United States
Environmental Protection
Agency
National Center for
Environmental Economics
Washington DC 20460
Version 2.0.0
December 23,2020
SAGE Model
Documentation
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For Further Information:
Copies of this documentation, source code for the model, and all publicly available data are available
at https://www.epa.gov/environmental-economics/cge-modeling-regulatory-analysis
Authors and Developers:
Alex Marten, PhD
U.S. Environmental Protection Agency
Office of Policy, National Center for Environmental Economics
Washington, DC
Andrew Schreiber, PhD
U.S. Environmental Protection Agency
Office of Policy, National Center for Environmental Economics
Washington, DC
Ann Wolverton, PhD
U.S. Environmental Protection Agency
Office of Policy, National Center for Environmental Economics
Washington, DC
Contact Information:
Questions related to this document should be addressed to Andrew Schreiber, U.S. Environmental
Protection Agency, Office of Policy, Washington, DC 20460 (email: schreiber.andrew@epa.gov).
Suggested Citation:
Marten, A., Schreiber, A., and Wolverton, A. 2020. SAGE Model Documentation (2.0.0). U.S.
Environmental Protection Agency: https://www.epa.gov/environmental-economics/cge-modeling-
regulatory-analysis.
Acknowledgements:
Richard Garbaccio contributed to the initial version of the SAGE model published in Marten and
Garbaccio (2018). David A. Evans provided invaluable ongoing review and comments on numerous
issues that arose during model construction.
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Contents
Executive Summary 5
What's New in Version 2.0? 8
1 Introduction 9
2 Model Structure 9
2.1 Trade 9
2.2 Production 13
2.2.1 Manufacturing and Service Sectors 13
2.2.2 Resource Extraction, Agriculture, and Forestry Sectors 17
2.3 Partial Putty-Clay Capital 18
2.4 Households 22
2.5 Government, Taxes and the Rest of World 26
2.6 Market Clearance 27
2.7 Closures 29
3 Calibration and Data 30
3.1 Benchmark Data 31
3.1.1 Crude Oil and Natural Gas Extraction Disaggregation 31
3.1.2 Filtering and Balancing Benchmark 32
3.1.3 Natural Resources 33
3.2 Taxes 35
3.3 Substitution Elasticities 40
3.3.1 Armington Elasticities 40
3.3.2 Production Elasticities of Substitution 43
3.3.3 Resource Extraction, Agriculture, and Forestry 44
3.3.4 Large Open Economy Elasticities 46
3.3.5 Partial Putty-Clay Elasticities 48
3.3.6 Consumption Elasticities 48
3.4 Dynamic Baseline 54
3.4.1 Productivity Growth 56
3.4.2 Population Growth 57
3.4.3 Government Accounts 57
3.4.4 Foreign Accounts 60
3.4.5 Baseline Energy Use 61
3.4.6 Baseline Visualization 65
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4 Solution 68
4.1 Multi-Year Timesteps 76
4.2 Calculating Welfare Effects 76
5 Modeling Regulatory Requirements 78
5.1 Compliance Requirements as a Productivity Shock 78
5.2 Modeling Explicit Compliance Requirements 79
5.3 Difference Between Productivity Shock and Explicit Compliance Requirements ... 81
6 Using the Model 83
6.1 Directory Structure 85
6.2 Building the Dataset 85
6.3 Running the Model 88
6.4 Solution Checks and Diagnostics 88
6.4.1 Numeraire Test 90
6.5 Examples of Adjusting or Using the Model 90
6.5.1 Adjusting Timesteps and Horizon 90
6.5.2 Example of a Hypothetical Regulation 91
6.5.3 Example of a Regulation with Phased In Requirements 92
6.5.4 Example of a Regulation in a Large vs. Small Open Economy 94
6.5.5 Example of Sector Specific Consumption Taxes 94
6.5.6 Additional Examples 96
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Executive Summary
In 2017, the EPA's Science Advisory Board (SAB, 2017) recommended that the Agency enhance
its regulatory analyses using computable general equilibrium (CGE) models "to offer a more com-
prehensive assessment of the benefits and costs" of regulatory actions. In response, the EPA has
invested in building capacity in this class of economy-wide modeling. A key outcome of this effort is
the EPA's CGE model of the U.S. economy, called SAGE. The SAGE model provides an important
complement to the analyses typically performed during rule development by evaluating a broader
set of economic impacts and offering a more complete estimate of costs.1
CGE models, such as SAGE, are aggregate representations of the entire economy. They assume
that for some discrete period of time an economy can be characterized by a set of conditions in
which supply equals demand in all markets. When the imposition of a regulation alters conditions
in one or more markets, the CGE model estimates a new set of relative prices and quantities for all
markets that return the economy to a new equilibrium.2 For example, the model estimates changes
in relative prices and quantities for sector outputs and household consumption of goods, services,
and leisure that allow the economy to return to equilibrium after the regulatory intervention. In
addition, the model estimates a new set of relative prices and demand for factors of production
(e.g., labor, capital, and land) consistent with the new equilibrium, which determines changes to
household income as a result of the regulation (EPA, 2010). In CGE models, the social cost of
the regulation is estimated as the change in economic welfare in the post-regulation simulated
equilibrium compared to the pre-regulation "baseline" equilibrium.
Unlike other analytic tools typically used to evaluate the costs of regulations, CGE models
account for how effects in directly regulated sectors interact with and affect the behavior of other
sectors and consumers. Specifically, they are designed to capture substitution possibilities between
production, consumption and trade; interactions between economic sectors; and interactions be-
tween a regulation and pre-existing distortions, such as taxes. Figure 1 uses a simplified circular
flow diagram to depict how input and output markets are generally connected to each other in
CGE models. Following a standard assumption in economics, the model assumes that households
maximize their wellbeing, while firms maximize their profits. Households supply factors of pro-
duction to firms in exchange for income (e.g. wages, profits, and interest payments). Firms use
the available factors of production and materials to produce outputs that are then bought and
consumed by households.
The SAGE model includes explicit subnational regional representation within the United States.
Each region contains multiple representative firms that vary by the commodity they produce and
1CGE models may also be able to provide additional information on the benefits of regulatory interventions, though
this is a relatively new but active area of research. Note that until the benefits that accrue to society from mitigating
environmental externalities can be incorporated in a CGE model, the economic welfare measure is incomplete and
needs to be augmented with traditional benefits analysis to develop measures of net benefits.
2 CGE models are generally focused on analyzing medium- or long-run policy effects since they characterize the
new equilibrium (i.e., when supply once again equals demand in all markets). Their ability to capture the transition
path of the economy depends on the degree to which they include characteristics of the economy the restrict its ability
to adjust instantaneously (e.g., rigidities in capital markets).
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Figure 1: Depiction of the Circular Flow of the Economy
have regional specific production technologies. Each region also has multiple representative house-
holds that vary by their income level and have region specific preferences. Within the economy
households and firms are assumed to interact in perfectly competitive markets. In addition to
households and firms, there is a single government in SAGE that represents all state, local and
federal governments within the United States. The government imposes taxes on capital earnings,
labor earnings, and production and uses that revenue (in addition to deficit spending) to provide
government services, make transfer payments to households, and pay interest on government debt.
Modeling domestic and international trade presents a unique challenge in that the model's
structure needs to account for the fact that the United States can be both an importer and an ex-
porter of the same good at both the national and regional level. SAGE handles these cases through
the use of the "Armington" approach, which assumes that imported and exported versions of the
same good are not perfect substitutes. In SAGE this assumption is applied to both international
and cross-regional trade within the United States. In addition, SAGE recognizes that the United
States is a relatively large part of the global economy and shifts in our imports and exports have
the potential to influence world prices.
SAGE is a forward-looking intertemporal model, which means that households and firms are
assumed to make their decisions taking into account what is expected to occur in future years and
how current decisions will impact those outcomes. In an intertemporal model care needs to be
taken to ensure that in response to a new policy the economy does not instantaneously jump to
a new equilibrium in a way that is inconsistent with the rate at which the economy can adjust
in practice. SAGE seeks to model a more realistic transition path, in part, by differentiating the
flexibility of physical capital by its age. Under this approach the model distinguishes between
existing capital constructed in response to previous investments and new capital constructed after
the start of the model's simulation. Existing capital is assumed to be relatively inflexible and is
used for its original purpose unless a relatively high cost is borne to alter its functionality. New
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capital is more flexible and easily adjusts to changes in the future. Independent of its vintage,
once capital has been constructed in a given region it cannot be moved to another region. While
physical capital is not mobile, households can make investments in whatever region of the country
they desire.
The dynamics of the baseline economy in SAGE are informed through the calibration of key
exogenous parameters in the model. Most importantly are population and productivity growth
over time. The model reflects heterogeneity in productivity growth across sectors of the econ-
omy consistent with trends that have been historically observed. In addition, the model captures
improvements in energy efficiency that are expected for firms and households going forward. Ad-
ditional baseline characteristics, such as changes to government spending and deficits and changes
to international flows of money and investments, are calibrated to key government forecasts or
informed by historical trends.
The SAGE model relies on a large number of data sources to calibrate its parameters. The
foundation is a state-level dataset produced by IMPLAN that describes the interrelated flows of
market goods and factors of production over the course of a year with a high level of sectoral
detail. When needed this dataset is augmented by information from other sources, such as the
Bureau of Economic Analysis, Energy Information Administration, Federal Reserve, Internal Rev-
enue Service, and the National Bureau of Economic Research. These data are combined with key
behavioral parameters for firms and households that are adopted from the published literature or
econometrically estimated specifically for the purposes of calibrating SAGE. The result is a static
dataset that describes the structure and behavior of the economy in a single year. To develop the
forward-looking baseline for the model, additional information on key parameters, such as produc-
tivity growth, future government spending, and energy efficiency improvements are incorporated
from sources including the Congressional Budget Office and Energy Information Administration.
To ensure that SAGE is consistent with economic theory and reflects the latest science, the
EPA initiated a SAB panel to conduct a high-quality technical review, completed in August 2020.
The SAB report commended the agency on its development of SAGE, calling it a well-designed
open-source model. The report included recommendations for refining and improving the model,
including several changes that the SAB advised the EPA to incorporate before using the model in
regulatory analysis (denoted as Tier 1 recommendations by the SAB). The SAB's Tier 1 recom-
mendations, including improving the calibration of government expenditures and deficits and the
foreign trade deficit; allowing for more flexibility in the consumer demand system; and representing
the United States as a large open economy, are incorporated as of version 2.0 of the model.3 A
number of the SAB's medium- and long-run recommendations have also been incorporated into
SAGE.
3SAGE, version 1.2.2 was peer reviewed by the EPA's Science Advisory Bord (SAB). The final report
is available at https : //yosemite . epa.gov/sab/sabproduct .nsf/0/511476D92CEF2AC7852585D6005D373C/$File/
EPA-SAB-20-010.pdf
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What's New in Version 2.0?
The current version of the model includes a number of major improvements, many of which imple-
ment the top-tier recommendations of the EPA's SAB (2020). Key improvements relative to the
previous version of the model (1.2.2) include:
• Improving the calibration of exogenous variables, including government and international
accounts.
• Allowing for more flexibility in the consumer demand system so the share of overall spending
on different goods varies with changes in income.
• Relaxing the assumption that the United States is a small open economy.
• Allowing for the implementation of variable time steps.
• Allowing for sector-differentiated productivity growth in the baseline.
• Providing additional diagnostic checks and illustrative examples.
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1 Introduction
SAGE is a computable general equilibrium (CGE) model of the United States economy developed
to aid in the analysis of environmental regulations and policies.4 It is an intertemporal model
with perfect foresight, resolved at the sub-national level. Each of the regions in the model has
five households reflective of national income quintiles. Each region has 23 representative firms,
with greater disaggregation in the manufacturing and energy sectors that are often impacted by
environmental policies. Production technologies are represented with nested CES functions, which
may include natural resource inputs. Capital for these firms is represented in a partial putty-clay
framework to aid in capturing transition dynamics. A single government agent levies taxes on labor
earnings, capital earnings, production, and consumption. The United States is treated as a large
open economy that relies on the Armington framework governing both domestic and international
trade.
In the following section, technical details on the structure of the model are presented. Section
3 describes the model's calibration. Section 4 discusses the solution algorithm. Section 5 discusses
potential options for representing regulations within the model. Section 6 provides a description of
how to run the model and describes the verification checks run by the model to test the solution.
For a more general description of the model and sensitivity analyses of the model's results we refer
the interested reader to Marten et al. (2019).
2 Model Structure
SAGE solves for the set of relative prices that return the economy to equilibrium after the imposition
of a policy or other shock, such that all markets clear. This section describes the model's basic
structure by first defining the markets in the model, followed by how firms, households, and the
government are represented. The section concludes by describing the market clearance conditions
that are used to determine equilibrium, where supply equals demand in all markets, along with the
closures applied in the model.
2.1 Trade
The United States is modeled as a large open economy. While SAGE does not include the rest of
the world explicitly, the model provides a reduced form mechanism to influence world commodity
4We use a recursive naming convention, where SAGE stands for SAGE is an Applied General Equilibrium model.
Note that CGE and AGE are often used in the economics literature to refer to the same class of models. Shoven
and Whalley (1984) describe AGE models as converting the simple two-sector general-equilibrium structure of Arrow
and Debreu to a more complex model of the economy that can then be solved computationally to evaluate the
welfare and distributional implications of different policies. CGE models have the same aim. Both rely on elasticity
estimates to parameterize and simplifying functional forms to solve the models. In addition, both types of models
are described as deriving from micro-theoretic foundations (e.g., cost minimization by firms, utility maximization
by households, all markets clear in equilibrium), though historically their solution algorithms have differed. AGE
models are solved iteratively to approximate the price vector that re-equilibrates the economy. CGE models use
macro balancing equations to close the model to solve for a unique solution (Horridge et al., 2013).
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Figure 2: SAGE Regions
prices. There are four subnational regions in the model matching the U.S. Census regions (see
Figure 2). Labor and natural resources are not mobile across regions. Capital once installed is not
mobile across regions; however, investment is mobile across regions.
Within a region, goods from different origins markets (regional, intra-national imports, interna-
tional imports) are aggregated using the Armington specification (Armington, f969). Intra-national
trade is pooled at the national level. That is, there exists a single market clearing price for com-
modities traded across regions, independent of the region of origin or destination.5 This structure
for intra-national trade is similar to other CGE models with subnational detail (e.g., Rausch et. al.
(2011); Ross (2014)).6 The Armington aggregate is based on first bundling regional output with
intra-national imports and then combining that bundle with international imports. A constant
elasticity of transformation (CET) function is used to differentiate regional output between differ-
ent destination markets (regional, intra-national exports, international exports). This structure is
presented in Figure 3.
To implement upward sloping rest of world supply curves for imports into the United States
and downward sloping rest of world demand curves for U.S. exports, the model uses a reduced
form approach without an explicit representation of the international economy. Specifically, the
international demand for U.S. exports and supply of imports into the U.S. market require the use
of a fixed factor, of which a rest of world agent, is endowed. This specification is not meant to
represent a physical process in reality, but is a reduced form assumption that allows the model's
BThe pooled approach for national trade is due to a lack of well established state-by-state bilateral trade data by
commodity.
6However, we note that there are examples where estimates of state-by-state bilateral trade matrices have been
applied (e.g., Balistreri and Rutherford (2001); Caron and Rausch (2013)).
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export demand and import supply curves to be calibrated to exogenous price elasticities. This
reduced form approach to modeling a large open economy follows Yuan et al. (2019).
More specifically, the Armington aggregate is defined as
tttyVyS d^VyS \ CS-Tlfr
•-nf-1
T^t,r,s,ftrd \ se-nf
m0.
]r,s,ftrd
+ (1 - cs-nfr>s)
cs-drir
mt,r,s,dtrd \ se~dn
rm^r,s,dtrd,
, (1)
+ (1 — cs-dnr>s)
H.r.s
d0r
( s e_n / — 1) s e-dn se-nf
se_n/(se.(in-l) | se-nf — 1
where at,r,s is the Armington composite in period t and region r for commodity s, mtyryS,trd are
imports from market trd, dt,r,s is domestic production consumed locally. Throughout this document
a 0 trailing a variable name denotes the value in the benchmark year; benchmark cost shares have
the prefix cs; and substitution elasticities have the prefix se. 7 The national market is denoted dtrd
and the international market is denoted ftrd. The parameter cs_n/r;S represents the international
imports share of the Armington composite, and cs-dnr>s represents the share of national imports in
the domestic-national composite. The substitution elasticity between international imports and the
domestic-national composite is sejnf and the substitution elasticity between domestic production
and national imports is se-dn. The inputs into the Armington aggregate are determined based on
minimizing the price of the composite good, pat,r,s, given the price in the domestic market, pdt,r,s,
the price in the national market, prit,s, and the price of foreign imports, pmt}S-
The CET function to differentiate domestic output across destination markets is defined as
Dt,r,s "i" y~€-%t,r,s — 2/0r
CS-dxrsA
't.r.s
d0r
~l~ CS-(lxr s dtrd
~l~ CS-d$rjSyftrd
te-dx-1-1
te-dx
te-dx-1-1
Xt,r,s,dtrd\ te~dx
x0.
'r, s, dtrd
$t,r,s,ftrd
(2)
xQ
r,s,ftrd
te-dx-\-l ~
te-dx
te-dx
te-dx-\-1
where yt,r,s is output from production with new capital, y-ext,r,s is output from production with
extant capital, xt,r,s,trd is exports to market trd, cs-dxr:S:mkt is the share of output destined for
market rrikt, and te-dx is the transformation elasticity. Within the production possibilities frontier
represented by equation (2), firms select the shares of production destined for each market based on
maximizing the price of output, pyt,r,s, given the price of the commodity in the different destination
markets.
In the model, most substitution elasticities vary across sectors as discussed in further detail in Section 3. However,
to simplify the exposition, in this document we forgo the sector subscript on substitution elasticities.
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Armington
Composite
International
Imports
Intra-national Local Intra-national International
Imports Goods Exports Exports
Output
Figure 3: Armington Trade Specification
The supply of imports from the rest of the world is characterized by a Cobb-Douglas production
function, defined as
ms,., E™ '•'•"'^{firnO,) \(52rmO,jtrd - /imO,) J
where mst,s is the supply of imports into the U.S. market in period t for commodity s, fimt,s
is the fixed factor input to import supply and ms-fxt,s is foreign imports less the fixed factor.
cs-ms denotes the calibrated cost share based on exogenous price elasticities for import supply (as
further explained in Section 3). The inputs into the supply of imports at price pmt,s are based on
minimizing the costs of the fixed factor, pfimt,s, and the price for foreign exchange, pfxt¦
Similarly, the international demand for exports (xd-fxt,s) is characterized by a Cobb-Douglas
production function combining exports from the U.S. market (xdt,s) and exports from the rest of
world agent treated as a fixed factor (fixt,s), defined as
= + ' (4)
where csJoejxs denotes the calibrated cost share based on exogenous price elasticities for export
demand. The inputs into the demand of international exports at price pfxt are based on minimizing
the costs of the fixed factor pfixt,s and the U.S. export price, pxt,s- Notably, when csJoejns = 0
and cs-loejxs = 0, the model is translated into a small open economy where pmt,s = pxt,s = pfxt-
Domestic
Goods
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We use a Cobb-Douglas function without loss of generality to pin down calibrated cost shares and
fixed factors based on exogenous price elasticities.
2.2 Production
Production in the model is aggregated to 23 sectors, with greater detail in manufacturing and
energy. The sectors in the model and their associated NAICS codes are presented in Table 1. This
default disaggregation represents sectors that have historically been the focus of environmental
regulations. This set of sectors also maps nicely into the industrial sectors of the U.S. Energy
Information Administration's (EIA) National Energy Model System (NEMS) that are used to
inform the baseline calibration.
2.2.1 Manufacturing and Service Sectors
In SAGE, perfectly competitive firms maximize profits subject to market prices and a given pro-
duction technology. Due to their parsimony and global regularity, nested constant elasticity of
substitution (CES) production functions have become widely used in applied general equilibrium
modeling (Brockway et al., 2017), and this is particularly true in the case of CGE models used to
analyze energy and environmental policies. Similarly, SAGE makes use of nested CES functions (in
calibrated share form) to define the production functions for the sectors represented. The policy
response of CGE models based on nested CES production functions may be sensitive to the ordering
of the nests, as this choice defines separability of the production functions amongst inputs (Lecca
et al., 2011). Thus, there has been much discussion about the hierarchy for nested CES production
functions, particularly with regards to capital, K, labor, L, and energy, E, inputs. Much of this
discussion has been based on heuristics, although the empirical work of Van der Werf (2008) is a
notable exception. Van der Werf (2008) studied the fit of different nesting structures given histori-
cal production data for 12 OECD countries between 1978 and 1996. Van der Werf (2008) finds that
the nesting structure combining K and L in the lower nest and the KL bundle with E in the top
nest, denoted KL(E), provides a significantly better fit to the data compared to the other possible
nesting structures. Furthermore, Van der Werf (2008) finds that the structure combining K and E
in the lower nest provided the worst fit for the data, a finding that has been corroborated in other
single country contexts (e.g., Dissou et al. (2015); Ha et al. (2012); Kemfert (1998)). Other multi-
and single-country studies have found that the KE(L) nesting structure may fit the data as well as
the KL(E) structure at the aggregate national level (e.g., Markandya and Pedroso-Galinato (2007);
Su et al. (2012)). However, Kemfert (1998) finds that in cases where the KE(L) nesting structure
finds support at the aggregate national level the specification may actually provide a worse fit than
the KL(E) structure when disaggregated sectoral production functions are estimated. We use a
structure that combines primary factors K and L in a lower nest, where that value-added bundle is
then combined with an energy composite. At the top level of the production function the KL(E)
composite is combined with a Leontief composite of material inputs. This structure is similar to
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Table 1: Model Sectors
Abbreviation
Description
NAICS Codes
NEMS IDM Code
agf
Agriculture, forestry, fishing and hunting
11
1, 2
gas
Natural gas extraction and distribution
211,* 213111,* 213112,* 2212,
4*
cru
Crude oil extraction
211,* 213111,* 213112*
4*
col
Coal mining
2121, 213113
3
min
Metal ore and nonmetallic mineral mining
2122, 2123, 213114, 213115
5
ele
Electric power
2211
NA
wsu
Water, sewage, and waste
2213
NA
con
Construction
23
6
fbm
Food and beverage manufacturing
311, 312
7
wpm
Wood and paper product manufacturing
321, 322
8, 19
ref
Petroleum refineries
32411
NA
chm
Chemical manufacturing
325
9
prm
Plastics and rubber products manufacturing
326
20
cem
Cement
32731
22
pmm
Primary metal manufacturing
331
12, 13
fmm
Fabricated metal product manufacturing
332
14
cpu
Electronics and technology
334, 335
16, 18
tem
Transportation equipment manufacturing
336
17
bom
Balance of manufacturing
3122, 313, 314, 316, 323, 32412, 3271, 3272, 32732,
32733, 32739, 3274, 3279, 333, 337, 339
10, 15, 21, 23
trn
Non-Truck Transportation
481, 482, 483, 485, 486, 4869, 487, 488, 491, 492, 493
NA
ttn
Truck transportation
484
NA
srv
Services
42, 44, 45, 51, 52, 53, 54, 55, 56, 61, 624, 71, 72, 81
NA
hit
Healthcare services
621, 622
NA
* Crude oil and natural gas extraction is included as a single sector in the benchmark data. However, we disaggregate this activity into separate sectors for crude oil and
natural gas. Details are available in Section 3.1.1.
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other CGE models used to analyze energy and environmental policies (e.g., Paltsev et al. (2005);
Rausch et al. (2011); Capros et al. (2013); Cai et al. (2015)).
For the energy composite we also use a nested CES function to represent available production
technologies. Initial work using energy-explicit CGE models typically combined all energy sources
- including primary energy sources and electricity - in a single nest, commonly with a unit substi-
tution elasticity (e.g., Borges and Goulder (1984)). Subsequent efforts separated electricity from
other primary energy sources in a two-nest CES structure that defined the energy composite (e.g.,
Van der Mensbrugghe (1994); Babiker et al. (1997); Paltsev et al. (2005); Rausch et al. (2011)
Bohringer et al. (2018)). The assumption of weak seperability between primary energy inputs and
electricity is representative of the primary energy choice across fuels for a sector being defined more
by the production process or regional fuel supply characteristics than by the price of electricity.
Some recent models have even gone a step further using a three-level CES nest to further disaggre-
gate the primary energy composite in order to impose separability between some of the fossil-fuel
use decisions in the cost-minimization problem (e.g., Burniaux and Truong (2002); Chateau et al.
(2014); Ross (2014)). However, the three-level CES nesting structure has not been applied consis-
tently across models, and evidence of weak separability in the data is lacking empirically (Serletis
et al., 2010a).
