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The Role of Locational Equilibria and Collective Behavior in Measuring the Benefits of Air Pollution Policies

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This research project uses the characteristics of a spatial equilibrium to estimate the economic value of reductions in air pollution. This equilibrium includes recognition of households? choices of residential locations based on site characteristics, environmental amenities, as well as the collective choice process determining the amount of community-provided local public goods. This spatial equilibrium estimator (SEE) allows estimates of benefits from air pollution policy to consider general equilibrium adjustments in response to policy. It also permits a behaviorally consistent description of a policy?s consequences. The objectives of this research project are to: (1) extend the SEE framework to include environmental public goods and to allow for a more detailed characterization of the observable sources of heterogeneity in household preferences; (2) apply the SEE framework along with conventional hedonic property value and simple (i.e., multinomial logit) readiness utilization maintenance (RUM) frameworks using current data for air quality (primarily ozone, nitrogen oxide, and particulate matter), housing prices, characteristics, as well as community characteristics in the Los Angeles (LA) area; and (3) compare the benefit estimates implied by each framework for a set of current policy alternatives and their respective sensitivities to their maintained hypothesis.


Principal Investigators:
Smith, V. Kerry
Sieg, Holger
Technical Liaison:
Research Organization:
North Carolina State University
Carnegie Mellon University
Funding Agency/Program:
Grant Year:
Project Period:
February 21, 2001 - February 20, 2004
Cost to Funding Agency:
Project Status Reports:
For the Year 2001

Task 1: Develop and Estimate Extension to Spatial Equilibrium Estimator. During this year, the majority of our efforts were in response to referees' comments, and revising papers prepared during the initial phases of the research. Two new review papers were prepared that include consideration of the conceptual issues associated with this research. The first was published in the International Yearbook of Environmental and Resource Economics (2002), edited by T. Tietenberg and H. Folmer. The second was a paper for a special issue of Environmental and Resource Economics for the World Congress of the Association of Environmental and Resource Economics (AERE) and the European Association of Environmental and Resource Economics (EAERE).

Task 2: Assemble Data for Modeling. Data for LA, Ventura, Orange, Riverside, and San Bernadino counties were assembled and used in several analyses associated with the project. These analyses include:

1. Development of the evaluation of price indexes for the SEE framework.

2. Estimation of the 36 community and the 92 community versions of the SEE
framework. Development of comparison of SEE with Bartik-Kanemoto Bounds.

3. Analysis of hedonic and RUM models for H. S. Banzhaf's thesis comparison of the role of air pollution when evaluated in this context.

4. Extension of the analysis to consider expansion in the LA Unified School District (expanding the choice set for benefit measurement from 92 to 102 communities).

5. The geo-codes for the RECLAIM areas were used to identify locations for the properties in our database (see attached Figure 1). However, aside from simple hedonic models, we have not yet undertaken the planned detailed analysis.

6. The final stages of analysis of the San Diego data are largely completed. Air pollution data were merged with the housing data and estimates of ambient concentrations comparable to our LA work were developed. In addition, information about open space, other land uses, and educational performance were geo-coded and merged with the housing data.

Rather than submit the LA data in isolation, we included the San Diego data files as well, and will submit the full information base at the end of the project period.

Task 3: Estimation of SEE Framework with Southern California Data. As noted in last year's report, the full 92 school district model was estimated by the end of last year. Programs were developed to compute locational equilibria for revised air pollution conditions. These programs were extended to consider expansions in the communities to 102 areas (with the break-up of the LA Unified School District into 11 sub-districts). In addition, the framework was extended to consider air quality conditions that correspond to the scenarios developed for the Environmental Protection Agency's (EPA) 1999 Prospective Report for the LA area. Figure 2 plots the predictions of the Urban Airshed Model (UAM-V) for ozone within our study area. Figures 3 and 4 plot the General Equilibrium (GE) solutions for these scenarios for 2000 and 2010 for baseline and control situations in comparison to the 1990 reference point used in the Prospective Analysis. Developing these linkages was a significant component of this year's activities.

Task 4: Estimation of Hedonic and RUM Frameworks. Hedonic models for the RECLAIM area, as fixed effects, were estimated last year and will be used in subsequent research. In addition, estimates of hedonic property value models for the San Diego area were also completed.

