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ENVIRONMENTAL ECONOMICS

Welfare Impacts of Ocean Acidification: An Integrated
Assessment Model of the US Mollusk Fishery

Christopher C. Moore

Working Paper Series

Working Paper # 11 -06
December, 2011

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g	ra National Center for Environmental Economics

s	z 1200 Pennsylvania Avenue, NW (MC 1809)

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Welfare Impacts of Ocean Acidification: An Integrated
Assessment Model of the US Mollusk Fishery

Christopher C. Moore

NCEE Working Paper Series
Working Paper # 11-06
December, 2011

DISCLAIMER

The views expressed in this paper are those of the author(s) and do not necessarily represent those
of the U.S. Environmental Protection Agency. In addition, although the research described in this
paper may have been funded entirely or in part by the U.S. Environmental Protection Agency, it
has not been subjected to the Agency's required peer and policy review. No official Agency
endorsement should be inferred.


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Welfare impacts of ocean acidification: an integrated assessment model of the US mollusk fishery

Christopher C. Moore
moore.chris@epa.gov

US EPA National Center for Environmental Economics
Abstract

As atmospheric carbon dioxide (C02) concentrations increase, the world's oceans are absorbing C02 at a
faster rate than at any time in the past 800,000 years. While this reduces the amount of the most prevalent
greenhouse gas in the atmosphere it also causes changes in seawater chemistry, collectively known as
ocean acidification. One of the known ecological impacts of ocean acidification is a reduced ability of
some marine calcifiers to form shells and skeletons. Mollusks and reef building corals are particularly
vulnerable. Understanding how these biophysical impacts affect social welfare is a critical step in
crafting and evaluating policies that reduce C02 emissions. There is an extensive body of literature
estimating the economic impacts of climate change but very little research has been done on how ocean
acidification could affect social welfare. This paper proposes an integrated biogeochemical-economic
model to estimate the social welfare impacts of ocean acidification in the US mollusk fishery. To
demonstrate the model two pathways for global greenhouse gas emissions are compared: a baseline path
and a policy path in which C02 and other greenhouse gas emissions are reduced. These pathways provide
input for integrated earth systems models, generating forecasts of changes to sea water chemistry and
mollusk production. A two-stage demand system estimates the utility function parameters needed to
calculate compensating variation for avoided increases in the prices of oysters, scallops, clams and
mussels. The model estimates annual compensating variation for the mitigation path relative to baseline
conditions.

JEL Classification: C33, Q22, Q54, Q57

Key Words: Ocean acidification, integrated assessment model, demand system estimation


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1. Introduction

The ocean is the Earth's largest sink of atmospheric carbon dioxide (C02) and has absorbed about one
third of the anthropogenic C02 emissions over the past 200 years (Sabine et al 2004). The increasing rate
at which the ocean is absorbing C02 is causing a number of changes to seawater chemistry, collectively
known as ocean acidification. C02, when absorbed into the ocean, acts as an acid lowering the seawater
pH and the aragonite saturation level (fiA)- As QA falls it becomes more difficult, and eventually
impossible, for many marine organisms to form shells and skeletons. Mollusks and reef building corals
appear to be particularly vulnerable while crustaceans, like lobsters and crabs, are not adversely affected
(Ries et al 2009). In addition to species that humans value directly, many important plankton species that
form the base of the marine food web are also calcifiers and have exhibited vulnerability to falling pH and
Qa (Guinette and Fabry 2008).

Regulations and agreements that reduce carbon dioxide emissions, such as fuel economy
standards in the US or the European Union's emissions trading system, mitigate the impacts of climate
change and ocean acidification. To develop efficient mitigation policy, decision makers should weigh the
expected social costs of these policies against the economic damages that are likely to be avoided as a
result. There is a large body of literature estimating the economic impacts of climate change caused by
C02 and other greenhouse gasses, but the impacts of ocean acidification are conspicuously absent from
that literature. Only recently have there been efforts to estimate ocean acidification's potential economic
impacts. So far they have examined revenues in the mollusk fishery (Cooley and Doney 2009; Narita et
al 2011) and ecosystem services provided by coral reefs (Brander et al 2009).

Welfare impacts of climate change are estimated using integrated assessment models (IAMs)
which link models of greenhouse gas (GHG) emissions, Earth systems dynamics, and economic damages
from temperature change. Policy makers would benefit from analogous models of ocean acidification
impacts in order to consider more comprehensive measures of damages from C02 emissions. It is useful


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to think of an impact pathway through which C02 and other greenhouse gas emissions affect social
welfare.

