United Slates Policy, Planning, EPA 230-05-90-078 Environmental Protection And Evaluation November 1989 Agency (PM-221) Contingent Valuation Assessment Of The Economic Damages Of Pollution To Marine Recreational Fishing A Printed on R*cycbdPmp*r ------- EPA-230-05-90-078 Contingent Valuation Assessment of The Economic Damages of Pollution to Marine Recreational Fishing Submitted to: Mary Jo Kealy Office of Regulatory Management and Evaluation U.S. Environmental Protection Agency Washington, D.C. 20460 Submitted by: Trudy A. Cameron Department of Economics University of California, Los Angeles 405 Hilgard Avenue Los Angeles, Ca. 90024 November, 1989 The information in this document has been funded in part by the United States Environmental Protection Agency under Cooperative Agreement No. CR 814656020. It has been subject to the Agency's peer and administrative review, and it has been approved for publication as an EPA document. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. ------- CONTINGENT VALUATION ASSESSMENT OF THE ECONOMIC DAMAGES OF POLLUTION TO MARINE RECREATIONAL FISHING (EPA Cooperative Agreement # CR-814656-01-0) Trudy Ann Cameron Executive Summary The research performed under this cooperative agreement is summarized in the contents of four papers. These are described in the following sections. 1. "The Determinants of Value for a Marine Estuarine Sportfishery: The Effects of ffater Quality In Texas Bays," (also Vorking Paper #523, Department of Economics, University of California at Los Angeles). This paper gives a detailed description of the data collected in the socioeconomic portion of the Texas Parks and Wildlife Creel Survey of over 10,000 recreational anglers between May and November of 1987. It also summarizes the auxiliary data sources used to augment these data, which include gamefish abundance estimates we have calculated from the data collected in the Texas Parks and Wildlife Resource Monitoring Program, water quality data from the Texas Department of Water Resources, and five-digit zip code sociodemographic averages from the 1980 Census. The objective in this first paper is to formulate special statistical models that produce estimates of each individual survey respondent's willingness to pay for access to the recreational fishery in the eight major bays along the Texas Gulf Coast. In this paper, no attempt is made to force these models to conform with formal economic theories. Instead, minimally sophisticated discrete choice econometric models are used in an attempt to establish the apparent systematic relationships between willingness to pay and whatever explanatory factors are available. These factors include: characteristics of the individual, their current catch, location and time of the interview, typical gamefish abundance, and coarse measures of several dimensions of water quality by time and location collected both by survey personnel and separately by the Department of Water Resources. The econometric methods used in this analysis are specially designed to accommodate the "limited dependent variable" nature of the data. The paper describes the method by which maximum likelihood logit estimates can be transformed to yield the implied parameters of an approximation to the demand function for recreational fishing access. In particular, we are interested in ------- price and income elasticities of demand. But we also focus in this study on the extent to which water quality, geographical and seasonal dummy variables, socioeconomic and other variables act as shifters of this demand function. For this portion of the study, there are mixed findings concerning the effects of water quality on the value of the recreational fishery. A wide variety of meteorological data and data on water quality is available. In most cases, however, it was necessary to aggregate these data up to the level of each of the eight major bays and for each month of the sample period. For example, we know about average temperature, dissolved oxygen, turbidity, etc., as well as nitrogen nitrate levels, phosphate levels, non-filterable residues, oil and gas in bottom deposits, and a wide array of other qualities. While several of our water quality variables appear to make statistically significant contributions to explaining willingness to pay for fishing access, many of them have counter-intuitive signs. It can be inferred that water quality probably varies inversely with other unmeasured attributes of anglers and the fishing resource that directly affect the value of the fishery. For example, if there are fewer substitute recreational opportunities in the Houston area, recreational fishing opportunities may be valued very highly, but simultaneously, the water quality may be very low. The reverse may be true in more remote areas of the coast. If we include water quality, but omit alternative recreational opportunities (for lack of data), then, it will appear that lower water quality implies higher social values of the fishery. I suspect that something like this is precisely what is happening. This study represents an heroic effort to assemble the most appropriate water quality data for the Texas Gulf Coast available from many different sources. Countless hours went into matching and merging all of this information with the survey responses. Unfortunately, it is an empirical issue whether or not the anticipated relationships will show up in these data. This paper concludes that it will be necessary to control for other important determinants of value before the residual variation attributed to measured water quality can be unambiguously identified. However, there is definite evidence that respondents perceptions regarding environmental quality are more immediate determinants of value than the actual measured quality of the water. While water quality apparently cannot be considered in this much detail with the current dataset, other coarser sociodemographic variables, such as income, appear to have strong and intuitively plausible effects on values. The apparent price elasticity of demand for fishing days (if a market existed) appears to be roughly -2.2, meaning that if access cost anglers 1% more, demand would decrease by 2.2%. The income elasticity appears to be just less than unity, implying that recreational fishing opportunities are borderline between being necessities and luxuries. There are other implications of these models, also conditional on the quality of the data. For example, geographical heterogeneity in the demand for recreational fishing days does seem to exist. The water quality variables, collectively, seem to explain quite a lot of this geographic variation, even if multicollinearity among these variables limits our ability to attribute value differences to specific individual dimensions of water quality. ------- The Vietnamese, as opposed to other cultural groups, seem to have markedly different preferences for fishing than the population as a whole. Money spent on associated market goods, once thought to be a reasonable proxy for the non-market value of a fishery, is positively related to the value of a fishing day (but typically completely unrelated to catch rates). Importantly, many other explanatory variables make strong contributions to explaining the annual value of fishing day access; reliance solely upon market expenditures could severely misstate resource values. The preliminary specifications explored in detail in this paper produced results that were sufficiently provocative to warrant further analysis of these data. It was decided that placing a little more structure on the model might help. Hence the next paper. 2. "Combining Contingent Valuation and Travel Cost Data for the Valuation of Non-market Goods," (a retitled major revision of Working Paper #503, Department of Economics, University of California at Los Angeles). This second paper takes advantage of the general sense of the data derived from the extensive exploratory modeling described in the first paper. It has been determined that there are several apparently robust systematic relationships between willingness to pay for access to the fishery and other measurable variables. Vith this established, one can be more confident that it is worthwhile to undertake further modeling that is more solidly founded upon neoclassical microeconomic principles. I am very pleased with the quality of this paper. It develops a new methodology, employing novel and very sophisticated econometric techniques appropriate to the special features of the data. The analysis is particularly careful and rigorous and many tangential issues are considered thoroughly. The simplest model of consumers' utility maximization posits that consumers have preferences defined over two types of commodities: the good in question (sportfishing days) and a composite of all other goods and services. More of both of these things makes them happier, but they are constrained by their budgets. They must trade off other goods and services in order to consume an additional fishing day, and vice versa. They allocate their limited budgets between fishing days and other things so as to maximize their level of happiness. All models of this type are, of course, dramatic simplifications of the real world, but they frequently provide very useful insights into the essential features of consumer behavior. Individuals with different sociodemographic characteristics, under different resource conditions, will make different consumption decisions. This type of variation allows us to calibrate a model which can then be used to simulate the likely responses of particular types of individuals if their decision making environment changes. While these models cannot be expected to do very well in predicting the actual response of a specific individual to some change, they can perform fairly well in the aggregate. ------- Earlier research employing these "utility-theoretic" models for the valuation of a non-market good such as sportfishing access occasionally used a technique known as the travel cost method. If fishing days can be considered as a single homogeneous good, information on the cost of a single trip and the number of trips taken can be combined to yield a model of demand for fishing days. This is the relationship between the implicit price of access and the number of days demanded, with accommodation for whatever shift factors (income, resource quality, etc.) can be quantified. Other attempts to value recreational fishing days have relied upon "contingent valuation" survey techniques, where survey participants are queried about the decisions they think they would make if a hypothetical market for fishing days existed (i.e. if they had to pay a per-day entrance fee or purchase a season's pass to fish). The discrete choice form of contingent valuation question was posed on the Texas Parks and Wildlife Creel Survey. Respondents' answers about whether or not they would be willing to pay an arbitrarily selected annual fee to continue fishing were analyzed in ad hoc models in the first paper discussed above. In the paper being described here, however, the mathematical form of the discrete choice model is carefully selected to conform to an underlying family of consumer preference functions with desirable properties from the point of view of economic theory. By doing this, the calibrated models can ultimately be solved to yield corresponding estimates of the formal welfare measures of value, including equivalent variation and compensating variation. The primary methodological innovation in this paper is to combine both travel cost and discrete choice contingent valuation data in one comprehensive model. Both methods of eliciting valuation information from survey respondents should provide insights regarding the same preference structure. We can combine the two different perspectives for a more thorough characterization of consumer behavior. In the basic model in this paper, all fishing days are treated as homogeneous and consumer choices regarding fishing access depend only upon their taste for fishing, their incomes, and the price of access to a fishing day. When this model is explored thoroughly and shown to be relatively successful, the assumption that all fishing days are identical is relaxed. The illustrative generalization explored in this paper is to allow preferences for fishing days (versus all other goods and services) to vary systematically with the zip code proportion of people reporting Vietnamese heritage on the 1980 Census. This is an imperfect measure of the respondent's own sociodemographic category, but we anticipate at least some correlation. The proxy turns out to be a significant shifter of preferences. The higher the proportion Vietnamese, the less willing is a representative consumer to trade off fishing days for other goods. Likewise, the greater will be their demand for fishing days at any relative price and the greater would be the cost to them of having to forgo some or all of their fishing access. The paper provides detailed empirical estimates of the welfare values associated with changes in fishing access. However, these dollar values are conditional upon the extent to which the data we are using actually capture the concepts prescribed by the microeconomic theory underlying the ------- specification. The data are far from ideal. Consequently, it would not be appropriate in this summary to uphold the dollar values as unambiguous. The Texas data are by far the best I had encountered up until that time. But it is crucial that this set of papers be regarded as demonstrations of the types of analyses that can be conducted. If results as satisfying as these can be achieved with mediocre ingredients, then subsequent surveys can be conceived and implemented to take maximum advantage of the methodological framework. These future studies will undoubtedly produce final empirical value estimates which can more confidently be used as a basis for policy making. With these qualifications, and others described carefully in the paper, some of the welfare estimates can be mentioned. For example, according to the basic model, if fishing days were curtailed by 10%, the average survey respondent would lose an amount of satisfaction roughly equivalent to the loss of $35 of income per year (although individual losses range from $19 to $52). A 20% curtailment would match an income loss of $139, on average. Simulating a complete loss of access is riskier and less realistic, but the model suggests that the average respondent would be hurt by about $3400. Generalizing the model to accommodate sociodemographic heterogeneity (proportion Vietnamese in zip code) shows how the fitted preference function is markedly different (for an otherwise typical respondent) when this proportion ranges from 0 to 2%. Plots of the estimated "indifference curves" and budget constraints make these differences particularly obvious. The paper also breaks new ground by freeing up certain parameter restrictions within the jointly estimated model so that the travel cost and contingent valuation data are allowed to imply different preferences. A scheme is also developed for allowing differential weightings in the pooling of these data, according to the perceived relative reliability of these two types of information. 3. "Using the Basic 'Auto-Validation' Model to Assess the Effect of Environmental Quality on Texas Recreational Fishing Demand: Welfare Estimates," (also Vorking Paper #522, Department of Economics, University of California at Los Angeles) The initial exploratory study described above (which employed all of the available data and used ad hoc models) suggested that measured objective dimensions of water quality did not always have clear cut and intuitively plausible effects on willingness to pay for access to sportfishing opportunities. An alternative possibility is that people's preferences for sportfishing are affected by their perceptions of environmental quality, not by what is actually out there. (What you don't know won't hurt you?) The creel survey asked respondents' subjective opinions about whether they were able to enjoy "unpolluted natural surroundings." Answers were recorded on a scale of one to ten. In this supplemental paper, we allow preferences to take on systematically different configurations depending upon these answers. Various welfare implications can be derived from the fitted model, again with the same caveats mentioned in the above two summaries. The amount of income loss that would be equivalent to a 10% cutback in access to the fishery is roughly $29 per year at the mean level of the subjective variable (8.07). ------- If environmental quality is perceived to be a 10, the loss would be about $37 per year. In contrast, if the quality is only 6, the loss of access would be only $23. For a complete loss of access, the decrease in value at the mean, at 10 and at 6 would be about $2400, $3000, and $1900 respectively. (Note that only a smaller subsample of the data could be used for these models, since not all respondents were queried regarding environmental quality.) Thus, we find that perceptions of environmental quality do affect preferences for fishing days as opposed to all other goods and services, and thus the value of access to the fishery will almost certainly be influenced by perceptible variations in water quality. Furthermore, we can show that respondents' answers to the "unpolluted natural surroundings" questions are statistically related to several of the measured water quality attributes examined in the first paper described above. However, it is clear that more research will be necessary to establish how objective water and environmental quality data can be translated into individual perceptions. With infinite and free computing resources, it would be desirable to allow preferences to differ systematically according to the levels of a whole range of shift variables. At present, however, there was no budget for such an elaborate model, so we were limited to exploring single shift variables independently. (Each shift variable adds five new unknown model parameters to be estimated.) 4. "The Effects of Variations In G&mefish Abundance on Texas Recreational Fishing Demand: Welfare Estimates." Keeping in mind the limitations on complexity, a second supplemental paper was also developed. Whether or not the value of this recreational fishery is dependent upon the abundance of gamefish is another question of vital interest to policy makers. Ideally, one would measure all of the major gamefish species (there are seven or eight, described in the first paper, above). For this illustration, however, we opt to concentrate upon red drum. As a measure of red drum abundance, we could have used each individual's reported catch of red drum on the fishing trip when they were surveyed, but this catch is dependent upon skill levels, which will be related to the individual's resource value. This is undesirable. Consequently, we rely upon data produced by the Parks and Wildlife Resource Monitoring program. We used data from the thousands of official samples collected by this program and aggregated up to average abundance measures by bay system and by month. These data are only proxies for the actual local abundance of red drum experienced by recreational anglers in each area and month, but they are completely unrelated to angler skill. Thus we hope to avoid simultaneity bias in the resulting estimates. This model, augmented to control for red drum abundance, lets us explore the likely changes in the social value of access to the fishery when the abundance of red drum changes. Again subject to extensive caveats, we find that the income loss that would be equivalent to a 10% reduction in fishing access is roughly $35 at mean abundance of red drum. If abundance was higher by 20%, the same reduction would hurt anglers by an average of $40. If abundance was lower by 20%, the decrease in access would be equivalent to ------- about a $32 decrease in income. A total loss of access would imply a loss of about $2800 at mean abundance, a loss of $3200 if abundance was 20% higher and of $2600 if abundance was 20% lower. If red drum abundance went to zero, a complete loss of access would still imply a loss of about $1800, presumably because there are several other gamefish species which can be sought. If anglers do not care directly about water quality, except to the extent that it affects catch rates of their preferred species, this type of model may be the most fruitful to pursue. Future studies might rely upon expert biological opinion regarding the expected effects on gamefish of changes in different attributes of water quality. Calibrated utility models such as those used in this series of studies could then be used to simulate the ultimate effects of these changes on social welfare. Again, all of these studies do undertake to provide point estimates of the dollar value of changes in consumer welfare corresponding to limitations on their access to recreational fishing or to changes in the quality of the fishing experience. However, due to the tenuousness of the data's ability to capture the theoretical concepts employed in these models, I elect not to cite all of these specific numbers outside the context of the papers, where the full range of caveats is laid out. Conditional upon the data available, I am confident of the validity of the findings. However, extensive detailed simulation sensitivity analyses would be required to put "true" confidence bounds on these estimates. The simple statistical precision of the estimates reported in the paper (as is usual in empirical work) presume that the data are exact measures of the desired quantities. ------- Work in progress Not for citation without permission 5/18/88 The Determinants of Value for a Marine Estuarine Sportfishery: The Effects of Water Quality in Texas Bays by Trudy Ann Cameron Department of Economics University of California, Los Angeles * We would like to thank the Texas Department of Parks and Wildlife for allowing us to use their survey. Jerry Clark and particularly Maury Osborn have been extremely helpful in overseeing the assembly and cleaning of the data. John Stoll contributed to the design of the survey. David Buzan and Patrick Roque at the Texas Department of Water Resources volunteered considerable effort in assembling water quality data from DWR records. David Brock at the Texas Water Development Board generously provided disks and documentation covering additional water data. ------- Work in progress Not for citation without permission 5/18/88 The Determinants of Value for a Marine Estuarine Sportfishery: The Effects of Water Quality in Texas Bays by Trudy Ann Cameron Department of Economics University of California, Los Angeles * We would like to thank the Texas Department of Parks and Wildlife for allowing us to use their survey. Jerry Clark and particularly Maury Osborn have been extremely helpful in overseeing the assembly and cleaning of the data. John Stoll contributed to the design of the survey. David Buzan and Patrick Roque at the Texas Department of Water Resources volunteered considerable effort in assembling water quality data from DWR records. David Brock at the Texas Water Development Board generously provided disks and documentation covering additional water data. ------- EPA-230-05-90-078 Contingent Valuation Assessment of The Economic Damages of Pollution to Marine Recreational Fishing Submitted to: Mary Jo Kealy Office of Regulatory Management and Evaluation U.S. Environmental Protection Agency Washington, D.C. 20460 Submitted by: Trudy A. Cameron Department of Economics University of California, Los Angeles 405 Hilgard Avenue Los Angeles, Ca. 90024 November, 1989 The information in this document has been funded in part by the United States Environmental Protection Agency under Cooperative Agreement No. CR 814656020. It has been subject to the Agency's peer and administrative review, and it has been approved for publication as an EPA document. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. ------- 2 The Determinants of Value for a Marine Estuarine Sportfishery: The Effects of Water Quality in Texas Bays by Trudy Ann Cameron ABSTRACT We use a large number of responses to an in-person creel and contingent valuation survey of recreational anglers collected in the bays along the Texas Gulf Coast between May and November of 1987, supplemented by concurrent and independently gathered water quality data and 1980 Census data. Using empirical techniques recently developed by this author (censored logistic regression by maximum likelihood), these data are employed to fit implied (non-market) demand functions for fishing days which incorporate shift variables for water quality, perceived pollution levels, ethnic heterogene icy, expenditures on related market goods, and catch rates. The price elasticity of demand for fishing days (if a market existed) appears to be roughly -2.2; the income elasticity appears to be just less than unity. Geographical heterogeneity in the demand for recreational fishing days is partially explained by water quality variables. The Vietnamese seem to have markedly different preferences for fishing than the population as a whole. Money spent on associated market goods, once thought to be a reasonable proxy for the non- market value of a fishery, is indeed positively related to the value of a fishing day (but typically completely unrelated to catch success). Importantly, many other explanatory variables make strong contributions to explaining the annual value of fishing day access; reliance solely upon market expenditures could severely misstate resource values. ------- 3 The Non-market Value of Water Quality Attributes: Estimates for Texas' Marine Estuarine Sportfishery by Trudy Ann Cameron 1. Introduction Decisions regarding the expenditure of public funds to enhance or restore environmental assets have frequently been made on the basis of purely normative arguments. Until recently, the non-market benefits enjoyed collectively by the consumers of environmental resources have been difficult to determine. The objective in this paper is to quantify the effects of variations in water quality upon the non-market value of the marine recreational fishery along the Texas Gulf Coast. Knowing how water quality affects the social value of this fishery will allow us to simulate changes in that value as a consequence of policies which improve water quality (or as a result of decisions to allow water quality to deteriorate). The "travel cost" method (TCM) for valuing non-market resources has been widely used but is frequently inappropriate for a marine sportfishery because the point-to-point distance for these fishing trips is often poorly defined. Destinations are diffuse and true opportunity costs for access are difficult to measure. These problems with the travel cost method have made hypothetical or "contingent" market surveys popular for eliciting resource values. In contingent valuation (CV) surveys, it seems to be particularly difficult for respondents to state the precise value they would place on the resource. Consequently, a variety of value elicitation techniques are employed. Different strategies are suitable depending upon whether the investigation relies upon personal interviews, telephone interviews, or mailed questionnaires. ------- One method is verbal "iterative bidding." An elaboration of this method, useful for in-person interviews or mail surveys, is the "payment card," where the respondent is merely asked to scan a card and to indicate the highest amount willingly paid (or lowest compensation willingly accepted) for access to the resource. An extreme form of the iterative bidding strategy involves only the first iteration: a single randomly assigned value is proposed and the respondent decides whether to "take it or leave it," much as in ordinary day-to-day market transactions. This "closed-ended CV" or "referendum" question format economizes greatly on respondent effort and minimizes strategic bias, but reduces estimation efficiency. The single offered sum is varied across respondents, which allows the yes/no responses to these questions to imply both the location and the scale of the conditional distribution of valuations. Many more responses are required to generate equally statistically significant parameter estimates for the valuation function, but it is suspected that this value elicitation technique minimizes the wide array of biases which have been argued to plague the other CV elicitation methods. At present, contingent valuation investigations are probably the most practical way to quantify the economic benefits to a recreational fishery of pollution control activities. CV questions can often be appended quite easily to regular creel survey instruments, so the marginal cost of gathering CV data is relatively modest. In CV valuation models, respondents' valuations of the resource are presumed to depend upon (a.) characteristics of the respondent and (b.) attributes of the resource (in this case, including the level of pollution and indirect manifestations of pollution levels such as the degree of urbanization and catch rates). A calibrated CV model can be used to simulate both (a.) the ------- 5 direct effects of changes in pollution levels--by imposing counterfactual changes in the quantities of pollutants and recomputing the fitted individual valuations; and (b.) indirect effects of changes in pollution levels--for example, by imposing predicted changes in catch rates and recomputing individual valuations. The difference in the population weighted sums of these individual valuations before and after the simulated reductions in pollution levels is a measure of the social benefit of the hypothesized clean- up program. This overall change in social value can be added to estimates of other relevant benefits (i.e. for market activities) and the total can be compared to the costs of the program in order to determine its economic advisability. For our Texas fishery, there is some concern at present about the proposed widening and deepening of the Houston Ship Channel, which is anticipated to have a substantial negative environmental impact. If statistically discernible effects of water quality upon the value of this recreational fishery can be found, our fitted models can simulate the changes in value resulting from changes in water quality due to projects such as this. Section 2 of this paper reviews the intuition and the details of the statistical model which we will use to fit valuation functions. Section 3 outlines the data. Section 4 considers "naive" specifications of the "valuation function" and explains how implied demand functions can be extracted from the estimated models. Section 5 presents some preliminary empirical results. Section 6 digresses to evaluate the determinants of catch success, an issue which is important to our ability to assume exogeneity of the explanatory variables in the valuation function. Section 7 examines respondents' claimed motivations for going fishing and their subsequent satisfaction levels, issues which are fundamental to the form of the basic ------- 6 utility functions which underlie the demand for fishing days. Section 8 takes advantage of explicit questions regarding perceived pollution levels to address whether pollution levels enter directly or indirectly into people's utility functions. We conclude with some tentative findings and a preliminary set of recommendations for improving subsequent surveys which might be used to assess the effects of water quality on the non-market value of recreational fishing. 2. Censored Logistic Regression Models for Referendum Valuation Data Before addressing this specific empirical project, it is helpful to outline the econometric estimation procedure which will be used to calibrate our model of valuation for this fishery. In Cameron and James (1987) , and in a forthcoming paper (Cameron, 1988) I have made the argument that initial estimates of utility-theoretic models of valuation in the spirit of Hanemann (1984) (or even entirely data-driven ad hoc valuation models) using referendum data can be obtained quite simply using packaged logit or probit maximum likelihood algorithms. Since the numbers of observations in the models explored in this study are large, and since the specifications involve a wide array of potential explanatory variables, I opt here to perform initial estimations using censored logistic regression models. The computations necessary to optimize the likelihood function underlying these models does not involve myriad evaluations of the non-closed-form integral for the cumulative normal density function. The optimization is faster and cheaper than it would be for a censored normal regression model. Furthermore, since the parameters of the censored logistic regression model can be solved-for from the parameter estimates produced by conventional packaged maximum likelihood logit models, and the SAS computer package provides ML logit routines in its MLOGIT module, we find it expedient to pursue initial trial specifications in the context of ------- 7 the SAS package. This also allows us to take advantage of the superior data- manipulation capabilities of this program. Based my earlier studies, the implicit valuation function parameter estimates produced by either the censored normal (probit-type) or censored logistic (logit-type) estimation procedures are very similar. The slight differences in the shape of the conditional density function for the regression errors makes only modest differences in the fitted values of the ultimate "regression" model. Hence it is safe to presume that explanatory variables which make a statistically significant contribution to the valuation function in the context of a simple logit specification will also be important under alternative distributional hypotheses. 2.1 Review of Censored Regression Models for Referendum Data Since the censored logistic model is not yet in the public domain, I will briefly reproduce the derivation of the model. "Referendum" survevs have recently become very popular as a technique for eliciting the value of public goods or non-market resources. Numerous • applications of these methods now exist. (For comprehensive assessments of these survey instruments and detailed citations to the seminal works and specific applications, the reader is referred either to Cummings, Brookshire, and Schulze (1986), or to Mitchell and Carson (1988). The referendum approach first establishes the attributes of the public good or the resource, and then asks the respondent whether or not they would pay or accept a single specific sum for access. (It is crucial that the arbitrarily assigned sums be varied across respondents.) This questioning strategy is attractive because it generates a scenario for each consumer which is similar to that encountered in day-to-day market transactions. A hypothetical price is stated and the respondent merely decides whether to ------- 8 "take it or leave it." This is less stressful for the respondent than requiring that a specific value be named, and circumvents much of the potential for strategic response bias. The challenge for estimation arises only because the respondent's true valuation is an unobserved random variable. We must infer its magnitude through an indicator variable (the consumer's "yes/no" response to the offered threshold sum) that tells us whether this underlying value is greater or less than the offered value. In formulating appropriate econometric methodologies for analyzing these data, it is important to begin by imagining how valuation might be modeled if we could somehow readily elicit from each respondent their true valuation. If valuation could be measured like other variables (i.e. continuously), we would simply regress it on all the things that we suspect might affect its level. The econometrically interesting complication with referendum data arises from the fact that we don't know the exact magnitude of the individual's valuation; we only know whether it is greater than or less than some specified amount. 2.2 Log-likelihood Function for Censored Logistic Regression Referendum data are not discrete choice data in the conventional sense (see McFadden, 1976, or Maddala, 1983). The procedure developed below is based upon the premise that if we could measure valuation exactly, we would use it explicitly in a regression-type model.1 The censoring of valuation to be "greater than or less than" a known threshold is a mere statistical inconvenience to be worked around. 1 Here, we would be using it explicitly in a "non-normal" regression model, namely, a regression model incorporating a two-parameter logistic density function. But that would be nothing special--econometric researchers have for several years been using maximum likelihood methods to explore Poisson regression, Weibull regression, and a host of other distributional assumptions as alternatives to the familiar normal model. ------- 9 Assume that the unobserved continuous dependent variable is the respondent's true willingness-to-pay (WTP)2 for the resource or public good, Y . We can assume that the underlying distribution of Y. , conditional on a vector of explanatory variables, xi (with elements j-l,...,p), has a logistic (rather than a normal) distribution, with a mean of g(xi,^) - xi'/3. In the standard maximum likelihood binary logit model, we would assume that: (1) - x.'0 + ut where Y is unobserved, but is manifested through the discrete indicator variable, I , such that: (2) It - 1 if Yt > 0 - 0 otherwise. If we assume that ui is distributed according to a logistic distribution with mean 0 and standard deviation b (and with alternative parameter k - bjl/n, see Hastings and Peacock (1975)), then (3) Pr(Ii - 1) - Pr (Yt > 0) - Pr(Ui > -x.'£) - Pr(u1A > -x^^/k) - 1 - Pr(V>1 < -x.'7) , where 7 - 0/k and we use ip to signify the standard logistic random variable with mean 0 and standard deviation b - n/J3. The formula for the cumulative density up to z for the standard logistic distribution is (4) F(z) - 1 - {1 + exp[z]}. 2 1 These models can be adapted very simply to accommodate willingness-to-accept (WTA). ------- 10 Therefore the log-likelihood function can be written as: (5) log L - 2 - log{1 + exp[ -x. ' 7]) + (1 - I.) log{exp[-x. '7]/(1 + exp[-x.'7])}. Simplification3 yields: (6) log L - 2 (1 - I.)(-xi,7) - log[l + exp(-x.'7)]. It is not possible in this model to estimate £ and k separately, since they appear everywhere as /3/k. The model must therefore be evaluated in terms of its estimated probabilities, since the underlying valuation function, x. '/3, cannot be recovered. With referendum data, however, each individual is confronted with a threshold value, t . Earlier researchers have included t as one of the x, 1 1 i variables in the conventional logit model described above. In our new model, we conclude by the respondent's (yes/no) response that his true UTP is either greater than or less than t1. We can assume a valuation function4 as in (1) with the same distribution for u^ but we can now make use of the variable threshold value t. as follows--in a new model which might be described as special form of "censored logistic regression": (7) It - 1 if Yt > t. - 0 otherwise, so that 3 Note that many textbooks (e.g. Maddala, 1983) exploit the symmetry around zero of the standard logistic distribution to simplify these formulas even further. We simplify this way to preserve consistency with the next model where we estimate k explicitly. * However, it is now straightforward to make the mean of the conditional distribution any arbitrary function g(x. ,/?). ------- 11 (8) Pr(Ii - 1) - Pr(Y. > t.) - Pr(u. > t. - xt'0) - Pr(u.//c > (ci - x.'/3)/*) - 1 - Pr(il>i < (t. - x.'£)/*). With this modification, the log likelihood function can now be written as: (9) log L - £ - I. log{l + exp[(ti - x.'£)/*]} + (1 - I.) log{exp[(t1 - x. '0)/k]/(1 + exp[(t. - x.'/3)/k])}. As before, this can be simplified to yield: (10) log L - Z (1 - - x.^0)/*] - log{l + exp[(ti - xl'/3)/k)). The presence of ti allows k to be identified, which then allows us to isolate 0 so that the underlying fitted valuation function can be determined. Note that if t - 0 for all i, (10) collapses to the conventional logit likelihood function in (6). The log-likelihood function in (10) can be optimized directly using the iterative algorithms of a general nonlinear function optimization computer program5 and this is undeniably the preferred strategy when the option is readily available. There exist function optimization algorithms which will find the optimal parameter values using only the function itself (and numeric derivatives). However, analytic first (and second) derivatives can sometimes reduce computational costs considerably. See Appendix I for a description of 5 We used a program called GQOPT - A Package for Numerical Optimization of Functions, developed by Richard E. Quandt and Stephen Goldfeld at Princeton University (Department of Economics). Roughly optimal parameter values are first achieved using the DFP (Davidon-Fletcher-Powell) algorithm; these values are then used as starting values for the GRADX (quadratic hill-climbing) algorithm to achieve refined estimates (i.e. to a function accuracy of 10~10) . We understand that the programs GAUSS and LIMDEP can also be adapted to optimize arbitrary functions. ------- 12 the gradient and Hessian components helpful in nonlinear optimization of this log-likelihood function. Maximization of the log-likelihood function in (10) will yield separate estimates of 0 and /c (and their individual asymptotic standard errors). However, estimates of -\/k and 0/k can, in the case of g(x.,/3) - x.',9, be obtained quite conveniently from conventional maximum likelihood "packaged" logit algorithms, although we emphasize that this is merely a handy "short- cut" to be used if a general function-optimization program is not available. If we simply include the threshold, t , among the "explanatory" variables in an ordinary (maximum likelihood) logit model (as has typically been done by earlier researchers using referendum data), it is easy to see that: (11) - (t,x') ¦1/K 0/* - -x*'7*, The augmented vectors of variables, x* and coefficients, 7*, may be treated as one would treat the explanatory variables and coefficients in an ordinary logit estimation. From 7*, it is possible to compute point estimates of the desired parameters fi and k. If we distinguish the elements of 7* as (a, 7) - (-l//e, 0/k) then k - -1/a and 0^ - - 1^/ot, j - l,...,p. However, accurate asymptotic standard errors for these functions of the estimated parameters are not produced automatically. If the conventional logit algorithm used allows one to save the point estimates and the variance-covariance matrix estimates for subsequent calculations, there are some alternative, relatively simple, methods for calculating approximate standard errors using only the information ------- 13 gleaned from a conventional logit model. (See the second portion of Appendix I.) 3. Data The Texas Parks and Wildlife Coastal Fisheries Branch has conducted a major creel survey of recreational fishermen from the Mexican border to the Louisiana state line during the period of May to November, 1987. The survey records detailed catch information, and appends a list of "socioeconomic" questions which make up the contingent valuation portion of questionnaire. Over 10,000 responses were collected; our admissibility criteria reduce the usable sample to 5526, which is still a very large number of responses. Hydrological data are collected simultaneously at each investigation sit£ along with the CV investigation. We merge these survey data with an assortment of data drawn from other sources, notably the Texas Department of Water resources and the 1980 Census. Extensive documentary information on variable construction is contained in Appendix II. The reader is referred to that section for details. A. Specifications 4.1 "Naive" Models As always, the very simplest model of fisheries valuation could presume that we only wish to know the marginal mean of the value of a year's fishing. If we include only the offered threshold as an explanatory variable in a logit model to explain the yes/no response, the fitted model will yield the marginal mean and marginal standard deviation of values (ignoring heterogeneity among respondents). This number is valuable if we can safely assume that the interview sample is a truly random sample of the "use" population, and if we know the size of the sample relative to the entire population. Under these ------- 14 limited circumstances, we can extrapolate from these per-person estimates to the total fitted "use" value of the fishery at the time of the survey and under the current conditions of the fishing population and the resource itself. If we were not concerned with forecasting the effects of changes in the fishing population or changes in resource attributes, this single point estimate and its standard deviation would tell us most of what we need to know. However, resource valuation models can be extremely useful for forecasting the anticipated effects upon resource values of changes in resource attributes. In this study, we are primarily concerned with changes in species abundance and changes in water quality. We will control for cross- sectional heterogeneity in anglers and in resource attributes. Having calibrated a model acknowledging this heterogeneity, we will have a fitted model which will be useful for predicting the effects on the value of the resource of a wide range of policy-induced changes in our explanatory variables. Where resource values are sensitive to water quality "parameters," we can determine the effect of a change in the level of each parameter on the social resource value of the resource. Comparing the social benefits of pollution control, for example, with the social costs of a cleanup program can provide a useful assessment of the economic efficiency implications of cleanup proposals. If resource values are sensitive to species abundance or size (either overall or by individual species), there will be important implications for fisheries management. Likewise, if access values are sensitive to the day of the week interacted with respondent characteristics, these valuation models could indicate how fishing licenses and closures could ------- 15 be decided in order to optimize both the resource base and the aggregate social value of access. One initial problem observed in the data concerns the distinction between willingness to pay and actual ability to pay. "Demand" in the economic sense might be limited to "effective" demand, not just wishful thinking. This distinction is unresolved at present, but must be addressed at some point during this study. The reason for raising this issue is that we observe in our sample that many of the people who claim to be willing to pay $20000 to continue fishing over the year come from zip codes where $20000 exceeds the median household income. While it may be that the respondent's household income is substantially larger than their zip code median, these responses cast some doubt on the accuracy of "effective" demands implied by responses to the $20000 referendum value. Fortunately, however, we have a very large sample, by contingent valuation standards. The referendum threshold values were assigned randomly to different respondents. Therefore, we will lose little except some estimation efficiency by dropping all respondents who were offered this extremely high threshold. It is quite possible that many of the respondents who respond that they would be willing to pay $20000 for a year's access to the recreational fishery are responding strategically, rather than realistically. Strategic biases from these responses can be quite high, so the results reported here exclude the $20000 offers, regardless of their yes or no response. (Current plans for the continuation of the survey call for this threshold to be dropped anyway. All specifications will eventually be estimated with the full sample, with $20000 threshold respondents deleted, and with thresholds exceeding $500, 2000, and $1500 deleted. This allows us to ------- 16 assess che sensitivity of the valuation function parameter estimates to survey design.) 4.2. Derivation of "Demand Functions" Underlying the Valuation Data In this survey, the underlying continuous dependent variable Y is the respondent's total valuation of a full year's access to the fishery, which we will designate as "total willingness to pay," TWTP. We can still estimate models for TWTP using censored logistic (or censored normal) regression implicitly via an ordinary MLE logit (or probit) algorithm. We can manipulate the estimated discrete choice coefficients to uncover the individual coefficients (/9) for any arbitrary underlying linear-in-parameters fitted total TWTP relationship, 0. However, the TWTP function must then be solved to yield the corresponding implicit demand function. To illustrate, suppose that our explanatory variables included only the number of fishing days per year, q, and other shift variables which we will denote by the "generic" variable X. Then the fitted quantity log(2¥TP) will be log(q) + X, where the parameters are now their estimated values and we ignore the stochastic component. The price willingly paid for a year's access is the total amount willingly paid for all trips. To determine the marginal WTP for one additional trip, we need to find the expression for the derivative: dTWTP/dq. Since 31ogTWTP/31og(q) is just 0Z, dTWTP/dq can be assumed to be 02 times the ratio of fitted TWTP (- expf/Sj + /92 log(q) + X]) to q. (To be strictly correct in treating this exponentiated fitted value of log(TWTP) as the fitted conditional mean of TWTP, we would scale this quantity by r(l+/c)T(l-/c) , but this term affects only the intercept of the resulting demand expression, so will will suppress it for simplicity of exposition.) If we consider dTWTP/dq to be p(q), the presumed demand relationship can be expressed as: ------- 17 (12) log p(q) - log 02 - log(q) + + 02 log(q) + 03 X. - (^ + log 02 + 03 X) + (0Z - 1) log(q) We can rearrange these formulas to isolate log(q) on the left-hand side: (13) log(q) - [(^ + log(02))/(l-02)] - [1/(1-j92) 1 log p(q) + [p3/a-fi2)\ x - a:* + a2* log p(q) + a3* X. We have thus arrived at point estimates for the implicit demand function corresponding to a log-log functional form for TWTP. The coefficients on log(p) have the straightforward interpretation of price elasticities of demand for fishing trips. If the X variables contain the logarithm of income, then the corresponding coefficient in the a3* vector gives the income elasticity of demand. Other variables making up the X vector will include respondent and resource attributes which shift the demand function. Of course, the p parameters in the above formulas are transformations of the original MLE logit parameters. It will certainly be possible to • "automate" the computation of all of the a* parameters of the implied demand function if we use software which allows us to save the fitted logit parameters to be used in subsequent computations (e.g. SHAZAM). Our initial exploratory models focus on the estimation of the 0 parameters, indirectly via the ordinary MLE logit approach. However, once promising specifications have been identified, and if one is willing (and able) to estimate a censored regression log-likelihood function directly, using non-linear optimization algorithms, it would be straightforward to reparameterize the censored regression likelihood function described above so that the elasticity parameter a2* and the other a3* parameters could be estimated directly. Note that 01 - - log[a2*/(l+a2*) ] - a:*/a2* (plus an additional term in T functions ------- 18 of k) and 02 - (1+a*)/a* and 03 - -a*/a*. The expression x.'