Task 5: Benefit Measurement and Estimation. As noted above, earlier research completed estimates of partial and general equilibrium benefit estimates with the SEE framework for the LA area. In addition, Bartik-Kanemoto bounds were estimated. We also obtained the air quality projections for California used in the EPA's (1999) Prospective Analysis, match them to our model's study area, and to develop a general equilibrium benefit analysis for research to be reported at National Bureau of Economic Research (NBER) Conference on Empirical Environmental Economics in May 2002.

The tasks envisioned in our initial research plan have been completed. We still are in the process of preparing new papers as well as revising earlier papers prepared with the project. Our success in keeping on-schedule allowed expansion in the project to consider a new area that was not anticipated in our original design. We have assembled the property value, education, air pollution information, as well as the price indices and distributional information needed to implement the SEE framework. We also added open space and a measure of related land uses into this database. An additional methodological extension is being considered. This extension would attempt to include moment conditions to characterize net in-migration into an area as a component of the equilibrium conditions. Before developing the details of the modeling, we are considering the basic data needs and our ability to meet them.

Figure 1. Boundaries for the RECLAIM Trading Areas.

Figure 2. LA Metropolitan School Districts and Environmental Protection Agency (EPA) Urban Airshed Model (UAM) Locations for Estimated Ozone Readings.

Figure 3. Computed General Equilibrium Prices for With and Without Clean Air Act Amendments (CAAA) 2000 Compared to Baseline 1990.

Figure 4. Computed General Equilibrium Prices for With and Without Clean Air Act Amendments (CAAA) 2010 Compared to Baseline 1990.

Future Activities:

We are now developing the conceptual and computational analysis necessary to estimate this expanded model. It is not clear if we will be able to complete this research before the conclusion of the project. There is a reasonable prospect if we do not attempt the methodological extension. There are no further resources available for the principal investigators. Thus, our ability to undertake the work rests on our ability to use research time not committed to other projects to this effort. Primary attention will focus on tasks related to the initial design of the project, including the:

• Completion of papers describing the research that has been finished and revising earlier papers for publication;

• Completion of the documentation of the data;

• Programming welfare analyses with the existing model to investigate its performance under different conditions; and

• Estimation and evaluation of the San Diego model as time and resources permit.

The working paper from submission will be revised. The team has to complete the writeup of the Bartik-Kanemoto bounds analyses. A paper on the San Diego work will be completed. We expect to expand the data documentation to include the San Diego data and to submit a CD-ROM with the LA and San Diego data and documentation.


Smith VK, Banzhaf HS. A diagrammatic exposition of weak complementarity and the Willig condition. American Journal of Agricultural Economics.

Sieg H, Smith VK, Banzhaf HS, Walsh R. Estimating the general equilibrium benefits of large changes in spatially delineated public goods. International Economic Review (submitted for review, 2002).

Smith VK, Pattanayak S. Is meta analysis a Noah's ark for non-market valuation? Environmental and Resource Economics (in press, 2002).

Smith VK, Sieg H, Banzhaf HS, Walsh R. Ozone improvement, household adjustments, and environmental policy analysis. Journal of Environmental Economics and Management (submitted for review, 2002).

Sieg H, Smith VK, Banzhaf HS, Walsh R. Using locational equilibrium models to evaluate housing price indeces. Journal of Urban Economics (in press, 2002).


Banzhaf HS, Smith VK. Estimating random utility models of housing choices: space, time, and budget. CEnREP Working Paper, March 2002 (under revision).

Banzhaf HS. Green price indices. Resources for the Future, Discussion Paper 02-09, March 2002.

Banzhaf HS. Quality adjustments for spatially delineated public goods: theory and applications to cost-of-living indices in Los Angeles. Resources for the Future, Discussion Paper 02-10, March 2002.


Sieg H, Smith VK, Banzhaf HS. Presented at the Spacial Externalities Symposium, Bren School of Environmental Science, University of California, Santa Barbara, CA, January 2001.

Sieg H, Smith VK, Banzhaf HS. Presented the Joseph Havileck Memorial Lecture in Applied Economics, Ohio State University, Columbus, OH, May 2001.