This paper develops an integrated biogeochemical-economic model to simulate the impact
pathway in figure 1 and project the potential impacts of ocean acidification on the US market for oysters,
scallops, clams, and mussels. The integrated model forecasts changes in consumer welfare through the
end of this century using the following models and data:

1.	Exogenous pathways for GHG concentrations and radiative forcing are used to project sea surface
temperatures (SST) under two different policy scenarios

2.	Exogenous pathways for C02 concentrations and the SST projections from Step 1 are used as
inputs to an ocean carbon model that calculates changes in the aragonite saturation state QA

3.	Species-specific growth rate responses to falling QA provide the biological impacts

4.	A Cobb-Douglas production function with environmental quality as an input allows the derivation
of the evolution of the price vector

5.	A two-stage demand system estimates the parameters of a representative household's expenditure
function that accounts for income changes and substitution between mollusks and other meats

6.	The estimated expenditure function is used to calculate compensating variation between two
alternative policy paths and the resulting evolution of the mollusk price vector

The two-stage budgeting model allows estimation of total income and price elasticities so that
mollusk expenditures can be modeled as functions of population and household income growth. The
almost ideal (AI) demand system, estimated in the second stage, allows substitution among mollusks that
exhibit different biological responses, and thus price changes, under the same set of ecological conditions
while the first stage expenditure model accounts for cross-price effects with other consumption
categories. The utility theoretic demand model allows estimation of social welfare changes as opposed to
previous economic studies of ocean acidification that project revenue losses. Estimated annual welfare


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impacts of the lower emissions path are initially small: about seven cents per household, on average. That
figure grows to nearly two dollars per household by the end of this century as demand for mollusks
increases and the divergence of projected ecological effects of ocean acidification between the policy and
baseline paths increases. The estimated present value of compensating variation for the emission
reduction examined in this paper is more than 700 million dollars when discounted at 5% through the year
2100.

This model can be expanded to estimate welfare impacts to global markets for mollusks and
finfish given sufficient market data and ecological response functions. Market and non-market impacts to
coral reefs are also needed for a comprehensive estimate of the potential economic impacts of ocean
acidification. This paper lays the groundwork for such an estimate by introducing an integrated
biogeochemical-economic model capable of estimating utility theoretic measures of welfare gains from
mitigating the some of the anticipated consequences of ocean acidification.

2. The biogeochemical model

The biogeochemical model simulates the impact pathway from GHG emissions to the biological
responses of the four mollusks species of interest to this model. Exogenous projections of C02 and other
GHG emissions and the resulting radiative forcing are taken from the representative concentration
pathways (RCP; Meinshausen et al 2010) which were generated for the IPCC Fifth Assessment Report.
The model developed in this paper will operate on two of the RCP scenarios, treating the high-emissions
pathway (8.5 w/m2 radiative forcing in 2100) as the baseline and the medium-high pathway (6 w/m2
radiative forcing in 2100) as the projected policy outcome (figure 2).

2.1 Sea surface temperature

The relationship between atmospheric C02 concentrations and ocean acidification is described, in part, by
Henry's Law, "at a constant temperature, the amount of a given gas that dissolves in a given type and


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volume of liquid is directly proportional to the partial pressure (PCO2) of that gas in equilibrium with that
liquid." However, when temperature is not constant the relationship changes and, in fact, as seawater gets
warmer with climate change it will absorb less C02 from the atmosphere. So in addition to the pathways
for atmospheric C02 concentrations, which are equivalent to pC02, the surface seawater temperature
(SST) is also required for accurate forecasts of QA-

To forecast sea surface temperature I use the simple upwelling diffusion energy balance model of
Baker and Roe (2009). The Baker and Roe model is an aspatial representation of the energy exchange
between the atmosphere and a well-mixed surface layer of the ocean which loses heat to the deep ocean
below. The resulting temperature of the surface layer (as well as the temperature anomaly) will depend
on the initial value for SST. To generate a single representative starting value for SST, I calculate a
market value-weighted 10 year average for the coastal regions of the US where mollusks are harvested
and cultured. Table 1 shows the annual average surface seawater temperature for the coastal regions of
the US (NOAA National Oceanographic Data Center) over the past 10 years and how much of the US
mollusk harvest value each region contributed in that time. The time path of temperature changes for
each of the RCP emissions scenarios are added to the weighted average of SST to generate representative
time paths of SST for the coastal regions of the US (panel A in figure 3).