/3 in che likelihood function should therefore be replaced by: (14) g(x.,£) - - log[a2*/ (l+a2*) ] - at*/a* + (l+a2*)/a2* log (q.) + X - g(a1*,Q2*,a3*,q1>X.) . The log-likelihood function to be optimized will now be: (15) log L - S (1 - Ii)((ti - g(a1*,Q2*)a3*)qi,X.))//c] - log(l + exp[(t. - g(a1*,a2*,a3*,qi,X.))/«]) . Since the individual parameters c^*, a2*> an<* a3* are identified, the nonlinear function optimizing program will produce the desired results. (The analytical gradient and Hessian formulas will be different and much more complicated, but as noted, many programs will compute their own numeric derivatives.) This model would produce not only direct point estimates of the demand elasticities, <*2*, and the other demand function derivatives, but also their directly estimated asymptotic standard errors. By the invariance property of maximum likelihood, the point estimates should be identical, so extremely accurate starting values for these nonlinear algorithms can be generated by transforming the ordinary logit point estimates. The nonlinear optimization of the likelihood function in (15), however, will yield asymptotic standard error estimates (and therefore t-ratios for hypothesis testing) which could only be approximated with considerable difficulty from the asymptotic variance-covariance matrix produced automatically for the ordinary logit parameter estimates. ------- 19 5. Preliminary Empirical Results 5.1 Unspecified Geographic Heterogeneity in Demand If we assume geographic homogeneity to begin with and estimate a TWTP model in log form simply as a function of the log of the total number of fishing trips (LTRIPS), the log of median zip code household income (LINC), and market expenditures (MON), we get the ordinary logit point estimates in Table la. To determine whether there exists systematic geographical variation in the demand function for fishing days, we then extend this model to include a set of qualitative dummy variables, one for each major bay system: MJ1 - Sabine-Neches MJ2 - Trinity-San Jacinto (Galveston Bay) MJ3 - Lavaca-Tres Palacios (Matagorda Bay) MJ4 - San Antonio-Espiritu Santo MJ5 - Mission-Aransas MJ6 - Corpus Christi-Neuces MJ7 - Upper Laguna Madre MJ8 - Lower Laguna Madre Since the Galveston Bay area accounts for Houston, we arbitrarily make MJ2 the omitted category when we enter sets of major bay dummy variables. Coefficients on the other dummies therefore represent shifts in the dependent variable relative to the values for MJ2. Individually, several of these dummy variables are statistically significant. Collectively, a likelihood ratio test for the incremental contribution of the complete set of dummy variables indicates that geographical variation in demand is statistically significant at the 10% level. If we take the ordinary logit parameter estimates from Table lb and transform them to yield the parameters of the log-log demand function corresponding to this TWTP function (shown in the last column of Table lb), we find that the price elasticity of demand for a fishing day, controlling for qualitative geographical variation via the set of major bay dummy variables, ------- Table la Extremely Simple Model: Geographic Homogeneity of Demand Variable Est. Coeff. Asy. t-ratio LOFFER -0.5608 -24.631 LTRIPS 0.3077 12.05 LINC 0.2488 2.316 MON 0.001734 6.167 constant 1.718 1.625 max LogL - -2550.6. Table lb Augmented Simple Model: with Geographic Heterogeneity (dummies) Variable Est. Coeff. Asy. t-ratio Demand fn q LOFFER -0.5638 -24.68 - LTRIPS 0.3095 12.08 - LINC 0.1278 1.058 0.5024 MON 0.001801 6.234 0.0071 MJ1 -0.1827 -0.7526 -0.7185 MJ3 -0.2589 -1.796 -1.018 MJ4 -0.03043 -0.1706 -0.1197 MJ5 -0.1167 -0.9230 -0.4587 MJ6 -0.3405 -2.819 -1.339 MJ7 -0.2878 -2.149 -1.131 MJ8 -0.3184 -2.478 -1.252 constant 3.119 2.563 - log(p) - - -2.217 max LogL - -2544.2 (LR test statistic for the set of seven major bay dummy variables is 12.8. x2(.05) critical value - 14.07; x2(-10) critical value - 12.01. ------- 20 is -2.217. The income elasticity of demand is 0.5024. the change in the log of fishing days for a one dollar increase in market expenditures is 0.0071. The seven bay dummies shift the log of fishing days by -0.72, -1.02, -0.12, - 0.46, -1.34, -1.13, and -1.25, respectively. 5.2 Quantifying Geographical Heterogeneity in Demand The evidence therefore suggests that geographical variation exists in the demand function for recreational fishing days in Texas. But in the model in the last section, the reasons for this geographical variation are non- specific. Demand could differ by bay system for a variety of reasons. First, systematically different types of people, with different preferences or constraints, might be utilizing each different bay system. (This is suggested by the drop in significance of the LINC variable when bay dummies are included.) The quality attributes of the resource could also vary across bay systems. If fish abundance affects TWTP, then variations in species abundance across bays could be captured by these dummy variables. If fishing conditions (weather and water conditions) vary systematically across bays, this effect could also be manifested in the dummy coefficients. In particular, however, we are curious to see whether measurable variations in water quality "parameters" exert any statistically discernible influence on TWTP. In lieu of a set of simple bay dummy variables, then, we begin to consider specifications employing variables which quantify the inter-bay differences in resource attributes. Table 2a augments the model in Table la by including a variable, TOTAL, for the total number of fish actually caught on the interview day. (In subsequent models, we will consider exogenous measures of abundance for individual species, by month and bay.) TOTAL current catch is not statistically significant, but it bears the anticipated sign, so we will ------- Table 2a Simple Model with Current Total Catch, No Water Quality Variable Est. Coeff.' Asy. t-ratio LOFFER -0.5617 -24.64 LTRIPS 0.3064 11.99 LINC 0.2504 2.331 MON 0.001735 6.156 TOTAL 0.003109 1.090 constant 1.718 1.625 max LogL - -2549.9. Table 2b Augmented Model: Geographic Heterogeneity in Water Quality Variable Est. Coeff. Asy. t-ratio Demand fn q LOFFER -0.5637 -24.63 - LTRIPS 0.3132 12.19 - LINC 0.2299 1.888 0.9177 MON 0.001675 5.953 0.00669 TOTAL 0.003603 1.243 0.01438 RESU 0.005401 2.138 0.02156 PHOS 1.076 2.685 4.296 CHLORA 0.02313 2.725 0.09233 LOSSIGN 0.005420 1.359 0.02163 CHROMB -0.009027 -0.969 -0.03603 LEADB -0.006231 -1.160 -0.02487 constant 3.119 2.563 - log(p) - - -2.250 max LogL - -2536.9 (LR test statistic for the set of six water quality variables is 26.0. x2(.05) critical value - 12.59. ------- 21 retain it in the model as a rudimentary control for "catch success." TOTAL will vary with individual fishing skill or effort, but it will also vary across major bays as species abundance varies. Of primary interest for the purposes of this study, of course, is the potential influence of water quality measures on TWTP, and hence on the demand function for recreational fishing days. Our supplementary data from the Texas Department of Water Resources provides sufficient sample on several common water quality parameters to allow us to generate monthly averages for each bay system. For others, however, the limited number of samples only allows reliable estimates of annual averages for each bay system. (This is particularly true for metals found in bottom deposits. We are awaiting further supplementary data on bottom deposits from the shellfish division of the Health Department.) In our first pass through the data, we examined pairwise correlations between species abundance and a wide range of water quality measures and selected several which seemed to have an obvious relationship to species abundance. (We have tangentially explored regressions of actual catch and monthly abundance of each species on all reliably measured water quality attributes, described in Section 6.) To illustrate the potential for water quality to affect TWTP for fishery access, we display in Table 2a some preliminary results for a rudimentary model incorporating a selection of water quality variables. (We emphasize that this model is by no means our last word on the subject. We have barely "scratched the surface" of a wide variety of potential specifications.) The water quality variables we include in Table 2b which are available as monthly averages for each bay system are RESU (total non-filterable residue, dried at 105C, in mg/1), PHOS (phosphorous, total, wet method, mg/1 as P), and CHLORA (chlorophyll-A, Mg/1. spectrophotometry acid method). ------- 22 Variables which can at present only be used as annual averages for each bay system are LOSSIGN (loss on ignition, bottom deposits, scaled to g/kg), CHROMB (chromium, total, in bottom deposits, mg/kg, dry weight), and LEADB (lead, total, in bottom deposits, mg/kg as PB dry weight). Transforming the ordinary logit parameter point estimates in Table 2b according to the formulas suggested above for solving such a model for the corresponding log-log demand function yield the demand parameters given in the last column of Table 2b. The price elasticity of demand for fishing days is now -2.250. The income elasticity of demand is now 0.9177. (The increase is probably attributable to the fact that we are not longer implicitly controlling for geographic income variation via the set of major bay dummy variables, so that this measure is probably more reliable.) A one dollar increase in market expenditures corresponds to a 0.0067 increase in the log of the number of fishing days demanded, suggesting that market goods associated with the fishing day (if typical) are complementary goods. An extra fish caught on the interview day affects demand by increasing the log of days demanded by 0.0144. Demand is higher where non-filterable residues are higher, where phosphorous concentrations are higher, where loss on ignition is greater, and where there are greater concentrations of chlorophyll-A. However, the presence of metals in bottom deposits, such as chromium and lead, corresponds to lesser demand for fishing days. 5.3 Controlling for Demographic Heterogeneity Among Respondents Having determined that there will be some water quality measures which appear to have a statistically significant impact upon the value of access to this recreational fishery, we now introduce three variables designed to control for interregional variations in demographics. We use PSPN0ENG, PVIETNAM, and PURBAN. To the extent that the demographic characteristics of ------- 23 anglers are correlated with the water quality in the areas where they fish, it will be important to allow for demographic effects in any attempt to identify the distinct effects on resource values of water quality measures. Table 3 gives the ordinary MLE logit parameter estimates with these additional explanatory variables. The last column of the table gives the point estimates of the parameters of the corresponding log-log demand function (and its shift variables). None of these three variables make statistically significant contributions to explaining resource values, but this may be an artifact of collinearity among the variables, so we retain them out of interest in determining point estimates of their effects on the demand function.6 The proportion of unassimilated Hispanic residents in the respondent's zip code (PSPNOENG) tends to decrease the log of fishing days demanded by about 1.5; the proportion of Vietnamese (PVIETNAM) has a dramatic effect on values (which persists through a variety of alternative specifications)--this variable increases the log of fishing days demanded by 31.8! People from relatively more urbanized areas apparently demand fewer fishing days. 5.4 Introducing Variations in Species Catch Rates, Species Abundance The total number of fish caught on the interview day has been included as an explanatory variable in several of the specifications discussed above. 6 Bear in mind that just because a particular variable is not statistically significantly different from zero for a particular sample of data does not imply that it is zero. We retain variables for which the coefficient estimates are stable across alternative specifications. With better data (e.g. with a more equal distribution of "yes" and "no" responses) there might have been enough information in this sample to reduce the sizes of the standard errors. Likewise, the error distribution may have an apparent dispersion larger than the actual dispersion because we are using group averages as proxies for several of our explanatory variables, including income. What could be an excellent "fit" with the true data could be converted to a poorer "fit" by the use of group averages. ------- Table 3 Augmented Model: Demographic Variables Variable Est. Coeff. Asy. t-ratio Demand fn q LOFFER -0.5637 -24.63 - LTRIPS 0.3132 12.09 - LINC 0.2281 1.512 0.9068 MON 0.001632 5.731 0.006488 PSPNOENG -0.3915 -0.5880 -1.556 PVIETNAM 8.000 1.237 31.80 PURBAN -0.1190 -1.400 -0.4732 TOTAL 0.003624 1.250 0.01441 RESU 0.005333 2.106 0.02120 PHOS 1.142 2.819 4.541 CHLORA 0.02235 2.631 0.08884 LOSSIGN 0.007762 1.686 0.03085 CHROMB -0.01300 -1.194 -0.05169 LEADB -0.004626 -0.8354 -0.01839 constant 1.404 0.9377 - log(p) - - -2.241 max LogL - -2534.9 ------- 24 Given that we have a wealth of data on the catch and on overall abundance, by individual species, it seems worthwhile to experiment with valuation models which discriminate among the effects of individual species on the annual value of access to the fishery. Perplexing results emerge as we include variables relating to the catch of individual species. There are seven major species in our working data set: REDS, TROUT, CROAK, SAND, BLACK, SHEEP, and FLOUND (See Appendix II for detailed descriptions). We have experimented with: a.) actual current day catch rates; b.) monthly average actual catch rates by bay system; c.) "annual" average actual catch rates by bay system; d.) monthly average abundance indexes by bay system from the TPW resource monitoring program; e.) annual average abundance indexes by bay system from thr TPW resource monitoring program For all of these measure; of catch rates, we find that for at least some species, often important ones, the coefficients in MLE logit models imply that greater catch rates or greater abundance decreases the value of the resource. This seems highly implausible, and points to the existence of important unmeasured variables, negatively correlated with catch rates, which are positively correlated with resource values and (by their omission) leave the catch rate variables with counterintuitive signs. Logically, since we are asking respondents to value a year's access to the fishery, it should b^ expected annual catch which influences their values. But anglers may be myopi-.. Actual average catch rates or abundance may be discounted in favor of current perceptions of catch rates. A variety of models have been estimated, but for illustration, we report our findings for one which uses monthly bay average catch rates. It is our inclination that average catch rates should be preferred to individual current catch rates because the latter does not control for individual expertise or fishing ------- 25 intensity. The monthly averages reflect the catch of the "average" angler, abstracting from individual differences in skill or enthusiasm. Results for a specification which replaces the TOTAL current catch variable with the full set of monthly catch averages for each bay system are presented in Table 4. The coefficients on MATROUT, MASAND, and MABLACK are negative, and the point estimate for the coefficient on MABLACK is relatively large. The set of catch variables collectively results in an improvement of only 3.0 in the log-likelihood function, which is not sufficient to reject by an LR test the hypothesis that the catch data should be excluded from the model. But perhaps we are not measuring the desired variables correctly. It is unfortunate that the survey did not collect information from post- trip respondents regarding their target species. If you only ever fish for one particular species, then the abundance if other species will not affect your value of access to the resource. In fact, of other species compete for the same biological niche as your preferred species, their abundance might detract from your value of the fishery. This angle will need to be explored. At one point, we made the heroic assumption that observed target proportions in each bay and month for pre-interview respondents carry over to the population as a whole (which is tenuous). Including these target proportions directly in a logistic regression model had no discernible effect, however, probably because the information was not specific to individual anglers (a severe errors in variables problem). Further investigation of the observable (and unobserved) correlates of catch rates is clearly warranted. At the time of this writing, we have not yet uncovered and explanation for these counterintuitive findings. The following section addresses catch rates explicitly, and describes the search ------- Table 4 Augmented Model: Monthly Average Catch Rates (by bay system) Variable Est. Coeff. Asy. t-ratio Demand fn q LOFFER -0.5636 -24.62 - LTRIPS 0.3129 12.09 - LINC 0.2158 1.432 0.8604 MON 0.001647 5.725 0.006566 PSPNOENG -0.3705 -0.5479 -1.477 PVIETNAM 7.421 1.142 29.58 PURBAN -0.1149 -1.343 -0.4580 MAREDS 0.05111 0.4234 0.2037 MATROUT -0.02823 -0.6157 -0.1125 MACROAK 0.001740 0.05004 0.006935 MASAND -0.02808 -0.5756 -0.1119 MABLACK -0.2094 -0.6973 -0.8346 MASHEEP 0.4165 1.331 1.660 MAFLOUND 0.06694 0.5238 0.2669 RESU 0.006257 2.328 0.02494 PHOS 1.185 2.671 4.723 CHLORA 0.02056 2.244 0.08195 LOSSIGN 0.006621 1.289 0.02639 CHROMB -0.009143 -0.7001 -0.03645 LEADB -0.005987 -0.9940 -0.02387 constant 1.5419 1.030 - log(p) - - -2.247 max LogL - -2532.7 ------- 26 for potential reasons for the results in Table 4 (and similar results for other models not reported in this paper). 6. Actual Current Catch versus Species Abundance: Regr^sjon Models It is not intuitively obvious whether exogenously measured species abundance, or actual catch rates by the respondent, should be the more appropriate determinant of valuation for the fishing season. Unfortunately, it is rarely easy to extract from respondents a reliable (retrospective) total of each species caught over the past year. We only have the current day's catch of each species in our present survey data. But exogenously measured abundance of each species is not necessarily a good predictor of variations in expected catch from the point of view of the individual who is being asked to value a year of access to the fishery. One reason is that Parks and Wildlife Resource Monitoring controlled samples are not "caught" using the same technology available to recreational fishermen. If fish are present, but are not "biting," they may still be swept up in the nets used by the Monitoring Program. Ideally, we would like to know the success rates (for each species) for a "standardized" recreational angler (with given skills and effort level). If we use individual respondents' actual catch rates, unobservable differences in skill will potentially bias the coefficients on the catch rate in the valuation equations. To determine what factors affect individual respondents' current catch rates, we ran a set of ordinary least squares regressions of each respondent's actual catch of each species (REDS, TROUT, CROAK, SAND, BLACK, SHEEP, and FLOUND) against the corresponding monthly and annual abundance indexes for that species, current market expenditures related to the fishing day (MON), specific fishing experience (SITETRIP, the annual number of trips to the site where the respondent was interviewed), non-specific fishing experience ------- 27 (NSWTRIP, annual trips to other saltwater fishing sites in Texas), and a number of demographic variables. The demographic variables reflect zip code average or median data drawn from the 1980 Census, so they do not necessarily capture concurrent demographics, but we will assume they are close. We include PRETIRED (the proportion of people in your zip code who are retired), PSPANISH (the proportion of people of Hispanic origin), PSPNOENG (the proportion speaking Spanish at home and little or no English--unassimilated immigrants), PVIETNAM (the proportion indicating Vietnamese origin, PURBAN (the proportion living in areas designated as urban), PTEXNATV (the proportion born in Texas--reflecting familiarity with the fishery or the environment), PFFFISH (the proportion working in forestry, fishing, or farming), and HHLDINC (median household income). These variables may affect catch rates for several reasons. First, demographic differences may influence the target species chosen. Alternatively, these variables may serve as proxies for fishing experience or skill. They may also proxy whether or not the objective of the fishing trip is purely recreational, or whether the catch is a significant supplement to the angler's diet. Demographic measures may also covary systematically with geographical regions and therefore with species abundance. Table A.l (at the back of this paper) displays the results of the seven OLS regressions. Interestingly, the exogenous abundance indexes (MMxxxxx and Axxxxx, computed from the Resource Monitoring data) are frequently significantly negatively related to the actual catch. Only for sand seatrout (SAND) do both abundance indexes enter positively. This result requires further investigation. In any event, if the fish are there, but you cannot catch them using legal recreational fishing gear, they may contribute considerably less to your value of the resource. ------- 23 For several species, money spent on market goods related to the fishing day is negatively related to the catch. (And it is interesting that MON is markedly uncorrelated, at 0.03, with zip code median household income.) Site- specific fishing experience (SITETRIP) significantly increases one's catch of red drum (REDS), spotted seatrout (TROUT), and black drum (BLACK). Non- specific fishing experience (NSWTRIP) significantly increase one's catch of sheepsheads (SHEEP) and southern flounder (FLOUND), but significantly diminishes one's catch of croakers (CROAK). PRETIRED insignificantly decreases the TROUT, CROAK, BLACK and SHEEP catch, significantly decreases the SAND catch, but has an insignificant positive effect on the FLOUND catch. People from zip codes with relatively large numbers of Vietnamese catch significantly (and substantially) fewer of several species, notable REDS, and SAND, but they catch dramatically larger numbers of CROAK. People from urbanized areas catch fewer REDS, but more CROAK, SAND, and FLOUND. Texas natives (or at least people from areas where relatively more people are Texas natives) catch significantly fewer REDS, but more TROUT, CROAK, BLACK, and FLOUND. If more of your neighborhood is employed in fishing, farming or forestry, you tend to catch significantly more REDS, SAND, and SHEEP, but significantly fewer CROAK. Higher neighborhood incomes mean higher REDS catch, but significantly lower CROAK and SAND catch rates. These differing results undoubtedly reflect the "sport" versus "food" values of different species. These tendencies might still reflect regional variations in fishing location, which might be correlated with demographic factors. To identify non-specific geographical and seasonal variations in catch rates, we also estimate OLS regressions of actual catch rates on a set of major bay dummies, MJ1 - MJ8, and a set of monthly dummies, MN5 - MN11 (where MN5 is May 1987, ------- 29 etc.). The results of these regressions are displayed in Table A.2. Clearly, there is considerable qualitative geographical and seasonal variation in catch rates for all species. Table A.3 therefore includes the quantitative variables from Table A.l (with the exception of Axxxxx, which takes on only one value per bay system), as well as the set of dummy variables MJ1 - MJ8. Geographical variation in resource stocks does not seem to explain completely the observed variations in catch rates. Tastes (demographics) still seem to matter in many cases. Since the abundance indexes derived from the Resource Monitoring data set do not seem to be a very good proxy for expected annual catch, we revert to using the information present in the contingent valuation sample. With over 5000 usable responses, we can average the actual current catch data for each respondent across all fishing trips to a particular bay system in a particular month. Likewise, we can generate annual average actual catch rates in each bay system. Tables A.4a through A.4c describe catch data based on the CV sample information. Table A.4a displays the differences in mean catch rates across bay systems for each species (AAxxxxx). Table A4.b explains the actual individual catch for each species using both monthly average catch rates and "annual" (May through November) catch rates, plus a variety of demographic variables. The monthly average catch is clearly the preferred indicator when both are included. (Its coefficient is always near one and highly significant.) However, if only annual catch rates are included, as in Table A.4c, these do an excellent job of explaining current individual catch. But sociodemographic, "experience," and market expenditure variables still contribute significantly to explaining individual catch rates for several species. In words, you don't just catch what everybody else catches--who you are makes a difference too. ------- 30 In subsequent work, we will contemplate using regression models like these to generate fitted reduced form estimates of individual catch to be used as explanatory variables in the logistic regression models for the demand equation. Purging catch rates of components which might be correlated the error term may improve the accuracy of the estimated coefficients. 