SAGE applies the two-level energy nesting with the bottom level nest combining refined petroleum
products (or by-products), coal, and natural gas. The second level nest combines the primary en-
ergy composite with electricity. This nesting structure is presented in Figure 4. More specifically,
the production function for manufacturing goods and services produced with new capital is
Dt,r,s — 2/0r
cs-klenir
( matter
\ mat0r
se-klem — 1
se-klem
+ (1 — cs-klemr}S)
t.r.s
( Me-
\kle 0r
se-klem — 1
se-klem
se-klem
se-klem — 1
(5)
where matt r s is the materials bundle, which is defined as
matt rs = mat0r s min T
id;
t,r,agf,s
id,
t.r.srv.s
id0r^agf^s id0r
(6)
idk,r,ss,s is the demand for intermediate good ss, and klet,r,s is the energy and value added composite,
which is defined as
klet r s = kle0r
csJtler s
enet>
\ eneOr
+ (1 — csJkler>s)
kl
t.r.s
kl0r
se-Kle
¦ (7)
enet,r,s is the electricity and primary energy composite, which is defined as
enet r s = ene0r
cs-ener s
se-ene— 1
em - - ^ se-ene
en0r
+ (1 — cs-eneT}S) -
id,
't.r.ele.s
idO
r.ele.s
se-ene— 1 ~
se-ene
(8)
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International
Intra-national
Local
Regional
Output
e-klem
Value Added-Energy
seMe
Value-Added
seJtl
International Domestic
Primary Energy Electricity Labor Capital
se-dn
se-en
Intra-national Local Coal
Refined Natural
Oil Gas
Figure 4: Manufacturing and Services Production Functions
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ent^r.s is the primary energy composite, which is defined as
— CTlO r^s CS-^T^ryColyS
CSSTl/f^gQ
(9)
where J2Sscs-enr,ss,s = 1- Finally, klt,r,s is the value added composite, which is defined as
where kdt,r,s is demand for new capital, and ldt,r,s is demand for labor. Recall that parameters with
the prefix cs are the relevant cost shares in the benchmark year, and parameters with the prefix se
are the relevant substitution elasticities.
Markets are assumed to be perfectly competitive, such that firms are price takers. Given market
prices, firms seek to maximize profits
where pyt,r,s is the output price based on maximizing returns across destination markets per equa-
tion (2), pat,r,s is the price of the Armington composite, prt>r is the rental rate for new capital,
plt,r is the wage rate, and tyt,r,s, and tkt,r are ad valorem taxes on output and capital income,
respectively.8
2.2.2 Resource Extraction, Agriculture, and Forestry Sectors
The resource extraction sectors (crude oil, natural gas, coal, and mining) have an additional primary
factor input, in this case representing the finite natural resource. In many cases, models have
included this resource in a top-level nest with a bundle of non-resource inputs (e.g., Ross (2005);
Paltsev et al. (2005); Sue Wing (2006); Rausch et al. (2011); Capros et al. (2013); Ross (2014);
Bohringer et al. (2018)). While some models allow for substitution between materials, energy, and
value-added in resource extraction sectors (e.g., Sue Wing et al. (2011); Capros et al. (2013)), other
models treat energy, labor, and capital as Leontief inputs (e.g., Ross (2014)), although in most
cases there is some substitutability allowed between labor and capital (e.g., Ross (2005); Paltsev
et al. (2005); Sue Wing (2006); Rausch et al. (2011)). Recent empirical evidence suggests non-zero
and statistically significant substitution elasticities between inputs in resource extraction industries
(Young (2013); Koesler and Schymura (2015)). Therefore, we maintain the same structure as in
8Payroll taxes are included as part of households' tax rate on labor income to capture the limit on Old Age and
Survivor's Insurance payments, which causes the marginal ad valorem tax rate to differ across employees based on
income.
(10)
(1 tyt,r,s) Pyt,r,syt,r,s ^^P(H,r,ss'i'dt,r,ss,s (1 "i" ^t,r) Pft,rkdt,r,s plt,rldt,r,si (H)
17
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the standard production nesting albeit with the addition of a fixed resource. The structure of the
production functions for the fossil fuel extraction sectors is presented in Figure 5.
We model the agriculture and forestry sectors using a similar production function with land as a
fixed factor input. We recognize that there has been an ongoing discussion in the literature related
to the degree of flexibility required by a production function to capture the separability, or lack
thereof, observed in empirical studies of agricultural sectors (e.g., Higgs and Powell (1990); Zahniser
et al. (2012); Simola (2015)). However, the decreasing returns to scale nature of production in the
sector, as captured in Figure 5, is common among approaches, independent of the nesting structure
applied.
For the resource extraction, agriculture, and forestry sectors the specific form of the production
function is
yt,r,s — y0r
se-rklem
se-rklem — 1 se-rklem — 1"
,, (rest,r,s\ /klemt,r,s
cs-rklemryS -^-L- + (1 — cs-rklemr^s) I
se-rklem
se-rklem —1
\resOrySJ ' \klemOr
(12)
where
klemtrs = klemOr
se-klem
s e-k I em — 1 s e_fc I em — 1 "
(matt,r,s\ se~klem , ;; x /klet,r,s\
cs-klemr g —— + (1 - csJtlemr,s) ,, n
\matOrsJ \kleOrsJ
se-klem — 1
(13)
and matt,r,s and klet,r,s are defined in (6)-(10). The fixed factors, rest,r,s, are sector specific and in
the baseline fixed at the benchmark level, rest,r,s = resOr}S Vi.
The resource extraction, agriculture, and forestry markets are also assumed to be perfectly
competitive, such that firms are price takers. Given market prices, firms seek to maximize profits
(1 tyt,r,s) Pyt,r,syt,r,s ^ *'yP(H,r,ss'i'dt,r,ss,s (1 "i" ^t,r) PVt,rkdt,r,s plt,rldt,r,s
ss (14)
- (1 + tkt,r) prest,r,srest,r,s,
where prest,r,s is the price of the fixed factor resource. It is assumed that returns to the fixed factor
face the same ad valorem tax rate as income from physical capital.
2.3 Partial Putty-Clay Capital
To better represent limitations associated with transitioning existing capital stock between sectors
or changing its production process, the model considers two capital vintages: existing stock in the
benchmark year and new capital formed after the benchmark year. Production with new capital
has the flexibility described in Figure 4 and 5. Production with extant capital has a Leontief
production structure, as shown in Figure 6.9 For a profit maximizing firm this means that output
9Given the Leontief structure of the production function with extant capital, the nesting pictured in Figure 6 is
unnecessary but is retained to make the figure more readable.
18
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International
Intra-national
Local
Regional
Output
se_rklem
Resource
Non-Resource
Bundle
Materials
Agriculture
se-klem
Value Added-Energy
seMe
se_
Value-Added
seJtl
International Domestic
Primary Energy Electricity Labor Capital
se-dn
se-en
Intra-national Local
Coal
Refined Natural
Oil Gas
Figure 5: Resource Extraction, Agriculture, and Forestry Production Functions
19
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of commodity s using extant capital is
kd-extrs
y-ext,r,s = yOr,s kdQ ' ' (15)
and demand for intermediate good ss, labor, and fixed factor resources to be used with extant
capital will be
• 7 • jn kd-ext,r,s
id-CXttrtSStS — idOf^gg^g
7 7 7 jn kd-eXtw _,N
ld-CXt ryS — ldOr s 7 ; (1 V
kdOr
Jr,s
and
kdjiXt r,s /1Q\
res.ext r s = resOr s————. (18)
' kdOr,s
In our partial putty-clay specification, extant capital is primarily sector specific, although it
allows a limited potential to shift extant capital across sectors at a cost. This feature is included to
match observations that some extant capital (e.g., structures) can be transferred across sectors. To
capture this characteristic, sector-specific extant capital, kd-ext>r,s is determined by a CET function
that transforms a region's extant capital, k-ext,r, with elasticity teJt-ex. More specifically, given
the rental rates for sector-specific extant capital the returns to the stock of extant capital are
maximized subject to the production possibilities frontier
k_ext r = kOr
csJtd.exr
te-k-ex
te-k-ex-1-1
kd_eXt r - ^ te-k^ex
kdOr
te_fc_ex +1
(19)
where ^scdJtd-exrtS = 1.
Capital, regardless of vintage, is assumed to depreciate at the annual rate 5. The law of motion
for extant capital reflects this ongoing depreciation, such that
k-ext+itr = (1 — S)k-ext,r, (20)
where k-exo,r = k0r. The law of motion for the new capital stock reflects both depreciation and
new regional investment, such that
kt+i,r = (1 - S)kt,r + invt,r, (21)
where invt>r is investment in region r in year t and ko,r = 0. The aggregate investment good is
composed of commodity output not otherwise used in final demand, government expenditures or
exported away. The formation of new physical capital via the aggregate investment good is assumed
20
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International Intra-national Local
Regional
Output
Materials
Value Added-Energy
Agriculture • • • Services
sejnf
International Domestic
Energy
Value-Added
Primary Energy Electricity Labor Capital
Intra-national Local Coal
Refined Natural
Oil Gas
Figure 6: Manufacturing and Services Production Functions with Extant Capital
21
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Table 3: SAGE Representative Households
Household Benchmark Income
hhl
hh2
hh3
hh4
hh5
< $25,000
$25,000-$50,000
$50,000-$75,000
$75,0004150,000
> $150,000
to operate through a CES function with an elasticity of substitution, seJnv, such that
invt>r = inv0r ^ cs-invr>s
se-inv — 1 ~
se-inv
(22)
where it>r,s is investment demand for commodity s, and csJnvryS = 1 for each region.
2.4 Households
Each region has five representative households differentiated by benchmark income. Benchmark
incomes for the representative households are presented in Table 3. Based on the underlying
economic data in our social accounting matrix, these represent the closest approximation to national
income quintiles possible.
Each representative household seeks to maximize intertemporal welfare, which is defined for
household h in region r as
where /3 is the discount factor, nt>r,h are the number of households represented by this agent, clt>r,h
is the consumption-leisure composite, and u(-) is the intra-temporal utility function. The discount
factor is defined as
where p is the pure rate of time preference.
The intra-temporal utility function is isoelastic, such that
where rj represents the inverse of the intertemporal substitution elasticity of full consumption. Intra-
temporal household preferences are defined by a nested CES-LES (linear expenditure system) utility
function as presented in Figure 7. The top level CES representation of the leisure-consumption
trade-off allows us to calibrate the elasticity of substitution to empirical labor supply elasticities.
This nested CES-LES approach also assumes weak separability between leisure and consumption of
other commodities (see Caron et al. (2017) for another example this type of utility function). Non-
(23)
(25)
22
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leisure consumption is assumed to follow a linear expenditure system (LES) demand structure. This
LES structure provides for non-homothetic preferences that can be calibrated to empirical income
elasticities while maintaining global regularity conditions that more flexible functional forms are
often missing (Ho et al., 2020; Sands et al., 2017; Lofgren et al., 2002).10 A linear expenditure
demand system allows for non-homothetic preferences with linear Engel curves that do not pass
through the origin when subsistence demands are positive (Stone, 1954). Engel curves describe the
proportion of income spent on a particular commodity as income changes.
Household
Utility
se.nf
International Domestic
Figure 7: Household Consumption
More specifically, this framework disaggregates non-leisure commodity demands into discre-
tionary (dcdtyryS,h) and subsistence demands {scdttrtS,h) such that total non-leisure commodity de-
mand (cdt,r,s,h) is defined as
cdt,r,s,/i — dcdt f g h -\- scdt f g fo. (26)
Each household in the model must achieve an exogenously specified minimum level of consumption,
denoted here as subsistence spending, for each commodity demand to contribute to positive utility
levels. To incorporate this demand sub-system into the model, calibrated subsistence demands
10Note that CES functional forms imply unitary income elasticities. This violates Engel's Law for food demand,
which states that consumers increase their expenditures for food products as their income grows at a decreasing rate.
Since household income is assumed to grow over time in the baseline, this assumption "imposes a baseline growth
path at odds with historical experience" (SAB, 2020). The LES functional form relaxes this assumption.
23
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(scdt,r,s,h) are held fixed and appear in the budget constraint but do not contribute to positive
utility levels (and are hence not included in Figure 7). Once agents have achieved the minimum
level of consumption, additional demand is endogenous in the model, denoted here as discretionary
spending, as captured in Figure 7. Aggregate discretionary consumption (dct>rth) is combined with
leisure in the top-level nest of the utility function using a CES function. More information about
the calibration of our demand system is presented in Section 3.3.6.
Intra-temporal household preferences over full discretionary consumption are defined as
dt,r,h — c/0r h
se-cl
se-cl — 1 se-cl — 1
, (let rh\ se-cl . , . / leist rh\ se-cl
CS-dr h ' ' ) + (1 - CS-dr,h) ( ' '
dcOrhJ \leis0rh
se-cl — 1
(27)
where leist,r,h is leisure and dct>r,h is the discretionary final goods consumption composite, defined
as
,1 _ ,1 n TT f c<^t,r,s,h ~ SCdt>r>s,h\ t'r'h's fr,o\
dct,r,h - dcOr>h n dcdOr>8>h J ' (28)
where csJtest,r,h,s is the value share for discretionary spending, adjusted for subsistence demands.
The subsistence portion of commodity demand, scdt,r,s,h, is assumed to grow at an exogenous rate
consistent with income growth so that the calibrated income elasticities are relatively stable over
the model's time horizon (see Section 3.3.6 for more details).
Households seek to maximize welfare in (23) subject to a budget constraint where sources
of income are represented on the right-hand side and expenditures on the left-hand side of the
equation, net of taxes. Disaggregation of exogenous government and international accounts implies
that the household budget constraint must also track these same categories of net transfers from
the government, net transfers from the rest of the world, and payments to service government debt.
'pkht+iinvhttrth + pclt}r}hclt}r}h + tCt^p(lt^r^sSdt,r,s,h) —
prhtkht,r,h + prh-extkh-ext,r,h + y^jprest>r,sreset,r,s,h
, (29)
^ (1 tfiCCLt,r,h) P^t,rt&t,r,h ~i~ (tlt,r,h j) plt,r^t,r,h
+ pfxt (inc-rowt,r,h + tran-rowt,r,h + curactbalt,r,h) intsharer>h
+ cpittransferst,r,h + cpit (gintt,r,h ~ deficitt,r,h + icnadjt,r,h) 9-sharer,h
In the household budget constraint, the left-hand side variables are defined as follows: pkht is the
price of new capital stock for households, invht,r,h is the level of investment in new capital stock
in period t, pclt>r>h is the unit cost of full consumption (i.e., discretionary consumption and leisure)
inclusive of any consumption taxes, and sdt,r,s,h is subsistence demand or the minimum amount of
demand required for positive utility levels.
The right-hand side of the budget constraint consists of several components. Earnings from new
capital are calculated as the after tax rate of return on new capital, prht, multiplied by household
24
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holdings of new capital stock, kht,r,h• Households also earn income from investments in extant
capital, which consists of the average national return on households' extant capital stock, prh-ext,
multiplied by their stock of extant capital, kh-ext,r,h-n prh-ext is further defined as
(30)
where pr-ex-aggt>r are the returns to extant capital in a region.
The model explicitly tracks investment returns by household and region in each time step.
To do this, we characterize a second "intermediary" household specific capital stock that allows
households to invest in capital formation in regions other than where they live. This capital stock
behaves consistently with the law of motion for capital and evolves according to
This capital stock reflects capital ownership by region, household and time period. It supplies a
national market for capital that is cleared by firm capital demands. Essentially, households invest
into a national investment fund that optimally (and without transaction costs) allocates those
investments across regions. Since new investment is mobile across regions there is a single price
for new capital investments by households and they earn a single rate of return that is inclusive of
regionally depreciating assets. These will be equal to the average price and rate of return to new
capital across regions.
Earnings from the ownership of fixed resources are captured in the household budget constraint
as the price of the fixed resource used by sector s, prest,r,s, multiplied by the household's endowment
of that fixed resource, reset,r,s,h-
To capture income from labor supply, tet>r,h is defined as the household's effective time en-
dowment, plt>r (i.e., the wage rate) is the price of labor, and lt,r,h is the household labor supply.
Since households are assumed to "purchase" leisure at its opportunity cost (i.e., the wage rate),
the household labor supply, lt,r,h, will be determined according to the time endowment constraint
The population and the time endowment are assumed to grow at exogenous rates, discussed in
further detail in Section 3.4.
Labor income must also be adjusted for taxes to be adequately represented in the budget con-
straint. Therefore, the value of a household's time endowment is (1 — tlt,r,h — tficat,r,h) plt,rtet>r,h,
which accounts for two taxes that are collected from households on labor: the personal income tax
on labor earnings and Federal Insurance Contribution Act taxes, with ad valorem rates tlt>r,h and
tficat,r,h, respectively. The FICA tax is collected in this manner, as opposed to a payroll tax on
nIt is assumed that past investment was also mobile across space, such that households have historically invested
nationally similar to the treatment of new capital. So the return households earn on their extant capital stock is a
weighted average of regional rental rates for extant capital stock.
kht+i,r,h = (1 - S)kht,r,h + invht,r,h-
(31)
tet}r}h —
(32)
25
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the firm side, to allow the effective FICA tax rate to incorporate the limit on the Old-Age, Sur-
vivors, and Disability Insurance tax. The additional component in the budget constraint related to
labor taxes, (tlt,r,h — tLavgt,r,h) pk,rk,r,h, adjusts the household's after tax income so that it only
reflects the average tax rate collected on labor supply, while continuing to allow the use of effective
marginal tax rates when modeling behavioral incentives. The adjustment represents the difference
in the tax payment that would be collected by the government on labor income using the marginal
tax rate for all labor income versus the average income tax rate. In the absence of this adjustment,
the excess tax collected at the marginal rates would be returned through incadjt,r,h and indexed
based on the consumer price index, which can affect welfare estimates and incidence in particular.
Households also receive net transfers from the rest of the world. These are calculated as the price
of foreign exchange, pfxt, multiplied by the sum of their share of net income from the rest of the
world, inc-rowttr,h, their share of net taxes and transfers from the rest of the world, tran-rowt>r,h,
and their share of the current account balance, curactbalttr,h- This sum is then adjusted by the
modeled incidence of those foreign transactions on households, int-shareTth-
Net government transfers to households are captured by trans ferst>rthi which is assumed to
be indexed to the consumer price index, cpit, as is the case with most federal government transfer
programs. Payments to service government debt are captured in the budget constraint through
the sum of the interest received on government debt, gintt,r,h, the purchase of government debt,
deficitt>r>h, and the balance of other inter-institutional transfers, incadjt,r,h• This sum is indexed
by the cpit and adjusted by the modeled incidence of those government transactions on households,
gsharer>h-
The consumer price index, cpit, is defined as
Er sA (1 + . .
°Plt = f, i * n N jn ' (33)
Er.sM1 +tcOr) cdOr>s>h
and cdt,r,s,h is demand for commodity s. intsharer>h and gsharer>h are defined as
int.share = ^s^sjtrd ~ xO^jtri (34)
Z_^r,s ™ r,s,ftrd xOr,s,ftrd Z_^h ^r,h
and
cOrh , .
g.share = = —, (35)
2^r,h cQr,h
such that the incidence is predominately assumed to follow the incidence of consumption.
2.5 Government, Taxes and the Rest of World
There is a single national government in the model that imposes ad valorem taxes on capital income,
production, wage income, and consumption, tkt,r, tyt,r,s, tlt,r,h, and tct,r, respectively. The taxes
are region specific, the production tax is also sector specific, and the labor income tax rates are
household specific. While they remain constant over time in the baseline, we allow for the possibility
26
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of future changes in tax rates in the policy simulations.
Government purchases in region r are assumed to be Leontief, such that
govt,r = govOr min ( ; (36)
s \gUr,sJ
where gt>r,s is public demand for commodity s in region r, and govt,r is the composite public
consumption good.
The government's budget constraint is
EwWr+ J] cpittransferst, r,h + cpitgintt + pfxtgint-rowt + cpitincadjt
r h
=£E tyt,r,sPyt,r,s (Ut,r,s y~£%t,r,s)
r s I.
+ tkt,r [prt,rkdt,r,s + pr-£Xt,r,skdjzxt,r,s + prest,r,s (rest,r,s + res-ext,r,s)} >
+ ££
r h
(tltyr,h t^typ^tyrysC'dtJrJsJh
+ cpitdef icitt>r,h,
(37)
where pgovt,r is the unit cost of government consumption based on (36).
The government's budget is balanced through lump sum transfers, incadjt, which are shared out
to households based on their share of national consumption in the benchmark dataset, as discussed
in Section 2.4. Exogenous government and international accounts have been disaggregated to
allow for differentiated assumptions about their growth and provide greater transparency over the
assumptions within the model. The specific level of disaggregation selected for these accounts also
allows the exogenous variables in SAGE to line up well with other government forecasts to which
these variables are calibrated (see Section 3.4 for more details).
A rest-of-the-world agent is characterized as being endowed with fixed factors for export de-
mands and import supplies that demands foreign exchange. The agent's budget constraint is
specified as
pfxtrowt = ^2 (Pfixt,sfixOs + p/imt;S/imOs j (38)
where pfxtrowt denotes the income level of the rest-of-the-world agent, such that rowt is the
rest-of-the-world demand for foreign exchange in each period.
2.6 Market Clearance
Given firm, household, and government behavior, along with the capital dynamics described in the
preceding sections, prices in equilibrium are assumed to clear all markets.
The price of the Armington aggregate, pat,r,s, is a composite price index derived from three
prices: the price for domestic output consumed regionally, pdt,r,s, the price of commodities imported
27
-------
from the national market, pnt,r,s, and the price for imported commodities from the foreign market,
Vmt,r,s¦ Vat,r,s clears the intermediary market for the aggregate demand of commodities, such that
(H,r,s = ^ ^(^t,-r,s,ss ~i~ id-6Xttr,s,ss) ~i~ ^ ^{,cdt,r,s,h) ~i~ H,r,s ~i~ 9t,r,s• (^9)
ss h
The price of domestic output consumed domestically, pdt,r,s, clears the domestic market, such that
iJ-eXt}r,s ~i~ Ut,r,s (pdt,r,s dttr,s (40)
y^r,s \Pyt,r,s J d0TjS
where the left hand side defines the optimal share of output supplied to the domestic market based
on the output transformation function in (2). The price of labor, plt>r, clears the labor market,
such that
^ ^ lt,r,h = ^ ^ ldt}r,s ~i~ ld-&Xttr,s- (41)
h s
The rental rate for sector specific extant capital, pr-ext,r,s, clears the market for extant capital,
such that
7 / \ teJc-ex 7 7
k-ext^r ( pr-extjryS \ _ kd-ext^s
k0r \pr-exjaggt,r J kdOr>s '
where the left hand side defines the optimal share of extant capital supplied to sector s based on
the extant transformation function in (19). The rental rate for new capital, prt,r, clears the regional
market for new capital, such that
kt,r = ^ ^ kdtjrjS. (43)
The price of new capital, pkt,r, clears the regional investment market, such that
kt-i,r (1 - 5) + invt-i,r = kt,r. (44)
The rental rate households' earn on their holdings, prht, clears the national investment market,
such that
^kht,r,h = ^kt,r. (45)
r,h r
The price of commodities on the national market, pnt>s, clears the market for national trade, such
that
^ ^ %t,r,s,dtrd = ^ ^ f^t,r,s,dtrd- (46)
r r
The price of imports, pmt,s, clears the market for foreign import market, such that
m*, = S>r,. (47)
r
The price of the import fixed factor, pfimttS, clears the market for foreign fixed import factors,
28
-------
such that12
fimOg = fimt,s. (48)
The price of exports, pxt,s, clears the market for foreign export market, such that
^2%t,r,s = xdk,s- (49)
r
The price of the export fixed factor, pfixt,s, clears the market for foreign fixed export factors, such
that
fixOs = fixt,s. (50)
The price of foreign exchange, pfxt, clears the foreign exchange market, such that
T: xd-fxt>s + inc-rowt + trarurowt — gint-rowt — curactbalt = ^ ms-fxt>s + rowt- (51)
S S
Finally, the rental rate for sector-specific fixed factors, prest,r,s, clears the market for sector-specific
fixed factors, such that
y, reset,r,s,h = rest,r,s + res-ext,r,s• (52)
h
Given that the CES and CET functions defining much of the model's structure are homothetic,
the prices for composite goods (e.g., pyt,r,s and pdt>r>h) are defined by their unit cost.
2.7 Closures
This section summarizes the main model closures, which are needed to ensure the model is well
specified and that there are enough equations to solve for the endogenous variables in the model.
These include the government account, trade accounts, intertemporal no-arbitrage condition, and
the terminal condition for the finite time horizon model. While some of these are presented above,
they are repeated here to provide a complete accounting in one section.
The government budget constraint in (37) is balanced through lump-sum transfers with house-
holds, where the endogenous transfers are distributed according to shares of benchmark consump-
tion per equation (35). The government budget is balanced via lump-sum transfers to avoid altering
the marginal incentives in the model through the speculative choice of which tax(es) to adjust.
The domestic trade account is closed each period with a single national price per commodity,
per the market clearance condition in (46). Each region's overall balance of payments (across all
commodities) in the domestic trade market is not required to be zero in a given period. Deviations
from zero are the result of net investment flows in or out of the region in combination with differences
between the region's tax payments and receipt of public funds.
The foreign trade account, across all commodities, is closed each period by the price of foreign
12Note that in the model, we let the fixed factors for imports and exports grow with the implicit growth rate.
fimOs and fix0S do not include a t subscript here for exposition purposes.
29
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exchange, per the market clearance condition in (51). The balance of payments is exogenously
specified.
To ensure that the model does not allow for intertemporal arbitrage opportunities, the following
constraint is placed on the price of capital
pkt,r =pn,r + 'pkt+iAl-$)¦ (53)
In other words, the price of capital in period t must equal the return it receives in period t plus
the present value of the depreciated asset in period t + 1. This is equivalent to an equilibrium
price of capital that is equal to the present value of returns it will earn over its lifetime. A similar
constraint is placed on the price of new capital stock held by households
pkht = prht + pkht+i(l — 5). (54)
To close the finite approximation to the infinite time problem we generally follow Lau et al.
(2002). The capital stock in the post-terminal period, ktr, is introduced as an endogenous variable
with associated price, pktr. The post-terminal capital stock is determined by requiring that regional
investment is growing at the rate of aggregate regional output growth, such that
iriVT,r ^2syT,r,s + y~eXT,r,s
(55)
inVT-l,r UT-l,r,s + y-eXT-l,r,s '
where T is the terminal period. The price of terminal capital stock is determined by requiring the
law of motion for capital to hold, such that
kr,r (1 — S) + invT,r = ktr, (56)
where households' share of the post-terminal capital stock is assumed to be equivalent to their
share of the capital stock in the last period of the model, such that
7 khT,r,h
khtrh = ^ , (57)
Lr.h khT,r,h
where the price of terminal capital for the households is equal to the weighted average price of
terminal capital
phht = (58)
r\iv
-------
stocks; tax rates; and the parameters defining the baseline projection. This section describes the
sources of each of these in turn.