2. 2 Ocean Carbon Chemistry

With projections of pC02 and SST I can forecast changes in seawater chemistry using the ocean carbon
model C02SYS (Lewis and Wallace 1998; van Heuven et al 2011). The C02SYS program performs
calculations relating parameters of the CO2 system in seawater. The program uses two of the four
measureable parameters of the CO2 system [total alkalinity, total inorganic CO2, pH and, pC02]
to calculate the two unknown parameters and QA at a given SST. The RCP scenarios and the ocean
heat uptake model of Baker and Roe have provided me with time paths for pC02 and SST. To complete


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the set of required inputs I need an initial value for either total alkalinity or total inorganic carbon after
which values will be determined within the model. I chose total inorganic carbon and used the C02SYS
model to calibrate that number to observed pC02 and pH levels in the year 2010. The resulting time
paths for ClA under the baseline and policy paths are shown in panel B of figure 3.

2.3 Mollusk responses to ocean acidification

As the ocean absorbs more C02 from the atmosphere the carbon equilibrium in seawater is shifting
toward C02 and away from carbonate ion (C032 ). The carbonate ion is a critical building block for
calcium carbonate shells and skeletons. Decreasing availability of carbonate ion will make it more
difficult and eventually impossible for some marine calcifiers to form shells and skeletons (Gazeau et al
2007).

The rate at which marine mollusks are able to build shells is not necessarily an economically
relevant measure of ocean acidification's impacts. Consumers care about what is inside the shell and how
much it costs. More relevant measures would be how tissue growth and population dynamics, such as
reproduction and predation, are affected. Unfortunately no empirical studies have examined these
impacts and so studies of shell growth under falling QA provide the only empirical relationships between
ocean acidification and mollusk production. Within that body of literature Ries et al (2009) provide the
most useful results for economic analysis.

Ries et al (2009) observe the response of different species of various age classes1 to changing QA
levels in controlled experiments. Eighteen different calcifying species were observed for 60 days at four
different levels of lA representing current conditions and two, three, and 10 times preindustrial
atmospheric C02 concentrations. Using regression Ries et al. test several functional forms, finding that

1 The fact that various age classes were observed is important because the results can be interpreted as average
changes over the life time of each species.


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over the range of lA observed, growth of the eastern oyster and bay scallop exhibited approximately
linear relationships with QA. Hard clams were largely unaffected by the increase to twice preindustrial
levels but further increases caused a precipitous decrease in growth rates. Blue mussels did not show any
statistically significant response to changes in QA even when increased to levels corresponding 10 times
the preindustrial C02 concentration. Table 1 summarizes the Ries et al results for the four types of
mollusk in the demand model. The regression results in table 2 provide the link in this integrated model
between the geochemical and biophysical components. Each of the empirical response functions operates
on the projected levels of lA to forecast changes in shell growth rates shown in figure 4.

3. Mollusk production and evolution of prices

The effect that ocean acidification may have on each mollusk price will be inferred from a production
function for a perfectly competitive industry that includes environmental quality as an input. This
approach has been used to estimate welfare impacts of habitat destruction on fisheries (e.g. Ellis and
Fisher, 1987; Barbier, 1994; Barbier and Strand, 1998) and air quality on agriculture (Kopp and
Krupnick, 1987). For each mollusk type i, I assume that production can be represented by the Cobb-
Douglas form

q,= AiXf'W,

where X is an input to production (e.g. harvest effort), E is a measure of environmental quality, and A, (3
and y are parameters. In this application E would be changing over time but I omit the time subscripts on
all arguments to simplify notation. The solution to the static profit maximization problem yields the cost
function


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Q = Wi

yA,E"j

where wt is the unit cost of input X,. Differentiating with respect to qt provides the marginal cost function
for mollusk i

MC,

dC; w;( 1 >

i

i-A

i 	 i

A F7i
vA-11 j

4i

A	(1)

dq{ fi.

which, under perfect competition, a reasonable assumption in the US mollusk markets, will also be equal
to price. The elasticity of price for mollusk i to changes in environmental quality is therefore found by

d In P y.

taking the natural log of (1) and differentiating with respect to ln(E),	L = L

3ln p.