7. Explicit Trio Motivation. Trip Goal Satisfaction The main objective of this project is to determine whether water quality has any statistically discernible effect upon the value of access to a recreational fishery. For a subset of respondents--those who were interviewed prior to embarking on their fishing trip--respondents were actually asked explicitly about how important it was to them to be able to "enjoy natural and unpolluted surroundings" on a fishing trip. The responses warrant investigation. In the pre-trip interviews, the TPW survey actually asked direct questions about a whole variety of potential motivations for going fishing. All respondents were asked to respond on a 10-point Likert scale (with 10 being "extremely important" and 0 being "not at all important") the importance they place upon recreational fishing as a way to: A - Relax (PRERELX) B - Catch Fish (PRECAT). The third motivation question was drawn at random from a selection of alternatives, including: C - Get away from crowds of people (NOPEOPLE), D - Experience unpolluted natural surroundings (NOPOLLUT), E - Do what you want to do (DOWHTWNT) , F - Keep the fish you catch (KEEPFISH), G - Have a quiet time to think (QUIETIME), H - Experience good weather (GOODWTHR), I - Spend time with friends or family (FRNDFMLY), and J - Experience adventure and excitement (ADVNEXCT). ------- 31 Since the latter eight goals were not asked of everyone, it was necessary to focus on the subsamples to which each question was posed. For pre-trip interviews which were not matched with post-trip interviews of the same anglers, we have a very limited amount of information. It is not possible to include demographic data, because zip codes were not collected. We therefore rely on whether the professed target species was red drum, trout, or flounder (TARGR, TARGT, or TARGF), upon major bay dummies, monthly dummies, and upon a dummy variable for weekend days. We use OLS regression of the recorded Likert scale response on these variables in an effort to detect factors affecting angler's objectives in going fishing. The results are contained in Table A.5. From Table A.5, we see that target species, geographic dummies, and seasonal dummies do not help at all to explain the NOPOLLUT motivation for going fishing. However, the target species do affect the NOPEOPLE motivation, the KEEPFISH motivation (red drum anglers seem to fish for sport; flounder anglers fish for food), and the GOODWTHR motivation (trout anglers enjoy the weather more; red drum and flounder anglers are less inclined to go out for the nice weather... they must be more serious). Red drum anglers are less likely to go fishing for its social aspects (FRNDFMLY). More weekend anglers claim to be strongly motivated by the desire for adventure and excitement (ADVNEXCT). Geographical and seasonal dummies occasionally make significant differences in the objectives of anglers. However, the values of the F-test statistics corresponding to these regression suggest that none of the models have particularly good explanatory power. Unfortunately, people who were interviewed prior to their fishing trips were not a random sample of anglers. Interviewing personnel did not begin to collect data until 10:00 a.m. in general, so pre-trip interviews sample ------- 32 individuals who do not embark on fishing trips until relatively late in the day. These are probably less avid fishermen. Consequently, what we learn from this sample cannot be reliably extrapolated to the entire sample. (It would have been helpful if the pollution question, in particular, had been posed to everyone, both pre- and post-trip.) Nevertheless, with this caveat in mind, we can examine the apparent relationships between attitudes and other variables. For the pre-trip interview sample which could be matched with corresponding post-trip interviews, we have both the attitudinal variables and the crucial zip code data which allow us to splice in data (by zip code) on our primary Census variables: median household income (HHLDINC), proportion of the population over 65 (PRETIRED), proportion of the population with birthplace in Texas (PTEXNATV), the proportion living in urban areas (PURBAN), the proportion of the population reporting Vietnamese origin (PVIETNAM), and proportion of the population speaking Spanish at home and speaking English not well or not at all (PSPNOENG). If we assume that zip code areas are relatively homogeneous, we can use median household income and these demographic proportions to control for a certain extent for the respondents demographic characteristics. To determine the extent to each motivation depends upon the characteristics of the respondent, we can attempt to interpret a number of OLS regressions. Other included explanatory variables are: number of fishing trips to the interview site over the last year (SITETRIP), number of saltwater fishing trips to other sites (NSWTRIP), and money spent on market goods during this fishing trip (MON). The results are presented in Table A.6. In the post-trip interviews, the TPW survey asked some direct questions concerning respondents' ability to achieve certain goals in going fishing. ------- 33 Again, all respondents were asked to respond on a 10-point Likert scale (with 10 being "completely" and 0 being "not at all") the extent to which they were able to achieve the same set of goals (A through J). All respondents were offered the first two goals, and one question from the remaining eight was asked of each respondent. In subsequent research, we may devote attention to the other attitudinal questions in the post-trip surveys, but for the present we will focus on the NOPOLLUT question, since this is most relevant to the issue at hand. For post-trip respondents' answers to the question "To what extent were you able to experience unpolluted natural surroundings," we obtained the regression results summarized in Table A.7. This OLS regression demonstrates that who you are (the demographic variables) has little to do with your perception of your ability to enjoy unpolluted surroundings. The only exception may be the PVIETNAM variable. On the other hand, geographic and seasonal dummies occasionally make a statistically significant contribution to explaining peoples responses. Anglers do seem to have differing perceptions of the level of pollution, especially across bay systems. The northern bays are perceived to be more polluted than are southern bays. It is unfortunate that this attitude question (NOPOLLUT) was not asked of the entire sample, so that this variable could be employed as a potential explanator for annual resource values. Nevertheless, we can experiment will a logistic regression specification based upon the 830 respondents who were posed both the NOPOLLUT question and the contingent valuation question. Table 5 summarizes the results of an ordinary logit model (without water quality variables or catch data) which includes the Likert scale value for the NOPOLLUT variable as a potential shift variable for the demand function. ------- 34 Since only a tiny subsample of the full dataset is being used in this case, we might expect some differences in the implication of the fitted models (especially if there was anything non-random regarding the choice of whom to ask each of the trip satisfaction questions--a factor which has not yet been investigated). However, the implied demand derivatives in Table 5 are highly consistent with those derived using the full dataset, except for the fact that the coefficient on PSPNOENG changes sign. The price elasticity of demand is typical, at -2.66; the income elasticity of demand is somewhat higher than in the full sample, at 1.589. However, in this subsample, the level of significance of LINC has dropped somewhat. Of particular interest is the coefficient on NOPOLLUT. This variable is statistically significant at the 10% level in the logit model. Adjustments in aspects of environmental quality (including water quality) which would increase a respondents' Likert scale choice by 1 unit (on the scale of 1 to 10) would therefore seem to increase the log of fishing days demanded by 0.28. Since the mean Likert scale value is approximately 8.2, this implies that the "elasticity of fishing day demand with respect to environmental quality" is roughly 2.2--an elastic response. 8. Perceptions of Pollution versus Measured Water Quality When we choose to specify a resource valuation model using water quality measures as explanatory variables, we are not being specific about whether water quality affects valuation of the recreational fishery direcdy or indirectly. For example, anglers may have no conscious perception of the dimensions of water quality when they go fishing, but water quality may be closely related to fish abundance and therefore to catch rates, so that water quality variables are proxies for other variables which do enter directly into ------- 35 individuals' utility functions. (At present, we are exploring OLS regression models for catch rates which include water quality variables.) To determine whether perceptions of environmental quality reflect actual levels of measured dimensions of water quality, we can select the subsample of respondents who were queried regarding their ability to enjoy unpolluted natural surroundings. We can then regress the NOPOLLUT variable on a range of water quality variables to see whether any statistically significant relationships emerge. If anglers appear to perceive water quality directly, then we can argue that water quality probably enters directly into their utility functions as a detectable resource attribute. If not, we would be inclined to say that appreciation of water quality variables is implicit, acting through other variables which are manifestations of water quality. Results for this experiment are given in Table A.8. There are 695 observations for which complete data exist for the initial set of explanatory variables we use here. Once again, monthly or annual averages for each bay system are used for the water quality variables, rather than conditions actually existing in the area on the specific day when the NOPOLLUT survey response was collected. This averaging process may considerably obscure an underlying close relationship between the date- and site-specific values of the water quality variables, had we been able to collect this information simultaneously with the creel survey. Consequently, the standard error for the parameter estimates may well be larger than they would be with more accurate data. Therefore t-tests for the statistical significance of coefficients are probably not conclusive. Table A.8 shows that several water quality measures bear estimated coefficients with t-values greater than unity. The two different measures of dissolved oxygen, MDO and DISO (from different data sources) enter oppositely ------- Table 5 Alternative Strategy: Use Reported Pollution Perceptions to Explain Value (n - 830) Variable Est. Coeff. Asy. t-ratio Demand fn q LOFFER -0.6639 -10.22 - LTRIPS 0.4145 5.946 - LINC 0.3966 0.9774 1.590 MON 0.004663 3.901 0.01869 TOTAL 0.003468 0.2962 0.01390 PSPNOENG 0.2828 0.1820 1.134 PVIETNAM 4.228 0.2686 16.95 PURBAN -0.2009 -0.8602 0.8051 NOPOLLUT 0.07043 1.753 0.2823 constant 0.08104 0.02007 - log(p) - - -2.661 max LogL - -357.53 ------- 36 and relatively significantly. Water transparency (TRANSP) significantly improves perceptions of low pollution. NH4 and PHOS and CHLORA are positively correlated with these perceptions; NITR is negatively related. CHROMB and LEADB detract from perceived environmental quality. (Other specifications reveal the consequences of the high correlations between OILGRS and LEADB: one or the other used alone is strongly negatively significant, but not both.) A tentative conclusion from these initial models is that people do seem to have perceptions of environmental quality that are somewhat related to actual measured dimensions of water quality. Loosely, then, policy actions designed to change the levels of arguments which probably figure significantly in regressions like that in Table A.8 will change anglers' perceptions of pollution levels. The censored logistic regression reported in Table 5 could then be used crudely in a "second stage" to infer the effects of such policies on the demand for fishery access and on the total social value of the fishery. 9. Tentative Findings and Directions for Continuing Research At this stage, of course, the results we have obtained reflect only our "first pass" through the data, to determine whether statistically discernible relationships among the variables of interest will assert themselves. Having achieved some success, it is now necessary to go back over all the data to verify the plausibility of the observed values and to "clean" the sample of additional influential observations which may be causing varying degrees of mischief in the estimation process. Occasional questionable values emerged during the work thus far. Usually, the statistical fit of the models is improved by correction of these problems. Some remarkable outliers among the water quality data on bottom deposits from the Department of Water Resources need to be examined before these "parameters" are included in the model. We also need to splice in the water ------- 37 quality data obtained from the Texas Water Development Board. Due to the absence of a crucial map, we are not able at present to distinguish accurately between the data for the Upper and Lower Laguna Madre areas. With that problem resolved, we will have at our disposal a number of other important dimensions of water quality. With tighter data, we will be able to employ the more refined econometric methods described in sections 2.2 and 4.2 of the paper. For now, we have been satisfied to obtain point estimates of the demand function parameters and to rely upon the statistical significance of the underlying MLE logit parameters to imply the significance of the corresponding demand function parameters. As is typical with survey analyses, the process of utilizing a data set reveals many ways in which the questionnaire could be improved from the point of view of using its results for particular tasks. We find that these data would have been much more useful if the range of offered threshold values had been manipulated during the course of the survey to ensure that fairly even proportions of "yes" and "no" responses were elicited. The efficiency of the estimation process is greater when one is better able to discriminate the shape of the distribution in the vicinity of the marginal mean of the distribution of implicit valuations. This sample has a disproportionate number of "no" responses, which means that the information we have frequently concentrates on the upper tail of the distribution, which is less helpful. For the pollution aspect of this study, our objectives would have been helped by asking all respondents direct questions about their water pollution perceptions and explicitly whether these perceptions affect their enjoyment of the fishing day (today or over the course of the year). ------- 38 It would have been desirable to elicit retrospective information from respondents on their approximate total annual catch of each species, their self-assess fishing ability, and especially, their target species (this was only asked in pre-trip interviews). We need to know more about the econometric literature on utilization of group means in lieu of individual values for explanatory variables. Since some of our earlier work with San Francisco Bay area data (Cameron and Huppert, 1988a, 1988b, and 1988c) has implied that individual income, for example, is correlated with Census median zip code income only at a level of roughly 0.3 to 0.4, much information may be lost by using these medians as proxies. On the other hand, there may be some valid arguments for treating zip code median income as a reasonable measure of "permanent income," or the operational level of total consumption for the individual relative to neighbors. This methodological issue still need to be explored. As we have pointed out in the paper, if information is being obscured by the use of group means or medians, the standard errors of the point estimates in our models could be artificially amplified, making parameters appear to be statistically insignificant at any of the typical (arbitrary) levels. With "real" data, the proxied variables might be strongly statistically significant. We don't know. A major unresolved issue, which has confounded us for some time, is the apparent negative effect of catch rates for some species on resource values. This is counterintuitive, since we have strong priors that better catch rates should imply a more desirable resource. We are confident that some explanation can be found. Certainly, five thousand Texans cannot be wrong. Effort thus far has been focused on determining the parameters of the demand functions corresponding to the fitted total valuation functions for a year of fishing access. The basic implications of microeconomic theory for ------- 39 the parameters of a log-log demand specification are readily satisfied. The price elasticity of demand for fishing days (if a market existed) appears to be roughly -2.2; the income elasticity appears to be just less than unity, implying that recreational fishing is borderline between being a necessity and a luxury. It is unfortunate that the lack of specific demographic data on our respondents prevents us from unambiguously identifying respondent characteristics which would let us segregate the sample and estimate separate demand functions for each group. We must content ourselves with using zip code averages as "shift" variables for a common demand specification. Geographical heterogeneity in the demand for recreational fishing days does seem to exist. Water quality variables seem to explain quite a lot of this geographic variation. The Vietnamese seem to have markedly different preferences for fishing than the population as a whole. Money spent on associated market goods, once thought to be a reasonable proxy for the non- market value of a fishery, is positively related to the value of a fishing day (but typically completely unrelated to catch success). Importantly, many other explanatory variables make strong contributions to explaining the annual value of fishing day access; reliance solely upon market expenditures could severely misstate resource values. ------- 40 APPENDIX I NONLINEAR OPTIMIZATION OF THE CENSORED LOGISTIC REGRESSION MODEL a.) Gradients and Hessian Elements for Nonlinear Optimization For the simplest version of the model, with g(x. ,/9) - x. ' f3, we can write out these derivatives by first defining the following simplifying abbreviations: (1) 0i - (tj_ - xt'P)/ k RA - l/(l+exp(-^)) Si - R^expC-^) The gradient vector for this model is then given by: (2) dlog L/d/3r - Z (x^A) {(Ii - 1) + R1 } r - 1 p dlog L/3k - Z (^/k) { (Ii - 1) + Rt } The elements of the Hessian matrix are: (3) 32logL/&l3vd0s - -(1 A2) Z xltXi> S. r,s-l p d2logL/d0rdK - -(1 A)2 Z xlr { (I1 - 1) + R4(l + <£,) } r - 1 p d2logL/dK2 - -(1A2) Z (2*t) ( (Ii - 1) + Ri } + Vi2Si The expectation of IA is [ l/Cl+expC^)) ] . The negatives of the expectations of the Hessian elements are as follows: (4) - E(d2logL/d/9r30s) - <1A2) 2 x.rxis St r,s - l,...,p - E(d2logL/d0rK) - (1A2) 2 xir^ S1 r - 1 p - E(d2logL/8K2) - (1A2) 2 ^2 St For models with more general forms of the valuation function, gCx^/9) , the gradient vector and Hessian matrix will have different formulas. In these ------- 41 situations, it may prove easier to substitute computing time for programming effort by using numeric derivatives in the optimization process. b.) Standard Error Estimate for Logistic Regression Parameters from Ordinary MLE Logit Algorithms One alternative is to use Taylor series approximation formulas for the variances of the desired parameters (Kmenta (1971, p. 444)): (5) Var(»c) - Var(- 1/a) - [1/a2]2 Var(a) Var (/9 ) - [7/a2]2 Var(a) + [-1/a]2 Var(7 ) J J J + 2 [7/a2] [-1/a] Cov(a,7 ) J J A second possibility is to use the analytical formulas for the Hessian matrix given in (3) in conjunction with the optimal values of 0 and k derived from 7*. The negative of the inverse of this matrix can be used to approximate the Cramer-Rao lower bound for the variance-covariance matrix for and k. Alternately, the expected values of the Hessian matrix elements are sometimes used in this process.7 Whichever way the point estimates are obtained, and by whatever method the asymptotic standard errors are determined, these ingredients are necessary for hypothesis testing regarding the signs and sizes of individual parameters. These can frequently be interpreted as derivatives (or as elasticities) of the inverse demand function (or ad hoc "valuation" function), and assessments of their probable true values are can be an important objective in many empirical investigations.8 7 The outer product of the gradient vector evaluated at the optimum is also sometimes used. However, since the expectation of the Hessian has simple formulas, it is probably preferred in this application. 8 Of course, if estimates are achieved by optimization of (10), hypothesis testing regarding the 0s (individually or jointly) is the same as in any maximum likelihood context: by likelihood ratio tests. ------- 42 APPENDIX II CONSTRUCTION OF ESTIMATING SAMPLE DATA I. Observations from the Texas P'arks and Wildlife Survey The "high use" season data set from the survey covers primarily the period from May 1987 to November 1987, although a few observations are included for December, 1987 and for January and February, 1988. We begin our analysis with the 9413 responses collected in post-trip interviews alone. Relatively fewer respondents were interviewed before their outings, since survey interviewers arrived later in the morning than most anglers leave for fishing trip. Also included are the 1094 respondents who were interviewed both before and after their fishing trip. These respondents were also posed the contingent valuation question; they will also be systematically different types of individuals because all are characterized by departing typically later in the day. This may be related to their implicit resource values. Variables from the survey which are available for use in this study include the following: MAJOR which of eight major bay systems (1 -north; 8-south) HOLIDAY whether the survey day was a holiday DAYTYPE 1st digit (holiday) 2nd digit (day of week) MONDAY year/month/day MINOR code identifying minor bay where survey was conducted STAT numerical code identifying survey site ID boat ID number INTTIME interview time TRIP ACT activity- recreational fishing or partyboat fishing PEOPLE number of people in the party COUNTY code for county or state of residence MINBAY minor bay where most fish were caught GEAR type of fishing gear used by party BAIT type of bait which caught the majority of fish REDS number of red drum landed LRED largest specimen landed and measured MLRED average length of <-6 specimens landed and measured TROUT number of spotted seatrout landed LTROUT ------- 43 MLTROUT " CROAK number of croakers landed LCROAK MLCROAK SAND number of sand seatrouc landed LSAND MLSAND BLACK number of black drum landed LBLACK MLBLACK SHEEP number of sheepshead landed LSHEEP MLSHEEP FLOUND number of South Atlantic flounder landed LFLOUND MLFLOUND TOTAL total landed, all species LTOTAL MLTOTAL SWTRIP number of saltwater fishing trips made in the last 12 months SITETRIP number of trips to the survey sight in last 12 months FWTRIP number of freshwater fishing trips in last 12 months SATISFY overall grade given to the fishing trip (0-10) POSTRELX answer to the post-trip question on extent person was able to relax answer to the post-trip question on extent person was able to catch fish; answer to alternating questions on other dimensions of fishing trip five-digit zip codes which will be used to merge survey data with census tract information on zip code areas for the approximately 90% of the sample with Texas residency implied. "What is the zip code where you currently live?" dollars spent on the fishing trip for non-capital market purchases: "How much will you spend on this fishing trip from when you left home until you get home ?" conveys the arbitrarily assigned threshold value proposed to each respondent and their yes/no response to the question: "If the total cost of all your saltwater fishing last year was dollars more, would you have quit fishing completely?" A "no" response therefore implies that the resource value is greater than the threshold. While the data set was quite well checked for consistency prior to our receipt of it, several unusable observations had to be deleted. Criteria for deletion were: POSTCAT POSTVAR ZIP MON CONTVAL ------- 44 - missing data on the contingent valuation question; - erroneous codes for the relaxation or catch satisfaction questions; - inadmissible codes for the post-trip varying satisfaction-oriented questions; - inadmissible levels for the relaxation or catch satisfaction questions; - inadmissible values for the response to the contingent valuation question; - more than 365 reported saltwater or freshwater fishing trips reported over the last year; - fractional numbers of salt- or freshwater fishing trips reported; - negative or greater than 365 trips per year; - satisfaction Likert scale values outside the 0-10 integer range; - trout catch greater than 300, total catch greater than 300; - zip codes greater than 99999; - no average abundance figures for this month or bay system. If preliminary specifications on this data set indicate that certain variables appear to have no statistically discernible effect on valuations, the presence or absence of valid values for these variables will be irrelevant, and some of these observations can be reinstated. Initial specifications do not incorporate sampling weights to offset any bias in estimated valuations which could result from systematic deletions of observations upon criteria which are correlated with resource values. If necessary, weights will be incorporated in subsequent specifications. 