3.1 Benchmark Data
The benchmark data is based on IMPLAN's 2016 database of the U.S. economy aggregated up
to the sectors in Table 1 for each of the regions in Figure 2, representative households in Table
3, and a single government.13 The data are used to define the benchmark year values and cost
shares. In addition, the benchmark dataset uses information from BEA's National Income and
Product Account tables for the government deficit, deficitO, government interest payments to
domestic agents, gintO, government interest payments to the rest of the world, gint-row0, the
current account balance, curactbalO, net income from the rest of the world, inc-row0, and net
taxes and transfers from the rest of the world, tranrow0.
The remainder of this section describes additional transformations and modifications made to
the database to conform to the structure of the model. Smaller transformations include:
• Household exports, which are primarily purchases by foreign tourists, are shared out across
commodities based on final good consumption shares and transferred from households to
sector-specific foreign exports.
• Government production (make and use) is integrated with private sector production.
• Investment demand, i0r;S, is determined as the residual that would lead the goods market
clearance condition in (39) to hold.
3.1.1 Crude Oil and Natural Gas Extraction Disaggregation
The underlying IMPLAN data does not distinguish between crude oil and natural gas extraction.
Therefore, we disaggregate the single IMPLAN oil and gas extraction sector into separate natural
gas extraction and crude oil extraction sectors. To determine the natural gas share of consump-
tion/use we assume that crude oil serves as an intermediate input only to the petroleum refining
sector and that natural gas is the only intermediate input (between the two) to all other sectors. We
make the same assumptions for household and government consumption and investment demand.
In the IMPLAN data, some of the intermediate inputs to the petroleum refining sector are natural
gas. To determine that share and the natural gas share of production and trade we minimize the
sum of squared deviations for those shares from observed values or assumed shares conditional on
market clearance conditions and the assumption of weakly positive domestic use of production.
The observed or assumed shares we try to match are derived as follows:
1. The observed share of natural gas production by region is defined using EI A data on crude
oil and natural gas production by state aggregated up to the regional level. To arrive at a
13IMPLAN Group, LLC, 16740 Birkdale Commons Parkway, Suite 206, Huntersville, NC 28078,
www.IMPLAN.com
31
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value share we multiply state-level production quantities by EIA data on state-level wellhead
prices for crude oil and city gate natural gas prices as a proxy for natural gas wellhead prices
(which are not available).
2. The shares of natural gas international imports and exports by region are defined using census
data on state-level international imports and exports of crude oil and natural gas aggregated
to the regional level.
3. A region's intra-national import share of natural gas is assumed to be similar to the region's
share of natural gas use relative to the region's total crude oil and natural gas use. A region's
intra-national export share of natural gas is assumed to be similar to the share of natural gas
production in the region.
4. The observed share of natural gas used as an intermediate input in the refining sector is
estimated based on national annual averages of crude oil and natural gas inputs to the sector
collected by EIA and converted to values using the Brent and Henry Hub average annual
prices as reported by EIA.
3.1.2 Filtering and Balancing Benchmark
To improve the computational performance of the model we, follow what is standard practice for
many CGE models and, filter out small values and rebalance the SAM. We remove any value less
than 5 x 10-5 and any intermediate input whose cost share is less than 5 x 10-5. This translates into
filtering values of less than $50,000 or less than .005% of the total costs of production, respectively.
The relatively small size of such values can impeed computational performance, while there removal
does not meaningfully affect the results of the model.
After filtering small values the SAM is rebalanced by minimizing the squared percent deviation
from the original values weighted by the original values. Specifically we solve for new values of in-
termediate input demand, id0r}SS}S, labor demand, ld0r}S, capital demand, kd0r}S, imports, m0rtSttrd,
exports, x0r>s>trd, household consumption, cd0r>s>h, government spending, g0r>s, investment, i0r;S,
capital endowment, labor endowment, household savings, and lump sum government transfers,
tran0ryh. This optimization is subject to the market clearance conditions in (39), (41), (43), and
(46), the budget constraints in (29) and (37), the balance of payment sharing in (34), the zero
profit condition
(1 - tyr,s)y0r,s = £ idOf^sSyS H~~ + (l + tkr) kd0rys, (^^0
the requirement that regional investment equals household savings
^ ^ ^0r,s — ^ ^ kh0t-\-lyr,h kh0tyr,hi (60)
s h
32
-------
consistent with the original data set, weakly positive domestic own use
y®r,s > ^ ^ XOr,s,trd> (61)
trd,
and where household savings is consistent with steady-state growth. The balancing occurs prior to
distinguishing between types of capital - new, extant - and fixed factor resources, as covered in the
next section. Therefore, the notation is somewhat simpler.
3.1.3 Natural Resources
Capital returns in the benchmark SAM are disaggregated into returns on man-made capital and
natural resources. The disaggregation is based on estimates of the returns to natural resources as
a share of gross surplus for those sectors. As described in greater detail below, these shares are
assumed to be approximately 25% for the oil and natural gas extraction sectors, 40% for the coal
mining sector, 40% for the agricultural and forestry sectors, and 40% for other mining sectors.
Through 2009, the U.S. Energy Information Administration (EIA) collected information on the
performance of major U.S. energy-producing companies. Based on the most recent survey, they
estimated that the total upstream costs (lifting costs plus finding costs) between 2007 and 2009 for
crude oil and natural gas companies included in the survey was $33.76 per barrel of oil equivalent
(EIA, 2011). EIA reports that the U.S. produced 1.95 billion barrels of crude oil14 and 3.67 billion
barrels of oil equivalent of natural gas15 in 2009.16 The U.S. Bureau of Economic Analysis (BEA)
estimates that in 2009 the output value for the oil and natural gas extraction sectors was $220
billion with gross operating expenditures of $123 billion.17 Combined, these estimates suggest that
the output value of the sector exceeded the upstream costs by $30 billion, which is 25% of the gross
operating surplus.
An alternative approach to defining the share of gross operating surplus due to rents paid to
natural resource ownership is to consider royalty payments. The United States has widespread
private ownership of minerals, including crude oil and natural gas. In 2012 an estimated 77% of
onshore crude oil and natural gas production revenue was associated with privately owned minerals
for which $22 billion in private royalties were paid (Fitzgerald and Rucker, 2016). In 2012, $8.5
billion in federal royalty payments were collected from onshore and offshore oil and gas production,
according to the U.S. Department of Interior's Natural Resources Revenue Data.18 The BEA
estimates that in 2012 value added for the crude oil and natural gas extraction sectors, less employee
compensation and production taxes, was $157 billion.19 Private and federal royalties represented
approximately 19% of this remaining value added. Brown et al. (2016) found evidence that private
14https://www.eia.gov/dnav/pet/PET_CRD_CRPDN_ADC_MBBLPD_A.htm
1Bhttps://www.eia.gov/dnav/ng/hist/n9070us2A.htm
16Natural gas was converted to equivalent barrels of oil at 0.178 barrels per thousand cubic feet following EIA
(2011).
17https://www.bea.gov/industry/input-output-accounts-data
https://revenuedata.doi.gov/explore/#federal-revenue
19https://www.bea.gov/industry/input-output-accounts-data
33
-------
royalty rates may not represent full rent on the natural resource, potentially due to monopsony
power and long-term contracts. Similarly, government royalty rates may not represent the full rent
associated with the nonrenewable resource. Therefore, 19% likely represents a lower bound on the
rents associated with crude oil and natural gas resources.
Sue Wing (2001), based on BEA rent estimates from 199420 and before the growth in shale
production, estimated resource rents to be approximately 45% for crude oil and natural gas pro-
duction. Technological progress such as horizontal drilling and hydraulic fracturing likely placed
downward pressure on the resource rents (e.g., Farzin (1992); Lin and Wagner (2007)). Given the
breadth of technical progress in these markets, 45% therefore may be a reasonable upper bound.
The share of gross surplus associated with coal resources is approximated using average ex-
traction cost estimates from Jordan et al. (2018) along with additional information on operation
costs for coal companies. Jordan et al. (2018) estimate average per-ton extraction costs for coal
by region based on 10-K filings from large publically traded coal companies (Figure 1 from their
paper). Based on there estimates of extraction costs and regional coal production levels, the ex-
traction costs for the industry in 2012 were approximately $37 billion. This value does not include
consumption of fixed capital, sales, or general administrative costs. Using the 10-K fillings for
the same publicly traded coal companies evaluated in Jordan et al. (2018), these additional costs
were on average 20% of extraction operating costs in 2012. BEA estimates that in 2012 the total
output value for the coal mining sector was $52 billion with $19 billion in gross operating surplus.21
Estimating the payments to the resource as the difference between the total output value and ex-
traction costs scaled to include other costs yields $8 billion, which is approximately 40% of gross
surplus for the sector. Notably, extraction operating costs may include some royalty payments,
which may represent returns to the resource, leading to an underestimated share of gross surplus
associated with resource payments. Conversely, the estimates of variable input costs do not include
expenditures associated with mine closures, which can be large, leading to an overestimate of the
share of gross surplus associated with resource payments. We note that, while based on data from
the early 1990s, Sue Wing (2001) similarly estimated resource payments to be 40% of gross surplus
in the coal sector.
Remaining mineral and metal mining activity is aggregated into another mining sector (rriin).
Approximately two-thirds of the output value from the sector is attributable to stone mining and
quarrying (NAICS 21231) or sand and gravel mining (NAICS 21232). Of the remaining third of
the sector's output value, copper ore mining (NAICS 212234) accounts for approximately half. Due
to a lack of recent data that would facilitate an exercise similar to those conducted for the other
mining sectors we assume the share of gross surplus attributable to the resource is 40%, following
the coal sector.
Disaggregating the returns to agricultural and forestry land as 40% of gross operating surplus is
consistent with rental data from the U.S. Department of Agriculture (USDA). The USDA estimates
20https://apps.bea.gov/scb/account_articles/national/0494od2/maintext.htm
21https://www.bea.gov/industry/input-output-accounts-data
34
-------
that the rental value in 2016 for cropland and pastureland is $136 and $13 per acre, respectively,22
and that there is approximately 245 million acres of cropland23 and 528 million acres of pasture-
land.24 The BEA estimates gross surplus in 2016 for the agricultural sectors to be $103 billion.
Using the USDA estimates to compute the total rent paid to agricultural land and dividing by
the BEA gross surplus estimate, suggests that land rental values are up to 40% of gross surplus
for the sector. It is worth noting that the USDA rent per acre estimates may include the returns
to some structures, potentially making them an overestimate of the returns to land. Since the
agriculture and forestry sectors are combined in the default aggregation of SAGE this assumption
is also implicitly applied to the returns to land for the forestry sector, which accounts for less than
9% of the gross surplus for the combined sector.
3.2 Taxes
As previously noted, the model explicitly includes business taxes/subsidies, tyr>s, personal labor
income taxes, tlr>h, and capital income taxes, tkr. The taxes are introduced into the dataset prior
to aggregation to the model's regions. When aggregating the dataset, taxes are set to keep the tax
revenue constant between the disaggregated and aggregated datasets. Production taxes net of any
subsidies, tyr>s, are based on the average rate observed in the IMPLAN database. The production
tax rates are presented in Table 4. Based on the design of the IMPLAN database these values also
include sales and excise taxes. A placeholder exists for consumption taxes, tcr, in the model's code
to allow for future development work that may move the sales and excise taxes out of production
taxes. In the current version of the model, explicit consumption taxes are set to zero. Therefore, as
it currently stands, sales and excise taxes are applied on the supply side of the market as opposed
to the demand side and are associated with the sector that submits the tax payment and not
necessarily the sector that produces the taxed commodity.
Personal income taxes on labor are differentiated across regions and households. Effective
marginal Federal Insurance Contribution Act (FICA) taxes are also differentiated across regions
and households. This allows the payroll tax rates to capture the annual limit on Old Age and
Survivor's Insurance (OASI) taxes, which would not be possible if the payroll taxes were collected
on the firm side due to the model's structure. Data from the U.S. Census Bureau's Current
Population Survey (CPS) Annual Social and Economic Supplement (ASEC) is used to create a
representative sample of tax returns. These sample returns are then run through NBER's Taxsim
model version 27 to estimate marginal tax rates for wage income and FICA for each sample return
(Feenberg and Coutts, 1993).25 For each region and household we compute the weighted average
effective marginal tax rate from the sample returns by weighting the Taxsim results by the CPS
22https://quickstats.nass.usda.gov/results/ABF12C63-5DDA-3745-A0B3-C91279A860Dl
23https://www.fsa.usda.gov/Assets/USDA-FSA-Public/usdafiles/NewsRoom/eFOIA/crop-acre-data/zips/
2016-crop-acre-data/2016_fsa_acres_data_aug2016_dr6.zip
https://www.nrcs.usda.gov/wps/portal/nrcs/detail/national/landuse/rangepasture/?cid=nrcsdevll_
001074
2Bhttp://users.nber.org/~taxsim/taxsim27/
35
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Table 4: Tax/Subsidy Rates on Production
nor
sou
mid
wes
agf
0.02
0.01
0.01
0.00
era
0.05
0.12
0.13
0.17
col
0.03
0.07
0.09
0.10
min
0.02
0.03
0.03
0.03
ele
0.09
0.08
0.08
0.08
gas
0.05
0.09
0.06
0.12
wsu
-0.09
-0.01
-0.04
-0.03
con
0.01
0.01
0.01
0.01
fbm
0.04
0.04
0.01
0.03
wpm
0.01
0.01
0.01
0.01
ref
0.01
0.01
0.01
0.01
chm
0.02
0.01
0.01
0.02
prm
0.01
0.01
0.01
0.01
cem
0.01
0.01
0.01
0.01
pmm
0.01
0.01
0.01
0.01
fmm
0.01
0.01
0.01
0.01
cpu
0.01
0.01
0.01
0.01
tem
0.01
0.00
0.00
0.00
bom
0.01
0.02
0.01
0.02
trn
0.03
0.03
0.04
0.04
ttn
0.01
0.01
0.01
0.01
srv
0.05
0.05
0.05
0.05
hit
0.01
0.01
0.01
0.01
36
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Table 5: CPS to NBER Taxsim Income Mapping
Taxsim Variable Description
CPS Variable(s)*
otherprop
transfers
gssi
dividends
stcg
ltcg
swage
pwage
ui
nonprop
pensions
Wage and salary income of primary taxpayer
Wage and salary income of spouse
Qualified dividend income
Short term capital gains or losses
Long term capital gains or losses
Other property income
Other non-property income
Taxable pensions and IRA distributions
Gross social security benefits
Unemployment compensation
Other non-taxable transfer income
ws.val, semp_val, frse.val,
-hiemp x phip_val
ws.val, semp_val, frse.val,
-hiemp x phip_val
quaLfrac x div.val
NA**
NA**
rnt_val,
(1 — quaLfrac) xdiv_val
oLval, ed_val
rtm_val
ss_val, ssi_val, srvs_val,
dsab_val
uc.val
paw.val, wc_val, vet_val,
csp_val, fin_val
* Except for the primary and spouse wage and salary income, for married taxpayers each Taxsim
variable is the sum of the CPS variables for both the primary taxpayer and their spouse.
** The CPS ASEC does not include information on imputed capital gains after 2010.
ASEC earned income and applying the supplement weights.
From the CPS, the filing status variable (filestat) and the dependent status variable (dep_stat)
are used to distinguish between single/head of household taxpayers and dependent taxpayers. All
married taxpayers are assumed to file jointly, and the person records for each couple are identified
using the a_spouse variable. The dep_row variable in the CPS is used to assign non-filing dependents
to taxpayers, along with the ages of the dependents. This information is used to populate the
Taxsim variables used to assess personal exemptions, the Dependent Care Credit, the Child Credit,
and the Earned Income Tax Credit.
The income variables in the CPS ASEC are mapped to the Taxsim variables as described in
Table 5. For married couples, all income values entered into Taxsim are joint earnings, except in the
case of wage and salary income, which are kept separate. In both cases the employee-paid portion of
employer-provided health insurance plans are subtracted from wages and saleries. Dividend income
reported in the CPS is split between qualified and ordinary dividends based on the aggregate share
of dividends that are qualified, quaLfrac, from the IRS individual income tax returns line item
totals.26 The CPS no longer includes imputed capital gains; therefore they are omitted from the
submission to Taxsim. This limitation may bias the weighted average effective marginal tax rates
downwards for the household representing the top income quintile (where nearly all capital gains
accrue) if the inclusion would cause some households to be in a higher tax bracket.
The implicit deductions for each filer are computed as the difference between adjusted gross
26https://www.irs.gov/pub/irs-soi/16inlinecount.pdf
37
-------
income (agi) and taxable income (tax_inc) as reported in the CPS minus personal exemption de-
ductions accounting for the phase out. From this value, we subtract property and state taxes. We
submit either this value or zero, whichever is higher, to Taxsim as potential sources of itemized
deductions. Property taxes in the CPS ASEC (prop.tax) are associated with household records so
we divide those taxes equally amongst all tax filing units in a household.
For each representative filer, Taxsim returns the effective marginal tax rate for primary earner
wage income. Using the CPS ASEC person weights and primary earner wages, a weighted average
of the effective marginal tax rates for wage income are computed for each region and representative
household in the model. Primary earner wages are used as the weight because each married couple
has two returns in our sample that are the same except for switching the primary and secondary
earner. Since the entire FICA tax is collected on the household side in the model the labor income
and FICA tax rates are adjusted to account for the fact that employees do not pay income or FICA
taxes on employer paid shares of the FICA tax.
The personal labor income tax rates by region and household are presented in Figure 8a, and
the FICA tax rates are presented in 8b.27 The crossbars represent the national income-weighted,
average effective marginal tax rate for the representative household.
The average individual income tax payment for household h in region r, tLavgOr>h, is computed
following the same procedure outlined above for the effective marginal individual income tax rate on
labor income. However, in this case the rate used is the average individual income tax rate calculated
by Taxsim. The average individual income tax rates by region and household are presented in Figure
8c. These estimates are consistent with recent estimates by the U.S. Congressional Budget Office
(CBO), noting that the estimates for SAGE are slightly higher due to the inclusion of state income
taxes (CBO, 2018).
The effective marginal tax rate on capital income is calculated as a weighted average of corporate
and personal income tax rates. The exercise described above for determining personal labor income
tax rates is replicated for qualified dividends, interest income, and other business income, such
as ordinary dividends and income from sole proprietorships and partnerships. In these cases, a
national weighted average for the effective marginal tax rate is calculated with weights based on
the income category being considered. The corporate income tax is based on an assessment of the
average effective marginal corporate income tax rate by the U.S. CBO (CBO, 2017). Specifically
the average effective marginal corporate income tax rate is set to 0.186. It is assumed that capital
income passed on to households in the form of interest payments or dividends are subject to both
the effective corporate income tax rate and the effective personal income tax rate for those types
of income. In contrast, capital returns associated with sole proprietorships and partnerships is
assumed to be only subject to the effective personal income tax rate on those types of income.
Based on those assumptions, the effective marginal tax rate on capital income, tkr, is calculated
27Recent CBO estimates of the effective marginal federal income tax rate on wages without the Tax Cut and Jobs
Act (TCJA) is approximately 20% in 2016, which is consistent with the income weighted average effective marginal
federal income tax rate of approximately 20% used in the SAGE calibration (https://www.cbo.gov/system/files/
2019-01/54911-MTRchartbook.pdf).
38
-------
0.35
"g 0.25
E 0.20
.:
hh3
Household
(a) Labor Income Effective Marginal Tax Rate by Household and Region
CO
o
£ 0.11
CO
Ct
•
West
X
£
•
Midwest
<
o
LL
•
South
Northeast
% .
hh3
Household
(b) FICA Effective Marginal Tax Rate by Household and Region
a
;
hh3
Household
(c) Average Individual Income Tax Rate by Household and Region
Figure 8: Household Effective Marginal Labor Tax Rates
39
-------
Table 6: Tax Rates on Capital Income
Region
tk
nor
0.33
sou
0.33
mid
0.33
wes
0.33
as a weighted average of the effective marginal tax rates on capital income distributed as interest,
qualified dividends, ordinary dividends, and other business income, where the weights are the IRS
individual income tax returns line-item totals for the types of capital income.28 The values of the
capital income tax rate based on these calculations are presented in Table 6.
3.3 Substitution Elasticities
In the calibrated CES and CET functions, the input-output data are used to define the benchmark
value shares, and the free parameters are defined by the substitution elasticity parameters. The
list of substitution elasticities included in the model is presented in Table 7.
3.3.1 Armington Elasticities
The sector-specific Armington elasticities between national and foreign goods, se_n/, are based
on the estimates included in the GTAP database (Hertel et al., 2008). The GTAP elasticities are
based on econometrically estimated substitution elasticities between imports across foreign sources,
se_m, by Hertel et al. (2007) and using the "rule of two." The rule, first proposed by Jomini et al.
(1991) and applied widely in CGE modeling, suggests that the elasticity of substitution across
foreign sources is twice as large as the elasticity of substitution between domestic and imported
commodities29, such that
t se-m
se-nf = —. (62)
In cases where more than one of the 57 GTAP sectors map into a single SAGE sector, we use value-
weighted averages based on GTAP v9 imports by the United States at world prices (Narayanan
et al., 2016).
To define the elasticity of substitution between domestic goods and intra-national imports we
follow the work of Caron and Rausch (2013). They provide a framework for estimating U.S.
intra-national trade elasticities of substitution based on empirical estimates of international and
domestic border effects. Specifically, they note that the relative strength of the intra-national and
international border effects, a, is defined by the ratio of one minus the substitution elasticities
28https://www.irs.gov/pub/irs-soi/16inlinecount.pdf
29Using a back-casting experiment, Liu et al. (2004) found no evidence to reject the rule of two, providing additional
support for its continued use.
40
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Table 7: Elasticity Parameters
Parameter Description
Trade
se-nf Elasticity of substitution between national and foreign goods
se-dn Elasticity of substitution between domestic goods and national imports
te-dx Transformation elasticity between domestically consumed and exported goods
Standard Production
seJklem Substitution elasticity between material inputs and energy-value-added
se-kle Substitution elasticity between energy and value added
seJtl Substitution elasticity between capital and labor
se-ene Substitution elasticity between electricity and primary energy
se_en Substitution elasticity among primary energy sources
Resource Extraction, Agriculture, and Forestry Specific
se-rklem Substitution elasticity between resource and materials-energy-value-added
Putty-Clay Capital
teJt-ex Transformation elasticity of sector differentiated extant capital
seJnv Substitution elasticity in aggregate investment bundle
Household
se-d Substitution elasticity between consumption bundle and leisure
eta Inverse intertemporal substitution elasticity of consumption
41
-------
Table 8: SAGE Elasticities
Sector se_kl se_kle se_klem se_ene se_en se_nf se_dn
agf
1.07
0.40
0.98
0.68
0.33
2.45
4.13
bom
0.36
0.19
0.56
0.68
0.33
4.01
7.06
cem
0.20
0.25
0.81
0.68
0.33
2.90
4.98
chm
0.24
0.72
0.94
0.68
0.33
3.30
5.73
col
0.79
0.42
0.22
0.68
0.33
3.05
5.26
con
0.17
0.15
0.61
0.68
0.33
1.90
3.12
cpu
0.10
1.06
0.64
0.68
0.33
4.40
7.79
cru
0.79
0.42
0.22
0.68
0.33
7.30
13.20
ele
1.00
0.46
0.68
0.01
0.23
2.80
4.80
fbm
0.22
0.19
0.63
0.68
0.33
2.66
4.53
fmm
0.18
1.01
0.11
0.68
0.33
3.75
6.57
gas
0.79
0.42
0.22
0.68
0.33
2.80
4.80
hit
0.58
0.16
0.80
0.77
0.10
1.90
3.12
min
0.79
0.42
0.22
0.68
0.33
0.90
1.25
pmm
0.18
1.01
0.11
0.68
0.33
3.74
6.56
prm
0.12
0.18
0.68
0.68
0.33
3.30
5.73
ref
0.73
0.38
0.42
0.68
0.33
2.10
3.49
srv
0.31
0.27
0.66
0.77
0.10
1.90
3.12
tem
0.18
0.16
0.38
0.68
0.33
3.46
6.02
trn
0.54
0.46
0.73
0.25
0.25
1.90
3.12
ttn
0.14
0.42
0.22
0.25
0.25
1.90
3.12
wpm
0.12
0.24
0.67
0.68
0.33
3.06
5.28
wsu
1.00
0.46
0.68
0.68
0.33
2.80
4.80
between intra-national sources, se.d, and international sources, se_m, such that
1 ~ se~d
a = . (63)
1 — se_m
Given an estimate for a and se_m, this relationship may be used to solve for the substitution
elasticity across domestic sources, se_d. We follow Caron and Rausch (2013) and apply the rule
of two to calibrate the substitution elasticity between locally produced goods in the region and
intra-national imports, such that se-dn = se-dj2. Given this relationship, along with (62) and
(63), we can solve for the substitution elasticity between locally produced goods
se-dn = ^ — a ^ — se.nf^J . (64)
Coughlin and Novy (2013) estimate both intra-national and international border effects for the
U.S. Based on their results we assume that a is 1.868. The SAGE values for se.nf and se-dn are
presented in Table 8.
We also follow Caron and Rausch (2013) in setting the transformation elasticity of output
42
-------
between domestic use, national exports, and international exports, te-dx, to 2.