The parameters [1 and y are the output elasticities of X and E. Since X is the only material input
to production, [1 indicates the return to scale. Identification of y will depend on how environmental
quality is defined in the model and the biological response of each mollusk to that metric. In principle,
this is an empirical question: How is the production of clams, oysters, scallops and mussels affected by
falling ClA levels, holding other inputs to production constant? Unfortunately for the researcher (not so
for the mollusks), the environmental conditions of interest have not been observed and so the data
required to answer this question directly are not available. Instead, following Cooley and Doney (2009),
I assume that changes in production for each type of mollusk, holding other inputs constant, are

proportional to changes in the calcification rate so that,	= 1 . If the metric for environmental

3 In s;


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quality in the production function is defined as the calcification rate for each mollusk, then
3 In qt d In qt

d In E d In e.

and y= 1 so that the evolution of the price vector is described by

ainff _ 1
Sing,, $

fi will be set equal to 1 for all i implying constant returns to scale in each mollusk fishery and unitary
price elasticity with respect to growth rates.

4. Two-stage demand model and welfare

The two stage budgeting approach models consumption as though households first allocate income
among expenditure groups and then decide how much of each group's allocation to spend on individual
commodities. Estimation requires that utility be weakly separable in these commodity groups so that a
price change for a given commodity only affects consumption of commodities in other groups through the
first stage allocation process, and that the proportional change in demand will be the same for each
commodity in a group. The advantage of multi-stage budgeting is that it allows identification of total
(unconditional) elasticities without having to estimate a complete demand system (i.e. a demand equation
for every commodity that households consume). This feature is particularly important for this model
because projections of welfare changes will reach the end of this century during which real incomes will
grow and mollusk prices will rise. The two stage model allows projected expenditures on each
commodity group to respond to income and prices based on elasticities estimated in the first stage. Those
commodity group expenditures and the coefficients of the second stage demand system are used to
calculate welfare impacts from expected changes in the mollusk price vector.


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4.1 First stage expenditure model

To estimate an expenditure function for the mollusk commodity group I estimate a linear household
expenditure model that is a function of disposable income, a price index for mollusks, logged prices for
substitutes and other conditioning variables. It is common to estimate a system of expenditure functions
in the first stage (e.g. Edgerton 1997, Jorgenson et al 1988) but because I am only interested in
expenditures on mollusks, expenditures on other commodity groups are not modeled here. The first stage
is a linear expenditure model with the functional form

where sy and //,- are the income and price elasticities of mollusk expenditures, 0 is a vector of parameters,
y is a vector of average household disposable income, p is a matrix of prices for mollusk substitutes, z is a
matrix of conditioning variables, and e is a vector of iid normally distributed errors. Quantity and prices
are time series data but I suppress the time subscript here to simplify notation. The form of the mollusk
price index in I' is taken from the almost ideal demand model estimated in the second stage and requires
coefficients estimated in that stage a0 and ak,

m	s

\nx = O0+y\ny + 7jp]nP + Yj^{pk) + YJjzj + e'

(3)

k=1

j=m

n

n n

(4)

Because coefficients from the demand system enter the price index equation the second stage must be
estimated before the first. While this may seem counterintuitive, or at least odd, it has no practical
implications on estimation or the results.


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4.2 Second stage demand system

The correct welfare measure to use when evaluating mitigation policy that will reduce prices relative to
their baseline path is compensating variation (Bockstael and McConnel, 1983). To estimate
compensating variation (CV) from an empirical demand system, the form of the demand functions must
be derived in a utility theoretic framework so that parameters of the expenditure function or indirect
utility function can be recovered. This model uses aggregate consumption data to model household
expenditure decisions, focusing attention on the aggregation properties of the underlying preferences.
The price indifferent generalized logarithmic (PIGLOG) class of preferences permits exact aggregation
over consumers (Muellbauer 1976) allowing inference on household optimization using aggregate data.
The PIGLOG expenditure function is of the form

In e(u,p) = a(p) + ub{p)	(5)

where u is the utility level and p is a vector of prices. Using the AI demand system (Deaton and
Muellbauer 1980) specification for the log expenditure function

n	Y n n

a(p) = aQ+Y4aj In p. +-Z ^ PjPk

j=i	1 j=i k=i

n

Hp) = w0IIp? '

k

where the vectors (/> and y/ are parameters. Invoking Shephard's lemma yields the estimable system of
expenditure shares (see Deaton and Meullbauer for the complete derivation)


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H' = ^x~ = a^. ^ ln (Pj)+ y/'ln {~py

Aggregation conditions imply ^ a{ = 1, ^ ^ = 0 and ^ y/t = 0, while homogeneity and symmetry

i	i	i

n

require ^ =0 and (j)^ = 0/(. Conditional on a fixed level of total expenditures x, the expenditure

elasticities of demand are

, W

^,x=l + 	(6)

m

and the conditional uncompensated price elasticities are

. Ytj fra,	,

, = <% + 		-UTij^Pj	(7)

wt wt wt j=i

where S!J = -1 if i = j and S!J = 0 il / / (Fan et al 1995).