2. Controlled Catch Rate Data: Resource Monitoring Data Set Another requirement of this study is some measure of "expected" catch rates by time and location. Actual catch associated with the fishing excursion during which the survey responses were collected are at best an imperfect indicator of catch expectations. Contemporaneous catch effects are also confounded by the possibility that the angler's expertise is unmeasured, and this expertise will simultaneously affect both their valuation of the resource and their current catch. This will result in misleadingly large estimates of the impact of catch rates on the total value of the year's access ------- 45 to Che sporcfishery if expertise, catch and resource valuation are all positively correlated (which seems likely). In order to avoid the omitted expertise variable's biasing effect on the catch rate coefficient, we take advantage of a supplementary data source which can be merged with the survey data. The Texas Department of Parks and Wildlife regularly collects information on individual species abundance, sizes, tagging, and other information. We elect to use this resource monitoring data for the period 1983 to 1986, for which 23,729 samples are available. Since we seek to reproduce a proxy for anglers' expectations about catch rates, the 1983-86 period would seem to provide a proxy for recent experience. Each observation in this large data file conveys information collected during a particular controlled harvest. Variables include, gear type (3 kinds), location, date, effort (which depends on gear type), meteorological data (including winds, cloud cover, rain, fog, water temperature, water depth, turbidity (TURB), salinity (SAL), dissolved oxygen (DO), barometric pressure, tide information, and wave height. The gear is applied to the fishery for a measured period of time. At the end of the sample period, the gear is removed and a count is taken of each type of organism collected. Mean lengths are also available. We focus on information for the major recreational target species of finfish: red drum (REDS), croaker (CROAK), black drum (BLACK), spotted seatrout (TROUT), sheepshead (SHEEP), sand seatrout (SAND), and southern flounder (FLOUND). In distilling this information into a catch expectation variable for each species, several manipulations are required. First, we standardize the catch using each of the three gear types to the mean number of effort units for each gear type. This controls for variations in catch rates due solely to ------- 46 differing sampling durations, yielding catch per unit effort (CPUE) for each type of gear, for arbitrary effort units. Once these "catch per unit effort" (CPUE) figures have been obtained, we compute overall means and standard deviations in CPUE for each species by gear type. We then use these means and standard deviations to "standardize" the individual CPUE figures for each species and each gear type. The resulting quantities are "indices" of CPUE. The different gear types do not necessarily yield additive estimates of catch rates, since they differ in effectiveness for any given number of hours of application. Therefore, we must resort to the standardized indices, which are unit-free (i.e. we subtract the overall mean CPUE for each gear type, and divide through by the overall standard deviation in CPUE for that gear type). The next step is to aggregate these indices across gear types to come up with a weighted average (across gear types) of the three indices of standardized CPUE. Our objective, initially, is to create indices of expected catch rates for each major species for each sample month and each major bay system along the Texas Coast. The weights we use are therefore the proportion of samples collected by each type of gear in each month and each major bay system. This implies that if one type of gear was only infrequently used in a given month or bay system, the CPUE index for this type of gear will receive a very low weight in the aggregation across gear types. Averages CPUE indices derived from large numbers of samples are presumed to be more reliable, and therefore receive larger weights. (DATA.CTCHIND2) In addition to the weighted average abundance indices by major bay and month, we also computed annual average catch rates for each major bay. (DATA.ANCATCH2) Since the survey of recreational anglers asked whether they ------- 47 would have given up fishing encirely if the access cost had been a particular specified amount, it will also be important to consider whether annual average expected catch is a better explanatory variable for resource valuation than actual catch on the current fishing trip or even monthly expected catch around the time when the survey response was elicited. However, various different measure of catch rates will be included in the valuation models, to determine which measure, statistically, seems to have the greatest effect of resource value. Bear in mind that the constructed abundance variables (MMxxxxx for monthly averages by bay system; Axxxxx for annual averages by bay system) are measured in standard deviation units. When these variables are used in regressions or logit an. yses, the coefficient reflects the consequences of a one standard deviation change in abundance. We may also take advantage of some of the dimensions of water quali ty collected along with the resource monitoring data. The 23,729 observations provides a rich quantity of information on turbidity, salinity, and dissolved oxygen. We compute average values of these measures for each month and each bay system, MTURB, MSAL, and MDO (DATA.TURSALDO), to be employed in regressions of pollution perceptions on measured water quality levels. 3. Texas Department of Water Resources Water Quality Data Dave Buzan and Patrick Roque of the Texas Department of Water Resources were kind enough to allow us to utilize information on the characteristics of a large number of water samples taken at diverse locations throughout the Texas estuarine/bay system for the purpose of monitoring water quality. We use only those observations on water quality measures for which a precise quantity is given. We excluded all observations for which it was only recorded that the amount of the substance was greater than a certain amount. ------- 48 For a few hundred observations, it was reported that the measured amount was less than a certain amount. For these cases, the threshold amount was very small, so we opted to record "zero" for these measures, so as not to bias upwards the mean quantities of these substances. While occasional water samples were taken on an incredible variety of water quality "parameters," consistent sampling focuses on transparency (TRANSP), dissolved oxygen (DISO), nonfilterable residues (RESU), nitrogen/ammonia (NH4), nitrate nitrogen (NITR), total phosphorous (PHOS), and chlorophyll-A (CHLORA). There were from 816 to 3884 observations on these quality measures; the other parameters all had fewer than 100 measurements, so that monthly averages by bay system were deemed to be less reliable. For these other water quality measures (having from 90 to 100 observations), we generate annual average levels for each bay system. These measures include "loss on ignition, bottom deposits" (L0SSIGN), oil and grease (OILGRS), and organic nitrogen (ORGNITR). In bottom deposits, a few records are available for each bay system on phosphorous (PHOSB), arsenic (ARSENB), barium (BARIUMB), cadmium (CADMIUMB), chromium (CHROMB), copper (C0PPERB), lead (LEADB), manganese (MANGANB), nickel (NICKELB), silver (SILVERB), zinc (ZINCB), selenium (SELENB) and mercury (MERCURB). These metals contamination data can be employed investigate whether amounts or perceptions of metal contamination appear to be statistically related to resource values. Locational information for these samples is recorded at the level of "stations," which we identified on maps and aggregated into each of the eight major bay/estuary systems along the Texas gulf coast. Subsequent research may disaggregate further, but for now, we rely on the presumption that each bay is a reasonably isolated aquatic system. There is considerable variation across bay systems in the average levels of these "parameters." [Early models use ------- 49 only those "parameters" which do not seem to involve questionable "outliers" among the samples. Further investigation of these outliers will be necessary before we can be confident about using bay average levels of contamination as accurate measures of true levels.] In siom, we have determined average levels for each of these basic water quality parameters for each bay system and for each month (DATA.DWRPARM). We also aggregate to determine annual averages for each bay system. (DATA.ANDWRPAR) For the metals and other parameters for which there are fewer observations, we have only eight observations, by major bay system. (DATA.HVYMETAL). 4. Hvdroloyical and Meteorological Data Collected at Survey Sites For each day at each survey site, TPW personnel recorded fairly detailed information about weather and surface conditions in the vicinity of the survey site. Both beginning of "day" and end of "day" values were recorded. We begin by considering only the beginning conditions (bearing in mind that this was approximately 10:00 a.m.). These data can be merged with the actual survey responses according to major bay, date, minor bay, and station numbers. Information from this data set which may prove pertinent includes: BWINDSP - beginning wind speed; BCLOUD - midpoints of cloud cover categories; BARO - beginning barometer reading; BRAIN - whether it was raining (0 - no, 1 - yes); BFOG - whether there was fog (0 - no, 1 - yes); BTEMP - temperature in Celsius; The temperature data contained obvious reporting errors, where temperatures had clearly been recorded in Farenheit instead of Celsius. Fortunately, there is very little potential for overlap in the two scales. We discredited any supposedly Celsius temperature over 40, presumed it was Farenheit, and converted it to the corresponding Celsius measure. Consistency checks ------- 50 confirmed that the corrected data were feasible, give the location and times of year. We merged these data (DATA.MDMETEOR) directly with the survey response records, based on day and location. We also constructed mean monthly levels of each of these weather and sea condition variables for each bay system (DATA.MMETEOR), as well as annual average levels for each bay system (DATA.AMETEOR). 5. Texas Water Development Board Water Quality Data David Brock of the Texas Water Development Board has been very helpful in providing us with some of his agency's data on water quality. At the time of this writing, we are still seeking additional information necessary for merging this information with the other data sets. The original merge criteria contained an error. The TWDB data measures many of the same water quality "parameters" as does the DWR data, plus some additional ones. The included data are: Water temperature (C) Turbidity (jksn ju) Transparency (secchi cm) Conductivity field @25 C-mmh Conductivity lab @25 C - micromh Dissolved oxygen mg/1 pH su Ammonia NH3-N mg/1 Nitrite N02-N mg/1 Nitrate N03-N mg/1 NitrogenT kjeldl mg/1 Phos-T P-wet mg/1 Phos-D ortho mg/1 Organ, carbon toe mg/1 Sulfate S04 mg/1 Chlorophyll-A mg/1 These data will be incorporated with the main data set as soon as the geographical definitions can be conformed accurately. ------- 51 6 . Health Department Data In February 1988, during a visit to Austin to confer with the other agencies mentioned in this Appendix, I met with Texas State Health Department data management personnel with Maury Osborn of the TPW Coastal Fisheries Branch. The Health Department maintains detailed historical records of water contamination, in particular for the purpose of determining shellfish "closures." We were informed that if a request for this data was issued by Jerry Clark of TPW directly to the Health Department, these data could be released to us. This formal request was made, but as yet, no data have materialized. We are not sure what accounts for this lack of cooperation, but we will persist. 7. Census Data (1980) for Texas, bv 5-Dlgit Zip Code The Inter-University Consortium for Political and Social Research (ICPSR) provided at nominal cost a tape containing detailed information about Texas residents aggregated to the level of 5-digit zip codes. Since all post- trip interviews attempted to collect the respondent's home zip code, we have a rich source of supplementary demographic data which we can exploit to reduce (to a certain extent) heterogeneity in valuation responses. By far the majority of respondents (over 90% of the sample) gave zip codes within Texas. For these respondents, then, we can augment our array of potential explanatory variables for the valuation models with Census information. It is extremely important to keep in mind that zip code proportions or medians for these variables are by no means identical to the respondents' actual characteristics. At best, we might assert that since 5- digit zip codes are very small areas, geographically, it is more plausible to use zip code demographic averages than, say, county or state averages, to control for demographic heterogeneity. ------- 52 The Census data which we suspect may be relevant to explain valuation responses were extracted from the Census tape and assembled in a file called DATA.TEXCENS1. Our variables are: HHLDINC - median household income in 1980 (TABLE69); FAMINC - median family income in 1980 (TABLE74); MEDINC - median individu.; income in 1980 (TABLE82) ; PURBAN - proportion inside urbanized areas (TABLE1); PRETIRED - proportion of individuals in zip code over the age of 65 (computed from TABLE15); PSPANISH - proportion of individuals in zip code claiming hispanic background (computed from TABLE13); PSPNOENG - proportion of over-18 individuals in zip code claiming to speak Spanish at home and to speak little or no English (computed from TABLE27); PVIETNAM - proportion stating "race" as Vietnamese (TABLE12); PFFFISH - proportion of individuals in zip code reporting to work in "forestry, fishing, or farming" sectors (TABLE66); PTEXNATV - proportion of individuals in zip code reporting birthplace outside Texas (TABLE33). We anticipate that household income (HHLDINC) will be the most appropriate explanatory variable reflecting income levels, although the other income measures will be explored. Since retired persons' opportunity costs of time for going fishing are smaller, we expect that if you come from a community with a large proportion of retired persons (PRETIRED), your likelihood of being retired yourself is larger, and your valuation of the fishery may be systematically different. The proportion of people in your zip code living in a designated urban area may also affect your motivations for going fishing, and hence your value of access. Cultural differences in tastes and preferences (for different species of game fish, or for recreation in general) may affect valuations. Especially since some people significantly supplement their diets with "game" fish, we would like to control for these differences. The PSPANISH variable includes people who have lived in the US or Texas for several generations; the PSPNOENG variable is intended to capture the proportion of recent immigrants from Mexico, since this is by far the most prominent immigrant group in the state. ------- 53 If PSPNOENG is significant where PSPANISH is not, this may reflect assimilation of the immigrant group, at least in terms of preferences regarding fish and recreation. Although this is 1980 Census data, significant numbers of Vietnamese immigrants had already settled in Texas by that time. PVIETNAM will be slightly outdated, but may nevertheless be important. Unfortunately, the Census tapes do not seem to identify individuals which consider themselves to be a member of the prevalent "Cajun" ethnic group. PTEXNATV is the proportion of the community which reports being born in Texas, versus elsewhere. This variable ignores the cultural background of individuals, and simply discriminates the proportion of the community which may have less familiarity with Texas recreational resources, fish species, angling techniques, etc. ------- 54 REFERENCES R.C. Bishop and T.A. Heberlein, Measuring values of extramarket goods: are indirect measures biased? Amer. J. Agr. Econom. 61, 926-930 (1979). R.C. Bishop, T.A. Heberlein, and M. J. Kealy, Contingent valuation of environmental assets: comparisons with a simulated market, Natural Resources J. 23, 619-633 (1983). T.A. Cameron, "A New Paradigm for Valuing Non-Market Goods Using Referendum Data: Maximum Likelihood Estimation by Censored Logistic Regression," forthcoming, Journal of Environmental Economics and Management, 1988. T.A. Cameron and D.D. Huppert, "OLS Versus ML Estimation of Non-Market Resource VAlues with Payment Card Interval Data," forthcoming, Journal of Environmental Economics and Management, 1989. T.A. Cameron and D.D. Huppert, "The Relative Efficiency of 'Payment Card' versus 'Referendum' Data in Non-market Resource Valuation," mimeo, Department of Economics, University of California, Los Angeles, 1988. T.A. Cameron and D.D. Huppert, "Measuring the Value of a Public Good: Further Remarks," mimeo, Department of Economics, University of California, Los Angeles, 1988. T.A. Cameron and M.D. James "The Determinants of Value for a Recreational Fishing Day: Estimates from a Contingent Valuation Survey," Department of Economics Discussion Paper #405, University of California, Los Angeles (1986). T.A. Cameron and M.D. James, Efficient estimation methods for use with 'closed-ended' contingent valuation survey data," Rev. Econom. Statist. (May 1987). R.G. Cummings, D.S. Brookshire, and W.D. Schulze (Eds.) "Valuing Environmental Goods: An Assessment of the Contingent Valuation Method," Rowman and Allanheld, Totowa, New Jersey (1986). W.M. Hanemann, Welfare evaluations in contingent valuation experiments with discrete responses, Amer. J. Agr. Econom. 66, 332-341 (1984). N.A.J. Hastings and J.B. Peacock, "Statistical Distributions," Wiley, New York (1975). J. Kmenta, "Elements of Econometrics," Macmillan, New York (1971). G.S. Maddala, "Limited-dependent and Qualitative Variables in Econometrics," Cambridge University Press, Cambridge (1983). D. McFadden, Quantal choice analysis: A survey, Ann. Econom. Soc. Measure. 5, 363-390 (1976). ------- 55 R.C. Mitchell and R.T. Carson, "Using Contingent Valuation Method," D.C. (forthcoming, 1988). C. Sellar, J.R. Stoll and J.P. Chavas, welfare change: a comparison 61, 156-175 (1985). Surveys to Value Public Goods: The Resources for the Future, Washington, Validation of empirical measures of of nonmarket techniques, Land Econom. C. Sellar, J.P. Chavas, and J.R. Stoll, Specification of the logit model: the case of valuation of nonmarket goods, J. Environ. Econom Management 13, 382-390 (1986). ------- SUPPLEMENTARY TABLES ------- Table A.l - Regressions of current catch on monthly and annual abundance measures for the species, market expenses, trip frequencies, and demographic variables by zip code. DEP VARIABLE: REDS VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP 0.55995251 0.30007121 MMREDS 0.36847595 0.23700779 AREDS -0.10965756 0.04224035 MON -0.000016971 0.000118226 NSWTRIP 0.000788784 0.000874304 SITETRIP 0.005368462 0.000797330 PRETIRED 0.85482835 0.72060800 PSPANISH 0.75937497 0.26831368 PSPNOENG 0.65719318 0.83394446 PVIETNAM -9.52181432 4.10336572 PURBAN -0.18475126 0.06936814 PTEXNATV -0.69407659 0.27218848 PFFFISH 4.39061789 1.80245578 HHLDINC 0.000012134 0.0000073043 1.866 1.555 -2.596 -0.144 0.902 6.733 1.186 2.830 0.788 -2.320 -2.663 -2.550 2.436 1.661 DEP VARIABLE: TROUT PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.32098798 0.96852747 0.331 MMTROUT 0.46025045 0.55181825 0.834 ATROUT -0.10727163 0.08659900 -1.239 MON 0.000344210 0.000391106 0.880 NSWTRIP 0.000856360 0.002804431 0.305 SITETRIP 0.008488526 0.002555053 3.322 PRETIRED -2.23625648 2.31717300 -0.965 PSPANISH 2.50439916 0.90968459 2.753 PSPNOENG -4.76702938 2.65016291 -1.799 PVIETNAM -10.54180776 13.22176053 -0.797 PURBAN 0.007574193 0.22341404 0.034 PTEXNATV 1.61013946 0.92900808 1.733 PFFFISH 4.43354471 5.80127597 0.764 HHLDINC 0.000016170 0.000023415 0.691 ------- Table A.l, continued DEP VARIABLE: CROAK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 3.30401254 0.98231253 3.364 MMCROAK -1.23508097 0.45744060 -2.700 ACROAK 0.08828395 0.09482006 0.931 MON -0.001526458 0.000391878 -3.895 NSWTRIP -0.006019254 0.002894183 -2.080 SITETRIP -0.001736803 0.002636454 -0.659 PRETIRED -3.96485185 2.37842920 -1.667 PSPANISH -9.44617850 0.91612331 -10.311 FSPNOENG 16.61375283 2.78349049 5.969 PVIETNAH 34.13699452 13.59965826 2.510 PURBAN 1.00645150 0.22970427 4.382 PTEXNATV 4.46549691 0.89550728 4.987 PFFFISH -26.83794821 5.96099955 -4.502 HHLDINC -0.000175471 0.000024158 -7.263 EP VARIABLE: SAND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 2.60203861 1.27890185 2.035 MMSAND 0.13525806 0.62965032 0.215 ASAND 0.34725560 0.12388076 2.803 MON 0.003049747 0.000506331 6.023 NSWTRIP 0.000772157 0.003762673 0.205 SITETRIP 0.002321740 0.003427697 0.677 PRETIRED -6.69928574 3.10020622 -2.161 PSPANISH -5.55781967 1.15362653 -4.818 PSPNOENG 8.36237511 3.52678402 2.371 PVIETNAH -37.14203944 17.67071748 -2.102 PURBAN 1.00236870 0.29815854 3.362 PTEXNATV 1.47548162 1.15738569 1.275 PFFFISH 18.26459246 7.73754036 2.361 HHLDINC -0.000122238 0.000031442 -3.888 ------- Table A.l, continued DEP VARIABLE: BLACK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP -0.21504911 0.15372003 -1.399 MMBLACK -0.03098885 0.11983304 -0.259 ABLACK 0.02454022 0.01586489 1.547 MON -0.000098978 0.000060809 -1.628 NSWTRIP -0.000610036 0.000452134 -1.349 SITETRIP 0.000872498 0.000411767 2.119 PRETIRED -0.51376786 0.37191902 -1.381 PSPANISH -0.88597982 0.13901951 -6.373 PSPNOENG 2.70210744 0.42860428 6.304 PVIETNAM -0.11057677 2.12731804 -0.052 PURBAN 0.04845612 0.03601018 1.346 PTEXNATV 0.66908968 0.13901599 4.813 PFFFISH 0.23180632 0.93050578 0.249 HHLDINC -.0000017218 .00000377165 -0.457 EP VARIABLE: SHEEP PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.06836968 0.21828737 0.313 MMSHEEP 0.12234247 0.15810969 0.774 ASHEEP -0.04147377 0.03175789 -1.306 MON 0.000139507 0.000087330 1.597 NSWTRIP 0.002547533 0.000636643 4.002 SITETRIP 0.000655088 0.000579990 1.129 PRETIRED -0.22178639 0.52319454 -0.424 PSPANISH 0.06904953 0.19867934 0.348 PSPNOENG -0.55274431 0.60979506 -0.906 PVIETNAM -2.34572452 3.01854217 -0.777 PURBAN 0.02545117 0.05043334 0.505 PTEXNATV -0.002006479 0.20671267 -0.010 PFFFISH 2.93979145 1.31880893 2.229 HHLDINC -.0000027911 .00000531521 -0.525 ------- Table A.l, continued •P VARIABLE: FLOUND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP -0.01970803 0.32426667 -0.061 MMFLOUND -0.61281021 0.20575268 -2.978 AFLOUND -0.15836960 0.03617201 -4.378 MON -0.000077295 0.000129670 -0.596 NSWTRIP 0.007868546 0.000943887 8.336 SITETRIP -0.000819604 0.000860134 -0.953 PRETIRED 1.13867584 0.78206752 1.456 PSPANISH -0.98520829 0.30517406 -3.228 PSPNOENG 2.04588931 0.91854214 2.227 PVIETNAM 1.06771366 4.44847267 0.240 PURBAN 0.16953815 0.07518352 2.255 PTEXNATV 0.63002837 0.30251588 2.083 PFFFISH -1.23657529 1.94501820 -0.636 HHLDINC -.0000037847 .00000789691 -0.479 ------- Table A.2 - Regressions of current catch on major bay and monthly dummy variables DEP VARIABLE: REDS PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.05034214 0.07581144 0.664 MJ1 0.09586074 0.16287253 0.589 MJ3 0.47034606 0.09943735 4.730 MJ4 0.41556795 0.12293509 3.380 MJ5 0.19918153 0.08094287 2.461 MJ6 0.19034190 0.07985535 2.384 MJ7 0.39698000 0.09674908 4.103 MJ8 0.87774944 0.08008518 10.960 MN5 0.04357481 0.09756501 0.447 MN6 0.04480128 0.09810146 0.457 MN8 0.20531995 0.08224176 2.497 MN9 0.38649084 0.08346977 4.630 MN10 0.39501347 0.08322912 4.746 MN11 0.26375298 0.10148514 2.599 :p VARIABLE: TROUT PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 2.02945978 0.24217103 8.380 MJ1 -0.30959043 0.52027779 -0.595 MJ3 0.60509801 0.31764131 1.905 MJ4 1.48200534 0.39270218 3.774 MJ5 -0.45785320 0.25856281 -1.771 MJ6 -0.23295552 0.25508884 -0.913 MJ7 1.81081777 0.30905394 5.859 MJ8 0.77603162 0.25582300 3.033 MN5 -0.19569724 0.31166034 -0.628 MN6 -0.61720332 0.31337396 -1.970 MN8 -0.37767862 0.26271195 -1.438 MN9 -0.51615104 0.26663468 -1.936 MN10 -0.43755749 0.26586596 -1.646 MN11 -0.08592488 0.32418277 -0.265 ------- Table A.2, continued DEP VARIABLE: CROAK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 1.80420655 0.25440856 7 .092 MJ1 0.15435967 0.54656879 0.282 MJ3 -1.44501071 0.33369255 -4.330 MJ4 -0.96835590 0.41254645 -2.347 MJ5 -1.22670089 0.27162867 -4.516 MJ6 0.12211734 0.26797915 0.456 MJ7 -0.80625121 0.32467124 -2.483 MJ8 -1.77502414 0.26875041 -6.605 MN5 -0.52584969 0.32740935 -1.606 MN6 -0.52478913 0.32920957 -1.594 MN8 1.30543161 0.27598747 4.730 MN9 0.54887768 0.28010843 1.960 MN10 0.24721955 0.27930087 0.885 MN11 -0.73844884 0.34056457 -2.168 EP VARIABLE: SAND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 1.49360615 0.32742378 4.562 MJ1 -1.75665494 0.70343395 -2.497 MJ3 -1.55240358 0.42946227 -3.615 MJ4 -1.25885186 0.53094723 -2.371 MJ5 -1.05708742 0.34958605 -3.024 MJ6 -1.56950545 0.34488913 -4.551 MJ7 -2.36323791 0.41785184 -5.656 MJ8 -1.87517327 0.34588174 -5.421 MN5 0.39706249 0.42137579 0.942 MN6 -0.32002563 0.42369266 -0.755 MN8 0.63333692 0.35519583 1.783 MN9 0.43997674 0.36049951 1.220 MNIO 0.84778208 0.35946017 2.358 MN11 2.84404560 0.43830655 6.489 ------- Table A.2, continued DEP VARIABLE: BLACK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.20731884 0.03932264 5.272 MJ1 -0.02152089 0.08448036 -0.255 MJ3 -0.12508682 0.05157716 -2.425 MJ4 -0.12285552 0.06376521 -1.927 MJ5 -0.15597693 0.04198426 -3.715 MJ6 -0.11956589 0.04142017 -2.887 MJ7 -0.13773178 0.05018278 -2.745 MJ8 -0.15204360 0.04153938 -3.660 MN5 -0.07209143 0.05060600 -1.425 MN6 -0.04345460 0.05088425 -0.854 MN8 -0.01226179 0.04265798 -0.287 MN9 0.02200455 0.04329494 0.508 MN10 0.14766722 0.04317011 3.421 MN11 0.05904913 0.05263933 1.122 DEP VARIABLE: SHEEP PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.12359373 0.05514031 2.241 MJ1 -0.19739614 0.11846289 -1.666 MJ3 -0.01479838 0.07232426 -0.205 MJ4 -0.06177563 0.08941499 -0.691 MJ5 -0.07825227 0.05887258 -1.329 MJ6 -0.14568843 0.05808159 -2.508 MJ7 -0.24692556 0.07036899 -3.509 MJ8 -0.15689291 0.05824875 -2.693 MN5 0.05152056 0.07096245 0.726 MN6 -0.007780611 0.07135262 -0.109 MN8 0.03604168 0.05981731 0.603 MN9 -0.004137654 0.06071048 -0.068 MN10 0.05014380 0.06053545 0.828 MN11 0.47535803 0.07381370 6.440 ------- Table A.2, continued IP VARIABLE: FLOUND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.82159657 0.08199456 10.020 MJ1 -0.31496533 0.17615627 -1.788 MJ3 -0.30390463 0.10754737 -2.826 MJ4 -0.63615308 0.13296157 -4.784 MJ5 -0.79315402 0.08754450 -9.060 MJ6 -0.79126378 0.08636828 -9.162 MJ7 -0.73886256 0.10463985 -7.061 MJ8 -0.63585291 0.08661686 -7.341 MN5 0.06951967 0.10552233 0.659 MN6 0.13816270 0.10610253 1.302 MN8 0.15535632 0.08894932 1. 