3.3.2 Production Elasticities of Substitution
Koesler and Schymura (2015) provide empirical estimates of the capital-labor substitution elas-
ticities (seJtl), (capital-labor)-energy substitution elasticities (seJtle), and (capital-labor-energy)-
materials substitution elasticities (seJtlem) at the industry level using a CES nesting structure
that is consistent with our standard production structure in Figure 4 and the resource dependent
sectors' production structure in Figure 5. The estimates are calculated with a panel dataset, cov-
ering 1995 to 2007, allowing for the estimation of long-run elasticities, which have been previously
applied to CGE modeling (e.g., Bohringer et al. (2016)). The 34 sectors estimated by Koesler and
Schymura (2015) are roughly consistent with our default aggregation, though notably they have
more detail in the service sectors and less detail in the resource extraction sectors. For cases where
a one-to-one mapping between their sectors and SAGE's sectors is not possible we use a weighted
average of the Koesler and Schymura (2015) elasticities, where the weighting is by the U.S. sectoral
output value in the last year of their dataset. For some sectors, the estimation routine of Koesler
and Schymura (2015) returned non-finite values for seJtl. Therefore, for the electricity and refining
sectors we use values from the recent study by Young (2013), which estimates sector-specific value-
added substitution elasticities for the United States30 Koesler and Schymura (2015) also reported
a non-finite value for seMe in the refining sector, in which case we apply the total industry value.
The SAGE values for se_kl, seJtle, and seJklem are presented in Table 8. In general, a larger value
for the substitution elasticity suggests a greater degree of substitutability between the inputs.
The interfuel substitution elasticities are based on estimates from Serletis et al. (2010a), which
provide the most recent estimates for the United States based on contemporary data disaggregated
across the industrial, commercial, electricity, and residential sectors. For the primary energy substi-
tution elasticity, se_en, in the industrial sectors we use the Allen elasticity across refined petroleum
and natural gas, as coal expenditures represent a small share of overall energy expenditures in those
sectors. For the electricity sector (ele), the primary energy substitution elasticity is set equal to
the estimate of the Allen substitution elasticity between coal and natural gas, as refined petroleum
inputs represent a very small share. The results of Serletis et al. (2010a) suggest there are few
substitution possibilities between refined petroleum and natural gas in the commercial sectors, so
the substitution elasticity in the services and healthcare sectors (srv and hit) is set to be commen-
surate with that finding. The substitution elasticity between the primary energy composite and
electricity, se_ene, is a weighted average of the Allen substitution elasticity estimates for electricity
and primary fuels from Serletis et al. (2010a). The weights represent the sector's national primary
fuel expenditures in the model's benchmark year based on EIA's State Energy Data System.31 We
assign values from the industrial sector to the manufacturing and resource extraction sectors in
the model.32 We assign values from the commercial sector to the services and healthcare sectors
30 We use the non-normalized generalized method of moments estimates from Young (2013).
31https://www.eia.gov/state/seds/
32Following this same procedure but using the meta-analysis results of Stern (2012) for the industrial sector produces
43
-------
(srv and hit). For the electricity sector we assume that the nest combining electricity and primary
energy inputs is essentially Leontief. For the transportation sectors we base the substitution elas-
ticities on the estimates of Serletis et al. (2010b) for high-income countries. The SAGE values for
se_en and se.ene are presented in Table 8.
3.3.3 Resource Extraction, Agriculture, and Forestry
In sectors with a fixed factor input, including the resource extraction sectors and the agriculture and
forestry sectors, the elasticity of substitution between the fixed factor resource and other inputs,
se-rklem, is calibrated to match a long-run supply elasticity based on the benchmark conditions,
similar to Balistreri and Rutherford (2001). In partial equilibrium with fixed prices for all non-
resource inputs and a fixed quantity for the resource, the elasticity of supply for a given sector is
given by
V = -Vres, (65)
where ares is the Allen own-price elasticity of substitution (Hertel and Tsigas, 2002). In the nesting
structure for sectors with a fixed factor, as depicted in Figure 5, the Allen own-price elasticity for
sector s in region r is
Ores = -se-rklemr,s {9~^res - l) , (66)
where 9r}S}res is the benchmark resource cost share of total costs (Keller, 1976). Combining (65)
and (66) provides the calibrated substitution elasticity for a given elasticity of supply
sejrklemryS = ^ . (67)
@r,s,res 1
The endogenous supply elasticity in the model is a function of the share of production from
new capital in the sector and the endogenously determined value shares, which differ from 9rtS}res.
As production with extant capital becomes a smaller share of total production over time, the
endogenous supply elasticity increases towards the long-run value to which the function is calibrated.
However, as demand for the sector's commodity expands over time the value share of production
from variable inputs increases (akin to a stock effect on marginal extraction costs), which in the
case of the CES production function places downward pressure on the endogenous supply elasticity.
Arora (2014) examines the natural gas supply elasticity in the United States before and after
the expansion of shale gas production through hydraulic fracturing, finding evidence of more elastic
supply in recent years. Based on these estimates, Arora and Cai (2014) suggest a long-run supply
elasticity of 0.5 for natural gas production as a reference case in CGE modeling. We apply a
long-run supply elasticity of 0.5 for the natural gas extraction sector (gas).
U.S. oil supply is also considered to be inelastic. Huntington (1992) reviewed expectations of
U.S. crude oil supply elasticities through the elasticities implicitly used in energy modeling systems
of the time and found an average long-run elasticity of 0.40. There is evidence that in recent
similar values for se_en and sesne.
44
-------
decades, the oil supply has been more inelastic than those implied expectations (Greene and Liu,
2015). Krichene (2002) estimates the long-run world crude oil supply elasticity to be 0.25 over the
period 1918-1999, with a lower elasticity estimates of 0.10 when the sample was restricted to the
later years. This is relatively consistent with recent estimates of short-run world crude oil supply of
0.10 by Caldara et al. (2018) and 0.15 by Baumeister and Hamilton (2019). Caldara et al. (2018)
provides evidence that short-run supply elasticities may be lower in non-OPEC nations relative to
the world value. However, Bj0rnland et al. (2017) finds that the supply elasticity for shale wells in
the U.S. (which are responsible for around 60% of U.S. oil production33) may be notably larger, in
the range of 0.3 to 0.9 depending on well characteristics. Finally, using a long-run supply elasticity
of 0.25, Beckman et al. (2011) find that the GTAP-E model was able to adequately capture the
variance of oil price responses to supply and demand shocks based on historical observations. Based
on this evidence, we apply a long-run supply elasticity of 0.15 for the crude oil extraction sector
(cru).
The supply of coal in the United States is generally thought to be elastic. For example, Balistreri
and Rutherford (2001) use a long-run supply elasticity of 1.9 to calibrate an energy-detailed CGE
model. This value is consistent with the long-run supply elasticity in other previous modeling
exercises (Golombek et al. (1995); Brown and Huntington (2003)). Empirical elasticities of coal
supply elasticities are limited. Dahl and Duggan (1996) survey the literature and find a range of
estimates between 0.05 and 7.9 for the United States, with a median value of 0.79. However, data
used in the included studies all end in the early 1970s. In a study of coal supply in Australia,
Beck et al. (1991) find a long-run supply elasticity of 1.9. Econometric analyses conducted by EIA
staff (EIA (2001)) find coal supply elasticities in the range of 1.5 to 3.0. Haggerty et al. (2015)
calculate an average supply elasticity of 2.4 from the results of econometric analyses underlying
recent versions of EIA's National Energy Modeling System. Based on this evidence, we apply a
long-run supply elasticity of 2.4 for the coal mining sector (col).
The long-run supply elasticity for the aggregate other mineral and metal mining sector (min)
is also likely to be elastic.34 Empirical estimates of supply elasticities for stone, sand, and gravel
mining are extremely limited. However, past investigations by the U.S. International Trade Com-
mission (ITC) found the short-run supply elasticity for cement and clinker to be between 2 and
4, suggesting the supply of stone inputs is likely to be fairly elastic (ITC, 2014a). There appear
to be no recent estimates of the supply elasticity for copper, though older estimates suggest that
the supply is elastic. For example, Foley and Clark (1981) estimate the long-run supply elasticity
of copper in the United States to be 6. While refractory minerals represent a smaller share of the
sector, a recent ITC investigation concluded the supply elasticity to be in the range of 5 to 7 (ITC,
2014b). Similarly, the ITC found that pure magnesium and alloy magnesium have a short-run
supply elasticity of 1.5 to 3 and 3 to 5, respectively (ITC, 2011). Based on this evidence, we apply
33https://www.eia.gov/tools/faqs/faq.php?id=847&t=6
34As reported previously, approximately two-thirds of the output value from the sector is attributable to stone
mining and quarrying (NAICS 21231) or sand and gravel mining (NAICS 21232). Of the remaining third of the
sector's output value, copper ore mining (NAICS 212234) accounts for approximately half.
45
-------
a long-run supply elasticity of 5 for the other mineral and metal mining sector (rriin).
The agriculture and forestry sector is dominated by crop and livestock production and therefore,
we focus on empirical estimates of long-run supply elasticities in those areas. The majority of U.S.
cropland is associated with the production of grains, with corn and soybeans as the dominant crops.
Kim and Moschini (2018) estimate the long-run supply elasticity of corn and soybeans in the United
States to be 0.4 and 0.3, respectively. These results are consistent with those of Hendricks et al.
(2014), who find a long-run supply elasticity for both corn and soybeans in the United States of 0.3.
While older studies also find a long-run supply elasticity for corn of 0.3, the estimate for soybeans
is higher at 1.6 (Shideed and White, 1989).35
For elasticities in livestock production, Kaiser (2012) estimates a long-run elasticity of hog
supply of 0.3. Boetel et al. (2007) estimate a long-run supply elasticity of breeding stock with
respect to the hog price of 0.6. Marsh (2003) and Sarmiento and Allen (2000) estimate long-
run cattle supply elasticities of 0.6 to 2.8 and 0.3 to 2.9, respectively. These ranges are roughly
consistent with previous estimates of cattle supply elasticities (e.g., Rucker et al. (1984) and Buhr
and Kim (1997)). Little empirical evidence exists for the long-run supply elasticity of poultry (e.g.,
broilers) in the United States.36 Based on this evidence, we apply a long-run supply elasticity of
0.5 for the agriculture and forestry sector (agf).
3.3.4 Large Open Economy Elasticities
Similar to the natural resource sectors, the large open economy assumption is operationalized by
calibrating the fixed factors in equations 3 and 4 so that model behavior is consistent with exogenous
price elasticities. The price elasticities used for international export demand and import supply
are produced by tracing out export demand and import supply functions with the GTAPinGAMS
package for 2011 (Lanz and Rutherford, 2016) and fitting an isoelastic function to the simulated
data. Table 9 reports the generated price elasticities for export demand and import supply by
sector (in columns labeled as GTAP). Import supply elasticities are noticeably higher indicating a
flatter supply curve (and in many cases well approximated by the small open economy assumption).
In equation 67, the elasticity of substitution is solved in terms of an exogenously set supply
elasticity and value shares derived from the underlying social accounting matrix. In this case,
however, the value shares of the export demand and import supply fixed factors are not known.
Therefore, the elasticity of substitution is set equal to one and the procedure solves for the value
shares. Rearranging terms, costs shares are solved for as,
cs-loejxs = —(68)
\^S I
3BIqbal and Babcock (2018) find global long-run supply elasticity estimates of 0.2 and 0.6, respectively. However,
Roberts and Schlenker (2013) find a slightly lower global supply elasticity for corn of around 0.1. For non-grain U.S.
agricultural production, a significant portion of production value in attributed to California. Russo et al. (2008)
study long-run supply elasticities of Californian horticulture and generally find estimates of less than 1, with values
of 0.7 for almonds, 0.2 for walnuts, and 0.4 for tomatoes.
36Kapombe and Colyer (1998), Holt and Aradhyula (1998), and Holt and McKenzie (2003) all find evidence of a
short-run supply elasticity of 0.1.
46
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Table 9: Large Open Economy Price Elasticities
Sector
Export Demand
Import Supply
GTAP SAGE
GTAP SAGE
agf
-4.02 -4.01
108.10 108.13
bom
-7.32 -7.32
192.47 192.47
cem
-5.27 -5.27
153.56 153.67
chm
-5.79 -5.79
194.73 194.73
col
-5.05 -5.05
725.14 727.77
cpu
-7.98 -7.98
188.47 188.47
cru
-10.15 -10.15
10.00 10.00
ele
-5.60 -5.60
210.53 210.53
fbm
-4.67 -4.67
140.24 140.23
fmm
-6.99 -6.99
193.31 193.32
gas
-27.04 -27.04
167.77 167.77
hit
-3.74 -3.74
37.10 37.10
min
-1.47 -1.47
231.66 231.93
pmm
-6.75 -6.75
215.72 215.72
prm
-5.79 -5.79
194.73 194.73
ref
-3.63 -3.63
65.03 65.03
srv
-3.77 -3.77
75.17 75.19
tem
-5.74 -5.74
156.73 156.73
trn
-2.12 -2.12
313.90 313.90
ttn
-3.21 -3.21
92.22 92.22
wpm
-5.61 -5.61
132.07 132.07
and
csJioe_mq =
1
(69)
1 + e™
where exs is the price elasticity of export demand for sector s and e™ is the price elasticity of import
supply for sector s. The reference levels of the fixed factors for exports (fixOs) and imports (fimOs)
are then defined as,
fixOs =
csdoejxs
(1 — csJoejxs)
I>°
r,s,ftrd
and
fimOs = csJoejns ^ mOr>sjtrd-
(70)
(71)
Given the dynamic baseline assumptions in the model, the model's endogenous price elasticities for
export demand and import supply are slightly different from the calibration points. Table 9 also
reports the average implicit price elasticities across regions in SAGE in the base year of the model.
47
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3.3.5 Partial Putty-Clay Elasticities
The elasticity of transformation for extant capital introduces a small amount of flexibility to shift
extant capital across sectors within a model region. We set this parameter to 1.5 to capture the
observation that some extant capital can be re-purposed in other sectors, though not excessively
so. Lacking good empirical work on this topic, we chose the elasticity to restrict the shift of a
given sector's extant capital stock for use in another sector to be roughly smaller than 5% (for non
fixed factor sectors) for reasonable sized policy shocks. The substitution elasticity in the aggregate
investment good bundle is set to be 0.05. Our formulation roughly follows Yuan et al. (2019), who
assume that aggregate investment is composed of fixed proportions of commodity output, while
allowing for a CES representation to explore this assumption in sensitivity.37
3.3.6 Consumption Elasticities
For non-leisure consumption, the model is calibrated to exogenous income elasticities as estimated in
the literature.38 The linear expenditure system requires that total commodity demand be divided
between discretionary and subsistence level spending. Because the underlying social accounting
matrix only reports total commodity demands, we determine subsistence levels that are consistent
with exogenously specified income elasticities. We illustrate this procedure in a simplified context.
Consider the LES utility function,
u (cdr>ith,cdr,n,h) = Yl(cdr>s,h ~ sd0rtSth)csJeSr-s-h. (72)
Maximizing this utility function subject to a budget constraint yields the following demand function,
j ia CS-lcSr s h{,Ir,h P$r s$dOr s h)
cdr^h = sdOr s h H - ! 5 ! L^, (73)
par,s
where par^s is the regional price for commodity s and Ir>h is the total income level for each agent.
This demand function for total non-leisure commodity expenditures is broken into the subsistence
demand component and the discretionary demand component. In this equation, there are two
unknowns: sdOr>Sth and csJesr>Sth- The benchmark data for SAGE only contains total commodity
demands, cdOr>Sth- Assuming reference prices are unity, algebra reveals the following LES budget
shares by rearranging equation 73,
cs les h - Cdr's'h ~ sd0r's'h (74)
1r,h 2-^/ss r,ss,h
37Data produced by the Bureau of Labor Statistics suggests that the composition of investment is to some extent
responsive to changes in prices over time (see: https://www.bls.gov/emp/data/input-output-matrix.htm). How-
ever, we are unaware of studies characterizing the magnitude of this price responsiveness and as such, provide the
option to perform sensitivity to the assumption made above.
38Technically, the model's implicit elasticity of consumption to aggregate consumption expenditures is calibrated to
match empirical estimates of the same behavioral response. But for simplicity of exposition, this elasticity is referred
to as the income elasticity in section 3.3.6.
48
-------
Income elasticities of demand are then defined as,
e[es = csJesr,s,h • (75)
Cu>r,s,h
Equations 74 and 75 are used to calibrate the nested non-leisure component of the demand system.
Note that we can substitute in benchmark levels of cdr>s>h {cdOr>s,h) and Ir,h directly from the un-
derlying social accounting matrix. We pin down the remaining degree of freedom using estimated
expenditure elasticities. To do so, we use the approach developed in Aguiar and Bils (2015) to
estimate expenditure elasticities using data from the Consumer Expenditure Survey (CEX) pro-
vided by the Bureau of Labor Statistics. Note that in our simple calibration above, income equals
aggregated non-leisure commodity expenditures. In SAGE, that is not the case. Therefore, we use
the approach in Aguiar and Bils (2015) to estimate expenditure elasticities that do not account
for leisure demand. The authors estimate log-linear Engel curves controlling for household demo-
graphics (etc. age, number of earners, family size) for different commodity groups and instrument
for total expenditures with total income to correct for reporting measurement error. The approach
identified by Aguiar and Bils (2015) has the advantage of not relying on price data jointly with
expenditure data to estimate a complete set of income elasticities (relative to estimating an LES
consumer demand system directly). The original estimates in the paper are reported using data
from 1994-1996. We update these estimates using CEX data from 2013-2017.39 We use this range
of data to capture income elasticities that correspond with the reference year (2016) in SAGE. In
our adapted estimation routine, we expand the set of commodity groupings relative to the origi-
nal paper to aggregate to SAGE sectors. Estimated elasticities are mapped to SAGE sectors as
weighted averages based on the Personal Consumer Expenditure (PCE) bridge file to input output
accounts provided by the BEA.40 Table 10 reports the reference elasticities used in this calibration
procedure and Table 11 reports the mapping shares between the CEX categories and SAGE sectors
as proxied by the PCE bridge file.
To ensure that the aggregate national subsistence demands are independent of the regional
aggregation used in the model, the calibration routine is first run at the national level with a single
household to generate total calibrated subsistence demands by commodity group. The calibration
for the default aggregation of the model (that is distinguished by both regional and household het-
erogeneity) is then conducted but constrained to match the subsistence demand totals as estimated
in the single region-household case. Because the system becomes over identified when constrain-
ing the aggregate subsistence demand levels to equal the values in the national model calibration,
we use a least squares calibration routine. This procedure will naturally allow calibrated income
elasticities to vary by region and income group. However, the least squares routine penalizes devi-
ations away from the empirically estimated elasticities while still being subject to the calibration
constraints (equations 74 and 75).
39For replication code from Aguiar and Bils (2015), see https://www.aeaweb.org/articles?id=10.1257/aer.
20120599.
40See: https://www.bea.gov/industry/industry-underlying-estimates.
49
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Table 10: Expenditure Elasticities
Estimated Expenditure Elasticities
(methodology from Aguiar and Bils (2015))
Mapped Elasticities
in SAGE
Sector Elasticity
CEX Category
Elasticity
Alcoholic Beverages
1.1
agf
1.02
Food and Other Beverages
0.85
min
1.27
Tobacco Products
0.34
ele
0.31
Clothing and Apparel
1.13
gas
0.32
Personal Care
1.07
wsu
0.26
Reading
0.74
fbm
0.86
Education
1.5
wpm
1.4
Medical Treatment
1.16
ref
0.65
Entertainment
1.39
chm
1.17
Electricity Utilities
0.31
prm
1.17
Natural Gas Utilities
0.32
cem
1.58
Heating Fuels
0.31
pmm
1.55
Telephone
0.65
fmm
1.41
Water Utilities
0.26
cpu
1.31
Housing
0.45
tem
1.07
Housing Supplies and Furnishings
1.58
bom
1.27
Vacation Home Rentals
0.6
trn
0.97
Transportation Fuels
0.66
ttn
1.58
Vehicle Maintenance
0.78
srv
0.79
Vehicle Financing
0.27
hit
1.17
Vehicle Services
1.1
Given the dynamic nature of the model and the baseline calibration that deviates from the
assumptions in the simplified static household problem above, the model's endogenous income
elasticities differ slightly from the calibration points. Figure 9 presents the income elasticities
implicit in the model's baseline along with the empirically estimated targets from the calibration
procedure. The largest, though still relatively small, deviations from the calibration targets occur in
sectors where the presence of fixed factors causes higher relative price growth in the outer simulation
years.
The consumption-leisure substitution elasticity is determined jointly with the time endowment
in the model to match observed estimates of the compensated and uncompensated labor supply
elasticities in a static setting. Consider the demand system in (27) and the simplified budget
constraint
pdt,r,hdt,r,h — (1 if plt,rt&t,r,h
where 7Tt,r,h represents non-labor income net of savings and tl-refundt,r,h represents a hypothetical
"refund" from the government to the household for the difference between the marginal and average
50
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Table 11: CEX to SAGE Mapping Shares
SAGE Sector
CEX Category
Share
SAGE Sector
CEX Category
Share
agf
Food and Other Beverages
0.69
ref
Transportation Fuels
0.94
agf
Entertainment
0.31
ref
Heating Fuels
0.05
cem
Housing Supplies and Furnishings
0.99
ref
Medical Treatment
0.00
cem
Vehicle Maintenance
0.01
prm
Vehicle Maintenance
0.45
chm
Medical Treatment
0.77
prm
Housing Supplies and Furnishings
0.44
chm
Personal Care
0.15
prm
Vehicle Services
0.04
chm
Housing Supplies and Furnishings
0.06
prm
Personal Care
0.02
chm
Entertainment
0.01
prm
Entertainment
0.02
chm
Reading
0.00
prm
Medical Treatment
0.02
chm
Food and Other Beverages
0.00
prm
Reading
0.01
chm
Heating Fuels
0.00
pmm
Housing Supplies and Furnishings
0.93
chm
Vehicle Maintenance
0.00
pmm
Vehicle Maintenance
0.04
chm
Transportation Fuels
0.00
pmm
Entertainment
0.03
cpu
Entertainment
0.47
srv
Housing
0.34
cpu
Housing Supplies and Furnishings
0.27
srv
Food and Other Beverages
0.12
cpu
Telephone
0.11
srv
Vehicle Financing
0.12
cpu
Clothing and Apparel
0.05
srv
Entertainment
0.10
cpu
Personal Care
0.05
srv
Education
0.07
cpu
Medical Treatment
0.03
srv
Medical Treatment
0.05
cpu
Vehicle Maintenance
0.02
srv
Vehicle Maintenance
0.04
cpu
Vehicle Services
0.00
srv
Housing Supplies and Furnishings
0.04
fmm
Entertainment
0.49
srv
Telephone
0.04
fmm
Housing Supplies and Furnishings
0.37
srv
Vehicle Services
0.03
fmm
Personal Care
0.11
srv
Personal Care
0.02
fmm
Vehicle Maintenance
0.03
srv
Reading
0.01
fmm
Vehicle Services
0.00
srv
Water Utilities
0.01
fbm
Food and Other Beverages
0.73
srv
Vacation Home Rentals
0.01
fbm
Alcoholic Beverages
0.13
srv
Clothing and Apparel
0.00
fbm
Tobacco Products
0.09
trn
Vehicle Services
0.71
fbm
Entertainment
0.04
trn
Vacation Home Rentals
0.22
hit
Medical Treatment
0.98
trn
Vehicle Maintenance
0.06
hit
Education
0.02
trn
Food and Other Beverages
0.00
min
Housing Supplies and Furnishings
0.63
trn
Housing Supplies and Furnishings
0.00
min
Food and Other Beverages
0.18
trn
Entertainment
0.00
min
Heating Fuels
0.13
tem
Vehicle Services
0.89
min
Entertainment
0.06
tem
Vehicle Maintenance
0.09
bom
Clothing and Apparel
0.52
tem
Entertainment
0.02
bom
Housing Supplies and Furnishings
0.26
ttn
Housing Supplies and Furnishings
1.00
bom
Entertainment
0.13
gas
Natural Gas Utilities
1.00
bom
Medical Treatment
0.06
wsu
Water Utilities
1.00
bom
Reading
0.01
ele
Electricity Utilities
1.00
bom
Personal Care
0.01
wpm
Housing Supplies and Furnishings
0.66
bom
Vehicle Maintenance
0.00
wpm
Clothing and Apparel
0.16
bom
Vehicle Services
0.00
wpm
Personal Care
0.15
wpm
Reading
0.02
wpm
Heating Fuels
0.01
wpm
Entertainment
0.01
tax rate. We use the notation of tl-refundt>rth in this section to emphasize that the tax rate relevant
for behavioral choices is the marginal rate. Assuming labor income taxes are constant over time,
tk,r,h + tficat,r,h = tlt+i,r,h + tficat+i>r,h V t, the Marshallian demand for leisure is
leistrh =leisOrh
ttOr,h + (1 — tlt,r,h — tficcLttr,h + plOrtLrefundOr>h) plOrteOrth J yplO
CS-Clr h
PCt,r,h
pcOrh
1—se.cl
+ (1 - CS-dr>h)
plt,r
plOr
1—se-cl
-1
— se-cl
(77)
51
-------
1.6
1.2
0.8
0.4
1.6
1.2
0.8
>>
B 0-4
(/)
jo
LU
(D
§1.6
o
_c
1.2
0.8
0.4
1.6
1.2
0.8
0.4
bom
LX it* •£*£->
chm
*u.xj:>*j Mm?
cpu
ele
fbm
fmm
gas
€<^*Q\S6^£X*
hit
^xr&£*rn'
Year
ow>
pmm
prm
ref
2020
2040
2060
2080
: m KMzm&t^msy
s»ouc«dk>
tem
trn
cxauiisi^
ttn wpm
#«. '«c
_i—i—i—i— —i—i—i—i—i— —i—i—i—i—i— —i—i—i—i—i— '/r ' y~ ~" •
hh1 hh2 hh3 hh4 hh5 hh1 hh2hh3hh4hh5 hh1 hh2 hh3 hh4 hh5 hh1 hh2 hh3 hh4 hh5 hh1 hh2hh3hh4hh5
Household
Figure 9: Calibrated Income Elasticities
The uncompensated price elasticity of leisure demand, may be obtained from (77), such that
leis — dl&iSt^r ,h Ph
rt.r.h —
9plt,r ldSt,r,h
(1 t^t,r,h plt,rt&t,r,h P^tyrtl-TCfUTldt^^
^tyryh (1 t^t,ryh t f ^C&t,r,h) P^t,rt^tyr,h plt,rtl-TCf UTldt^,h
se_cl—1
- (1 - cs-dr h)
plOf
plt,r
^ {P^t,r,hi Pit,;
\ 1—se-cl
+ se-cl
Id \ se-c^~ 1
(1 - cs-clr h) ( ) e {pct^h,plt,r)l~se~d - 1
pit,
r.h
(78)
where
^ {PCt;r,hi plt,r) —
CS-Cl
r.h
pCt,r,h
PC0r,h
1—se_cl
+ (1 - CS-Clr h)
plt,r
pl0r
1—se_cl
(79)
52
-------
The first two components of (78) define the income elasticity of leisure,
(1 tfiCCLf^r^}i)pltyrtGtjr,h~\~ pltptl-TCfUTldt^fo
^t,r,h ~l~ (1 ^ f ic&t r h) pltyrt&t,r,h H~ P^tyrtl-TCfundi^h
7n n se_cZ-1
plOr\ ^ 7 se-cl
^t,r,h
- (1 - cs-clr>h) J e (?"V,/i, pk
and the third component represents the substitution effect, or the compensated price elasticity of
leisure demand,
leislcl 7
^t,r,h = se~cl
se-cl—1
(f - CS-dr,h) ( ) eipCt^Pkr)1 ^ ~ 1
(81)
This may be verified through the Hicksian demand function via the Slutsky equation. Given the
definition of labor supply, tet,r,h — leist,r,h, the compensated labor supply elasticity, or substitution
effect, is
l\cl leis\cl ldSt,r,h /oo\
elr,h = ~Vt,r,h 7- J— • (82)
tet,r,h ~ ieiSt,r,h
And the uncompensated labor supply elasticity is
l _ leis le"ist,r,h ,„o\
et,r,h H't,r,h_L i ¦ >
tet,r,h ~ ieiSt,r,h
which, may be written as
I _ ( I , leis\d\ leist,r,h /s4x
et,r,h \^t,r,h ' ^t,r,h I x„ * (84)
V ' ' / tet,r,h ~ ieiSt,r,h
We define the share of the time endowment spent on leisure as t,r,h leis\d
c • — /or\
t,r,h i A ^t,r,h (85)
J- - h CS~° r'h
Assuming that in the benchmark prices are normalized to unity such that the effective labor price is
53
-------
(1 — tiotrth — tficaotrth) and given the definition of cs-clrth and an estimate of the income elasticity
of labor, e1, (76) and (88) may be substituted into (87) to yield the calibrated benchmark value of
leisure
leisOrh = dcOryh^ —— —^
(1 - tl0>r>h - tfica0,r,h) (1 + eJ) + "fo!"