Combining the results of the first and second stage models allows estimation of total
(unconditional) elasticities. Fan et al (1995) also estimate a two-stage demand system and show that the
total (unconditional) income elasticity commodity i is

 = , 	(8)

i i\x y

and the total (unconditional) price elasticity for commodity i is


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Vij=Vij\x + i\^j^ + Vp)

(9)

4.3 Compensating variation

Realizing that a utility maximizing consumer will ensure e(u,p) = x expression (5) can be inverted for the
indirect utility function

, , In (x)-a(p)

k

If the vector of prices is unchanged and the indirect utility function is plugged into expression (5), after
cancelling terms, the result is simply In e(u, p) = In x. However if p" represents the original vector of

prices and p' is a new price vector, then substituting u (x, p) into e(u, pl j will yield the minimum

expenditure level required to reach the original level of utility when facing the new vector of prices, so
that

, / i\ / i\ ln(x)~a{p0)r-r( i\^

In e(u,p) = a(p)+	YI(Pj) 

11 \Pk) >

k

The difference between the original level of expenditures x and the minimum level required to achieve
the same utility under a new set of prices e(u,p1} is the compensating variation (CV)


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CV = x- exp

<(p')

+

ln(jc)-a(

ayp

0\n

nw>

-nwr

(10)

5. Data and Methods

The two stages of the budget allocation demand model rely on similar data except that in the first stage
mollusk expenditures are aggregated and household disposable income is included as an independent
variable. Domestic consumption of mollusks is calculated using monthly landings data from 1990
through 2010 and subtracting net exports of live or fresh mollusks (National Marine Fisheries Service).
Dockside prices are used because of the lack of data on retail prices and linear interpolation of quarterly
observations of disposable income provides monthly observations (Bureau of Economic Analysis).
Monthly wholesale prices for beef, chicken, and pork are used as conditioning variables in the first stage
expenditure model. And because the harvest and consumption of most mollusks varies seasonally, a
cosine function that peaks in December and reaches a minimum in June is used to estimate both stages of
the model. Finally, a logged year index captures a diminishing time trend that is orthogonal to income
and price effects.

The first stage expenditure equation is estimated via ordinary least squares. The second stage
demand system is estimated using nonlinear seemingly unrelated regression (NLSUR) while constraining
the coefficients on logged prices to satisfy symmetry restrictions. Only n-1 equations of the system are
estimated directly to avoid singularity of the error variance-covariance matrix. The homogeneity and
adding-up restrictions are used to recover the coefficients of the n"1 equation.


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Finally, in order to forecast expenditures on the mollusk commodity group via equation 3,1 use
the 2009 Stanford Energy Modeling Forum's (EMF 22) projections of US gross domestic product (GDP)
and population from the IMAGE modeling group and assume that households will maintain their recent
10-year average of 2.57 people and disposable income being 70% of GDP. The resulting forecast of
households and disposable income is summarized in table 4.

6. Results

In this section I present the results of the two-stage demand model and use them to forecast total mollusk
expenditures for the income and baseline price projections. The projected baseline mollusk expenditures
and time paths of the mollusk price vector are then used in expression (10) to calculate annual
compensating variation for the emissions reductions realized by moving from the high RCP emissions
path to the medium-high path.

6.1 Estimation results

The log-log specification of the first-stage expenditure model means that the coefficients on income and
prices (Table 5) can be interpreted as elasticities for total expenditures on the mollusk commodity group.
The first-stage income and price elasticities are of the expected sign, with only the chicken cross price
elasticity being statistically insignificant. Beef and pork appear to be substitutes for mollusks so far as
increases in those prices are correlated with an increase in expenditures on the mollusk group. Over the
span of the time series, holding all else equal, there has been a negative but diminishing trend in mollusk
expenditures. And though different types of mollusks in the commodity group have different harvesting
seasons, there is a statistically significant seasonal cycle in total expenditures.