747 MN9 0.05658948 0.09027749 0.627 MN10 0.23391866 0.09001721 2.599 MN11 0.78029069 0.10976219 7.109 ------- Table A.3 - Regressions of current catch on monthly abundance index, demographic variables, and major bay dummy variables DEP VARIABLE: REDS PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.08249090 0.30620085 0.269 MMREDS 0.31460321 0.24591373 1.279 MON -0.000126631 0.000119475 -1.060 NSWTRIP 0.000997362 0.000871506 1.144 SITETRIP 0.005338593 0.000792004 6.741 PRETIRED 0.40792992 0.72216553 0.565 PSPANISH 0.94774237 0.29027646 3.265 PSPNOENG -1.92730218 0.94335117 -2.043 PVIETNAM -6.30008634 4.13511627 -1.524 PURBAN -0.17926668 0.06960719 -2.575 PTEXNATV -0.35985526 0.28079594 -1.282 PFFFISH 4.06562241 1.79684467 2.263 HHLDINC 0.000014557 .00000727471 2.001 MJ1 0.22117083 0.16308096 1.356 MJ3 0.41258319 0.10128207 4.074 MJ4 0.29340746 0.11918553 2.462 MJ5 0.11045001 0.08697339 1.270 MJ6 0.14403815 0.08637686 1.668 MJ7 0.36564235 0.09914413 3.688 MJ8 0.80571613 0.09778452 8.240 DEP VARIABLE: TROUT VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP 0.32926072 0.98058040 MMTROUT 0.72672191 0.51692313 MON 0.000418306 0.000383818 NSWTRIP 0.001301984 0.002790464 SITETRIP 0.009021724 0.002535271 PRETIRED -1.40101257 2.31274943 PSPANISH 2.38954617 0.93836731 PSPNOENG -6.87307423 3.02935838 PVIETNAM -5.11369468 13.24493296 PURBAN -0.08751728 0.22300185 PTEXNATV 1.51843888 0.90477954 PFFFISH 1.66646879 5.76057977 HHLDINC 0.000014731 0.000023296 MJ1 -0.12522173 0.51372014 MJ3 0.46603374 0.32238217 MJ4 1.42956747 0.38169115 MJ5 -0.73896336 0.29216032 MJ6 -0.56608140 0.27586664 MJ7 1.58614179 0.30245190 MJ8 0.62707082 0.32306103 0.336 1.406 1.090 0.467 3.558 -0.606 2.546 -2.269 -0.386 -0.392 1.678 0.289 0.632 -0.244 1.446 3.745 -2.529 -2.052 5.244 1.941 ------- Table A.3, continued EP VARIABLE: CROAK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 2.66756373 1.00525808 2.654 MMCROAK -3.98638283 0.40759600 -9.780 MON -0.001477013 0.000392887 -3.759 NSWTRIP -0.006107054 0.002860786 -2.135 SITETRIP -0.001945570 0.002599357 -0.748 PRETIRED -2.84572618 2.37166305 -1.200 PSPANISH -10.44237560 0.96981335 -10.767 PSPNOENG 21.96652769 3.12265143 7.035 PVIETNAM 42.50799742 13.57571203 3.131 PURBAN 0.88205153 0.22857272 3.859 PTEXNATV 4.60465670 0.92367915 4.985 PFFFISH -25.60229589 5.90128326 -4.338 HHLDINC -0.000159420 0.000023899 -6.671 MJ1 -1.32428223 0.52467711 -2.524 MJ3 -1.26997939 0.32994369 -3.849 MJ4 -1.09222587 0.39260972 -2.782 MJ5 -0.23015884 0.28546340 -0.806 MJ6 2.96516199 0.32860335 9.024 MJ7 -0.10117965 0.31440281 -0.322 MJ8 -0.30969034 0.32172324 -0.963 EP VARIABLE: SAND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 3.49528262 1.33092771 2.626 MMSAND 0.72768171 0.58049126 1.254 MON 0.003208116 0.000516215 6.215 NSWTRIP 0.000111362 0.003769108 0.030 SITETRIP 0.002300422 0.003424049 0.672 PRETIRED -6.18159589 3.12377497 -1.979 PSPANISH -4.92447442 1.25551174 -3.922 PSPNOENG 8.32102379 4.07928230 2.040 PVIETNAM -43.08458320 17.88205173 -2.409 PURBAN 0.98033470 0.30113908 3.255 PTEXNATV 1.59438668 1.21376362 1.314 PFFFISH 20.77898656 7.76855507 2.675 HHLDINC -0.000125297 0.000031474 -3.981 MJ1 -1.26918171 0.70113740 -1.810 MJ3 -1.80970744 0.44122254 -4.102 MJ4 -1.69999347 0.55660418 -3.054 MJ5 -0.93288233 0.41761009 -2.234 MJ6 -1.51242967 0.37264711 -4.059 MJ7 -1.47083745 0.46585384 -3.157 MJ8 -1.88560063 0.44713447 -4.217 ------- Table A.3, continued i? VARIABLE: BLACK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP -0.06527348 0.15959629 -0.409 MMBLACK -0.03127245 0.12061281 -0.259 MON -0.000069184 0.000062054 -1.115 NSWTRIP -0.000675180 0.000452805 -1.491 SITETRIP 0.000844350 0.000411388 2.052 PRETIRED -0.38407660 0.37526227 -1.023 PSPANISH -0.81824332 0.15091174 -5.422 PSPNOENG 2.86581250 0.49012528 5.847 PVIETNAM -1.20317407 2.14842043 -0.560 PURBAN 0.04742877 0.03617276 1.311 PTEXNATV 0.58276254 0.14602230 3.991 PFFFISH 0.39924427 0.93388199 0.428 HHLDINC -.0000024413 .00000378035 -0.646 MJ1 -0.04210067 0.08343432 -0.505 MJ3 -0.12673404 0.05401686 -2.346 MJ4 -0.15692987 0.06429929 -2.441 MJ5 -0.11390689 0.04643952 -2.453 MJ 6 -0.06697295 0.04542878 -1.474 MJ7 -0.10752456 0.04999241 -2.151 MJ8 -0.21494500 0.05137572 -4.184 EP VARIABLE: SHEEP PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.18397633 0.22424085 0.820 MMSHEEP 0.19706534 0.16868340 1.168 MON 0.000146931 0.000087682 1.676 NSWTRIP 0.002501075 0.000638205 3.919 SITETRIP 0.000654810 0.000579796 1.129 PRETIRED -0.10899880 0.52896178 -0.206 PSPANISH 0.18634607 0.21297531 0.875 PSPNOENG -0.98841053 0.69064803 -1.431 PVIETNAM -3.18386372 3.02844868 -1.051 PURBAN 0.02463802 0.05097815 0.483 PTEXNATV 0.03107763 0.20624852 0.151 PFFFISH 2.90768177 1.32049588 2.202 HHLDINC -.0000038586 .00000532886 -0.724 MJ1 -0.11879970 0.11723539 -1.013 MJ3 -0.08906114 0.07379417 -1.207 MJ4 -0.18881993 0.09180317 -2.057 MJ5 -0.11501370 0.06391136 -1.800 MJ6 -0.16932811 0.06321095 -2.679 MJ7 -0.21894058 0.06971473 -3.141 MJ8 -0.22701709 0.08198620 -2.769 ------- Table A.3, continued :P VARIABLE: FLOUND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 0.21204966 0.33183132 0.639 MMFLOUND -0.49321815 0.21939866 -2.248 MON -0.000066724 0.000129246 -0.516 NSWTRIP 0.007551138 0.000943757 8.001 SITETRIP -0.000819620 0.000857429 -0.956 PRETIRED 1.36027395 0.78225188 1.739 PSPANISH -0.71324691 0.31584173 -2.258 PSPNOENG 0.81296362 1.02514679 0.793 PVIETNAM 0.52069004 4.47714546 0.116 PURBAN 0.16554232 0.07538672 2.196 PTEXNATV 0.93747057 0.30394040 3.084 PFFFISH -0.37430053 1.94690673 -0.192 HHLDINC -.0000050267 .00000787969 -0.638 MJ1 -0.35044016 0.17397636 -2.014 MJ3 -0.43350722 0.10925459 -3.968 MJ4 -0.80589558 0.12901976 -6.246 MJ5 -0.65223380 0.10370180 -6.290 MJ6 -0.63117761 0.09957913 -6.338 MJ7 -0.55085946 0.10597766 -5.198 MJ8 -0.42631471 0.10855894 -3.927 ------- Table A.4a - Average "Annual" Actual Catch Rates by Sample Respondents (for May-Nov 1987); by Major Bay System MAJOR AAREDS AATROUT AACROAK AASAND AABLACK AASHEEP AAFLOUND 1 2 3 4 5 6 7 8 0.35000 0.21942 0.70226 0.57912 0.42059 0.45898 0.62898 1.16386 1.44286 1.68155 2.34292 3.36027 1.29244 1.45691 3.56847 2.48221 1.63571 1.92039 0.46612 0.99663 0.75575 2.21288 1.31051 0.33708 0.75714 1.93689 0.19713 0.36364 1.05586 0.63344 0.15446 0.23034 0.214286 0.219417 0.117043 0.090909 0.062432 0.115265 0.057325 0.086142 0.064286 0.172816 0.119097 0.060606 0.118291 0.055036 0.007962 0.014045 0.785714 0.982524 0.603696 0.202020 0.205915 0.236760 0.340764 0.331461 Table A.4b - OLS Regressions of Actual Individual Catch Rates on Average Rates for Sample Anglers (for each bay and month, MAxxxxxx, and for each bay, AAxxxxxx). DEP VARIABLE: REDS PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP -0.12266561 0.29823802 -0.411 MAREDS 0.95085659 0.08092220 11.750 AAREDS -0.05043007 0.12278424 -0.411 MON -0.000092812 0.000115702 -0.802 NSWTRIP 0.000923382 0.000857973 1.076 SITETRIP 0.005093002 0.000781527 6.517 PRETIRED 0.45725770 0.70551913 0.648 PSPANISH 0.72133204 0.26179804 2.755 PSPNOENG -1.22854525 0.82771249 -1.484 PVIETNAM -4.92451856 4.04183705 -1.218 PURBAN -0.18016933 0.06794174 -2.652 PTEXNATV -0.34731022 0.26481849 -1.312 PFFFISH 2.72013126 1.76799000 1.539 HHLDINC 0.000013987 .00000716232 1.953 ------- Table A.4b, continued DEP VARIABLE: VARIABLE INTERCEP MATROUT AATROUT MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC TROUT PARAMETER ESTIMATE -1.36523478 0.98197610 0.006042790 0.000286035 0.001863515 0.008918273 -1.43720691 1.43940886 -3.82852658 -2.07403981 -0.07554478 1.53446304 -1.98870119 0.000010671 STANDARD ERROR 0.94998077 0.10033556 0.14070736 0.000370669 0.002757012 0.002511557 2.26629296 0.84354198 2.58495718 12.94627157 0.21864170 0.84795042 5.68333396 0.000023018 DEP VARIABLE: VARIABLE INTERCEP MACROAK AACROAK MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC CROAK PARAMETER ESTIMATE 1.81057461 0.83774972 0.11396771 -0.001215592 -0.005338101 -0.001572947 -1.90685717 -8.60976875 18.04502300 31.27438550 0.82502684 3.72817129 -21.13769899 -0.000159098 STANDARD ERROR 0.97371072 0.06864557 0.13693499 0.000383033 0.002844955 0.002590113 2.34453169 0.88171963 2.73232498 13.34679054 0.22594926 0.87567771 5.86344930 0.000023783 T FOR HO: PARAMETER-0 -1.437 9.787 0.043 0.772 0.676 3.551 -0.634 1.706 -1.481 -0.160 -0.346 1.810 -0.350 0.464 T FOR HO: PARAMETER-0 1.859 12.204 0.832 -3.174 -1.876 -0.607 -0.813 -9.765 6.604 2.343 3.651 4.257 -3.605 -6.690 ------- Table A.4b, continued DEP VARIABLE: SAND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 1.04106408 1.26437786 0.823 MASAND 0.98233478 0.07436923 13.209 AASAND 0.11303100 0.18715312 0.604 MON 0.003017771 0.000497673 6.064 NSWTRIP -0.001733434 0.003701859 -0.468 SITETRIP 0.000968215 0.003369551 0.287 PRETIRED -5.89965190 3.04239513 -1.939 PSPANISH -4.58440729 1.14376694 -4.008 PSPNOENG 7.47884232 3.46885734 2.156 PVIETNAM -46.01016400 17.40831290 -2.643 PURBAN 0.91626869 0.29301929 3.127 PTEXNATV 1.94350416 1.13489728 1.712 PFFFISH 18.23397447 7.61793262 2.394 HHLDINC -0.000110765 0.000030901 -3.585 SP VARIABLE: BLACK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP -0.29092946 0.15268688 -1.905 MABLACK 0.96665317 0.09114036 10.606 AABLACK -0.09573732 0.25278827 -0.379 MON -0.000071042 0.000060670 -1.171 NSWTRIP -0.000674880 0.000447214 -1.509 SITETRIP 0.000671392 0.000407375 1.648 PRETIRED -0.26273281 0.36938636 -0.711 PSPANISH -0.61890961 0.14299078 -4.328 PSPNOENG 2.06309845 0.43075110 4.790 PVIETNAM -0.74833926 2.10625389 -0.355 PURBAN 0.04133539 0.03551921 1.164 PTEXNATV 0.53988053 0.13864906 3.894 PFFFISH 0.35225404 0.92028645 0.383 HHLDINC -5.35967E-07 .00000374053 -0.143 ------- Table A.4b, continued DEP VARIABLE: VARIABLE INTERCEP MASHEEP AASHEEP MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC SHEEP PARAMETER ESTIMATE -0.09047019 0.99441736 0.04962667 0.000051587 0.002201864 0.000382545 0.05006948 0.01381854 -0.32208556 -3.32365172 0.04434566 0.04907053 2.55337512 -.0000014707 STANDARD ERROR 0.20353089 0.03670434 0.31134446 0.000080557 0.000597400 0.000544200 0.49119093 0.18550590 0.55982006 2.82850803 0.04734667 0.18406197 1.22902375 00000499508 DEP VARIABLE: VARIABLE INTERCEP MAFLOUND AAFLOUND MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC FLOUND PARAMETER ESTIMATE -0.61623401 0.97594742 -0.02153132 -0.000030626 0.006652809 -0.001277307 1.44956602 -0.43520381 0.72106186 -1.86240792 0.09270761 0.70903598 -0.33088056 -4.07689E-07 STANDARD ERROR 0.31048537 0.05182762 0.10986631 0.000124319 0.000914079 0.000831043 0.75447296 0.29352799 0.88677081 4.30327459 0.07250692 0.28266255 1.87895111 00000763403 T FOR HO: PARAMETER-0 -0.445 27.093 0.159 0.640 3.686 0.703 0.102 0.074 -0.575 -1.175 0.937 0.267 2.078 -0.294 T FOR HO: PARAMETER-0 -1.985 18.831 -0.196 -0.246 7.278 -1.537 1.921 -1.483 0.813 -0.433 1.279 2.508 -0.176 -0.053 ------- Table A.4c - OLS Regressions of Actual Individual Catch Rates on "Annual" Average Catch Rates (by bay system, AAxxxxxx) DEP VARIABLE: VARIABLE INTERCEP AAREDS MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC DEP VARIABLE: VARIABLE INTERCEP AATROUT MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC REDS PARAMETER ESTIMATE -0.17221294 0.88499989 -0.000142307 0.001071111 0.005384716 0.33591552 0.82939290 -1.50245838 -6.08247392 -0.17038106 -0.32388801 4.01044819 0.000014969 TROUT PARAMETER ESTIMATE -1.46919676 0.97625433 0.000416560 0.001431302 0.009029381 -1.53660877 2.05603824 -5.21985591 -4.62037204 -0.07380018 1.39479051 1.56510528 0.000015985 STANDARD ERROR 0.30189259 0.09463395 0.000117054 0.000868480 0.000790784 0.71415935 0.26486900 0.83760654 4.09055782 0.06877599 0.26808275 1.78637790 00000725031 STANDARD ERROR 0.95805247 0.10071020 0.000373599 0.002780255 0.002533030 2.28566892 0.84838605 2.60313817 13.05445151 0.22051315 0.85508754 5.72027055 0.000023209 T FOR HO: PARAMETF.R-0 -0.570 9.352 -1.216 1.233 6.809 0.470 3.131 -1.794 -1.487 -2.477 -1.208 2.245 2.065 T FOR HO: PARAMETER-0 -1.534 9.694 1.115 0.515 3.565 -0.672 2.423 -2.005 -0.354 -0.335 1.631 0.274 0.689 ------- Table A.4c, continued DEP VARIABLE: CROAK PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 2.28572714 0.98589955 2.318 AACROAK 0.91638532 0.12171787 7.529 MON -0.001416135 0.000387781 -3.652 NSUTRIP -0.006336075 0.002881682 -2.199 SITETRIP -0.001620966 0.002624632 -0.618 PRETIRED -2.73498544 2.37478506 -1.152 PSPANISH -10.42514263 0.88066463 -11.838 PSPNOENG 22.06274250 2.74857122 8.027 PVIETNAM 35.64921090 13.51980165 2.637 PURBAN 0.87878673 0.22891726 3.839 PTEXNATV 4.15492950 0.88664122 4.686 PFFFISH -26.48857430 5.92496424 -4.471 HHLDINC -0.000177231 0.000024053 -7.368 EP VARIABLE: SAND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 1.41489731 1.28379481 1.102 AASAND 1.08298286 0.17483291 6.194 MON 0.003137767 0.000505358 6.209 NSWTRIP 0.000235592 0.003756601 0.063 SITETRIP 0.002220311 0.003420799 0.649 PRETIRED -6.59692145 3.08942598 -2.135 PSPANISH -4.84730866 1.16144683 -4.174 PSPNOENG 7.61299788 3.52299589 2.161 PVIETNAM -43.06236011 17.67862787 -2.436 PURBAN 0.98954192 0.29754040 3.326 PTEXNATV 1.73664712 1.15250486 1.507 PFFFISH 20.49016673 7.73491401 2.649 HHLDINC -0.000123535 0.000031368 -3.938 ------- Table A.4c, continued DEP VARIABLE: VARIABLE INTERCEP AABLACK MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAH PURBAN PTEXNATV PFFFISH HHLDINC BLACK PARAMETER ESTIMATE -0.26300398 0.84957965 -0.000073271 -0.000649917 0.000826483 -0.40638490 -0.70453147 2.21811495 -1.10922521 0.04450246 0.59054447 0.35238792 -.0000025102 STANDARD ERROR 0.15420014 0.23893440 0.000061280 0.000451707 0.000411208 0.37285190 0.14419906 0.43483440 2.12716746 0.03587531 0.13996088 0.92954552 00000377348 DEP VARIABLE: VARIABLE INTERCEP AASHEEP MON NSWTRIP SITETRIP PRETIRED PSPANISH PSPNOENG PVIETNAM PURBAN PTEXNATV PFFFISH HHLDINC SHEEP PARAMETER ESTIMATE -0.03535211 1.14481671 0.000147038 0.002511729 0.000648276 -0.16218767 0.14164609 -0.72252764 -3.27210423 0.03013284 0.01242447 2.98360822 -.0000038444 STANDARD ERROR 0.21662870 0.32859181 0.000085663 0.000635759 0.000579156 0.52276013 0.19738974 0.59566819 3.01068062 0.05039299 0.19591140 1.30807122 00000531597 T FOR HO: PARAMETER-0 -1.706 3.556 -1.196 -1.439 2.010 -1.090 -4.886 5.101 -0.521 1.240 4.219 0.379 -0.665 T FOR HO: PARAMETER-0 -0.163 3.484 1.716 3.951 1.119 -0.310 0.718 -1.213 -1.087 0.598 0.063 2.281 -0.723 ------- Table A.4c, continued DEP VARIABLE: FLOUND PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP -0.59237667 0.32028494 -1.850 AAFLOUND 0.92591610 0.10075174 9.190 MON -0.000037291 0.000128243 -0.291 NSWTRIP 0.007522444 0.000941733 7.988 SITETRIP -0.000864638 0.000856981 -1.009 PRETIRED 1.39301161 0.77828601 1.790 PSPANISH -0.65905648 0.30254645 -2.178 PSPNOENG 1.15633766 0.91445592 1.265 PVIETNAM -0.40499133 4.43841383 -0.091 PURBAN 0.16577954 0.07468882 2.220 PTEXNATV 0.77931103 0.29156099 2.673 PFFFISH -0.12527303 1.93823814 -0.065 HHLDINC -.0000051086 .00000787083 -0.649 ------- Table A.5 - Precrip Motivation Questions: OLS Regressions DEP VARIABLE: N'OPEOPLE F-TEST 0.943 OBS 603 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP TARGR TARGT TARGF MJ1 MJ3 MJ4 MJ5 MJ 6 MJ7 MJ8 MN5 MN6 MN8 MN9 MN10 MN11 WKND 7.59185247 0.52836370 -0.34403082 0.47487337 0.64433020 0.84117457 0.23616653 0.34060028 0.27210277 0.27241992 0.46534192 -0.04077979 -0.04905820 -0.37063712 0.32841948 -0.19742662 -0.09581740 -0.01828012 0.44738621 0.24653310 0.24382515 0.47290029 0.41974765 0.46032060 0.44200330 0.46624780 0.50602718 0.54607083 0.41754746 0.38895224 0.34417911 0.35045962 0.39216770 0.36166775 0.44172970 0.21044572 16.969 2.143 -1.411 1.004 1.535 1.827 0.534 0.731 0.538 0.499 1.114 -0.105 -0.143 -1.058 0.837 -0.546 -0.217 -0.087 DEP VARIABLE: NOPOLLUT T-TEST C 791 OBS 429 PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 9.28862007 0.32744825 28.367 TARGR -0.06010503 0.19483745 -0.308 TARGT 0.02721384 0.18658810 0.146 TARGF -0.18077773 0.37549661 -0.481 MJ1 0.13636153 0.30518053 0.447 MJ3 0.06243266 0.36528564 0.171 MJ4 -0.18281956 0.27396226 -0.667 MJ5 -0.40245959 0.35735465 -1.126 MJ6 -0.14210375 0.33100665 -0.429 MJ7 0.02401744 0.32870964 0.073 MJ8 0.08025961 0.27896454 0.288 MN5 -0.007657418 0.31921439 -0.024 MN6 0.08823009 0.32933579 0.268 MN8 0.19207957 0.25276985 0.760 MN9 0.25429200 0.27247807 0.933 MN10 -0.39582402 0.27040307 -1.464 MN11 -0.28337536 0.32430722 -0.874 WKND 0.10035740 0.19787569 0.507 ------- DEP VARIABLE: DOWHTWNT F-TEST OBS 1.385 503 VARIABLE INTERCEP TARGR TARGT TARGF MJ1 MJ3 MJ4 MJ5 MJ 6 MJ7 MJ8 MN5 MN6 MN8 MN9 MN10 MN11 WKND PARAMETER ESTIMATE 7.70993748 -0.19641401 0.10541805 0.26082970 0.80886667 1.33626023 0.77824468 0.80050893 0.48155068 1.08142499 0.89569917 0.50210737 0.09873351 0.60081590 -0.13628211 0.002551616 0.19458545 0.14459588 STANDARD ERROR 0.44125530 0.21523229 0.21296736 0.39672252 0.48840354 0.43315279 0.43810012 0.42618053 0.40874203 0.43207201 0.44663572 0.40968952 0.31592841 0.37690952 0.31189957 0.35379013 0.39803834 0.25298011 T FOR HO: PARAMETER-0 17.473 -0.913 0.495 0.657 1.656 3.085 1.776 1.878 1.178 2.503 2.005 1.226 0.313 1.594 -0.437 0.007 0.489 0.572 DEP VARIABLE: KEEPFISH F-TEST OBS 2.619 536 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP TARGR TARGT TARGF MJ 1 MJ3 MJ4 MJ 5 MJ 6 MJ7 MJ8 MN5 MN6 MN8 MN9 MN10 MN11 WKND 8.09163143 -0.63493893 -0.03000512 1.16005118 -0.67785857 -0.89785739 -0.21607825 -1.01361087 -1.04931986 -0.41688883 -0.25730722 -0.14119910 0.22085293 -0.63595454 1.45515992 0.18826575 -0.67293081 0.21160550 0.39754566 0.28813687 0.28608262 0.51360011 0.48409302 0.42731459 0.51354355 0.52192311 0.49730779 0.45091149 0.45696247 0.54846485 0.39028515 0.36390967 0.48851570 0.36217584 0.44317159 0.26132905 20.354 -2.204 -0.105 2.259 -1.400 -2.101 -0.421 -1.942 -2.110 -0.925 -0.563 -0.257 0.566 -1.748 2.979 0.520 -1.518 0.810 ------- DEP VARIABLE: QUIETIME F-TEST OBS 1.579 482 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP TARGR TARGT TARGF MJ1 MJ3 MJ4 MJ5 MJ6 MJ7 MJ8 MN5 MN6 MN8 MN9 MNIO MN11 WKND 8.33047553 -0.14268653 •0.18754912 0.03336624 •0.73609622 •0.70451833 •0.56445054 •1.14804492 •1.34006483 ¦0.29360849 0.04573877 ¦0.81118400 ¦0.09321641 0.08157845 •0.10180406 0.22701246 •0.45980224 •0.05979884 0. 0. 0.58638878 0.29999957 0.30534004 0.48896232 0.69983581 .71501660 .70372958 0.69315901 0.68904331 0.69167542 0.74465338 0.47981448 0.41382943 0.44580404 0.53428439 0.40778226 0.53274809 0.32476937 14.206 -0.476 -0.614 0.068 -1.052 -0.985 -0.802 -1.656 -1.945 -0.424 0.061 -1.691 -0.225 0.183 -0.191 0.557 -0.863 -0.184 DEP VARIABLE: GOODWTHR F-TEST OBS 2.759 381 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP TARGR TARGT TARGF MJ1 MJ3 MJ4 MJ5 MJ 6 MJ7 MJ8 MN5 MN6 MN8 MN9 MNIO MN11 WKND 7.09707233 -0.48646878 0.51229235 -1.49302896 0.40571747 1.09149043 0.72597107 0.48019072 1.23645655 -0.26498057 0.22708658 -0.31701387 1.28035717 0.14411618 1.14428728 0.49489729 0.57428481 0.34439790 0.43106770 0.32599391 0.33760558 0.49194356 0.49441812 0.56904719 0.44476911 0.58953742 0.46327764 0.44679878 0.46512018 0.38871104 0.60295514 0.46022680 0.46974240 0.43572265 0.45843956 0.25591639 16.464 -1.492 1.517 -3.035 0.821 1.918 1.632 0.815 2.669 -0.593 0.488 -0.816 2.123 0.313 2.436 1.136 1.253 1.346 ------- DEP VARIABLE: FRNDFMLY F-TEST OBS 1.233 406 VARIABLE INTERCEP TARGR TARGT TARGF MJ1 MJ3 MJ4 MJ5 MJ6 MJ7 MJ8 MN5 MN6 MN8 MN9 MN10 MN11 WKND PARAMETER ESTIMATE 8.54110823 -0.59800573 0.15487751 0.46287229 0.20963175 0.66950705 0.25996020 0.46650183 0.60614119 -0.09825039 0.17366924 -1.35708719 0.35442366 0.09749444 0.15200115 0.45811705 0.19319351 0.13095893 STANDARD ERROR 0.46254806 0.25565774 0.25328885 0.40689201 0.44760664 0.46462665 0.42541605 0.43289498 0.55775904 0.43264822 0.40604008 0.70293279 0.34017854 0.32599378 0.39173057 0.33971443 0.47315411 0.23814544 T FOR HO: PARAMETER-0 18.465 -2.339 0.611 1.138 0.468 1.441 0.611 1.078 1.087 -0.227 0.428 -1.931 1.042 0.299 0.388 1.349 0.408 0.550 DEP VARIABLE: ADVNEXCT F-TEST OBS 1.267 443 VARIABLE INTERCEP TARGR TARGT TARGF MJ1 MJ3 MJ4 MJ5 MJ6 MJ7 MJ8 MN5 MN6 MN8 MN9 MN10 MN11 WKND PARAMETER ESTIMATE 7.25608143 0.23528665 -0.26195517 -0.14838342 0.03723037 -0.92314231 -0.04891245 1.01363017 -0.83621541 0.03118484 0.49056525 -0.01289834 0.04472742 -0.34816497 -0.55696234 -0.20256002 0.49999921 0.44184453 STANDARD ERROR 0.61347890 0.31342257 0.30524996 0.47233401 0.54138594 0.71890424 0.51960706 0.56859825 0.60606846 0.49129926 0.53133745 0.53358967 0.49114189 0.46015875 0.54623163 0.52433722 0.52655699 0.26438608 T FOR HO: PARAMETER-0 11.828 0.751 -0.858 -0.314 0.069 -1.284 -0.094 1.783 -1.380 0.063 0.923 -0.024 0.091 -0.757 -1.020 -0.386 0.950 1.671 ------- Table A,5, continued DEP VARIABLE: PRERELX F-TEST 1.585 OBS 3722 PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 8.78987067 0.13274228 66.218 TARGR -0.08702046 0.08311952 -1.047 TARGT -0.02271869 0.08253455 -0.275 TARGF -0.05306643 0.14142803 -0.375 MJ1 -0.009755689 0.13606929 -0.072 MJ3 -0.25145705 0.14111326 -1.782 MJ4 -0.36764056 0.13622517 -2.699 MJ5 0.03227412 0.14489392 0.223 MJ6 0.008712145 0.14303434 0.061 MJ7 0.05884559 0.13821775 0.426 MJ8 -0.003183858 0.13112852 -0.024 MN5 0.01144559 0.12708450 0.090 MN6 -0.02560113 0.11183769 -0.229 MN8 0.13506010 0.10587769 1.276 MN9 0.01645299 0.12161881 0.135 MN10 0.12827553 0.10739298 1.194 MN11 0.08320163 0.13371926 0.622 WKND -0.01423466 0.06462206 -0.220 DEP VARIABLE: PRECAT F-TEST 2.063 OBS 3722 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T FOR HO: PARAMETER-0 INTERCEP 6.56236349 0.17428059 37.654 TARGR 0.09004818 0.10912966 0.825 TARGT 0.12237258 0.10836163 1.129 TARGF 0.52153433 0.18568432 2.809 MJ1 0.15331075 0.17864870 0.858 MJ3 -0.17609374 0.18527106 -0.950 MJ4 0.17431650 0.17885337 0.975 MJ5 0.15514299 0.19023478 0.816 MJ6 0.54007251 0.18779330 2.876 MJ7 0.15005384 0.18146947 0.827 MJ8 0.30449474 0.17216185 1.769 MN5 -0.10320669 0.16685235 -0.619 MN6 -0.22755882 0.14683444 -1.550 MN8 0.04694627 0.13900941 0.338 MN9 -0.14802188 0.15967631 -0.927 MN10 -0.10164869 0.14099887 -0.721 MN11 0.05654611 0.17556329 0.322 WKND 0.11237509 0.08484389 1.324 ------- Table A.6 - For sample interviewed both before and after fishing trip; demographic, geographic, and seasonal variables and their effects on extent to which "unpolluted natural surroundings are a motivation for going fishing. DEP VARIABLE: NOPOLLUT F-TEST 1.569 OBS 85 PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 19.31015380 26.92078701 0.717 HHLDINC -0.000493022 0.000514831 -0.958 PRETIRED -42.07217646 41.08032759 -1.024 PTEXNATV -1.35518067 28.42559659 -0.048 PSPNOENG 6.58063295 39.05040280 0.169 PVIETNAM -109.12039 406.35400 -0.269 PURBAN 0.18671766 5.03175573 0.037 SITETRIP 0.04004085 0.01082416 3.699 NSWTRIP 0.02132592 0.10230115 0.208 MON 0.005535399 0.01279516 0.433 MJ1 -4.17274793 8.79692225 -0.474 MJ3 -9.84498903 9.81685770 -1.003 MJ4 1.22590283 8.62253424 0.142 MJ5 -2.43125737 8.03930377 -0.302 MJ6 4.13690974 6.64660300 