From (81), the benchmark uncompensated leisure demand elasticity is
Vo?r,hl = ~se-d ¦ C.S-Clr,h- (90)
Substituting (90) into (85) yields the calibrated version of the elasticity of substitution between
consumption and leisure,
el\dclOr hlOr h , x
se-cl = , . „ , , (91)
leisOrftdcOrft
where e^d is the empirical estimate of the substitution elasticity. The observed labor earnings are
combined with the calibrated benchmark value of leisure in (89) to determine the time endowment
^cOr^h = ^0r^h ldsOr^.
To calibrate the time endowment and the substitution elasticity between consumption and
leisure, we use the conclusions from the literature review by McClelland and Mok (2012) on esti-
mates of the income and substitution effects for the United States. Specifically, they conclude that
estimates on the order of e1 = —0.05 and el^cl = 0.20 are representative of the most recent empirical
evidence. Given the dynamic nature of the model and the baseline calibration that deviates from
the assumptions in the simplified static household problem above, the model's endogenous labor
supply elasticities differ slightly from the calibration points. Figure 10 presents the substitution
and income effects implicit in the model's baseline.
In the households' welfare maximization problem the additively separable nature of the in-
tertemporal welfare function in (23) and the isoelastic form of the intra-temporal utility function
(25) mean the elasticity of intertemporal substitution will be 1/rj. In a recent review of over 1,400
estimates of the elasticity of intertemporal substitution for the United States, Havranek et al. (2015)
find a mean value of 0.6. Based on this evidence, we set the value of rj to 1.66.
3.4 Dynamic Baseline
The model's baseline is a result of the economic structures and parameters previously defined, along
with exogenous growth assumptions regarding: productivity, population, government accounts,
foreign accounts, and energy use. Each of these components is discussed in turn, followed by a
presentation of baseline indicators from the default version of the model.
As discussed in Section 2.7, the model is closed using a terminal condition that assumes the
economy converges to a steady state in the very long-run. Because the model includes fixed factors
of production, achieving convergence to a steady state requires that growth trends to zero in the
very long-run and all quantities and prices remain constant. The assumptions that allow the model
54
-------
0.2
w
(0
~ 0.1
>*
Q.
D
CO
0.0
** *** k---
A 4 *A v
^ A ^ * A # A A
A AA A A4Ai
• . - V/ • {W'.VN "vV v"-"---
A
Effect
• Income
A Substitution
Year
• 2020
2040
2060
• 2080
v.-
- I- - ^*4 - .>* ¦
-0.1
hh1
hh2
hh3
Household
hh4
hh5
Figure 10: Calibrated Labor Supply Elasticities
to meet these terminal conditions are described in each of the Subsections below. Care is taken
to ensure that the assumptions required for the model's terminal conditions do not meaningfully
impact the results of the model in the time frame typically considered in regulatory analysis.
However, in instances where a particularly long time-horizon is relevant for the analysis these
specification can be revisited if necessary.
Also relevant to the baseline are assumptions regarding the initial private return to capital,
rbar, which is set to 0.045. The interest rate reflects the average after-tax rate of return on private
capital. Given the capital tax in Section 3.2 the social return on private capital in the model is
approximately 0.07, which is consistent with the average pre-tax rate of return on capital observed
between 1960 and 2014 (CEA, 2017). The depreciation rate, 5, is set to 0.05, which is the average
U.S. capital depreciation rate from 1950 to 2014 as estimated by Feenst.ra et al. (2015). This rate
is applied to both new and extant capital.
The pure rate of time preference, p, for households is a determinant of their savings rate and
therefore, important for defining the baseline. Based on the isoelast.ic form of the intra-temporal
utility function, the pure rate of time preference, p, in (24) is calibrated via the Ramsey formula
given the specification of rj, rbar, and the expected labor productivity and population growth rates
over the first four model periods. Based on these assumed parameter values, p is about 0.018.
Opinions on the most appropriate value for p vary. Some argue on ethical grounds that it should
be equal to or very near zero (e.g., Ramsey (1928), Stern (2007)). Others rely on descriptive
approaches to backout the implied pure rate of time preference, which typically imply somewhat
higher values between 0.02 and 0.03 (Nordhaus, 2007). See Arrow et al. (2013) for a summary of
these different approaches.
55
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3.4.1 Productivity Growth
The foundation for productivity growth in the model is Harrod neutral (i.e., labor augmenting)
technological progress. Aggregate economy-wide labor productivity growth is calibrated to match
the estimates used in the CBO Long Term Budget Projection, which extends to 2050.41 As previ-
ously noted, to meet the terminal conditions for the solution algorithm, growth in the very long-run
needs to converge to zero. Therefore, the aggregate labor productivity growth rate in the last pe-
riod of the CBO projection is extrapolated to 2060 at which point it linearly declines to zero by
2080.
Future productivity growth is not expected to be uniform across the sectors of the economy.
To calibrate exogenous labor productivity growth, Lprodt,s, in SAGE historic differences in labor
productivity growth across sectors are extrapolated in a manner consistent with the assumptions
regarding economy-wide productivity growth based on the CBO projection.
The Integrated Industry-level Production Account data from BEA and the U.S. Bureau of Labor
Statistics (BLS), covering 1998 to 2017, provide estimates of historic integrated labor productivity
growth by sector in addition to data on gross output. This information is used to developed output-
weighted average labor productivity growth estimates for each of the SAGE sectors. Prior to 2050,
the baseline assumes that these historic differences in productivity will persist. After that point,
the variance across sectors is calibrated to linearly decline to zero by 2070 (i.e., the productivity
growth rate in each sectors converges to the mean growth rate).
In each model year, the sector-specific distribution of growth rates is then scaled by a constant
proportion so that the aggregate economy-wide labor productivity growth matches the calibrated
aggregate projections previously discussed. This scaling to match the aggregate productivity growth
assumption is conducted conditional on relative labor demand across sectors in the benchmark year
and persisting throughout the modeling horizon. This condition will not hold in the baseline as
heterogeneity in sectoral growth rates alone will cause sectors' shares of aggregate labor demand to
shift over time. However, simultaneously solving for both the model's baseline and these calibrated
scaling parameters is computationally infeasible. While restricting sectors' share of labor demand
to the benchmark levels in this scaling procedure will lead the baseline growth rate of aggregate
labor productivity to be higher than the intended calibration point from the CBO projections,
in practice the difference is relatively small. Figure 11 presents the growth rate of economy-wide
labor productivity in the SAGE baseline and the CBO calibration points. The differences due to
use of the benchmark labor shares will be most prevalent in the later years. The larger differences
between the SAGE baseline and the CBO calibration points in the first two simulation periods are
due to the representation of large but short-term COVID related impacts on labor markets in 2020
in the CBO projection. The SAGE baseline smooths out these impacts due to the larger time steps
and forward looking nature of the model.
Figure 12 presents the exogenous sector specific labor productivity growth rates for SAGE in
addition to the historical growth rates used for the calibration. While there is temporal heterogene-
41https://www. cbo.gov/data/budget-economic-data
56
-------
2020
Source
SAGE
CBO
2030
2040
2050
Year
Figure 11: Aggregate Labor Productivity Growth in SAGE Baseline and CBO Target
ity in the exogenous growth rates the figure presents average annual growth rates over two periods
to more easily facilitate a comparison.
3.4.2 Population Growth
Population in the model is assumed to grow at an exogenous rate equal to the growth rate of the
labor force in the CBO Long-Term Budget Outlook, which extends to 2050. As previously noted,
to meet the terminal conditions for the solution algorithm growth in the very long-run needs to
converge to zero. Therefore, the population growth rate in the last period of the CBO projection
is extrapolated to 2060 at which point it linearly declines to zero by 2080.
Assumed population growth is presented in Figure 16.
3.4.3 Government Accounts
The government agent, in SAGE represents all federal, state, and local governments in the United
States. Real government expenditures are exogenously specified as is the level of deficit financing.
The relevant expenditure variables are government consumption, govt,r, interest, payments, gintt
and gint-rowt, and transfer payments, transferst,r,h- Where possible we calibrate the variables to
CBO's budget, projections.42 However, CBO's budget, projections only cover the federal portion of
the government, expenditure variables and in many cases are only presented in the 10-yea.r budget,
outlook, requiring extrapolation for the longer time horizon in SAGE.
42https://www. cbo.gov/da.ta/budget-economic-data
57
-------
con
fbm
cem
ttn
fmm
hit
prm
wsu
ele
trn
bom
o
o chm
(D
CO
agf
min
col
wpm
srv
ref
gas
pmm
tern
cru
cpu
2 4
Annual Labor Productivity Growth [%]
Figure 12: Historical and Calibrated Sectoral Labor Productivity Growth Rates
58
-------
To set the government deficit we follow an approach similar to Jorgenson et al. (2013). Initially,
the federal deficit is calibrated to grow at the rate projected in the CBO 10-year budget projection.
In the benchmark year, state and local governments have a small deficit which is assumed to follow
real GDP growth over the 10-year budget projection period. At the end of that projection period
all government deficits are assumed to linearly decline to zero over the next 40 years, after which
point they remain at zero.
The growth of interest payments both domestically, gintt, and to the rest of the world, gint-rowt,
are based on the growth of government debt. Since the current level of all government debt is not
part of the SAM, the U.S. Federal Reserve estimates of federal debt43 and state and local government
debt44 are used to set the starting point for total public debt. The growth of debt is based on the
deficit projection described above. Total interest payments are then assumed to follow the growth
of debt. The baseline does not attempt to project changes in the share of debt held domestically
compared to the rest of the world. Therefore, domestic interest payments and foreign interest
payments are assumed to grow at the same rate.
Both real federal government consumption and transfer payments follow a similar calibration
process. In both cases they are assumed to initially grow at a rate consistent with the CBO 10-
year budget projection.45 Afterwards, federal government consumption and transfer payments are
assumed to grow at the rate of GDP. There are no comprehensive authoritative projections for
state and local government accounts equivalent to CBO's projections for the federal government.
Therefore, we assume the state and local government consumption and transfers will grow at the
rate of real GDP throughout the time horizon.
The real GDP growth rate projection used to calibrate these exogenous payment projections is
based on the extended projection in the CBO Long-Term Budget Projection out to 2050 and the
implied growth rate based on aggregate labor productivity and population growth rate assumptions
beyond 2050. The latter portion ensures that the projection of government expenditures and trans-
fer payments is consistent with the exogenous assumptions regarding productivity and population,
which is particularly important for ensuring that the terminal conditions in the model will hold.
An alternative approach to projecting government accounts would be to exogenously specify the
government accounts as a share of GDP and allow the level to be endogenously determined. Since
government consumption does not directly enter the utility functions for agents in the model, the
baseline for SAGE uses exogenously projected levels to facilitate consistent changes in welfare when
modeling policy changes. For a similar reason, the government budget constraint is endogenously
balanced through lump sum transfers with households.
43https://fred.stlouisfed.org/series/GFDEBTN#0
44https://fred.stlouisfed.org/series/SLGSD0DNS#0
4BFor historic years that may be included in the baseline due the benchmark year, CBO estimates of realized values
are used.
59
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Figure 13: Historical Net Income and Net Transfers from Rest of the World as Percent of GDP
3.4.4 Foreign Accounts
There are four variables associated with the rest of the world that are exogenously specified: the
current account balance, curactba.lt, net. taxes and transfers from the rest of the world, tranjrowt,
net income for the rest of the world, incjrowt, and government interest paid to the rest of the
world, gint-rowt-
To set the current account balance, curactbalt, we follow an approach similar to Jorgenson
et. al. (2013) and the one used for the government deficit. Initially, the current account balance is
calibrated to grow at the rate projected by the CBO in their economic projections. At the end of
that projection period the current account balance is assumed to linearly decline to zero over the
next 40 years, after which point it remains at zero.
Both net taxes and transfers from the rest of the world, tran-rowt, and net income for the rest
of the world, incjrowt, are calibrated in a similar fashion. Historically, net taxes and transfers from
the rest of the world have been a roughly constant relative to GDP at around 0.5%, see Figure 13.46
Net income from the rest of the world relative to GDP was consistently around 1% from 1990 until
2008, after which it increased to around 2% where it has remained for the last decade. Given the
relatively stable relationship over the last decade for both variables, they are calibrated to follow
real GDP growth similar to the method described in Section 3.4.3.
The exogenous projection of government interest paid to the rest of the world is described in
Section 3.4.3.
46Figure 13 is based on data from the BEA National Income and Product Account tables.
60
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3.4.5 Baseline Energy Use
The cost shares in the production functions are adjusted to capture expected technological change
in the energy intensity of production based on EIA's Annual Energy Outlook (AEO) forecast.47
To get the unit energy consumption (UEC) we divide the total energy consumption in the AEO
by the real value of shipments for each sector. The National Energy Modeling System (NEMS)
used for the AEO only allows for limited fuel switching within the industrial sectors, so changes
in the UEC over time predominately represent exogenous forecasts regarding technological change
in energy efficiency. We use the average growth rate of the UEC in the AEO over SAGE model
periods to calibrate the cost shares in the production function. The UEC relative to its value in
the benchmark year is denoted as ene-growthtyS.
The change in energy efficiency is assumed to be capital embodied. Therefore, the change is
represented as a shift from energy use to capital such that the "benchmark" values for intermediate
and capital inputs as well as the cost shares are time dependent. The partial putty-clay framework
needs to be accounted for to ensure that the overall UEC trend in SAGE is consistent with AEO,
since only production with new capital is associated with the improvements and the goal is to match
the overall UEC trend in AEO. The energy-related intermediate inputs and capital benchmark
values for production with new capital are calibrated, such that
and
where
idOt,r,ss,s = ene-f actort,sidOotr,ss,s ss e sene (92)
= M0„„, + _ (93)
ene.factort,s = "j (Q4)
ene-growthtySqJbaset — (1 — 5)*
qJbaset — (1 — 5f
sene e (col,gas,ref,ele) is the set of primary energy commodities plus electricity, and q-baset
reflects an approximation of general growth of the economy by capturing the cumulative growth of
the effective labor force (i.e., aggregate economy-wide labor productivity growth plus population
growth). The relevant cost shares, csJtle and csJtl, become time dependent and are adjusted to
be consistent with (92) and (93).48
The mapping from the AEO sectors to the SAGE sectors is presented in Table 12. For the
non-truck transportation sector, trn, the UEC growth rate is based on the average growth rate of
air transportation fuel efficiency as forecast by the AEO, since this represents a large share of the
energy consumption for the sector. For the truck transportation sector, ttn, the UEC growth rate
is based on the average growth rate of truck freight transportation fuel efficiency as forecast by the
AEO. No changes in the energy intensity of the electricity sector are assumed.
47The calibration is conducted with the most recent AEO forecast that includes a representation of the benchmark
year for SAGE.
48Outside of this section we exclude the time subscript on the benchmark values and cost shares to simplify the
exposition.
61
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Table 12: Unit Energy Consumption SAGE and AEO Mapping
SAGE
AEO
Sector
Sectors
agf
agg
col
ming
min
ming
ele
gas
ming
era
ming
wsu
bmf
con
ens
fbm
fdp
wpm
ppm, wdp
ref
ref
chm
bch
prm
pli
cem
cem
pmm
ism, aap
fmm
fbp
cpu
cmpr, eei
tem
teq
bom
bmf, ggr, mchi
trn
ttn
srv
comm
hit
comm
62
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Figure 14 presents the exogenous sector-specific UEC growth rates for SAGE. While there is
temporal heterogeneity in the exogenous growth rates the figure presents average annual growth
rates over two periods to more easily facilitate a comparison.
Household and government energy consumption shares are assumed to change over time to
match the energy intensity forecasts in AEO (the same assumption is used for subsistence demands).
Consumption shares of electricity and natural gas are assumed to grow at the same average rate
as in the AEO forecast, and are reflected by the indices cd-ene-growtht,eie and cd-ene-growtht,gas,
respectively. The consumption share of refined petroleum is assumed to grow based on the average
consumption share growth rate of light-duty vehicle fuel expenditures, and is reflected by the
index cd-ene-growtht,ref • This is assumed to represent a shift towards other consumption goods in
proportion to their benchmark consumption shares, such that
cdOt,r,h,s = cd-ene-growtht,scdOo,r,h,s s G sene (95)
and
cdOt,r,h,s = cd%,r,h,s + < [1 - cd-ene-growtht,ss} cdOo>r,h,ss > ^—cd0°>r>h>s s g sene_
y ssEsene J ^ssgsene cdvO,r,h,ss
(96)
Figure 15 presents the exogenous household UEC growth rates for SAGE. While there is temporal
heterogeneity in the exogenous growth rates, the figure presents average annual growth rates over
two periods to more easily facilitate a comparison. The same assumption is used for both discre-
tionary and subsistence demands. Government consumption is subject to the same treatment and
growth rates.
The growth of natural gas consumed per unit of electricity produced in the baseline is roughly
consistent with forecasts from AEO. However, the growth of coal consumed per unit of electricity
produced, absent any adjustment, would be higher than AEO forecasts due to regulatory and
market changes. Therefore, we adjust the cost share of coal in electricity production to be consistent
with the share of electricity generated from coal in the AEO forecast. The parameter coLele-growth
represents the share of fossil fuel inputs from coal in the electricity sector based on the AEO forecast.
The reduction in the cost share is offset by an increase in the cost share of capital and labor, which
would be associated with the alternative non-fossil fuel sources of generation growing in the AEO
forecasts. Specifically, the intermediate, capital, and labor inputs are adjusted over time, such that
idOtrCol,ele COl-dC-f (lCtOVtid0()rcoieie} (97)
kdOt,r,eie = kd%,rfiie + [1 - coLele-f actortid%,rfi0ifiie\ fef/n°'r'efe > (98)
Kl\jrele
and
— IdOo~I- [l coLele-f actortid%, r,col,ele}-r^^, (99)
Kl\jrele
63
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Period
2021-2036
2036-2051
-2 -1
Annual Unit Energy Consumption Growth [%]
Figure 14: Calibrated Sectoral Unit Energy Consumption Growth Rates
64
-------
-4
-3
-2
-1
0
Annual Unit Energy Consumption Growth [%]
Figure 15: Calibrated Household Unit Energy Consumption Growth Rates
where
col-ele-f actor t,s
coLele-growthtq-baset — (1 — S)
(100)
qJbaset — (1 — 5)*
and qJbase-t reflects an approximation of general growth of the economy by capturing the cumulative
growth of the effective labor force (i.e., aggregate economy-wide labor productivity growth plus
population growth). The cost shares cs-en, cs-ene, and cs-kle are also adjusted accordingly.
3.4.6 Baseline Visualization
This section presents plots for how a number of key variables and indicators evolve over the model's
baseline. Figure 16 presents the growth rates of key economic variables including real GDP, the
capital stock, realized economy-wide labor productivity (i.e., real GDP per unit of labor input),
labor supply (i.e., total hours worked), and population.
Figure 17 presents the expenditure side GDP accounts as a percent of GDP in the baseline.
Figure 18 presents the government accounts as a percent of GDP in the baseline. Figure 19 presents
the foreign transaction accounts as a percent of GDP in the baseline.
Figure 20a presents the average annual growth rates of output by sector for the near- and
medium-term in the baseline. While there is temporal heterogeneity in the exogenous growth
rates, the figure presents average annual growth rates over two periods to more easily facilitate
a comparison. Figure 20b similarly presents the average annual growth rate of real prices by
commodity in the national market.
65
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Variable
Real GDP
Capital Stock
Labor Productivity
Labor Supply
Labor Force
2020
2030
2040
2050
Year
Figure 16: Growth Rate of Key Baseline Variables
2020
2030
2040
2050
Year
Account
Consumption
Exports
Government
Imports
Investment
Figure 17: Expenditure-Side GDP Accounts in Baseline
66
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30
20
CL
Q
CD 10
2020 2030 2040 2050
Year
Figure 18: Government Accounts in Baseline
2
2020 2030 2040 2050
Year
Figure 19: Foreign Accounts in Baseline
Account
Deficit
— — Gov. Consumption
Interest
¦ ¦ ¦ ¦ Tax Revenue
- ¦ Transfers
Account
Current Account Bal.
— — Gov. Interest
Net Exports
¦ ¦ ¦ ¦ Net Income
- — - Net Transfers
67
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0 1 2 3 -1.0 -0.5 0.0 0.5 1.0 1.5
Annualized Output Growth [%] Annualized Price Growth [%]
(a) Change in Sectoral Output (b) Change in National Market Prices
Figure 20: Sectoral Change in Baseline
4 Solution
To solve the model, the primal version of the problem in Section 2 is converted to a series of
non-linear equations that define profit maximizing firm behavior, welfare maximizing household
behavior, market clearance, balanced budgets, and perfect competition following Mathiesen (1985)
and Rutherford (1999).