One of the implications of the AI specification of the second stage demand system is that the
magnitude, statistical significance and sign of an individual coefficient do not have practical meaning.
For example, a positive coefficient on the log of own-price does not imply that price has positive effect on


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the quantity consumed. The results of the second stage AI demand system are reported in table 6, but
discussion should be reserved for price and expenditure elasticities which are functions of multiple
parameters (equations [6] through [9]). To conduct inference on the results of the second stage model, I
simulate distributions for the conditional price and expenditure elasticities via bootstrapping. Table 7
reports the means and standard deviations of the bootstrapped sample based on 5,000 draws of the second
stage coefficients. These elasticities indicate how consumption of each type of mollusk tends to change
in response to a price increase while holding total mollusk expenditures fixed. Three out of the four own-
price elasticities have the expected sign and are statistically significant. The conditional demand for
mussels does not appear to be responsive to price. This pattern is repeated in the expenditure elasticities;
the demands for oysters, scallops, and clams tend to increase with total mollusk expenditures but the
demand for mussels does not.

Total price and income elasticities draw on the results of the first and second stage models and
can differ substantially from the conditional elasticities which are based on the second stage results alone.
Total elasticities will generally be smaller in magnitude than conditional elasticities because expenditures
on the commodity group will adjust with prices and income. Table 8 reports summary statistics of
bootstrapped samples of the total elasticities based on 5,000 draws of the first and second stage
coefficients. Again, mussel demand is not responsive to own-price changes but its income elasticity is
positive, albeit small, and statistically significant. The income elasticities for oysters, scallops, and clams
are also statistically significant.

6.2 Simulation and welfare results

The price and income elasticities are not used directly in the welfare calculation but they are a convenient
way to judge the identification strategy of the two-stage demand model. Instead, the first stage is used to
forecast total mollusk expenditures as a function of disposable income and the baseline price index for


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mollusks. The coefficients of the second stage are used in the welfare calculations and to identify the
price index. However, a necessary input into both the expenditure and welfare simulations is the time
paths for mollusk prices. Using the growth rate changes of figure 4 and the price evolution equation (2),
baseline and policy price projections are plotted in figure 5. Recall Ries et al (2009) did not observe a
response from mussels to falling QA, so I assume their dockside price will remain constant at the recent
10-year average of $0.72 per pound of meat and is not plotted in figure 5.

Evaluating equation (4) along the baseline price projection vector provides the baseline price
index which, along with the household income projections in table 4, is needed to forecast household
expenditures on mollusks. Assuming the prices of beef, chicken and pork remain constant in real terms,
baseline mollusk expenditures are expected to increase with income but not as quickly as the income
elasticity ey alone would suggest. There is also downward pressure on mollusk expenditures from the
rising prices via the price index elasticity ///< and the logged time trend 04. However, baseline utility is
falling over time so expenditures required to maintain baseline utility when prices increase more slowly
will also decrease, all else being equal. Figure 6 plots household minimum expenditures on mollusks
required to achieve baseline utility and shows that is indeed the case here for much of the time horizon.
The vertical distance between these two curves is the undiscounted annual measure of CV at a given point
in time. Table 9 summarizes the results of the welfare calculation using equation (10) for compensating
variation. Annual CV for households and the US as a whole are both increasing because the price
differential between the baseline and policy cases grows over time, but the total CV for the US grows at a
faster rate due to population growth. The present value of CV is found using a 5% discount rate.

7. Conclusion

It is not yet clear how estimates ocean acidification damages will compare with those of climate change.
The goal of this line of research is to remove ocean acidification from the list of "unqualified benefits"


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of reducing C02 emissions. Filling this gap in the literature and, by extension, analysis of domestic and
international carbon policy should be a research priority. While the estimates produced here reflect just a
fraction of total damages from ocean acidification, the methodology can be used to value market impacts
to global finfish and shellfish markets.

One major caveat is that the geochemical, biological, and economic models that form the
integrated model are not equal in their reliability. The two-stage demand system is based on well-
established methods and estimated with reliable data. Likewise, the ocean carbon model is based on well-
understood deterministic relationships relating atmospheric C02 concentrations to aragonite saturation
levels. The projected time paths for C02 concentrations and sea surface temperature are based on
sophisticated equilibrium and climate models but are, nonetheless, long-term projections involving highly
uncertain variables. The Ries et al. study relating changes in mollusk growth rates to falling QA levels is
the best of its kind for the purposes of this study because it (1) examines the most popular species in US
markets (2) uses levels of pC02 and C1A that we are likely to witness this century and (3) observes the
subjects over a 60-day period. Many studies of this type examine non-harvested species under extreme
conditions and do so over a period of just a few hours.

The most tenuous link in the integrated model is the relationship between changes in growth rates
to the evolution of mollusk prices. This study presumes, via Cobb-Douglas production with
environmental quality as an input, that changes in growth rates will have a proportional effect on the
marginal cost of mollusk production. Ideally, an empirical study of how falling QA affects the harvest
and culture of mollusks would inform the modeled relationship. The relationships assumed here serve as
placeholders until more data are available.