0.622 MJ7 -5.69727465 6.63558981 -0.859 MJ8 -15.01756379 8.27448287 -1.815 MN5 9.44642008 7.95520190 1.187 MN6 4.20898200 7.25488897 0.580 MN8 8.30827846 6.19106440 1.342 MN9 4.44008039 6.2385 3464 0.712 MN10 0.94326577 5.99986399 0.157 MN11 11.91217331 6.72034145 1.773 WKND 2.07968018 4.75885531 0.437 ------- Table A. 7 - Extent to which respondents were able to "Experience Unpolluted Natural Surroundings." (n-858) IF VARIABLE: NOPOLLUT PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 8.42190686 1.00903630 8.346 HHLDINC -0.000011214 0.000022673 -0.495 PRETIRED 1.58102890 1.96850152 0.803 PTEXNATV -0.61188444 0.85289639 -0.717 PSPNOENG -1.28938826 1.51495547 -0.851 PVIETNAM 19.42599903 11.87295215 1.636 PURBAN 0.08369006 0.19819351 0.422 MJ1 -0.86422020 0.36986443 -2.337 MJ3 0.32246599 0.38965319 0.828 MJ4 0.64005519 0.25369335 2.523 MJ5 1.01771109 0.35532066 2.864 MJ6 0.10662209 0.31278854 0.341 MJ7 0.46076012 0.29608459 1.556 MJ8 0.88094389 0.32441647 2.715 MN5 0.22148059 0.35923225 0.617 MN6 -0.69695574 0.29829741 -2.336 MN8 -0.02393900 0.22370082 -0.107 MN9 -0.18379131 0.27529979 -0.668 MN10 -0.02430656 0.26243870 -0.093 MN11 0.45402552 0.35517060 1.278 WKND -0.16900558 0.19266161 -0.877 ------- Table A.8 - OLS Regression of "Ability to Enjoy Unpolluted Natural Surroundings" on Measured Water Quality Variables DEP VARIABLE: NOPOLLUT F-TEST 4.192 OBS 695 PARAMETER STANDARD T FOR HO: VARIABLE ESTIMATE ERROR PARAMETER-0 INTERCEP 7.65156764 1.88693837 4.055 MTURB 0.000064889 0.01043748 0.006 MSAL 0.01185356 0.01791982 0.661 MDO -0.22131054 0.13894215 -1.593 TRANSP 0.02299990 0.01366888 1.683 DISO 0.26350825 0.10926245 2.412 RESU 0.009595514 0.007438127 1.290 NH4 3.99552741 3.69437706 1.082 NITR -1.40780844 1.18960581 -1.183 PHOS 0.14529883 1.41691553 0.103 CHLORA 0.009712722 0.02752364 0.353 LOSSIGN -0.01482662 0.02449996 -0.605 CHROMB -0.003165001 0.01881366 -0.168 LEADB -0.04634034 0.01468208 -3.156 ------- Combining Contingent Valuation and Travel Cost Data for the Valuation of Non-market Goods by Trudy Ann Cameron Department of Economics University of California, Los Angeles ABSTRACT Contingent valuation (CVM) survey methods are now being used quite widely to assess the economic value of non-market resources. However, the implications of these surveys have sometimes met with a degree of skepticism. Here, hypothetical CVM data are combined with travel cost data on actual market behavior (exhibited by the same consumers) to internally validate the implied CVM resource values. We estimate jointly both the parameters of the underlying utility function and its corresponding Marshallian demand function. Equivalence of the utility functions implied by the two types of data can be tested statistically. Respondent and/or resource heterogeneity can be accommodated readily. A sample of Texas recreational anglers illustrates the technique. * This project has benefited greatly from helpful comments and suggestions provided by E.E. Learner and by B.C. Ellickson, W.M. Hanemann, J. Hirshleifer, D.D. Huppert, K.E. McConnell, R.E. Quandt, M. Waldman, and seminar participants at UCLA, the 1988 SEA meetings, the University of British Columbia, and Simon Fraser University. J. Clark and the Texas Department of Parks and Wildlife generously provided the results of the survey (designed in consultation with J.R. Stoll of Texas A&M). M. Osborn at TPW prepared the data. The Inter-university Consortium for Social and Political Research provided Census data. This research is supported in part by EPA cooperative agreement # CR-814656-01-0. ------- Revised: April 21, 1989 Combining Contingent Valuation and Travel Cost Data for the Valuation of Non-market Goods Economists have long been skeptical about the reliability of consumers' stated intentions, as opposed to their actions in the marketplace. The notion that "actions speak louder than words" underlies much of the criticism of survey methods as a basis for demand forecasting. In some situations, however, market demand activity cannot be directly observed. Surveys and other indirect methods are the only glimpses of demand relationships we have. In these circumstances, it is valuable to explore methods by which researchers can combine survey responses and other available information to formulate the best possible characterization of demand when actual market observations "in the field" are unattainable. For a wide variety of environmental resources and public goods, the absence of markets makes it extremely difficult to establish a monetary value for access to these commodities. Whenever a proposed change in policy affects the quality or availability of these non-market goods, either explicit or Implicit cost-benefit analysis must be undertaken at some point in the decision process. For some time, economists have experimented with alternative methods of eliciting or inferring the social value of these non- market goods. The familiar travel cost method (TCM) popularized by Clawson and Knetsch (1966) has been widely applied in an extensive array of empirical studies. This method interprets variation in travel costs to a particular site where a ------- non-market good is consumed as equivalent to the effect of a per-trip entrance fee to the same location. Subsequent research has provided numerous extensions and qualifications to the original travel cost method. A somewhat newer, competing approach to valuation involves directly asking individual consumers of the non-market good about its value. A hypothetical market scenario is described to each respondent and their professed behavior under that scenario is recorded. To avoid the connotations of hypotheticality, this has been dubbed the "contingent valuation method" (CVM). Despite the potential for a variety of biases in poorly designed CVM surveys (described in detail in surveys by Cummings, Brookshire, and Schulze, 1986, or Mitchell and Carson, 1988) there are still many situations where more realistic methods (such as market simulations or actual market experiments) are prohibitively difficult, and where some of the other potential methods, such as hedonic housing price models or hedonic wage models, are inappropriate. In these cases, it has generally been conceded that CVM surveys, when interpreted cautiously, can provide useful information about the characteristics of demand for a good not presently priced and traded in a real market. The CVM technique has also been widely applied. Despite the semantic care in naming the CVM, the data it produces have still been criticized as "hypothetical answers to hypothetical questions." Consequently, "external validation" of empirical applications of CVM has received considerable attention in the literature. Some of these compare CVM and TCM; others compare CVM with other valuation methods. For example, Bishop and Heberlein (1979) and Bishop, Heberlein and Kealy (1983) pit CVM estimates against TCM and the results of simulated market experiments. They conclude that CVM mechanisms produce "meaningful--albeit inaccurate --economic information." CVM and TCM are also compared by Sellar, ------- 3 Stoll and Chavas (1985), who conclude that the two methods do provide comparable estimates of consumer surplus, and that whenever possible, both methods should be used in future studies as a validity check on the results. Schulze, d'Arge, and Brookshire (1981) determine that "all evidence obtained to date suggests that the most readily applicable methodologies for evaluating environmental quality--hedonic studies of property values or wages, travel cost, and [CVM] survey techniques--all yield values well within one order of magnitude in accuracy. Such information...is preferable to complete ignorance." Brookshire, Thayer, Schulze, and D'Arge (1982) compare CVM estimates with a hedonic property value study. Regarding CVM, they conclude that "[a]lthough better accuracy would be highly desirable, in many cases where no other technique is available for valuing public goods, this level of accuracy is certainly preferable to no information for the decision-making process." Brookshire and Coursey (1987), on the other hand, compare hypothetical non-market CVM responses with market-like elicitation processes (Vernon Smith's public good auction experiments in the laboratory and in the field). Compared to CVM, the marketplace appears to be "a strong disciplinarian" in terms of limiting the tendency for certain types of inconsistencies in valuation responses. In all these previous studies aimed at external validation of the values for non-market goods produced by CVM, the alternative measures of value were obtained either by indirect methods (the travel cost approach or hedonic wage or rent functions) or by small simulated market experiments. The point estimates of value produced by each technique are generated by completely separate models which are sometimes even applied to completely separate ------- samples of data. This makes rigorous statistical comparisons of the different value estimates impossible. The new joint models introduced in this paper also appeal to the marketplace to "discipline" contingent valuation estimates, while at the same time, the CVM information provides insights into the probable behavior of respondents under conditions which are far removed from the current market scenario. The innovation is that the validation occurs in the context of a single joint model applied to a single sample of respondents. Since we collect both CVM and TCM information from each respondent, the joint model can be estimated both with and without restrictions, allowing the consistency of the CVM information and TCM information to be tested in a statistically rigorous fashion. 1 The new joint models described in this paper will be appropriate for a whole spectrum of non-market resource valuation tasks wherever CVM or TCM have been used separately before. For concreteness in this paper, however, we concentrate on an empirical application concerning the non-market demand for access to a recreational fishery. The U.S. Fish and Wildlife Service estimates that economic activity associated with recreational fishing generated $17.3 billion in 1980 and $28.1 billion in 1985, and there are at least 60 million Americans who fish regularly (reported in Forbes, May 16, 1988, pp. 114-120). Recreational fisheries valuation has therefore attracted considerable policy-making interest over the past few years.2 There are many 1 The conceptual framework for the econometric implementation is similar to models of discrete/continuous choice employed by Hanemann (1984) and by Dubin and McFadden (1984), but in the present case, the discrete choices are purely hypothetical. 2 Among current related policy issues, for example, is the quantification of the social costs of acid precipitation (which kills fish and decreases the consumer surplus associated with recreational fishing). These costs are ------- 3 theoretical examinations and empirical attempts at valuation extant.3 One factor accounting for the proliferation of empirical analyses is the availability of vast quantities of survey data collected regularly for fisheries management purposes. Section I of this paper develops the logic whereby a discrete-choice direct utility function can be modified into an indirect utility difference function (defined over fishing days and a composite of all other goods). Then this function and the corresponding Marshallian demand function for fishing access days can be modeled jointly. Section II describes a sample of CVM and TCM data used to demonstrate this technique. Section III describes alternative stochastic specifications. Section IV provides a general outline of the types of results these models generate. Section V goes into detail regarding the specific empirical results for a basic model and some useful extensions. I. THE JOINTNESS OF CONTINGENT VALUATION AND TRAVEL COST RESPONSES A rigorous utility-theoretic tradition in the analysis of "discrete- choice" CVM data was initiated by Hanemann (1984b), who elaborated substantially upon earlier estimation procedures used by Bishop and Heberlein (1979). The discrete choice (or "referendum") format for CVM survey questions is often argued to be less subject to some of the usual CVM biases than are other formats. Rather than asking the respondent to place his own specific generally considered to be one of the most substantial components of acid rain damages. 3 To cite only a few of the more recent recreational fisheries studies: McConnell, 1979, Anderson, 1980, Samples and Bishop, undated, McConnell and Strand, 1981, Vaughn and Russell, 1982, Morey and Rowe, 1985, Rowe, Morey, Ross, and Shaw, 1985, Samples and Bishop, 1985, Donnelly, Loomis, Sorg, and Nelson, 1985, Morey and Shaw, 1986, Cameron and James, 1986, 1987, Thomson and Huppert, 1987, Cameron 1988a, Cameron and Huppert, 1988, 1989, Agnello, 1988, and McConnell and Norton, undated. ------- 6 dollar value on access to the resource, a single threshold value is offered and the respondent is asked to indicate whether his personal valuation is greater or less than this amount. For the survey available for this study, the referendum CVM question seems most easily interpreted as asking whether the respondent would entirely cease to use the resource if the annual access fee ("tax") were equal to T.4 Let Y be the respondent's income, let q be the current number of trips per year to the recreation site, and let M be the respondent's typical travel costs (i.e. market cost of access and incidental expenses on complementary market goods associated with one trip).5 With cross-sectional data, it is convenient to begin by assuming a common utility function wherein access to the recreational resource can be traded off against a composite of all other goods and services, z, for which the price can be normalized to unity. If market goods (travel, etc.) are consumed in fixed proportions with the number of recreation trips, then only the number of trips appears separately in the utility function: U(z,q) - U(Y- Mq.q). Suppose a respondent to the CVM question indicates that he would continue fishing under the hypothetical two-part tariff with fixed tax T and marginal price M. This implies that his maximum attainable utility when paying the tax and enjoying access exceeds his utility when forgoing all trips 4 A possible alternative interpretation of the question is addressed in Appendix I. 5 These data do not allow accurate imputation of the opportunity costs of travel time. Rather than invoking a completely arbitrary guess about time •.osts, we opt to ignore this component while acknowledging that the empirical .esults will certainly reflect this decision. To the extent that time costs are important, the social values of access implied by the travel cost portion of the model will be underestimated. ------- and thereby avoiding both the tax and the travel costs associated with each trip: (1) AU(Y.M.T) - max, U(Y-M,.T.,) - U ------- 8 for U(z,q) is an adequate representation of the preferences of individuals in this sample, this supposition will be used to impose parameter constraints across the two parts of the model. Requiring that respondents' professed behavior in a hypothetical context be consistent with their observed behavior in real markets should attenuate the degree of bias due to the hypothetical nature of the CVM question. In turn, the CVM information allows the researcher to "fill in" some information about demand that is not captured by the range of the currently observable demand data and it can temper biases in the travel cost information due to underestimation of the true opportunity costs of access. One key question to be addressed in this study is whether CVM and TCM data do indeed elicit the same preferences. When parameter constraints are imposed across two models, it is also possible to allow the corresponding parameters to differ, taking on any values the data suggest. This option allows for a rigorous statistical comparison of the different utility configurations implied by the CVM and the TCM data. Contingent on the validity of the assumption of quadratic utility, one can test statistically the hypothesis that the corresponding parameters in the two models are the same. This is implicitly a test of whether professed behavior in the hypothetical market is consistent with observed behavior in a real market. If utility parameter equivalence is rejected, then one might suspect that the contingent valuation technique and/or the travel cost method might be unreliable in this specific application. Travel cost models seem to enjoy broader acceptance than CVM models, although rudimentary travel cost models like the one employed here can also have serious deficiencies. Fortunately, if the researcher harbors prior opinions regarding the relative or absolute reliability of these two types of ------- 9 information, these priors can be readily incorporated into the estimation process. Consequently, even if parameter equivalence is rejected initially, there will be some recourse. In addition to these basic issues, this paper describes a number of extensions which demonstrate the flexibility of this model as a prototype for subsequent work in non-market resource valuation. II. AN ILLUSTRATIVE EXAMPLE Between May and November of 1987, the Coastal Fisheries Branch of the Texas Department of Parks and Wildlife conducted a major in-person survey of recreational fishermen from the Mexico border to the Louisiana state line. The "socioeconomic" portion of the survey is most pertinent here. The specific CVM question asked of respondents was: "If the total cost of all your saltwater fishing last year was more, would you have quit fishing completely?" At the start of each survey day, interviewers randomly chose a starting value from the list $50, $100, $200, $400, $600, $800, $1000, $1500, $2000, $5000, and $20,000. On each subsequent interview, the next value in the sequence was used. Therefore, offered values can be presumed to have no correlation whatsoever with the characteristics of any respondent. In addition to this question, respondents were asked "How much will you spend on this fishing trip from when you left home until you get home?" The survey also established how many trips the respondent made over the last year to all saltwater sites in Texas.7 Five digit zip codes were collected, which allows establishment of residency in Texas. 7 Unfortunately, the duration of each trip is unknown, so it must be assumed that the majority are one-day trips, which may or may not be entirely plausible. Here, the term "trip" is used synonymously with "fishing day." ------- 10 Income data were not collected from each respondent, but the five-digit zip codes allow merging of the data with 1980 Census median household incomes for each zip code. Zip codes cover relatively homogeneous "neighborhoods," at least when compared to income data on the county level, for example. Individuals' consumption patterns tend to conform somewhat to those of their neighbors, so median zip code income may be a better proxy for "permanent" disposable income than actual current self-reported income. There is high variance in median incomes across zip codes, so the Census income variable may actually make a substantial and accurate contribution to controlling for income heterogeneity among the survey respondents.8 In other work utilizing the entire dataset (Cameron, Clark, and Stoll, 1988) it has been determined that subsets of individuals in the sample exhibit extreme behavior. The full sample has therefore been filtered somewhat for use in this demonstration study. Since the initial models presume identical underlying utility functions for all individuals, those who report more than sixty fishing trips per year are discarded from the sample. It is relatively likely that these individuals are atypical, since 90% of usable sample reports fewer than this number of days. The median number of trips reported is between eleven and twelve. This research is therefore clearly directed at "typical" anglers. It is also the case in the full usable sample from the survey that some individuals respond that they would keep fishing if the cost had been $20,000 higher when $20,000 exceeds the median household income of their zip code. 8 While the use of group averages instead of individual income information undeniably involves errors - in-variables complications in the estimation process, the distortions may in fact be not much greater than they would be with the use of self-reported income data in an unofficial context. It is well known that many individuals have strong incentives to misrepresent their incomes if they do not perceive a legal requirement to state them correctly. ------- 11 Since the assignment of value thresholds was completely exogenous, the estimating sample includes only those respondents who were posed values up to and including the $2000 offer. Everyone offered values greater than this was excluded, regardless of their answer to the CVM question. The final criterion for inclusion in the sample for this study was that a respondent should not report spending more than $100 on this fishing trip. Again, a very large proportion of the sample passes this criterion. When market expenditures are reported to be much larger than this, it seems reasonable to suspect that capital items have been included, so that it would be invalid to treat these costs as "typical" for a single fishing trip. Current expenditures over $2000 were reported by several respondents. Descriptive statistics for the variables used in this paper are contained in Table I. III. THE STOCHASTIC SPECIFICATION It may be helpful to think of the model developed in the following sections as a nonlinear analog to a more familiar econometric model. The conceptual framework is similar to a system of two equations with one right- hand side endogenous variable, cross-equation parameter restrictions, and a non-diagonal error covariance matrix. However, one of the dependent variables is continuous and one is discrete, both equations are highly nonlinear in parameters, and the simultaneity in the model involves an endogenous variable which is not observed directly, but must be counterfactually simulated. In order to have the option of constraining the coefficients of the utility function (and hence the indirect utility function) as well as those of the corresponding Marshallian demand function to be identical, the discrete :hoice model and the demand equation must be estimated simultaneously. To fix ------- Table I Descriptive Statistics for the Variables (n - 3366) Acronym Description Mean Std. dev. median household income for respondent's 5-digit zip code (in $10,000)* (1980 Census scaled to reflect 1987 income; factor-1.699) 3.1725 0.6712 M current trip market expenditures, assumed 0.002915 0.002573 to be average for all trips (in $10,000) T annual lump sum tax proposed in CVM scenario 0.05602 0.04579 (in $10,000) q reported total number of salt water fishing 17.40 16.12 trips to sites in Texas over the last year I indicator variable indicating that respondent 0.8066 0.3950 would choose to keep fishing, despite tax T PVIET proportion of population in respondent's 0.002497 0.006217 5-digit zip code claiming Vietnamese ancestry a Dollar-denominated quantities are expressed in $10,000 units throughout the study, so that squared income and squared net income do not become too large, resulting in extremely small probit coefficient estimates which thwart the optimization algorithm. ------- 12 ideas, it is helpful to begin by considering the two components of the joint model completely separately, ignoring any potential error correlation. A. A Separate CVM Choice Model The decision to work within the framework of direct, rather than indirect, utility functions buys easy characterization of the shapes of consumer indifference curves. Under the hypothetical CVM scenario, the respondent is asked to choose between ceasing to use the resource and paying no lump-sum tax, or continuing to consume a revised optimal quantity of access q(Y-T,M) at a new lower net income. Unless one can assume that there is no income effect, q(Y-T,M) will probably be less than the current optimal quantity, q(Y,M). But if, for the initial exposition, it is temporarily assumed that the income elasticity of demand for access is zero, one can begin by considering how the CVM component of the joint model should be estimated. It will be convenient to model the discrete choice elicited by the CVM question using conventional maximum likelihood probit (rather than logit) techniques, where the underlying distribution of the implicit dependent variable, the true utility difference, is presumed to be Normal. Since AU(Y,M,T) in equation (1) can at best be only an approximation, assume that for the ifch observation, AUi - AUj* + e , where is a random error term distributed N(0, a2). AUt*, the systematic portion of the utility difference on the right hand side of equation (1) will be represented in what follows as f(xi,^). In conventional probit models, AUa is unobserved, but if AUt is "large" (i.e. AU£ > 0), one observes an indicator variable, It (the "yes/no" response), taking on a value of one. Otherwise, this indicator takes the value zero. In constructing the likelihood function for this discrete response variable, the following algebra is required: ------- 13 (3) Pr( IA - 1 ) - Pr ( AU. > 0 ) - Pr ( ^ > - fCx^/9) ). Since eL has standard error a, dividing through by a will create a standard normal random variable, Z, with cumulative density function (4) Pr( et > - Xi'£ ) - Pr ( Z > - f(x.lt0)/o ) - Pr ( Z < f(xi,^)/a ) - 9 (f(xi,^)/a), by the symmetry of the