Given the assumption of constant returns to scale, one can solve for the constant unit cost
function of producing good z denoted as Clr z. Perfect competition may then be represented along
68
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with profit maximization by zero-profit conditions that assume the unit cost function under optimal
behavior is at least as great as the price for the good. If it is the case that the unit cost function is
greater than the price such that profits are negative, it must be the case that the quantity produced
is zero, providing the complementarity condition. This will hold for production with both new and
extant capital and provision of the Armington aggregate, government goods, and investment. The
zero-profit conditions associated with these activities are
Ct,r,s (Pat,r >agfj * * * ; P&tyrysrv j prt,r,prestos,pit,r,tkt,r,tyt,r,s) >PVt,r,i -L Dt,r,i > 0, (101)
Clr,i (Pa*> ryagfj * * * j P&tyrysrv j pV-eXt:r,S7PV&St:r,S7plt,r7tkt:r7tyt:r,s} ^ PUt,r,i -L D-&%t,r,i ^ 0,
(102)
(pdt,r,i,pnt,i,pfxt) > pat,r,i -L at,r,i > o, (103)
C9t r (pat, r,agfi • • • i P&t,r,srv^) ^ pgovt,r -L govt,r > 0, (104)
Ct,r (Pat,r,agf, ¦ ¦ ¦ ,P(H,r,srv) > pmVt,r -L %nVt,r > 0, (105)
Ct,s{pfixt,s,pxt,s) >pfxt -L x(Lfxt,s> 0, (106)
and
C™s(pfimt,s,pfxt) >pmt,s -L mst,s > 0, (107)
where C\rs is the unit cost function for production of s using new capital based on (5) and (12),
ctZ is the unit cost function for production of s using extant capital based on (15), C£r s is the
unit cost function for the Armington aggregate based on (1), Cfr is the unit cost function for the
government good based on (36), C\r s is the unit cost function for the investment good based on
(22), C^s is the unit cost function for the open economy representation for exports (4), and is
the unit cost function for the open economy representation of imports (3). A similar condition can
be established for the "price" of full consumption
&t,r,h (p(H,r >agfj * * * ; P&tyrysrv j tltyr,hi tficat,r,h,tct,r) >pclt,r,h -L clt,r,h > 0, (108)
where et,r,h is the unit expenditure function for full consumption based on the intra-temporal
preferences in (27). Following Section 2.7, the final zero-profit condition requires that for investors
to hold capital the price must equal the present value of returns, such that
ph,r > pn,r + (1 - S)pkt+l,r -L h,r- (109)
A similar condition must also hold for the national new captial stock fund into which households
invest, such that
pkht > prht + (1 — 6) pkht+i -L pkht. (110)
From Shepard's lemma the Hicksian demands for each input is the partial derivative of the unit
cost function with respect to the price of the input times the level of the activity. As such, the
69
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input demands for profit maximizing firms using new capital, conditional on the equilibrium level
of production, are
9CLa
idtrsss — Ut,r,sj (HI)
dpat,
,,r,ss
dCL.
kdt,r,s = ' ' yt,r,s, (112)
dprt,r
dCl
dph
and
ldt,r,s = ,, (113)
dprest,r,s
Similarly inputs to production using extant capital are defined as
9Ctrs , ^
rest,r,s = ^ - Vt,r,s- (114)
p,r,y-ex
t r s
id-CXf^r^ss^s = — U-CXt^^s, (115)
C)pOjt,r,ss
Q(jy-ex
kd-ext,r,s = o2/-ea;t,r,s, (116)
dpr-ext,',
dC%
dph,,
Q(jy-ex
ld-ext,r,s = „ ;r's y-ext,r,s (117)
and
p,r,y-ex
t T S
res-ext,r,s = t; -—y-ext>r,s- (118)
oprest,r,s
The inputs to the formation of capital and government consumption may be similarly defined as
9C?r
9t,r,s = o —gOVt,r (119)
and
r
k,r,s = —invt,r• (120)
opat,r,s
The inputs to the large open economy representation can also be defined as
xdt,s = ^——xdJxtyS, (121)
U'[)Xtys
9Cfs , x
fixt,s = T—^r2—xdjxt>s, (122)
opfixt,s
dC7i
ms-fxt,s = gpfXtmSt>s> (123)
70
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and
dC™ , ,
fimt,s = p. t. '—msts- (124)
dpfimt,s
Given the equilibrium level of full consumption, the demands for final discretionary consumption
goods are
dcdt,r,h,s = ®et'r'h clt r,hi (125)
opat,r,s
where leisure demand can be similarly defined as
leist,r,h = clt,r,h- (126)
dpk,r
Total commodity demands are defined as,
— dcdf^r^}i^s -\- (127)
where scdt>rth,s is exogenous. Imports and domestically-sourced use are defined conditional on the
equilibrium level of the Armington aggregate as
dC^r s , ,
dt,r,s = p. ' ' at>r,s, (128)
dpdt,r,s
9C?rs , x
^t r,s,dtrd — TJ ^t,r,s> (129)
dpnt,r
and
dCfr s
1Tlt,r,s,ftrd = ~7\ &t,r,s- (1^0)
dpmtyS
Exports are determined from the CET function in (2), such that
, / \ te-dx
_ y~ext,r,s + Ut,r,s ( pnt,r \ /iqiA
%t,r,s,dtrd — n I ) (131)
U®r,s \Pyt,r,s J
and
, / \ te-dx
_ y~ext,r,s + Vt,r,s ( PXt,s \ /i oo\
%t,r,s,ftrd — I I i (1^2)
y0r,s \pyt,r,s J
where the right hand side defines the optimal share of output supplied to the export markets based
on the output transformation function in (2).
Given the Hicksian demands conditional on equilibrium activity levels, the market clearance
conditions in Section 2.6 can be defined. If any of the conditions in (39)-(52) holds with strict
inequality it would imply that supply exceeds demand in equilibrium, such that the price of that
activity's output must be zero. This leads to a series of complementarity conditions, which define
the market clearance conditions. The price of the Armington aggregate, pat,r,s, clears the goods
71
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market, such that
dt,r,s ^ ^^(idt,r,s,ss ~i~ id~CXttr,s,ss) ^ cdt,r,s,h) "i" it,r,s ~i~ 9t,r,s -L P&t,r,s ^ 0. (133)
ss h
The price of domestic output consumed domestically, pdt,r,s, clears the domestic market, such that
y~eXtr,s + 2/t,r,s /pdtr,s\ ^ dfr,s , , ^ „ /i,,\
> -L pdt,r,s > o, (134)
y0r,s \pyt,r,sj do
where the left hand side defines the optimal share of output supplied to the domestic market based
on the output transformation function in (2). The price of labor, plt,r, (i.e., the wage rate) clears
the labor market, such that
ldt,r,s + ld-ext,r,s -L ph,r > 0. (135)
h s
The rental rate for sector specific extant capital, pr-ext,r,si clears the market for extant capital,
such that
7 / \ te-kjex 7 7
k-extyr ( pr-ext^s \ . kd-ext)riS ,
> —r~^ -L pr-ext,r,s > 0 (136)
Jr,s
k0r \pr-ex-aggt,r J kdOr
where the left hand side defines the optimal share of extant capital supplied to sector s based on
the extant transformation function in (19). The national weighted average rental rate households
earn on their past investments in the extant capital stock is
prJuex, > ^P^.aS9t,,k.exv ± ^ (1W)
k-ext,r
The regional rental rate for new capital, prt,r, clears the market for new capital in that region, such
that
kt,r > J2kdt,r,s -L prt,r > 0. (138)
The price of regional new capital, pkt>r, clears the investment market in that region, such that
kt-i,r (1 ~ 5) + invt-i>r > kt,r -L ph,r > 0. (139)
The rental rate for new capital investments clears the national market for new capital, ensuring
the households savings are consistent with investment in new capital across the regions, such that
^2kht,r,h>^2kt,r -L prht > 0. (140)
r.h r
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The price of foreign exchange, pfxt, clears the foreign exchange market, such that
y, mst>s + rowt > ^ xdt,sjtrd + inc-rowt + trari-rowt — gint-rowt — curactbalt _L p/a;t > 0.
(141)
The price of internationally imported commodities, pmt>s clears the import market
Y, mt,r,s,ftrd > mst.s -L pmt,s> 0. (142)
r
The price of internationally exported commodities, clears the export market
^ ^ ^tyVySyftrd — % df -L P%t,s — 0* (1^3)
r
The price of the fixed factor for internationally imported commodities, pfimt,s clears the market
fimOs > fimt,s -L pfimt,s > 0. (144)
The price of the fixed factor for internationally exported commodities, pfixt>s clears the market
fixOs > fixt,s -L pfixt,s > 0. (145)
The price of commodities on the national market, pnt>s, clears the market for national trade
^ ^ %t,r,s,dtrd ^ ^ ^ n^t,r,s,dtrd -L P^t,s ^ 0. (146)
r r
The rental rate for sector specific fixed factors, prest,r,s, clears the market for sector specific fixed
factors, such that
^2reset,r,s,h> rest,r,s +res-ext,r,s -L prest,r,s > 0. (147)
h
In addition, the problem requires that households maximize intertemporal welfare in (23). The
Karush-Kuhn-Tucker conditions for the welfare maximization problem are
> Xt,r,hPClt,r,h -L clt,r,h > 0, (148)
. nt,r,h J
Pt-\-l,r,hX-t-\-l,r,h ^ flt,r,h^t,r,h -L ^ 0) (149)
73
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and
pkht+iinvht,r,h >prhtkht,r,h + (1 - tlt,r,h ~ tficat>r>h)plt,rtet>r>h
+ prh-extkh-ext,r,h + y^prest,r,sreset,r,s,h
S
+ Pfxt (inc.rowtyr,h + trarurowt^h + curactbalt^h) int.sharer^
+ cpittransferst)r,h + cpk (gintt)r)h - deficittjr,h + icnadjt^h) gshareryh (150)
(tltfr,h tl-ClVCft r h) P^tyr^t,r,h
pd't,r,hd't,r,h ^ ^ (1 ~l~ tCf^ fJ(lt^r^sSCdf^ g h
s
-L > 0.
where the level of labor supply is determined by the time constraint, such that
t&t,r,h — ldSt,r,h It,r,h -L It,r,h — 0) (151)
and the new capital stock held by households is determine by investment according to
kht,r,h (1 - 5) + invht,r,h > kht+i,r,h -L invt,r,h > 0. (152)
The terminal level of capital kh,T+i,r,h is equal to khtT:h, which is define below by the model closures.
The problem requires that the government budget constraint holds, as described in Section 2.5,
such that
YJV90Vt,r90Vt,r+ cpittransferst, r,h + cpitgintt + pfxtgint-rowt + cpitincadjt
r h
tyt,r,sPyt,r,s (yt,r,s H~ y~&%t,r,s)
r s {
+ tkt,r \prt,rkdt,r,s + pr^ext,r,skd^ext,r,s + prest,r,s (rest,r,s + res.ext,r,s)] j
+ EE (flt,r,h ^ plt,r^t,r,h tCttrPCht,r,s^dt,r,S,h ^PHdcfidtf^.^
r h L
_L incadjt > 0.
(153)
It must also be the case that the rest of world budget constraint associated with income from
the fixed factors in the reduced form large open economy specification holds, such that
pfxtrowt > ^ (pfixt,sfix0S + pfimt,sfim0s j _L rowt > 0. (154)
Finally, we include the conditions to close the finite time approximation to the infinite time
74
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problem. As noted in Section 2.7, the post-terminal capital stock is determined by requiring that
investment grows at the rate of aggregate consumption growth, such that
inyT,r > VT,r,s + y~eXT,r,s
inVT-l,r ~ J2syT-l,r,s + y-e%T-l,r,s
_L ktr > 0.
(155)
The price is determined based on the law of motion for capital, such that
kr,r (1 ~ 5) + invT,r > ktr _L pktr > 0,
(156)
where households' share of the post-terminal capital stock is assumed to be equivalent to their
shares of the capital stock in the last period of the model
and price of terminal capital for the households is equal to the average price of terminal capital
The equations (101)-(158) define the equilibrium conditions of the model. The problem is
formulated in the General Algebraic Modeling System (GAMS).49 The model is solved using the
PATH solver (Ferris and Munson, 2000). We set the numeraire to the price of foreign exchange,
pfxo, in the initial period.50
In this documentation all variables are defined in levels for ease of exposition and interpretation.
The model in the code is mathematically equivalent to what is laid out in this documentation.
However, in the implementation most variables are defined as indices relative to the benchmark
value instead of in levels. This provides for a fairly well scaled problem with only limited need for
scaling of equations and variables prior to the solve. This implementation does not affect the model
solution, but does mean that some of the equations as implemented in the code may differ slightly
from what is laid out in the documentation.
49GAMS Development Corporation. General Algebraic Modeling System (GAMS) Washington, DC, USA, 2014.
boSAGE solves for a set of relative prices through the selection of a numeraire, or a chosen price level used to
denominate other prices in the model. Here, price changes are characterized relative to the foreign exchange rate in
the initial period. A numeraire is required in this class of economic models to satisfy Walras' Law. A competitive
general equilibrium is homogeneous of degree one in prices, meaning that the equilibrium level price vector scaled by
a common factor is also a solution to the model. This indeterminacy is solved by fixing a single price to align the
number of equations and variables in the model. In SAGE, we drop equation 141 for t = 0, though this condition is
verified to hold post-solve. Notably, in intertemporal dynamic CGE models, only one price level in a single year is
needed as a numeraire. For recursive dynamic formulations, a numeraire price can be assigned in every period if the
model is homogeneous of degree one in prices within each period.
= pr > khtr>h _L khtr>h > 0
l^r,h kn,T,r,h
(157)
pkht > T.rPktrkU ± ^ Q
Er r
(158)
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4.1 Multi-Year Timesteps
In this documentation the equations are written assuming an annual timestep for simplicity. How-
ever, solving the default version of the model at an annual timestep for a long enough time horizon
to achieve convergence to the steady state is not computational feasible. Therefore, we use multi-
year time steps to reduce the computational burden. To do so we adopt a step function approach
to defining investment investment over a timestep. When defining the laws of motion for regional
capital in equation (139) this translates to
kt-i,r (1 ~ §yntervalt _|_ intervaltinvt-i,r > kt,r -L Ph,r > 0, (159)
where intervalt is the number of years between model period t and t + 1. Consistent with this
adjustment the intertemporal no arbitrage condition in equation (109) needs to be updated to
ph,r > intervaltprt^r + — fi)mtervalt pkt+i,r -L kt,r- (160)
Similar adjustment is required for the laws of motion in equations (152) and (156) and the in-
tertemporal no arbitrage condition in equation (110).
Additional straight forward adjustments are needed to the exogenous temporal parameters in
the model and the household discount factor relative to the annual timestep presentation in this
documentation. These adjustments are made automatically by the model based on the simulation
years selected. Section 6.5.1 provides details on setting the timesteps and time horizon when using
the model.
4.2 Calculating Welfare Effects
Households' willingness to pay to avoid the costs of the policy requirements, that is the social costs
associated with the policy, are estimated using equivalent variation (EV). EV is estimated as the
amount of additional income households would require under baseline prices and still achieve the
same level of welfare as simulated in the policy case. More specifically, EV is calculated as the
difference between expenditures (on all goods including leisure) in the case where households face
baseline prices but are constrained to the welfare level achieved in the policy case and expenditures
in the baseline. This will be positive if the components of the policy modeled are on net an
improvement in welfare and negative if they are on net a reduction in welfare.
The households' optimization problem described by (23)-(32) yields optimal levels of consump-
tion and leisure given prices, taxes, transfers, and shadow prices on their budget constraint, At,r,h-
For simplicity of exposition, let be a vector of all prices, taxes, and transfers faced by house-
hold h in region r, where sim denotes the given simulation: base for baseline and pol for policy.
The optimal levels of consumption and leisure are then given by
cdt™s,h = dcdt,r,s,h (z r,h> Xr*h) + Scdt,r,s,h (161)
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and
leis?™h = leist>r>h (zX A$*) , (162)
where is a vector of shadow prices over the simulation's time horizon. Households' expenditures
on full consumption are then defined as
expenditure (z££\ Xf™) = ^ (i - tl%™h - tfica%™h) pls™leisst™h + (l + tc%™) pas™scdst™th,
t S
(163)
noting that since the prices are relative to the numeraire in the initial period they are already in
present value terms.
From the first order conditions to the household optimization problem in (149), the evolution
of the shadow price is defined as
PKTl,r,h = (164)
where (5 is the discount factor defined in (24). Therefore, given a terminal value AT,r,h, the sequences
of shadow prices can be determined. Given a vector of prices, taxes, and transfers and a vector of
shadow prices, (161) and (162) define the paths of consumption and leisure. Based on those paths,
(23) defines the households' welfare. Computing EV is therefore reduced to a problem of finding
a value that, along with z^e, leads to a level of welfare equal to the level in the policy
simulation. Given this value, define
cdt"r,s,h = dcdt,r,s,h (zbrahe, + scdt^Sth (165)
and
= leist,r,h (zbrahe, A^) • (166)
EV is then defined as
EVr>h = expenditure (z^e, A^j — expenditure (z^e, A^ej . (167)
The value of EV defined in (167) is reported in the model output under the name ev and is
based on the simulation years in the model and a finite time horizon. Two additional measures
of EV are also standard outputs for a policy simulation. These include ev_annual, which linearly
interpolates (163) between simulation years to estimate EV over all years covered by the policy
simulation, and ev_inf, which extends ev_annual from a finite to an infinite time horizon based on
the assumption that quantities and prices follow their steady state paths after the terminal period
in the model. Measures of baseline expenditures on full consumption (consumption and leisure) are
also output under the names cl_base, cl_base_annual, and cl_base_inf, with analogous temporal
definitions, so that the user may compute EV as a share of baseline full consumption if desired.
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5 Modeling Regulatory Requirements
Environmental regulations can vary over many dimensions. For example, EPA (2015) describe four
categories of regulations commonly promulgated to address air pollution: single sector emission rate
limits or technology standards; regional or state-implemented emission targets; multi-sector boiler
or engine-level emission limits or technology standards; and federal product standards. Each of
these categories has unique characteristics that may affect how the compliance requirements of the
regulations and incentives created by the regulation should be modeled. Environmental regulations
addressing additional pathways for pollution (e.g., land, water) have many similarities with the
aforementioned categories but also have additional attributes that may be relevant for how they
are modeled. Thus, the appropriate approach to introduce the requirements of a regulation into
the model will depend on the specific details of the policy.
In practice, with the exception of federal product standards or prohibitions, environmental reg-
ulations are typically source-level technology standards, performance-based emission-rate limits, or
workplace standards. In each case, sources are required to undertake abatement and monitoring
activities in addition to their regular production activities. As a starting point for reflecting hetero-
geneity across regulatory approaches, the default version of the model has two built-in approaches
for simulating abatement requirements on producers that may be calibrated to engineering or par-
tial equilibrium estimates of compliance costs: a productivity shock and an explicit abatement
activity. Each approach is discussed below, followed by an example that highlights the differences
between them.
5.1 Compliance Requirements as a Productivity Shock
The production functions in the model, as described in equations (5)-(10), are of the calibrated
share form in which the inputs are entered relative to the benchmark values. In other words, the
production function in (5)-(10) can be described as
To generalize this discussion, (168) introduces the index v e (new, extant) to describe the vintage
of capital used in the production function. Under the case v = extant, (168) represents the Leontief
production function for production with extant capital implicitly described by (15)-(18).
(168)
78
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In the code an additional parameter, prod-indt,r,z,s,v, is introduced to allow for modeling of a
productivity shock on input z. The implementation essentially redefines (168) as
f I f ( "idt,r,agf,s,v idt.
yt,r,s,v = Jy I Jmat
r.srv.s.v
pTOd-indtyr,agf,s,vid0r^agf^s P^od-indf^r^srv^s/vidOr^sro^s
i'dt r.ele.s.v
/<
pvod-indt}r,eie,s,vidOr^eie
ft
idt^coi.s.v idt ,r,gas,s,v
fkl
prod-indt,r,coi,s,vidOrtCOitS pfod-indt,r,gas,s,vidOr,gas,s
kdt r s v ldt,r,S,V
(169)
prodJndt rks vkdOr,s prodJndt r i s vldOr
where in the baseline prodJndt,r,z,s,v = 1, in which case (168) and (169) are equivalent.
The interpretation of this additional parameter is that increasing prod And for a specific input
from 1 to 1 + A and holding all other inputs fixed would require a A x 100% increase in the
affected input to continue producing the baseline level. Based on this interpretation one can define
an approach to calibrating the value of prodJnd to reflect the compliance requirements associated
with a regulation. For example, suppose an engineering cost analysis estimates that a regulation
impacting sector s will require additional expenditures on input z of costt,r in year t and region r to
produce the baseline level of output at new production sources, yt,r,s,new This may be represented
by
prodJndt,r,z,s,new = 1 + '"°St*'r y°r>s ; (170)
V-L i Tz) Zur,s Ut,r,s,new
where z0r,s is the benchmark value of input z and tz represents any potential ad valorem tax on
input 2 paid by producers (e.g., taxes on capital returns). This calibration would yield a situation
where holding the output level and all other inputs fixed at their baseline levels, consistent with
the setup in most engineering cost analyses, would require additional expenditures (gross of taxes)
of costt,r on input z. However, it should be noted that, after implementing the shock, firms may
substitute away from the now less productive input towards other inputs. Based on the nature of
the productivity shock these implicit substitution possibilities in the compliance activity are defined
by the substitution elasticities in the regulated sector's production function.
5.2 Modeling Explicit Compliance Requirements
The model also allows for the explicit specification of input requirements for regulatory compliance.
This is accomplished by extending the nesting structure of the production function depicted in Fig-
ures 4-6 to include a top level Leontief nest that combines production of saleable goods and services
with pollution abatement activities. For the standard manufacturing and services production func-
tions with new capital, this extended production function is presented in Figure 21. Production
then requires both the traditional production activity and an abatement activity, which is itself a
79
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Leontief function of inputs used in regulatory compliance.
International Intra-national Local
Output
Goods
Production
Abatement
se-klem
Materials
Value Added-
Energy
Agriculture
Services Labor Capital
Figure 21: Manufacturing and Services Production Functions with Abatement
With the implementation of the extended production function to account for potential compli-
ance activities, output in the manufacturing and service sectors that is not associated with a fixed
factor resource is defined as
. ( klem.tr s abatet
Vt,r,s = y r,s mm yklem0t 'ry abate0t
.r,s
r.s
(171)
where klemt>r,s represents the traditional production activity defined in Section 2.2.1, such that
klem.tr s = klemOr s
f matt,,
cs_klemr s I -
V matOt
se-klem — 1
se-klem
+ (1 — cs-klemr,s)
(
kle
t.r.s
\kle 0;
t.r.s
sejzlem — l'
se-klem — 1
(172)
The abatement activity is defined as a Leontief function of intermediate inputs, labor, and new
80
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capital, such that
id-abatettr,agf,s id-abatet,r,srv,s ld-abatet,r,s kd-abatet,r,s
abatet r s = abateOt r s min
id-abateOt r agf s' ' id-abateOt r srv s' Id-abateOt r s' kd-abateOt r s
"(173)
where id-abatet,r,ss,s, ld-abatet,r,s> and kd-abatet,r,s are inputs of commodity ss, labor, and capital
for abatement activities, respectively. The "benchmark" values in (173) include time subscripts
because the required level of abatement activities or the inputs associated with the abatement
activity may change over time, for example due to a phase in of the regulation. With the extended
production function that includes abatement activities, firms are assumed to maximize profits
inclusive of the abatement inputs,
(1 tyt,r,s) Pyt,r,syt,r,s V&t,r,ss (idttr,ss,s "i" ^d-Cbb(lt6t,r,ss,s)
(174)
— (1 + tkt,r) Pft,r (kdt,r,s + kd.abatet,r,s) — vh,r (ldt,r,s + ld-abatet,r,s) >
subject to the production function defined by (171)-(173) and (6)-(10). Similar extensions are
implemented for production with extant capital and sectors associated with fixed factor resources.
In the case of production associated with extant capital, abatement activities are still assumed to
make use of new capital in (173).
The solution approach outlined in Section 4 is easily extended to accommodate the expanded
production structure inclusive of abatement activities. While the default implementation repre-
sents abatement activities as Leontief technologies, alternative functional forms can be adopted if
warranted. It is also possible to represent abatement activities as substitutes for emissions in a
CES function where the elasticity is calibrated to match available estimates of marginal abatement
cost curves following Kiuila and Rutherford (2013), allowing more complex regulatory designs to
be modeled.
5.3 Difference Between Productivity Shock and Explicit Compliance Require-
ments
There are two main differences between modeling compliance requirements as a productivity shock
versus a nesting structure that explicitly represents the abatement activity. First, the substitution
possibilities allowed between inputs for compliance differ. The productivity shock implicitly as-
sumes that compliance inputs have the same substitution elasticities as the underlying production
technology for the regulated sector. Alternatively, explicit representation of abatement require-
ments, at least as defined in Section 5.2 and the default version of the model, does not allow
flexibility in how the abatement requirements are met. Second, the explicit abatement requirement
assumes that any capital inputs for compliance activities are always new capital investments regard-
less of whether the regulation affects new or existing sources of production. For the productivity
shock, capital requirements associated with compliance activities at existing sources are implicitly
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assumed to be repurposed extant capital.51
To highlight the main differences between these approaches to modeling regulatory requirements
the example examples/regulatory_modeling_approach.R simulates an identically-specified regu-
lation under both approaches. For this example, as well as the others presented in Section 6, we
use a hypothetical regulation in the primary metal manufacturing (pmm) sector loosely calibrated
to an initial round of regulations that were promulgated about 20 years ago under section 112 of
the Clean Air Act. Section 112 of the Clean Air Act (CAA) requires the EPA to list industrial
categories of major sources of one or more hazardous air pollutants (HAPs) and to then establish
a national emissions standard for those categories (also referred to as a NESHAP). Major sources
of HAPs are defined as new or existing facilities that emit 10 tons or more annually of any single
HAP or 25 tons or more annually of a combination of HAPs. A NESHAP is typically based on an
assessment of the degree to which emission reductions have been achieved at the best performing
facilities in a particular source category using existing abatement control techniques. This standard
is referred to as a Maximum Achievable Control Technology or MACT floor because it specifies the
minimum level of HAPs control required. Specifically, the Clean Air Act requires the NESHAP to
reflect the maximum degree of reduction in HAP emissions that is achievable, taking into consid-
eration the cost of achieving the emission reductions (as well as a few other factors). For existing
sources, the MACT floor is the average emission rate of the least-emitting 12 percent of facilities
within that industry at the time of promulgation.
For primary metal manufacturing, it was estimated that the abatement technology available
to meet the initial emission limits for integrated iron and steel manufacturing and primary and
secondary aluminum manufacturing would require capital investments equivalent to approximately
0.4% of those sector's capital stock and annual operating costs equivalent to approximately 2.0% of
those sector's labor expenditures at the time. Since the goal is to provide a hypothetical scenario to
test the behavior of the model and not to develop quantitative impact estimates for a specific policy,
we make many simplifying assumptions to keep the example as clear as possible. For example, costs
as a share of benchmark capital and labor inputs are assumed to be uniform across regions; costs
scale with output over time; operating costs are assumed to be associated with labor only; new and
existing sources are assumed to face the same compliance costs; the other primary metal production
activities included in the default aggregated pmm sector are assumed to face similar compliance
costs for abating HAP emissions; and the policy is assumed to begin in the second modeling period.
The details of how this scenario is run are presented in Section 6.