When evaluating domestic policies that affect greenhouse gas emissions the US government uses
a measure that reflects the global benefits of mitigating climate change (Social Cost of Carbon TSD


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2010). The most immediate and useful extension of this work is to develop a global measure of welfare
impacts in markets for mollusks. Over the past ten years 12 countries consumed more than 90% of the
global shellfish harvest (FAO Fisheries Database), so it is possible to quantify the vast majority of
benefits by focusing on just a dozen countries. The direct impact to shellfish markets is just one of the
three categories of impacts to consider. Direct impacts to coral reefs will include market and nonmarket
measures of benefits. Estimating potential impacts to finfish stocks requires modeling of trophic
interactions and migration that, while possible on a local level, is not currently feasible for a fishery as
large as the US market.

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Bockstael, N. & McConnell, K. 1983. Welfare measurement in the household production framework. The
American Economic Review 73 (4) 806-814

Brander, L.; Rehdanz, K.; Tol, R. & Beukering, P. 2009. The economic impact of ocean acidification on
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Figures

Green house
gas Emissions

Changes to
seawater
chemistry

Biological
responses

Social welfare
impacts

Figure 1 Ocean Acidification Impact Pathway

o
O

OnI

O
O

1000
900
800
700
600
500
400
300

	Baseline Scenario

	Policy Scenario

2020

2040 2060
Year

2080

2100



01 
.E 6

TD
^ *

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A	B

Figure 3 Projections of SST and C1A


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0.13

0.11

o 0.09
CD

0.07

0.05

Oyster

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year

Clam

0.05

f 0.04

< 0.03

0.02

0.35

0.3

0.25

o

g 0.2

0.15

Scallop

0.1

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year

	Baseline Scenario

	Policy Scenario

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
Year

Figure 4 Projections of annual mollu.sk growth rates

* Ries et al (2009) observed mollusk growth over a 60-day period. The growth rates shown in this figure are estimated with the regression
equations in table 1 and then adjusted to reflect annual growth rates.


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	Baseline Scenario

	Policy Scenario

Figure 5 Mollusk price projections


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Figure 6 Household expenditures required to reach baseline utility

Tables

Table 1 Market value-weighted average of initial SST

US Coastal Region

Average Proportion of
Mollusk Market Value

10-year Average SST (C)

New England
Mid-Atlantic
South Atlantic
Gulf of Mexico
North Pacific

0.48
0.24
0.03
0.15
0.10

Market value-weighted average initial SST

11.45
15.12
22.18
23.45
11.45
14.52


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Table 2 Growth rate responses to different levels of D.A (Ries et al 2009)

Mollusk Name	Regression liquation R~

liaslern Oyster	#, = 0.840^-0.23	0.76

Bay Scallop	= 2.73^0.97	0.34

Hard Clam	= -10.3c"+0.94	0.81

Blue Mussel	No response

Iixpecled 60-day '/< change in weight

Qa=2.13	Qa=1 .53	Qa= 1.13

Current p('()	2 x Prcindustrial	3 x Preinduslrial

2.019	1.515	1.179

6.018	4.596	3.648

0.962	0.458	-0.254

3.7	3.7	3.7


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Table 3 Summary of demand model data

Sid

Variable

Description

Mean

Dev

Min

Max

Wscallops

scallops expenditure share

0.547

0.136

0.255

0.883

W oysters

oysters expenditure share

0.214

0.096

0.057

0.513

Wclams

clams expenditure share

0.211

0.089

0.021

0.449

W mussels

mussels expenditure share

0.029

0.020

0.003

0.111

Pscallops

scallops dockside price per pound

2.61

0.58

1.62

4.23

Poysters

oysters dockside price per pound

5.60

1.29

3.16

9.10

Pclams

clams dockside price per pound

0.83

0.26

0.54

2.45

Pmussels

mussels dockside price per pound

0.58

0.28

0.27

1.84

Pbeef

beef wholesale price per pound

1.92

0.29

1.47

2.72

Pchicken

chicken wholesale price per pound

1.14

0.12

0.81

1.49

Ppork

pork wholesale price per pound

0.63

0.08

0.49

0.89

InM

log of mollusk expenditures per 1.000 households

5.69

0.29

4.97

6.19

InP

AI price index lor mollusks

5.83

0.17

5.51

6.35

Y

average household disposable income

68.264

15.445

44.510

95.614

Year

index for year

10.5

5.77

1

20

cos(nionth)

cosine on month index

0

0.71

-1

1

Table 4 Socioeconomic projections

Year Household Disposable Income Households in IJS
(thousands of dollars)	(millions)