standard normal distribution. At best, in cases where f(x ,0) is linear-in-parameters, the vector 0 can only be identified up to a scale factor, since it only ever appears in ratio to a. (However, this is quite acceptable, because the solutions to the consumer's utility maximization problem are invariant to monotonic transformations of the utility function.) The probability of observing It - 0 is just the complement of Pr^ - 1), namely 1-4 (f (xA ,$)/ ------- 14 B. A Separate Demand Model The systematic portion of the TCM Marshallian demand function resulting from the optimization problem in (2) will be denoted by gCx^/9) . In estimating this model separately, one might assume that q1 - gCx^) + r^, where r) N(0, vz) . This suggests that nonlinear least squares (by maximum likelihood) is an appropriate estimation method. The log-likelihood function associated with the demand model is therefore: (6) log L - -(n/2)log(2ir) - n log v - (1/2) Zt{ [q4 - g(x1(0)]/u}2 Again, there exist packaged computational routines to estimate such nonlinear models, but this application requires a general function optimization program to allow for subsequent constrained joint estimation of this model and the utility difference model. C. Constrained Joint Estimates, Independent Errors To impose the requirement that the two decisions (one real and one hypothetical) reflect the identical underlying utility function, the CVM and TCM models must be estimated simultaneously. With independent errors, it is simple to combine the two specifications by summing the two separate log- likelihood functions and constraining the corresponding Pi coefficients in each component to be the same: (7) log L - -(n/2)log(2w) • n log u - (1/2) ^ { [qt - g(x1,^)]/v}2 + S, { I, log [* (f(x1,/9)/a)] + (1 - I4) log ( 1 -[* (f(xlf0)/a)] ) }. D. Constrained Joint Estimates, Correlated Errors Realistically, unobservable factors which affect respondents' answers to the CVM discrete choice question are simultaneously likely to affect their ------- 15 actual number of fishing days demanded. To accommodate the influence of unmeasured variables, one can allow for a correlation, p, between the ei error terms in the discrete choice model and the »; error terms in the demand model.9 Assume that these errors have a bivariate normal distribution, BVN(0, 0, a2, v2, p). In empirical discrete/continuous choice models, it is frequently more convenient not to work directly with the joint distribution of the errors. Instead, one can take advantage of the fact that the joint density can be represented equivalently as the product of a conditional density and a marginal density. In order to derive the model with nonzero p, one can exploit the fact that for a pair of standardized normal random variables, say Wj and W2, the conditional distribution of W2, given W " w , is univariate Normal with mean (p wt) and variance (1 - p2) . When allowing for nonzero values of p, then, the term #(f(x ,/9)/a) in the discrete-choice portion of equation (7) will be replaced by: (8) * { [(f(xlf0)/a) + p ZJ / (1 - p2)1/2 } where Zi - [q± - g(xlt)9)]/u, the standardized fitted error in the demand function, evaluated at the current parameter values. Clearly, if p - 0, this model collapses to the model with independent errors described in the previous section. IV. AN EXPLICIT FUNCTIONAL FORM AND CLASSES OF RESULTS The basic model proposed in this paper (and its variants) uses a quadratic direct utility specification for U(z,q). Other discrete/continuous If the estimated value of the error correlation, p, is substantial and statistically significant, one probably ought to generalize the specification, if possible, to accommodate systematic heterogeneity across respondents. Section V will address this issue. ------- 16 modeling exercises have begun with an indirect utility function, since commodity prices (rather than quantities) are more plausibly assumed to be exogenous for the typical consumer. In the present context, however, we desire to maintain the geometric intuition behind direct utility functions and their associated indifference curves.10 We have selected the quadratic form for the direct utility function because of its simplicity and because a number of other familiar specifications are unsuitable for the derivation of associated Marshallian demand functions (also discussed in Appendix II). For identical consumers, the simplest quadratic direct utility specification is: (9) U(z,q) — f}^ z + f)2 q + z2/2 + zq + q2/2 Under the current scenario for the respondent, consumption of the Hicksian composite good z is (Y - Mq) and q will be non-zero for anyone being interviewed, so the utility function in (9) is really a function of Y and q.11 (9') U(Y, q) - 0l (Y-Mq) + 02 q + (Y-Mq)2/2 + (Y-Mq)q + 05 q2/2. The specific form of the utility difference which dictates a respondent's answer to the CVM question will be linear in the same parameters as U: (10) AU(Y,M,T) - f(xt,0) - ^ {[Y-Mq-T] - Y} + fi2 q + 03 {[Y-Mq-T]2 - Y2)/2 + ^ [Y-Mq-T] q + 05 (q)2/2. 10 A quadratic indirect utility version of the model is discussed in Appendix II. Unfortunately, the calibrated model does not satisfy the regularity conditions for valid indirect utility functions. 11 In-person CVM surveys typically sample only current users of the resource. When access price increases ( or simply positive access prices) are being contemplated, this does not pose much of a problem. However, when projected scenarios involved improved resource attributes, one must really survey potential users as well as current users to elicit an accurate measure of aggregate demand responsiveness. ------- 17 The first order conditions for the Lagrangian in equation (2) yield a corresponding Marshallian demand for q of: (11) q(Y,M) - g(xt ,0) - [ 02 + Y - 0l M - 03 Y (M) ] / [ 20k (M) - M2 - 05 ]. Since every additive term in both the numerator and denominator of this expression contains a multiplicative 0 coefficient, the demand function is of course invariant to the scale of the 0 vector. Consequently, it is necessary to adopt some normalization of the demand function parameters (for example, 02 - 1, an entirely arbitrary and inconsequential choice). Thus the form of the demand function actually estimated will be: (12) q(Y,M) - [ 1 + (0*) Y - (y91*)(M) - (0*) Y (M) ] / [ 2(0*)(H) - (03*) (M)2 - 0* ]. where 0* - 0^/02. This demand function is highly non-linear in M. Crucially, when we endogenize the q in equation (10) by substituting the formulas for q(Y-T,M) based on the calibrated demand models in (11) or (12), we are effectively converting the direct utility specification into an indirect utility specification! But if the indirect utility function V(Y-T,M) - U(Y-T,q(Y-T,M)) were to be written out in full, it would be a complex and unappealing formula. Instead, we will describe our results in terms of the implied direct utility function U(z,q). The central empirical results in this study are the estimates of the 0 parameters of the assumed underlying quadratic direct utility function. All of the economically interesting empirical measurements in this paper are derived from this calibrated utility function. Throughout, the empirical ------- 18 utility function should exhibit properties which are consistent with economic intuition about plausible shapes for these functions. First, the derivatives of the underlying direct utility function are: (13) au/az - + £3z + 04q a2u/az2 - p3 d\J/dq - p2 + /3,z + 05q a2U/3q2 - 05 d2U/dzdq - The marginal utilities of the composite good z and of access days q will depend on the local values of z and q. Whether or not each marginal utility is increasing or decreasing will be revealed by the signs of fi3 and 05. If both 03 and are negative, the fitted utility function will be globally concave, and a globally optimal combination of z and q will be implied. The budget constraint will be binding unless the implied global optimum is attainable inside the budget set. The formulas for the global optimum will be strictly in terms of the estimated coefficients: (14) qa"u - [-fi2 + (^ V*3>] / ^5 " <0*2/03>l " - (-^ . 0kq*)/03 Admissible fitted quadratic utility functions are not necessarily strictly concave, however. The bundle at which both marginal utilities go to zero may correspond to a saddle point of the complete fitted utility function. But only quasi-convexity in the positive orthant is required. To assess compliance with this regularity condition, one can easily examine the configuration of the fitted utility function's indifference curves. An indifference curve through any arbitrarily chosen bundle (z',q') can be identified by first determining the level of utility this bundle represents: ------- (15) U' - 01 z' + 02 q' + ^ z'2/2 + z'q' + 05 q'2/2. To find all other bundles (z,q) which provide utility U', one merely sets up the quadratic formula for z: (16) (Pz/2)z2 + + 04q)z + [/32q + ($,/2)q2 - U'] - 0 Plots of empirical indifference curves are highly intuitive and relatively novel and will be used throughout the discussion to highlight the differences in estimated preference structures. Once the corresponding Marshallian demand function has been calibrated by joint estimation of the utility parameters, we are usually curious about the implied price and income derivatives: (17) 3q/3M — ( -a^M-^M^K^+^Y) - 2(^-^M) ] / [2^M-/93M2-05]2 3q/3Y - [/V03M] / [2/3aM-/33M2-/95]2 . From the demand curves, policy makers are also sometimes interested in estimates of the reservation price. One simply sets q - 0 in equation (11) and solves the resulting quadratic formula for (M). Given the current level of M, the reservation level of any additional potential per-day access charge can readily be determined. One of the ultimate empirical objectives of this research concerns estimation of the total social value of recreational access to this fishery. One measure of value is the equivalent variation, E, which can be viewed as the fixed tax which would make these anglers just indifferent between paying the tax and continuing to fish, or not paying the tax and forgoing their ------- 20 fishing opportunities. Algebraically, E is given by the equation maxq U(Y-Mq- E,q) - U(Y,0). But completely depriving everyone of access to the resource is an extremely drastic proposition. So we also consider the equivalent variation formulas that give the social costs of limiting access to a proportion a of current (fitted) access levels, where 0 < a < 1 . The equivalent variation for such partial restrictions is given by maxq U(Y-Mq-E,q) - U(Y-aMq,aq). Letting D - (2/9.M - ^M2 - , R - <02+/84Y-01M-03MY)/D and S -------- 21 A general formula for partial loss of access could easily be devised, but this paper will focus on the equivalent variations. V. SPECIFIC EMPIRICAL ESTIMATES A. The Basic Model The "basic model" constrains the quadratic direct utility parameters and the corresponding parameters in the Marshallian demand function for fishing days to be identical. The model initially assumes equal reliability of the two types of information (CVM and actual market demand), and allows the post- tax quantity demanded in the discrete choice model to be determined endogenously according to the same demand function. The model also allows for correlated errors in the two decisions. The first pair of columns in Table II give these results (the second pair of columns will be discussed later). Both the estimated quadratic direct utility function parameters and the corresponding implied (normalized) Marshallian demand parameters are provided. The utility function Implied by these parameter estimates is globally concave, with a slightly positively sloped principal axes for the ellipses that form its level curves. (The relevant lower left portions of these curves are interpreted as indifference curves). Of course, the quadratic form is merely a local approximation to the true utility function. Nevertheless, if the entire surface of the true utility function was quadratic, the apparent global optimum of that function would be located at 28.4 fishing days and $289,823 in median zip code income (compared to sample means of 17.4 fishing days and $31,725 in income). Thus the utility function is well-behaved in the relevant region. At the means of the data, the two marginal utilities are positive. The implied price elasticity of demand at the means of the data is -0.074 and the income elasticity is 0.078, although these elasticities change substantially with deviations away from the sample mean values. To establish------- Table II Fitted Quadratic Direct Utility Parameters (with and without parameters constrained to be identical for CVM and TCM portions of model) Parameter Constrained 0s Point Est. (Asymp. t-ratio) Implied **- P/P2 Unconstrained $s Point Est. (Asymp. t-ratio) Implied 0*- P/P, (z) hP3 (z2/2) (zq) (q2/2) *1 *-^2 3.309 (8.237)a 0.1192 (19.55) -0.1167 (-1.836) 0.002579 (2.006) -0.006837 (-22.80) 16.01 (81.98) 0.2315 (9.086) 27.76 1.0 -0.9790 0.02164 -0.05736 1.276 (0.7457) 28.17 (2.573) 1.498 (2.834) 2.263 (2.147) -502.3 (-1.311) 75.89 (5.756) 1.0 -10.89 (-2.428) -0.01749 (-0.9029) -0.04739 (-14.97) 15.97 (82.04) 0.2505 (9.749) 0.04530 1.0 0.05318 0.08033 -17.83 max Log L -15708.17 -15640.61° a Asymptotic t-ratios in parentheses. b CVM utility parameters do not satisfy regularity conditions. 0 Likelihood ratio test statistic for four parameter restrictions - 115.12. Equivalence of utility parameters is soundly rejected.------- 22 a visual benchmark for this basic model, for art individual with mean income and travel costs, an indifference curve for the empirical quadratic utility function, the budget constraint through (my.O). and the fitted maximum attainable indifference curve are shown in Figure 1. Using the basic constrained model that assumes one common utility function for all respondents, it is possible to use equation (18) to compute fitted values for the equivalent variation (either for each respondent, or at the means of the data). Across the 3366 respondents in this sample, the fitted values of E for a complete loss of access appear in the first row of Table III (a - 0).12 Over the estimating sample, the average point estimate for the equivalent variation for a complete loss of access is $3451 (or, alternatively, at the means of the data, it is $3423). Minimum and maximum values in the sample are also provided. Table III also gives the model's estimates for the equivalent variation associated with successively smaller restrictions on days of access (a denotes the proportion of current consumption to which each individual's access days are restricted).13 For an across-the-board 10% reduction in fishing days, for example, the average calculated utility loss by these respondents would be only $35, although values as high as $52 and as low as $19 can obtain, due solely to different incomes and travel costs faced by different respondents. The main policy interest in equivalent variations for partial restrictions on access stems from the need to make optimal allocations of finite fish stocks between recreational anglers and commercial harvesters. If 12 For the single individual with average characteristics in Figure 1, this quantity would be determined by taking the parallel downward shift in the budget constraint which would leave the new constraint just tangent to the lower indifference curve. 13 The computed equivalent variation, plotted as a function of a, is convex when viewed from below.------- other goods ($'0000) 3.9 EMPIRICAL PREFERENCES 3.6 \ . maxU(Y.M) 3.0' 2.7"1- 0.8 \ V \ U(Y,0) budgec constraint ^q(Y,M) 6.0 12.0 13.0 24.0 30.0 36.0 fishing access days Figure 1 - Indifference curves at optimum and at zero access days, for respondent with mean income and travel costs.------- Table III Fitted Individual Equivalent and Compensating Variation Estimates* for the Basic (Constrained) Model (Table II) Valuation mean max min Measure: Equivalent Variation a - 0.0b $ 3451 $ 5132 $ 1857 a - 0.1 2799 4166 1505 CM O 1 a 2214 3298 1190 a - 0.3 1697 2529 912 a — 0.4 1248 1861 670 a - 0.5 867 1294 465 a - 0.6 555 829 298 0 1 0 313 467 168 a - 0.8 139 207 75 a - 0.9 35 52 19 Compensating Variation a - 0.0 $ 3560 $ 5361 $ 1899 * Since the sane utility function is presumed for all respondents, individual variations in these quantities stem solely from differences in income and travel costs. k For access days restricted to the fraction a of fitted current access days.------- 23 faced with a proposal to cut back on recreational access, it would be necessary to quantify the social losses to recreational anglers, compare these losses to the anticipated gains accruing to commercial harvesters, and then to argue that such a redistribution of the catch would result in a potential Pareto improvement.1* The final row of Table III provides, for comparison, the corresponding compensating variation for a complete loss of access (i.e. for a - 0 only). As is typical, the compensating variation for the loss is larger than the equivalent variation for the same loss. Here, however, the difference is largely an artifact of the quadratic form chosen for the utility function. The concentric ellipses which form the level curves of a globally concave utility function can be expected to have this relationship. B. Different Preferences Implied by Real versus Contingent Data We require both a constrained and an unconstrained specification if we plan to use a formal likelihood ratio test statistic to determine whether the utility parameters implied by the CVM data alone are consistent with those estimated jointly using both CVM and TCM data. The constrained specification (the basic model just described) appears in the first pair of columns in Table II. For the unconstrained model, the demand information necessary to compute the endogenous quantity in the CVM discrete choice model is calculated using only the utility function parameters for the CVM portion of the model. We therefore allow the discrete choice CVM model exclusively to imply values for 14 In a richer specification, with enough shift variables to more closely capture the variations in quantity demanded, it would be an interesting exercise to assess total aggregate losses due to restrictions of access to specific numbers of days. The present data are not appropriate for simulating these policy changes.------- 0X, P2, 03, and 05. The observed TCM demand decisions will imply separate values for and fi5*. The second pair of columns in Table II displays results for an unconstrained model corresponding to the first pair of columns in the same table. The point estimates do not bode well for the consistency of the preferences elicited by the two types of responses. First of all, it is especially unsettling to note that the quadratic direct utility function implied by the CVM data alone does not even conform to the regularity conditions expected of a valid utility function. At the means of the data, the implied marginal utility from an additional access day is negative; there is also increasing marginal utility with respect to the composite good. The TCM quadratic direct utility parameters, however, are thoroughly acceptable. (The only link between the two submodels is the estimated error correlation, P¦) Nevertheless, there must still be some information about preferences in the CVM data, and the recorded responses on these surveys dictate these particular parameter values. We can certainly still compare the maximized value of the log-likelihood in the constrained and unconstrained models in order to assess whether the imposition of cross-equation parameter restrictions is tenable. A likelihood ratio test for the set of four parameter restrictions embodied in the "basic" model soundly rejects these restrictions.13 For this quadratic specification, the CVM- and TCM-elicited preference functions are different. 15 It may be suspected that the TCM estimates systematically understate the true value of access (due to underestimates of the actual opportunity costs of access) and that the CVM estimates systematically overstate the true value of access (due to the incentives embodied in the way the question was posed). If data deficiencies make it too implausible to force compatibility of these responses with a common underlying set of preferences, the researcher would of course be free to report the two types of value estimates separately.------- 25 For a respondent with mean characteristics, Figure 2 shows the empirical indifference curves passing through the bundle (0,Y) for (i.) the "basic" constrained model and (ii.) the demand portion of the unconstrained model. The greater curvature of the indifference curve for the restricted parameters implies that E (the equivalent variation) based on the joint model, will be substantially larger than E based on observed TCM market demand behavior alone. For the unrestricted TCM demand parameters, the fitted equivalent variation at the means of the data is only $1686 (versus about $3451 for the constrained model). The implied inverse demand functions corresponding to the different sets of preferences implied by the joint model and by the unconstrained TCM model are shown in Figure 3. When the CVM responses and observed TCM demand behavior are constrained to reflect the same set of quadratic preferences, the reservation price is about $409. The unrestricted TCM demand behavior implies a much lower reservation price. Thus the CVM (i.e. hypothetical market) scenario does seem to invite respondents to overstate the strength of their demand for resource access, as one might suspect (and/or the TCM indirect market data understates the strength of demand). C. Differing Reliability for Real versus Contingent Data The basic model (with or without the utility parameters constrained across the two sub-models) reflects the presumption that the decisions which respondents claim they would make under the hypothetical scenario proposed in the CVM question deserve to be treated as equally credible when compared to their actual market behavior regarding number of fishing days demanded. This need not be the case. In other research on CVM (Cameron and Huppert, 1988), Monte Carlo techniques were used to demonstrate the wide range of referendum CVM value------- EMPIRICAL PREFERENCES budget constraint TCM preferences 2.91 joint model preferences 0.0 4.0 9.0 12.0 20.0 24.0 q Figure 2 - U(Y,0) for respondent with mean travel costs, according to constrainted joint model preference parameters and according to TCM portion of model with separate sets of preference parameters (CVM parameters fail to satisfy regularity conditions and are not shown).------- fishing 20.0]T access days (q) ft EMPIRICAL INVERSE DEMAND CURVES i\ 15. fl] \\ 19.0 5.0 TCM \ preferences joint model preferences \ 0.8 0.0 125.0 251.0 375.0 i i r' 500.0 625.0 750.0 total price of access (M) Figure 3 - Inverse demand curves corresponding to constrained joint model preference parameters, and according to TCM parameters from unconstrained model, for respondent with mean income and travel costs. (CVM parameters do not satisfy regularity conditions and are not shown.)------- 26 estimates which can result simply as an artifact of the arbitrary assignment of the threshold values on the questionnaires. One conclusion in that study was that researchers should probably insist on vastly larger samples for referendum CVM data, in order to offset the inefficiencies in estimation which result from the highly diffuse information in referendum responses. By itself, this property of referendum data might be sufficient to warrant a discounting of its credibility when it is combined with "point" information from the same sized sample. Fortunately, researchers are free to use their own prior opinions to adjust the relative credibility of each type of information. This can be done in an ad hoc fashion, by employing non-unitary weights on the respective terms in the log-likelihood function (see Appendix IV). Alternately, it can be done more rigorously, by making assumptions about the variances of the distributions of the estimated /9 parameters around the "true" mean of the £ vector.16 In the discussion that follows, we assume that CVM data are presumed to be less reliable than travel cost data, since this has been a typical sentiment among researchers in this area. However, the demand information inferred from the travel cost data is also likely to be unreliable, especially since TCM applications often assume that the opportunity cost of access is constant as access days increase. If opportunity costs rise, as they most likely do, TCM will underestimate the implicit value of access, perhaps severely.17 Also recall that we do not impute an arbitrary value of travel 16 We owe this helpful suggestion to Ed Learner. 17 If increasing opportunity costs of access can be captured in the data, there exist econometric strategies for dealing with non-linear budgets sets which could undoubtedly be adapted to this type of problem. (See Hausman, 1985.)------- 27 time in this study. Depending upon the relative qualities of the two types of data, then, appropriate discounting of each type of information can be decided ex ante. Utilizing Explicit Priors on the Distributions of 0 and 0* Let 0 continue to denote the utility parameter estimates derived from the CVM data, and let 0* be the utility parameter estimates from the TCM data. Let 0r signify the true but unknown utility parameter vector. (Without loss of generality, we can normalize the second element, 02, to unity in all three cases.) Now assume that conditional on the true 0T, 0 and 0* are statistically independent and that the elements of 0/0T are distributed N(l,a2) and the elements of 0*/0r are distributed N(l, |