For each modeling approach we consider three policy simulations in which the regulatory re-
quirements apply to 1) all sources of production; 2) only production associated with extant capital;
and 3) only production associated with new capital.52 As previously noted, there are two potential
B1For example, where part of an existing structure must be repurposed for compliance activities.
B2In the default specification of abatement requirements in SAGE, abatement activities experience productivity
growth equal to the economy-wide average as described in Section 3.4.1. However, to simplify the comparison between
the two regulatory modeling approaches the scenarios presented here assume no productivity growth in the compliance
activities.
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Table 13: EV Comparison Across Modeling Approaches [Billion $]
Affected
Productivity
Abatement
Sources
Shock
Requirement
All
-45.8
-45
Existing
-8.3
-8.4
New
-37
-36.1
differences between the approaches to modeling abatement requirements: differences in the substi-
tution possibilities in the abatement activity, and the vintage of capital required for compliance.
When only production associated with new capital is subject to the regulatory requirements, then
new capital is required for compliance in both cases, and differences between the two approaches
are driven by varying assumptions about substitution possibilities in the abatement activity. On
the other hand, because production associated with extant capital is modeled as Leontief, if only
production associated with extant capital is subject to the regulatory requirements, then neither
modeling approach provides any substitution possibilities in the abatement activity and differences
across the two approaches are due to the vintage of capital required for compliance.
Figure 22 presents the simulated percent change in output and labor demand (inclusive of abate-
ment requirements) for the regulated sector under the different scenarios. There is little difference
in output between the two modeling approaches independent of which sources of production are
subject to the abatement requirements. When the abatement requirements fall on existing sources
and there is no difference in the assumptions about substitution possibilities in the abatement
activity, the change in labor demand is approximately the same. In the other cases the labor inten-
sity of production is lower in the case of the productivity shock relative to the explicit abatement
requirement as firms substitute away from labor under this approach.
In a first best setting, we expect that the additional compliance flexibility assumed under the
productivity shock approach would lower the social costs of the regulation, but in a second best
setting the differential effect on the real wage rate leaves the direction of the difference ambiguous
a priori. Table 13 presents estimates of EV under both approaches to represent the hypothetical
regulation on the pmm sector (i.e., productivity shock and explicit abatement activity), varying
which sources are affected (i.e., all, existing sources only, or new sources only).53 For this example,
regardless of which sources are affected, the EV for the two approaches to representing abatement
requirements are within 0.5% of each other.
6 Using the Model
The core SAGE package is composed of 1) a build routine for constructing the model's database and
2) the modeling files for performing simulations. The programs are written to allow flexibility in
how the datasets are constructed and provide options for including different modeling assumptions.
B3The values presented represent the infinite time horizon approximation of EV discussed in Section 4.2 and
contained in the output variable ev_inf.
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2020
2040
2060
2080
Year
(a) Change in Output in Regulated Sector
2020
2040
2060
2080
Year
Version
Abatement
Productivity
Sources
All
Existing
New
Version
Abatement
Productivity
Sources
All
Existing
New
(b) Change in Labor Demand in Regulated Sector
Figure 22: Effect of Approach to Modeling Abatement Requirements
The build routine constructs a consistent set of value shares based on IMPLAN data and compiles
all other exogenous data parameters (including elasticities, growth rates, population totals, tax
rates, and oil and gas production data) to form the necessary inputs to run the model. The build
routine is only run once for a given release to generate the model's datasets. Afterwards, conducting
an analysis only requires running the model itself.
The SAGE model is run in a sequence and is intended to be used to compare the impacts
of a policy shock against a specified reference case. The user must run the model to calculate
the baseline level of all model variables, design a policy shock that alters the reference equilibrium
point, and rerun the model to compare the resulting equilibrium with baseline values for computing
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the economy-wide impacts.
6.1 Directory Structure
The build routine, model, and all examples are designed to be run from the package's top directory
level. The package is composed of the subdirectories in Table 14.
Table 14: Directory Structure
Subdirectory Description
build
utilities
data
model
diagnostics
examples
output
do cument at i on
Subdirectory contains data and files for constructing the bench-
mark dataset. The build routine relies on a mixture of
GAMS and R routines. The launching program is called
build_default_datasets .R
Subdirectory for custom R routines and functions for compiling
external data sources and running model code. This code is refer-
enced throughout the build routine and modeling examples.
Subdirectory containing reconciled benchmark data and exoge-
nous parameter files.
Subdirectory containing the core SAGE modeling file.
Subdirectory containing scripts for running model and data diag-
nostic tests.
Subdirectory holding examples using the model.
Place holder subdirectory for generated model results.
Subdirectory containing documentation for the model. The docu-
mentation source is available in the latex file documentation.tex,
while a typeset pdf version of the documentation is available in
documentation.pdf.
6.2 Building the Dataset
The data compilation routines in the build stream includes programs written in both R and
GAMS.54 Some custom R routines are included (see the utilities subdirectory) to automate the
download of external data sources and facilitate their subsequent compilation. External R packages
used by SAGE but not currently available on the the system are automatically installed when the
build stream is run, or may be installed separately by running utilities/install_R_packages .R.55
The build routine is controlled through the launch program, build_default_datasets .R, in
the build subdirectory. The build script is designed to be run for the top-level directory of the
B4R and GAMS must be included in the PATH environment variable. The current build stream was tested with
GAMS 24.9 and R 3.5.
BBNote that by default the package "fiftystater" is not installed, though this package is necessary for using the
utility to create state choropleths with results or Figure 2. Instructions for how to install this package are included
in utilities/install_R_packages. R.
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SAGE package. Note that an internet connection is required for running the routine as it relies on
external data sources for calibration.
The major steps in the build stream are as follow:
1. Initially, builcLparameters .R compiles preference and technology parameters outside of the
SAM (e.g., elasticities) from included and downloaded data files and creates data/parameters .gms.
2. builcLbaseline .R compiles the exogenous projections that help define the model's baseline
and creates data/baseline.gms.
3. Additional external data sets needed for the creation of the SAM are downloaded and pro-
cessed by get_additional_economic_data.R, get_oil_and_gas_data.R, and get_population_data.R.
4. Data on effective marginal tax rates are processed by get_tax_data.R. Note that aside from
reconciling data from the Current Population Survey, get_tax_data.R submits the compiled
data to the NBER TAXSIM model to derive weighted marginal tax rates.
5. IMPLAN data is extracted using build/data/implan by read_implan_state.gms, which
partitions each state data file into its submatrix components.56
6. Resulting state-level GDX outputs are merged and fed into build_benchmark. gms to create
the SAM and disaggregate the oil and gas extraction sectors.
7. The SAM is aggregated to the requested levels in aggregate_benchmark.gms based on the
aggregation defined in aggregation_f ile at the top of the launching program.
8. The SAM is filtered and rebalanced in balance_benchmark.gms, imposing microconsistency
on the dataset (i.e. data satisfying all needed accounting identities in the modeling frame-
work) as well as other calibration assumptions on the dynamic structure of the model. The
aggregated dataset is balanced and filtered using a least squares optimization framework with
options as listed in Table 15.
9. Using the calibrated data, subsistence demands are estimated consistent with Section 3.3.6
as implemented in calibrate_les.gms. The build routine first generates the national data
file to constrain the recalibration procedure when imposing regional disaggregations in the
model.
The build routine relies on both IMPLAN data and data from external sources (e.g., EIA and
U.S. Census Bureau). The build stream requires that the state-level IMPLAN data files (*.gms) are
stored in build/data/implan at the time of compilation.57 All other data files are included with the
B6The process for constructing a SAM from the IMPLAN dataset is based on the IMPLANinGAMS package (Rausch
and Rutherford, 2009). The original version of this software can be found at: http://www.mpsge.org/implan98.htm.
B7IMPLAN is a proprietary data set and is therefore, not included in the publically available version of SAGE.
Given a licensed version of IMPLAN for SAGE's benchmark year, to build the SAGE data sets first follow the
instructions in build/data/implan/implan_data_instructions. txt to add the necessary IMPLAN data files into
the SAGE directory structure.
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Table 15: Selected Options in Data Set Build Stream
Place
Option
Description
Default Value
Launch
aggregati on_f ile
Name of the mapping file that
default _aggregat ion. gms
characterizes the level of sector,
region, and household aggrega-
tion. Mapping files are located
in build/aggregation_map. Al-
ternative mappings can be used
to modify the dimensionality of
the dataset.
aeo.year
Year of the EIA's AEO to use in
Most recent AEO that in-
the calibration.
cludes benchmark year
aeo.scenario
AEO scenario to use in the cali-
pasteO("REF",aeo.year)
bration.
balanced_growth
Binary flag to calibrate bench-
1
mark investment levels consis-
tent with a balanced growth
path.
Matrix
filter_small
Binary flag to filter out small
1
Balancing
numbers.
include_taxes
Binary flag to allow tax rate ad-
0
justments in balancing.
threshold
Filter threshold for smallest
5e-4
value allowed in benchmark
dataset.
frac_deviations
Binary flag to minimize percent
1
deviations rather than absolute
deviations.
SAGE package in build/data or downloaded from the internet throughout the routine. Following
the successful completion of these routines, the file build/data/satellite_data_versions.csv
is generated, which includes versioning information for downloaded data from API (Application
Programming Interface) requests, the current population survey, and the TAXSIM model. Im-
portant options for controlling the build stream are located in the launch program and the SAM
filtering and rebalancing script (build/balance_benchmark.gms). These options are described in
Table 15 and are listed at the top of the associated programs. Once the build stream is finished,
the resulting balanced dataset and generated parameters file containing all elasticities and assumed
dynamic parameters are stored in the data subdirectory at the top level of the package's directory
structure.
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6.3 Running the Model
The model itself is written in GAMS and located in model/sage.gms. The model is designed to be
run from the package's top directory and requires the PATH solver to be installed and licensed. The
model is designed to run a single scenario, either a baseline scenario or a policy scenario. Therefore,
the general process will be to first solve the model for the baseline solution and then rerun the model
to solve for the counterfacutal policy solution, sage.gms is written to minimize the need for user
adjustments to core model code (i.e. equations and data declarations) when solving counterfactual
scenarios. Instead, the model offers multiple points during the execution where additional code can
be included to change the specification or behavior of the model (examples below).
The model can be run through the GAMS IDE, but is designed to be run from the command
line to take advantage of command line arguments to specify options including additional code
to be included during counterfactual simulations. Running the model is done with a command
line call to GAMS: gams model/sage.gms. The available command line options are presented in
Table 16 and may be applied when running the model with the syntax gams model/sage .gms
—optionl=choicel —option2=choice2 ....
After each simulation all model variables are saved in both .csv and .gdx format. These files
are written to the output/ subdirectory. While these files are very similar in their contents, the
CSV file contains additional output based on post-processing of the solution results, such as GDP,
EV, etc. It is also worth noting that the quantity/activity variables in the GDX file are indices
relative to the benchmark levels, while in the CSV file these indices have already been multiplied
by the benchmark levels for the convenience of working with the output.
6.4 Solution Checks and Diagnostics
After each simulation the model performs a set of verification checks on the solution. The results of
these post-solve diagnostics are reported in the GAMS listing file. This set of diagnostics includes
checks that:
1. Nominal gross domestic product is the same when calculated based on expenditures and value
added;
2. Accounting identities hold in the post-solve social accounting matrix; and
3. No arbitrage opportunities exist between the national new capital price for household invest-
ments and the regional capital prices.
Following a simulation, a new social accounting matrix is constructed based on the computed post-
policy equilibrium. This constructed matrix serves to verify that all of the accounting closures
hold. These accounting closures include a check on commodities (the value of production and
imports less exports must equal demand), activities (the value of production must equal the costs
of labor, capital, intermediate inputs, and tax obligations), households (the value of consumption,
investment, and tax payments must equal factor income and transfers), government (the value of
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Table 16: Command Line Options for the SAGE Model
Option
Description
Default Level
benchmark_f ile
putty_clay
parameter_file
baseline_file
gdx_baseline_file
balancecLstart.values
policy_file
gdx_save
gdx_results_file
output_file
prologue
epilogue
perturb_start
File containing the benchmark dataset. The default aggregation is spec-
ified in Section 2.
Binary flag for enabling the partial putty-clay specification. With a
value of 0, capital is fully malleable.
File containing the elasticities and additional technology and preference
assumptions.
File containing the time steps and exogenous baseline assumptions.
A gdx file containing the results of a previous model solve. May be
used to set the starting values and/or define baseline prices to calculate
equivalent variation.
Binary flag to set the starting values based on a balanced growth path
solution independent of whether a baseline file was provided.
Optional file containing GAMS code to define the policy changes in the
model. If NULL the baseline is run.
Binary flag for saving model results in a GDX file. The resulting
GDX file is stored in the file specified by the environment variable
gdx_results_file.
Provides the location and output name of the GDX file where the model
results will be stored.
Provides the location and output name of the CSV file where the model
results will be stored.
Optional file with GAMS code to be included before any data processing
and model declaration. Useful for adjusting parameters.
Optional file with GAMS code to be included after the model solution
and any post-processing. Useful for additional post-processing of results.
Debugging option to additively and uniformly perturb initial starting
values on yt,r,s- Value specifies the size of the perturbation.
data/def ault_aggregat ion.gdx
1
data/parameters.gms
data/baseline.gms
1
output/results.gdx
output/results.csv
-------
government purchases less transfers equals tax income), and the rest of the world (the value of
imports equals exports plus an exogenously defined balance of payments deficit). While the listing
file contains the numerical values for each of these checks, for convenience the log file reports if a
given check has "FAILED" based on a selected tolerance, which has a default value of 10~4 (i.e.,
$100,000). If no error messages are reported, then all checks were passed.
6.4.1 Numeraire Test
The previous solution checks illustrated instances of hypothetical policy shocks that satisfied post
equilibrium adding up conditions. One other form of model validation concerns test simulations
where the outcome of the simulation is already known. One such test suggested by Dixon and
Rimmer (2013) is to test the model's homogeneity assumptions. As described above, SAGE is
homogeneous of degree one in prices and hence a numeraire is assigned to represent equilibrium
prices as relative. The level of the numeraire is typically fixed to 1. Because the model relies on
relative prices, perturbing the numeraire from 1 to (1+/?) should adjust all baseline price and value
variables by the same perturbation factor (/?) while quantity variables remain unchanged.
To test that this assumption holds in SAGE, the "policy" file, diagnostics/numeraire_test .gms,
contains an adjustment to the numeraire by a perturbation factor of fi = 0.2. "Policy" is writ-
ten in quotes because the purpose of this test is to compare two separate baselines (not a policy
case vs. a baseline) differed only by the magnitude of the numeraire, but can be functionally
implemented with a policy file. Notably, the chosen value of fi is arbitrary.58 The example may
be run from the command line in a similar fashion those already described or from the R script,
diagnostics/numeraire_test.R.
6.5 Examples of Adjusting or Using the Model
The following sections present a information or examples for adjusting specifics of the model or
conducting policy analysis.
6.5.1 Adjusting Timesteps and Horizon
The default parameterization of the model uses five year timesteps between 2016 and 2081. The
simulation years for the model are defined by the set t in the baseline file. This default assumption
can be changed in the default baseline file (data/baseline.gms). Alternatively, a new baseline
file can be created with the updated simulation years and specified by the command line option
—baseline_f ile when running the model. The default aggregation of the model does not support
annual timesteps. Maintaining the end year of 2081 with annual time steps increases the dimen-
sionality of the model and poses computational intractabilities. Use of annual time steps with a
more aggregated version of the model (e.g., no regional representation) is feasible. The model does
not require that the timesteps be evenly spaced.
B8While this value is arbitrary, a large level of /3 may cause issues for the model's solver.
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6.5.2 Example of a Hypothetical Regulation
The file examples/sample_abatement.requirement .gms contains a representation of the hypothet-
ical regulation in the primary metal manufacturing (pmm) sector that is described in Section 5.3.
As previously stated, the hypothetical scenario assumes compliance with the regulation requires
capital investments equivalent to approximately 0.4% of the regulated sector's capital stock and
annual operating costs equivalent to approximately 2.0% of the regulated sector's labor expendi-
tures; cost shares are uniform across regions; costs scale with output across time; operating costs
are associated with labor only; and new and existing sources face the same compliance costs.
As noted in Table 16, the model provides options for including GAMS code in the model at
multiple points during its compilation. The policy_file command line option allows the user
to define a file containing GAMS code that will be included right before the model's solve state-
ment. The file examples/sample_abatement_requirement .gms (see Listing 1) defines compliance
requirements for the hypothetical regulation in the pmm sector based on the explicit abatement
requirement approach of Section 5.2 and is intended to be used with the policy_f ile option.59
Listing 1: examples/sample_abatement_requirement .gms
> ... the primary metal
> msnu fact in:inq sector and have ,s.n engineering cost estimate thai, compliant.-.
> ¦¦¦ . , : : . ¦... . , ¦¦¦¦ ' . , '.. , ¦¦¦ ... . ,
> ...... ¦¦¦ ... ¦¦¦ .... .
> . ¦¦ : ¦¦¦ ¦¦¦¦. . the requirements are assumed to be the same for
> pro-duct ion with new and extant capital,
lcLabateO (t, r, "pirun v) $ (ord (t) gt 1 or ord (t) eq card (t) ) = 0.020*ld0 (r, "pmm") *
l_prod_agg (t) ;
kd_abate0 (t,r, "pnrniv)$(ord(t) gt 1 or ord(t) eq card(t)) = 0.004*kd0(r, "pmm");
The variables ld_abateO(t,r,s,v) and kd_abateO(t,r,s,v) define the labor expenditures
and capital stock required for compliance when producing the benchmark level of output, yO(r,s),
in period t, region r, and sector s with capital of vintage v. There is an analogous variable for
intermediate inputs of commodity ss for compliance, id_abateO(t,r,ss,s,v). Care needs to be
taken to ensure that the abatement costs are entered in the correct format, that is, the compliance
costs at sources of vintage v when output from those sources is at the benchmark level.
In this example, the labor inputs are multiplied by l_prod_agg(t), which reflects the aggregate
labor productivity growth in the economy. By default the model assumes that labor productivity in
abatement activities will grow at this rate. Therefore, by increasing the costs at rate l_prod_agg(t)
one is essentially negating that productivity growth and instead assuming that there is no produc-
tivity growth in the abatement activity. This is done only to keep this example the same as the
one presented in Section 5.3 to maintain consistency throughout the examples.
B9For an example that implements the compliance requirements as a productivity shock, see
examples/regulatory _modeling_approch. R.
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In this example, the average compliance expenditures per unit of output in a region are assumed
to remain constant over time. In addition, the compliance requirements are assumed to begin in
the second period, hence the conditional ord(t) gt 1. The second part of the conditional is to
ensure that the example will work with the static version of the model, which by definition only
has one time period.
To analyze the hypothetical regulation the baseline is first calculated, after which the model is
run with the hypothetical regulation. This can be accomplished from the command line using the
commands presented in Listing 2.
Listing 2: Running the Sample Abatement Requirement from the Command Line
gams model/sage.gms —gdx_results_file=output/baseline.gdx
—output_file=output/baseline_resuits.csv
gams model/sage.gms —gdx_baseline_file=output/baseline.gdx
—policy_file=examples/sample_abatement_requirement.gms
—output_file=output/regulation.results.csv
In calculating the baseline in the first model run, the command line option gdx_results_f ile
defines the GDX file where the results of the model solve will be saved. The command line option
output_file defines a CSV file where the baseline results will be stored. The GDX file is used
to define the baseline in the policy run using the gdx_baseline_f ile command line option. In
this case, the baseline is used to both set the starting values and provides the baseline prices for
calculating EV. The output_file command line option defines a CSV file where the results of
the model run with the abatement requirement will be saved. The two output files may be used
to calculate the changes in variables between the two simulations. Policy impacts should only be
compared to their corresponding baseline.
Once the post policy equilibrium solution is determined, the SAGE listing file (sage. 1st) will
include the diagnostic checks described above. The diagnostics help determine if the model solution
satisfies the necessary closures.
The model's use of command line options and compile time code inclusions allows the model
to be easily run from scripts. The modeling package includes a series of R utilities that are located
in the file utilities/R_utilities.R, which provides functions to run the model and process
the results from R. The file examples/basic_example .R shows how this hypothetical abatement
requirement may be run and results processed from an R script. An analogous example of how
such routines can be built in GAMS is included in examples/basic_example.gms.
6.5.3 Example of a Regulation with Phased In Requirements
The previous example focused on a hypothetical regulation where the compliance requirements
were assumed to begin in the second period of the model and where the average compliance expen-
ditures per unit of output in a region are assumed to remain constant over time. It is possible to
model situations where the average compliance costs per unit of output are expected to vary over
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time. One example of this regulatory context is when a regulation is phased in over time. This
section describes the implementation differences from previous examples to accommodate temporal
variation in compliance cost model inputs.
The policy file examples/sample_phased_in_abatement_requirement .gms contains a modified
representation of the hypothetical regulation described in Section 6.5.2 where the average compli-
ance costs per unit of output in the second period of the model are 50% of their expected value once
the regulation is fully implemented starting in the third period of the model. This scenario assumes
compliance with the regulation requires capital investments equivalent to approximately 0.2% of
the regulated sector's capital stock and annual operating costs equivalent to approximately 1.0%
of the regulated sector's labor expenditures in the first year of compliance (second model period).
Subsequent years of compliance (third model period and thereafter) requires capital investments
equivalent to approximately 0.4% of the regulated sector's capital stock and annual operating costs
equivalent to approximately 2.0% of the regulated sector's labor expenditures. All other aspects of
the hypothetical regulation match the example described in Section 6.5.2.
Listing 3 presents the policy file for this phased in version of the example regulation. The
variables ld_abateO(t,r,s,v) and kd_abateO(t,r,s,v) define the labor expenditures and capital
stock required for compliance when producing the benchmark level of output, yO(r,s), in period
t, region r, and sector s with capital of vintage v. In this case, there is a definition for the two
phases of the hypothetical regulation: the first phase denoted by ord(t) eq 2 (the model's second
period) and the second phase denoted by ord(t) gt 2 (all model periods after the second). The
second part of the conditional for the second phase costs is to ensure that the example will work
with the static version of the model, which by definition only has one time period and is assumed
to be associated with the full implementation costs in this example.
Listing 3: examples/sample_phased_in_abatement_requirement .gms
> tills is a ' ¦¦¦¦
> , ¦¦¦ . ¦¦¦ . " ¦¦¦
> • . . , ¦¦¦ '
> ' ' , : ¦¦¦ , . . ' ¦¦¦ ¦¦¦ ' , . ,1.'
> baseline capital expenditures and 2% of labor .¦<..¦¦¦ . - . .¦;¦¦¦¦ : ¦...¦¦ ¦.
> ¦¦¦ ¦¦¦ ¦¦¦ ¦¦¦ ,
> ¦¦¦ . , , . . ¦¦¦;¦ ¦ i. ¦ . " ¦¦¦ . .
> ¦¦¦ ¦¦¦ ¦¦¦ ¦ ¦¦¦ . ¦ , .....
> be the same for production with new and extant capital,
> ... : :. ' ¦ ¦¦¦ ¦ . ¦ . : . first phase (second mo-del period)
lcLabateO (t, r, , v)$( (t) 2) = 0.010*ld0(r, "piran ") * l_pr ocLagg (t) ;
kd-abateO (t, r, *«.«.. ,v) $ (t) 2) = 0.002*kd0(r, "pmm") ;
>
ld-abateO (t,r, "pmm",v)$(ord(t) gt 2 or ord(t) eq card(t)) = 0.020*ld0(r, "pmm") *
l_prod_agg (t) ;
kd_abate0 (t, r, "pimn v) $ (ord (t) gt 2 or ord (t) eq card (t) ) = 0.004*kd0 (r, "pmm") ;
This example may be run from the command line in a similar fashion to Listing 2 by updating
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the name of the policy file. The R script examples/policy_phase_in_example .R runs a comparison
between the phased in policy and the immediate implementation version in Section 6.5.2. Imple-
menting a phased in regulation as a productivity shock would be accomplished in a similar fashion
by defining the productivity shock (represented by the parameter prod_ind) for each phase using
a conditional argument for t.
6.5.4 Example of a Regulation in a Large vs. Small Open Economy
In this section, we illustrate the importance of the large open economy assumption in SAGE for the
aforementioned hypothetical regulatory scenario. A model switch has been integrated into the code
to convert the model to a small open economy where the United States is treated as a price taker
in the world market for commodities with perfectly elastic demand for its international exports
and perfectly elastic supply for international imports. This assumption can be toggled from the
command line as illustrated in Listing 4 (note that previous commands for running the baseline
and policy case still apply here).
Listing 4: Running the Model as a Small Open Economy
gams model/sage.gms —loe=0
We run the hypothetical environmental regulation for all sources in the primary metal manufac-
turing sector (pmm). As before, we assume that compliance with the regulation requires additional
capital and labor inputs to production. Functionally, the large open economy formulation imposes
a non-zero slope in the international demand for U.S. export curve and supply of international
imports into the U.S. market curve. The steepness of these curves are evaluated in Table 9. Figure
23 reports the percent change in imports and exports across all model years for each sector in the
economy. Because estimated elasticities are high for imports, the percent change across the two
formulations are almost equivalent. Both model formulations estimate increases in the imports for
primary metals due to import substitution from relatively more expensive domestic output. The
story is different for exports. Estimated elasticities are smaller in absolute value for exports and
therefore the large open economy modeled results diverge more significantly from the small open
economy results. Imposing a downward sloping demand curve for exports mutes quantity impacts
in the export market and therefore percent changes in the large open economy formulation are
smaller than in the small open economy case.
While quantity changes are muted in the large open economy case, export and import prices
differentially change for each commodity. This contributes to larger social costs estimated in the
large open economy framework relative to the simpler alternative as reported in Table 18.