2010;|

86.5

120.1


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2020

99.X

131.0

2030

1 13.0

141.0

2040

126.6

149.0

2050

141.4

155.5

2060

157.3

158.3

2070

174.4

161.4

2080

192.7

163.6

2090

212.5

165.2

2100

233.6

166.4

~Observed (US Department of Commerce Bureau of Economic Analysis)


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Table 5 - First stage results

Dependent Variable: log of mollusk expenditures (In M)

n = 240
R-squared: 0.7077

Variable

Parameter

Coefficient
listiniate

Standard lirror

In (y)

y

0.555**

0.255

InP

Vp

-0.181*

0.107

In (p v, )

0i

0.324**

0.161

In (Pchicken)

02

-0.065

0.576

In (Ppork)

03

0.477**

0.147

In (year index)

04

-0.100*

0.057

cos (month index)

05

-0.260

0.019

constant

00

0.503

2.483

* significant at the 90% confidence level

** significant at the 99% confidence level


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Table 6 Second Stage Constrained Nonlinear SUR

Dependent variable: expenditure share Oi)
liquation Variable Parameter

listimate

n = 240
Standard lirror

Oysters

constant

al

0.222**

0.019

R: = 0.967

In (poyster)

7n

0.128**

0.013



In (Pscallop)

fl2

-0.088**

0.012



In (Pclam)

713

-0.036**

0.009



In (Pmussel)

714

-0,004

-



ln(M/P)

(h

-0.140**

0.013



In (year index)

-

0.072**

0,006



cos(nionth index)

-

-0.01 1*

0.005

Scallops

constant

2

0.409**

0.035

&

to

II

o

oo

In (Pscallop)

722

0.078**

0.018



In Pdam)

723

0.034**

0.013



In (pmussel)

724

-0.025

-



ln(M/P)

fh

0.254**

0.019



In (year index)

-

-0.054**

0.009



cos(month index)

-

0.112**

0.008

Clams

constant

a3

0.290**

0.019

K: = 0.945

In (Pdam)

733

0.005

0.013



In Pmussel

734

-0.003

-



ln(M/P)

&

-0.084**

0.015



In (year index)

-

-0.017*

0.007



cos(nionth index)

-

-0.110**

0.006


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Mussels constant	a4	0.079

In (Pmussel)	744	0.032

ln(M/P)	fl4	0.030

* significant at the 90% confidence level
** significant at the 99% confidence level

Table 7 Conditional Price and Expenditure Elasticities

$

Quantity^^^

Oysters

Scallops

Clams

Mussels

Expenditures



-0.245**

-0.251**

-0.011

0.139**

0.346**

Oysters

(0.095)

(0.059)

(0.044)

(0.032)

(0.081)



-0.368**

-1.06**

-0.148**

-0.254**

1.470**

Scallops

(0.039)

(0.037)

(0.051)

(0.026)

(0.051)



-0.046

0.280**

-0.845**

0.1 12**

0.590**

Clams













(0.071)

(0.082)

(0.103)

(0.035)

(0.103)



-0.128

-0.868**

-0.082

0.127

-0.048

Mussels













(0.127)

(0.105)

(0.123)

(0.106)

(0.127)

* significant at the 90% confidence level
** significant at the 99% confidence level

Table 8 Total Price and Expenditure Elasticities

$

Oysters

Scallops

Clams

Mussels

Income

Quantity^.












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-0.181**

-0.088

0.051

0.147**

0.423*

Oysters













(0.086)

(0.074)

(0.050)

(0.031)

(0.241)



-0.096**

-0.368**

0.120**

-0.120**

1.83*

Scallops













(0.041)

(0.114)

(0.042)

(0.043)

(0.987)



0.060

0.555**

-0.740**

0.126**

0.733*

Clams













(0.065)

(0.096)

(0.101)

(0.034)

(0.411)



-0.136

-0.891**

-0.073

0.127

-0.064

Mussels













(0.121)

(0.105)

(0.126)

(0.105)

(0.177)

* significant at the 90% confidence level

** significant at the 99% confidence level

Table 9 Annual compensating variation

Year

2020

2040

2060

2080

2100

NPV discounied al 5%

1 Iousehold

$0.07

$0.41

$0.85

$1.28

$1.78

$4.83

IJS (Millions)

$9.6

$61.6

$134.9

$209.8

$295.5

$734.6


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