6.5.5 Example of Sector Specific Consumption Taxes
To further augment the section on sensitivity simulations, we illustrate model results for hypothet-
ical sector specific consumption tax scenarios. The simulations estimate the equivalent variation of
94
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Imports
-0.5
E
3
E
0.0
0.5
1.0
wsu
wpm
ttn
trn
tem
srv
ref
prm
pmm
min
hit
gas
fmm
fbm
ele
cru
cpu
con
col
chm
cem
bom
agf
Exports
1.5
% change
¦E
]
3
?
Figure 23: Percent Change in Imports and Exports
Table 18: EV Comparison Across Trade Assumptions [Billion
Large Open
Small Open
Economy
Economy
-44.98
-41.67
sector specific consumption taxes that raise an additional $10 billion in total government revenues
in each time step of the model based on the output value in the baseline (this revenue target repre-
sents approximately 2% of government revenue from sales and excise taxes in the benchmark year).
95
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This suite of simulations is run via the R program, examples/consumption_tax.r that relies on
a policy file called examples/consumption_tax.gms (also reported in Listing 5). The policy file
selects the taxed sector as controlled by the R script and imposes a hypothetical addition to the
existing consumption tax for the selected sector equal to the specific amount of government revenue
raised in each period.
Listing 5: examples/consumption_tax.gms
> implements consumption tax ch.an.qe
-v
> s..tsx; taxed sector set by defininq s...:t a x ( "xxx " i = YES;
> shock.size: initial year valuer of the shock in billions
-v
set
s_tax(s) taxed sector;
parameter
shock.size value of the shock in billions
tax addition to tax rate;
'
s.tax (s) = no;
> load the shock specification
$include examples/tax_definition.gms
> tax amount
tax(t,s_tax)$ sum((rr,h), pa.l(t,rr, s.tax)*cd.1(t,rr,s_tax,h)* cd_base(t,rr,s_tax,h)
)
= shock.size/sum( (rr,h), pa.1 (t,rr,s.tax)*cd.1 (t,rr,s.tax,h)*cd.base (t,rr,s.tax,
h) ) ;
> augment exist ina consumption tax
tc (t, r, s.tax) = tc (t, r, s.tax) + tax (t, s.tax) ;
display tax;
Figure 24 reports the calculated social costs as characterized by changes in equivalent variation.
These results are for diagnostic purposes only and should not be interpreted as the results of a
specific policy. The social cost is dependent, in part, on the use of the revenue, where in these
examples the recycling occurs through the models standard government budget constraint.
6.5.6 Additional Examples
Other examples are included in the examples subdirectory and are listed in Table 19. These
relatively simple examples are designed to demonstrate basic features of the modeling framework
and their general impact on simulation results. The examples are intended to be run from the top-
level directory of the SAGE package. Most of the routines listed in Table 19 use the R programming
96
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-------
Table 19: Additional Simulation Examples
File Name
Description
static_vs_dynamic .R
putty-clay _vs_putty-putty. R
national_vs_regional .R
regulatory_modeling_approach.R
open_economy.R
scenario_analysis.R
consumption_tax.R
plot_results.R
Compares the results from the sample abatement re-
quirement using a dynamic vs. static version of the
model.
Compares the results of the sample abatement re-
quirement under the default partial putty-clay capital
framework vs the case of fully malleable capital under
the putty-putty assumption.
Compares the results from the sample abatement re-
quirement from the dynamic model with and without
regional delineation.
Compares the output of the sample abatement require-
ment when modeled as a productivity shock vs. an ex-
plicit abatement requirement per unit of output. Pro-
duces the comparisons in Figure 22.
Compares the output of the sample abatement require-
ment when assuming a large vs. small open economy
in international trade. Produces the comparisons in
Figure 23.
Runs sensitivity analyses around hypothet-
ical regulations similar to those consid-
ered in Marten et al. (2019). Uses the file
examples/productivity_shock.gms as the pol-
icy file to define a variety of hypothetical regulations
as productivity shocks.
Runs sensitivity analyses for hypothetical sector spe-
cific consumption tax increases as reported in Figure
24. Uses the file examples/consumption_tax.gms as
the policy file to define the hypothetical scenarios.
Illustrates custom plotting functions designed to or-
ganize and display results from SAGE outputs. For
function code, see R_utilities.R.
References
Aguiar, M. and Bils, M. (2015). Has consumption inequality mirrored income inequality? American
Economic Review, 105(9):2725-56.
Armington, P. S. (1969). A theory of demand for products distinguished by place of production.
Staff Papers (International Monetary Fund), 16(1):159-178.
Arora, V. (2014). Estimates of the price elasticities of natural gas supply and demand in the United
98
-------
States. Munich Personal RePEc Archive, MPRA Paper No. 54232.
Arora, V. and Cai, Y. (2014). US natural gas exports and their global impacts. Applied Energy,
120:95-103.
Arrow, K. J., Cropper, M., Collier, C., Groom, B., Heal, G. M., Newell, R. G., Nordhaus, W. D.,
Pindyck, R. S., Pizer, W. A., Portney, P., et al. (2013). How should benefits and costs be
discounted in an intergenerational context? the views of an expert panel. The views of an expert
panel (December 19, 2013). Resources for the future discussion paper, (12-53).
Babiker, M. H., Maskus, K. E., and Rutherford, T. F. (1997). Carbon taxes and the global trading
system. University of Adelaide, Center for International Economic Studies, Seminar Paper 97-08.
Balistreri, E. J. and Rutherford, T. F. (2001). Dynamic general equilibrium analysis at the state
level: Assessing the economic implications of the Kyoto Protocol. Presented at the 4th Annual
Conference on Global Economic Analysis, Purdue University, June 27-29.
Baumeister, C. and Hamilton, J. D. (2019). Structural interpretation of vector autoregressions
with incomplete identification: Revisiting the role of oil supply and demand shocks. American
Economic Revievj, 109(5):1873-1910.
Beck, T., Jolly, L., and Loncar, T. (1991). Supply response in the Australian black coal industry
(no. 91.1). Canberra, Australia: Australian Board of Agricultural and Resource Economics.
Beckman, J., Hertel, T., and Tyner, W. (2011). Validating energy-oriented CGE models. Energy
Economics, 33(5):799-806.
Bj0rnland, H., Nordvik, F., and Maximilian, R. (2017). Supply flexibility in the shale patch:
Evidence from North Dakota. Norges Bank Research Working Paper 9.
Boetel, B. L., Hoffmann, R., and Liu, D. J. (2007). Estimating investment rigidity within a threshold
regression framework: The case of US hog production sector. American Journal of Agricultural
Economics, 89(1):36-51.
Bohringer, C., Carbone, J. C., and Rutherford, T. F. (2018). Embodied carbon tariff's. The
Scandinavian Journal of Economics, 120(1):183-210.
Bohringer, C., Schneider, J., and Asane-Otoo, E. (2016). Trade in carbon and the effectiveness
of carbon tariffs. University of Oldenburg, Department of Economics, Discussion Papers in
Economics, No. V-388-16.
Borges, A. M. and Goulder, L. H. (1984). Decomposing the impact of higher energy prices on long-
term growth. In Scarf, H. E. and Shoven, J. B., editors, Applied General Equilibrium Analysis.
Cambridge University Press.
99
-------
Brockway, P. E., Heun, M. K., Santos, J., and Barrett, J. R. (2017). Energy-extended CES aggregate
production: Current aspects of their specification and econometric estimation. Energies, 10(2).
Brown, J. P., Fitzgerald, T., and Weber, J. G. (2016). Capturing rents from natural resource
abundance: Private royalties from U.S. onshore oil & gas production. Resource and Energy
Economics, 46:23 - 38.
Brown, S. P. and Huntington, H. G. (2003). Terms of trade and OECD policies to mitigate global
climate change. Federal Reserve Bank of Dallas Economic and Financial Policy Review, 2(1) :1—
25.
Buhr, B. L. and Kim, H. (1997). Dynamic adjustment in vertically linked markets: the case of the
US beef industry. American Journal of Agricultural Economics, 79(1):126-138.
Burniaux, J.-M. and Truong, T. P. (2002). GTAP-E: an energy-environmental version of the GTAP
model. Purdue University, Center for Global Trade Analysis, GTAP Technical Paper No. 16.
Cai, Y., Newth, D., Finnigan, J., and Gunasekera, D. (2015). A hybrid energy-economy model for
global integrated assessment of climate change, carbon mitigation and energy transformation.
Applied Energy, 148:381-395.
Caldara, D., Cavallo, M., and Iacoviello, M. (2018). Oil price elasticities and oil price fluctuations.
Journal of Monetary Economics, 103:1-20.
Capros, P., Van Regemorter, D., Paroussos, L., Karkatsoulis, P., Fragkiadakis, C., Tsani, S., Char-
alampidis, I., and Revesz, T. (2013). GEM-E3 model documentation. European Commission
Joint Research Centre, JRC Technical Report 26034 EN.
Caron, J., Karplus, V. J., and Schwarz, G. A. (2017). Modeling the income dependence of household
energy consumption and its implications for climate policy in china.
Caron, J. and Rausch, S. (2013). A global general equilibrium model with US state-level detail for
trade and environmental policy analysis-technical notes. MIT Joint Program on the Science and
Policy of Global Change, Joint Program Technical Note 13.
CBO (2017). International comparisons of corporate income tax rates. U.S. Congressional
Budget Office, https://www.cbo.gov/system/files/115th-congress-2017-2018/reports/
52419-internationaltaxratecomp.pdf.
CBO (2018). The distribution of household income, 2014. U.S. Congressional
Budget Office, https://www.cbo.gov/system/files/115th-congress-2017-2018/reports/
53597-distribution-household-income-2014.pdf.
CEA (2017). Discounting for public policy: Theory and recent evidence on the
merits of updating the discount rate. Council of Economic Advisers Issue Brief.
100
-------
https://obamawhitehouse.archives.gov/sites/default/files/page/files/201701_
cea_discounting_issue_brief.pdf.
Chateau, J., Dellink, R., and Lanzi, E. (2014). An overview of the OECD ENV-Linkages model:
Version 3. OECD Environment Working Papers, No. 65.
Coughlin, C. C. and Novy, D. (2013). Is the international border effect larger than the domestic
border effect? Evidence from US trade. CESifo Economic Studies, 59(2):249-276.
Dahl, C. and Duggan, T. E. (1996). US energy product supply elasticities: A survey and application
to the US oil market. Resource and Energy Economics, 18(3):243-263.
Dissou, Y., Karnizova, L., and Sun, Q. (2015). Industry-level econometric estimates of energy-
capital-labor substitution with a nested CES production function. Atlantic Economic Journal,
43(1):107-121.
Dixon, P. B. and Rimmer, M. T. (2013). Validation in computable general equilibrium modeling.
In Handbook of Computable General Equilibrium Modeling, volume 1, pages 1271-1330. Elsevier.
EIA (2001). Model documentation: Coal market module of the National Energy Modeling System.
DOE/EIA-M060(2001).
EIA (2011). Performance profiles of major energy producers 2009. Report Number: DOE/EIA-
0206(2009).
EPA (2010). Guidelines for preparing economic analysis. U.S. Environmental Protection Agency.
Washington, DC.
EPA (2015). Economy-wide modeling: Social cost and welfare white paper, https://yosemite.
epa.gov/sab/SABPRODUCT.NSF/0/07E67CF77B54734285257BB0004F87ED.
Farzin, Y. H. (1992). The time path of scarcity rent in the theory of exhaustible resources. The
Economic Journal, 102(413):813-830.
Feenberg, D. and Coutts, E. (1993). An introduction to the TAXSIM model. Journal of Policy
Analysis and Management, 12(1): 189-194.
Feenstra, R. C., Inklaar, R., and Timmer, M. P. (2015). The next generation of the Penn World
Table. American Economic Review, 105(10):3150-82.
Ferris, M. C. and Munson, T. S. (2000). Complementarity problems in GAMS and the PATH
solver. Journal of Economic Dynamics and Control, 24(2):165-188.
Fitzgerald, T. and Rucker, R. R. (2016). US private oil and natural gas royalties: Estimates and
policy relevance. OPEC Energy Review, 40(l):3-25.
101
-------
Foley, P. and Clark, J. (1981). US copper supply: An economic/engineering analysis of cost—supply
relationships. Resources Policy, 7(3):171-187.
Golombek, R., Hagem, C., and Hoel, M. (1995). Efficient incomplete international climate agree-
ments. Resource and Energy Economics, 17(l):25-46.
Greene, D. L. and Liu, C. (2015). U.S. oil dependence 2014: Is energy independence in sight?
Energy Policy, 85:126-137.
Ha, S. J., Lange, I., Lecca, P., and Turner, K. (2012). Econometric estimation of nested production
functions and testing in a computable general equilibrium analysis of economy-wide rebound
effects. University of Stirling, Division of Economics, Stirling Economics Discussion Papers
2012-08.
Haggerty, M., Lawson, M., and Pearcy, J. (2015). Steam coal at an arm's length: An evaluation
of proposed reform options for US coal used in power generation. Manuscript, Headwaters
Economics and Montana State University.
Havranek, T., Horvath, R., Irsova, Z., and Rusnak, M. (2015). Cross-country heterogeneity in
intertemporal substitution. Journal of International Economics, 96(1):100-118.
Hendricks, N. P., Smith, A., and Sumner, D. A. (2014). Crop supply dynamics and the illusion of
partial adjustment. American Journal of Agricultural Economics, 96(5):1469-1491.
Hertel, T., Hummels, D., Ivanic, M., and Keeney, R. (2007). How confident can we be of CGE-based
assessments of free trade agreements? Economic Modelling, 24(4) :611-635.
Hertel, T. W., McDougall, R., Narayanan, B., and Aguiar, A. H. (2008). Behavioural parameters.
In Narayanan, B. and Walmsley, T. L., editors, Global Trade, Assistance, and Production: The
GTAP 7 Data Base. Center for Global Trade Analysis, Purdue University.
Hertel, T. W. and Tsigas, M. (2002). Primary factor shares. In Dimaranan, B. V. and McDougall,
R. A., editors, Global Trade, Assistance, and Production: The GTAP 5 Data Base. Center for
Global Trade Analysis, Purdue University.
Higgs, P. J. and Powell, A. A. (1990). Forecasting small-area agricultural incomes using a CGE
model of the Australian economy. The Annals of Regional Science, 24(l):43-59.
Ho, M., Britz, W., Delzeit, R., Leblanc, F., Roson, R., Schuenemann, F., and Weitzel, M. (2020).
Modelling consumption and constructing long-term baselines in final demand. Journal of Global
Economic Analysis, 5(1):63-108.
Holt, M. T. and Aradhyula, S. V. (1998). Endogenous risk in rational-expectations commodity
models: A multivariate generalized ARCH-M approach. Journal of Empirical Finance, 5(2):99-
129.
102
-------
Holt, M. T. and McKenzie, A. M. (2003). Quasi-rational and ex ante price expectations in com-
modity supply models: An empirical analysis of the US broiler market. Journal of Applied
Econometrics, 18(4):407-426.
Horridge, M., Meeraus, A., Pearson, K., and Rutherford, T. F. (2013). Solution software for com-
putable general equilibrium modeling. In Handbook of computable general equilibrium modeling,
volume 1, pages 1331-1381. Elsevier.
Huntington, H. G. (1992). Inferred demand and supply elasticities from a comparison of world
oil models. In Sterner, T., editor, International Energy Economics. International Studies in
Economic Modelling, Springer, Dordrecht.
Iqbal, M. Z. and Babcock, B. A. (2018). Global growing-area elasticities of key agricultural crops
estimated using dynamic heterogeneous panel methods. Agricultural Economics, 49(6):681-690.
ITC (2011). Magnesium from China and Russia. Investigation Nos. 731-TA-1071-1072 (Review)
Publication 4214.
ITC (2014a). Gray portland cement and cement clinker from Mexico. Investigation No. 731-TA-451
(Final) Publication 2305.
ITC (2014b). Silica bricks and shapes from China. Investigation No. 731-TA-1205 (Final) Publi-
cation 4443.
Jomini, P., Zeitsch, J. F., McDougall, R., Welsh, A., Brown, S., Hambley, J., and Kelly, J.
(1991). SALTER: A general equilibrium model of the world economy, Volume 1, Model structure,
database and parameters. Industry Commission, Canberra.
Jordan, B., Lange, I., and Linn, J. (2018). Coal demand, market forces, and US coal mine closures.
RFF Working Paper 18-13.
Jorgenson, D. W., Goettle, R. J., Ho, M. S., and Wilcoxen, P. J. (2013). Double dividend: Envi-
ronmental taxes and fiscal reform in the United States. MIT Press.
Kaiser, H. M. (2012). An economic analysis of the national pork board checkoff program. Report
prepared for the National Pork Board.
Kapombe, C. M. and Colyer, D. (1998). Modeling US broiler supply response: A structural time
series approach. Agricultural and Resource Economics Review, 27(2):241-251.
Keller, W. J. (1976). A nested CES-type utility function and its demand and price-index functions.
European Economic Review, 7(2):175-186.
Kemfert, C. (1998). Estimated substitution elasticities of a nested CES production function ap-
proach for Germany. Energy Economics, 20(3):249-264.
103
-------
Kim, H. and Moschini, G. (2018). The dynamics of supply: US corn and soybeans in the biofuel
era. Land Economics, 94(4):593-613.
Kiuila, O. and Rutherford, T. F. (2013). Piecewise smooth approximation of bottom-up abatement
cost curves. Energy Economics, 40:734-742.
Koesler, S. and Schymura, M. (2015). Substitution elasticities in a constant elasticity of substitution
framework—Empirical estimates using nonlinear least squares. Economic Systems Research,
27(1):101-121.
Krichene, N. (2002). World crude oil and natural gas: A demand and supply model. Energy
Economics, 24(6):557-576.
Lanz, B. and Rutherford, T. F. (2016). Gtapingams: Multiregional and small open economy models.
Journal of Global Economic Analysis, 1(2): 1-77.
Lau, M. I., Pahlke, A., and Rutherford, T. F. (2002). Approximating infinite-horizon models in a
complementarity format: A primer in dynamic general equilibrium analysis. Journal of Economic
Dynamics and Control, 26(4):577-609.
Lecca, P., Swales, K., and Turner, K. (2011). An investigation of issues relating to where energy
should enter the production function. Economic Modelling, 28(6):2832-2841.
Lin, C.-Y. C. and Wagner, G. (2007). Steady-state growth in a Hotelling model of resource extrac-
tion. Journal of Environmental Economics and Management, 54(1):68 - 83.
Liu, J., Arndt, C., and Hertel, T. W. (2004). Parameter estimation and measures of fit in a global,
general equilibrium model. Journal of Economic Integration, 19(3):626-649.
Lofgren, H., Harris, R. L., and Robinson, S. (2002). A standard computable general equilibrium
(CGE) model in GAMS, volume 5. Intl Food Policy Res Inst.
Markandya, A. and Pedroso-Galinato, S. (2007). How substitutable is natural capital? Environ-
mental and Resource Economics, 37(1):297-312.
Marsh, J. M. (2003). Impacts of declining US retail beef demand on farm-level beef prices and
production. American Journal of Agricultural Economics, 85(4):902-913.
Marten, A. and Garbaccio, R. (2018). An applied general equilibrium model for the analysis of
environmental policy: Sage vl.O technical documentation. NCEE Working Paper 2018-05.
Marten, A. L., Garbaccio, R., and Wolverton, A. (2019). Exploring the general equilibrium costs
of sector-specific regulations. Forthcoming in Journal of the Association of Environmental and
Resource Economists.
Mathiesen, L. (1985). Computational experience in solving equilibrium models by a sequence of
linear complementarity problems. Operations research, 33(6):1225-1250.
104
-------
McClelland, R. and Mok, S. (2012). A review of recent research on labor supply elasticities.
Congressional Budget Office, Working Paper 2012-12.
Narayanan, B., Aguiar, A., and McDougall, R. (2016). An overview of the gtap 9 data base. Journal
of Global Economic Analysis, l(l):181-208.
Nordhaus, W. D. (2007). A review of the stern review on the economics of climate change. Journal
of Economic Literature, 45(3):686-702.
Paltsev, S., Reilly, J. M., Jacoby, H. D., Eckaus, R. S., McFarland, J., Sarofim, M., Asadoorian,
M., and Babiker, M. (2005). The MIT Emissions Prediction and Policy Analysis (EPPA) Model:
Version 4. Joint Program Report Series, Report 125.
Ramsey, F. P. (1928). A mathematical theory of saving. The Economic Journal, 38(152):543-559.
Rausch, S., Metcalf, G. E., Reilly, J. M., and Paltsev, S. (2011). Distributional impacts of a U.S.
greenhouse gas policy: A general equilibrium analysis of carbon pricing. In Metcalf, G. E., editor,
US Energy Tax Policy. Cambridge University Press.
Rausch, S. and Rutherford, T. F. (2009). Tools for building national economic mod-
els using state-level implan social accounts. Unpublished manuscript. Available online at:
http://www.cepe.ethz.ch/people/profs/srausch/IMPLAN2006inGAMS.pdf.
Roberts, M. J. and Schlenker, W. (2013). Identifying supply and demand elasticities of agri-
cultural commodities: Implications for the US ethanol mandate. American Economic Review,
103(6):2265-95.
Ross, M. T. (2005). Documentation of the Applied Dynamic Analysis of the Global Economy
(ADAGE) Model. RTI International Working Paper 05-01.
Ross, M. T. (2014). Structure of the Dynamic Integrated Economy/Energy/Emissions Model:
Electricity Component, DIEM-Electricity. Duke University, Nicholas Institute for Environmental
Policy Solutions, Working Paper NI WP 14-11.
Rucker, R. R., Burt, O. R., and LaFrance, J. T. (1984). An econometric model of cattle inventories.
American Journal of Agricultural Economics, 66(2):131-144.
Russo, C., Green, R. D., and Howitt, R. E. (2008). Estimation of supply and demand elasticities
of California commodities. Agriculture and Resource Economics Working Papers, Department
of Agricultural and Resource Economics, UCD, UC Davis.
Rutherford, T. F. (1999). Applied general equilibrium modeling with MPSGE as a GAMS subsys-
tem: An overview of the modeling framework and syntax. Computational economics, 14(1-2) :1
46.
105
-------
SAB (2017). SAB advice on the use of economy-wide models in evaluating social costs, benefits, and
economic impacts of air regulations. EPA-SAB-17-012. U.S. Environmental Protection Agency.
Washington, DC.
SAB (2020). Technical review of epa's computable general equilibrium model, sage. EPA-SAB-20-
010. U.S. Environmental Protection Agency. Washington, DC.
Sands, R., Malcolm, S., Suttles, S., Marshall, E., et al. (2017). Dedicated energy crops and com-
petition for agricultural land. Economic Research Report-Economic Research Service, IJSDA,
(223).
Sarmiento, C. and Allen, P. G. (2000). Dynamics of beef supply in the presence of cointegration: A
new test of the backward-bending hypothesis. Review of Agricultural Economics, 22(2):421-437.
Serletis, A., Timilsina, G. R., and Vasetsky, O. (2010a). Interfuel substitution in the United States.
Energy Economics, 32(3):737-745.
Serletis, A., Timilsina, G. R., and Vasetsky, O. (2010b). International evidence on sectoral interfuel
substitution. The Energy Journal, 31(4): 1-29.
Shideed, K. H. and White, F. C. (1989). Alternative forms of price expectations in supply analysis
for US corn and soybean acreages. Western Journal of Agricultural Economics, 14(1836-2016-
150808):281.
Shoven, J. B. and Whalley, J. (1984). Applied general-equilibrium models of taxation and interna-
tional trade: An introduction and survey. Journal of Economic literature, 22(3):1007-1051.
Simola, A. (2015). Intensive margin of land use in CGE models-Reviving CRESH functional form.
Land Use Policy, 48:467-481.
Stern, D. I. (2012). Interfuel substitution: A meta-analysis. Journal of Economic Surveys,
26(2):307-331.
Stern, N. (2007). The Economics of Climate Change: The Stern Review. Cambridge University
Press.
Stone, R. (1954). Linear expenditure systems and demand analysis: an application to the pattern
of british demand. The Economic Journal, 64(255):511-527.
Su, X., Zhou, W., Nakagami, K., Ren, H., and Mu, H. (2012). Capital stock-labor-energy substi-
tution and production efficiency study for China. Energy Economics, 34(4):1208-1213.
Sue Wing, I. (2001). Induced technical change in computable general equilibrium models for climate-
change policy analysis. PhD thesis, Massachusetts Institute of Technology.
106
-------
Sue Wing, I. (2006). The synthesis of bottom-up and top-down approaches to climate policy
modeling: Electric power technologies and the cost of limiting US C02 emissions. Energy Policy,
34(18) :3847-3869.
Sue Wing, I., Daenzer, K., Fisher-Vanden, K., and Calvin, K. (2011). Phoenix Model Documenta-
tion.
Van der Mensbrugghe, D. (1994). GREEN-the reference manual. OECD Economics Department
Working Papers, No. 143.
Van der Werf, E. (2008). Production functions for climate policy modeling: An empirical analysis.
Energy Economics, 30(6):2964-2979.
Young, A. T. (2013). US elasticities of substitution and factor augmentation at the industry level.
Macroeconomic Dynamics, 17(04):861-897.
Yuan, M., Rausch, S., Caron, J., Paltsev, S., and Reilly, J. (2019). The mit us regional energy
policy (usrep) model: The base model and revisions. Joint Program Technical Note TN, 18.
Zahniser, S., Hertz, T., Dixon, P., and Rimmer, M. (2012). The potential impact of changes in
immigration policy on U.S. agriculture and the market for hired farm labor: A simulation analysis.
U.S. Department of Agricuture, Economic Research Service, Economic Research Report Number
135.
107
------- |