Sieg H, Smith VK, Banzhaf HS. To be presented at the National Bureau of Economic Research Workshop on Empirical Environmental Economics, May 2002.

Project Reports:
The overall objectives of this research project were to: (1) extend a new framework (developed by Epple and Sieg [1999]) for estimating consumer preferences for spatially delineated public goods so that the approach could be evaluated for use with environmental resources; (2) develop the data and implement a large-scale application of the framework for estimating consumer preferences for air quality in southern California; (3) evaluate the feasibility of computing the general equilibrium responses of housing prices (because of household adjustment) to exogenous changes in air quality conditions; (4) compare general and partial equilibrium welfare measures for these exogenous changes in local public goods; and (5) compare the results from the locational equilibrium framework with results from hedonic and random utility models previously used in policy analysis.

The Epple-Sieg approach describes household behavior within a framework that has a long history in economics. It suggests that when public goods are spatially distinct, it should be possible to observe households moving to different locations seeking public goods that more closely align with their preferences. If analysts are prepared to specify how public goods such as air quality contribute to well being, the Epple-Sieg analysis suggests that if there are measures of the spatial amenities and disamenities along with housing costs, it should be possible to estimate consumer preferences for these amenities.

This research developed four extensions to the Epple-Sieg approach: (1) a methodology for measuring price indices that adjusts for heterogeneous housing; (2) a framework that includes a range of restrictions implied by locational adjustment that are used with aggregate data on the types of households located in specific communities; (3) a method for using the preference estimates to compute the new prices that would result from an exogenous change in amenities reflecting the adjustments households would make in response to that change; and (4) an analysis of the issues that arise in measuring partial and general equilibrium welfare measures (willingness to pay [WTP]) for large-scale policy changes.

To our knowledge, this research is the first effort to provide a practical resolution for measuring changes in welfare when there are general equilibrium implications of large changes in spatially differentiated public goods.

Methods and Data

The empirical implementation of the model focuses on the Los Angeles, CA, metropolitan area, which consists of the area west of the San Gabriel Mountains and includes parts of five counties: Los Angeles, Orange, Riverside, San Bernardino, and Ventura. We assume that the school district corresponds to the community selected by a household when making its locational decisions.

A comprehensive database on housing markets in the Los Angeles metropolitan area was assembled based on housing transactions collected by a firm, Transamerica Intellitech, that sells access to these data to realtors and financial institutions. These data contain housing characteristics and transaction prices for virtually all housing transactions in southern California between 1989 and 1991. Table 1 reports means of the main variables in the housing sample by counties for these years.

Table 1. Descriptive Statistics of the Housing Sample
Los Angeles
San Bernardino
Number of Observations
Market Value of House
Number of Bathrooms
Number of Bedrooms
Lot Size (square feet)
Building Size (square feet)
Swimming Pool (proportion)
Fireplaces (proportion)
1 Mile of Coast (proportion)
3 Miles of Coast (proportion)
Commute Time (minutes)

The data used to derive the housing price indices are based on housing sales and do not necessarily match the housing stock in the area. According to the 1990 U.S. Census (the year closest to our sample), 70 to 80 percent of all households change houses within 10 years. In our sample, 15 percent of the houses were built within 1 year, whereas in the 1990 Census for the area, only 3 percent were built in 1989-1990.

One approach to address differences between our transaction sample and the U.S. Census is to construct weights for the transaction sample. The basic idea is to assign large weights for the observations in the transaction sample that appear to be undersampled based on estimates from the 1990 U.S. Census and small weights to observations that are relatively oversampled. We construct these weights such that the transaction sample matches three attributes of the stock of all owner-occupied housing in the U.S. Census: location, the number of bedrooms, and the age of the house. Hence, the observations on the housing sales are weighted by the relative weight of their school district. Conditional on school districts, they are weighted by the number of bedrooms (in 5 categories) and the age of the house (8 categories), assuming age and bedrooms are independent (the correlation between bedrooms and age was not available). We estimate the price indices and the quartiles for housing using both weighted and unweighted samples (as discussed below, air pollution readings are assigned to each house based on its location in relation to air pollution monitors. The weights applied for housing expenditures also were applied in estimating the average pollution readings in each school district). We estimate the community-specific price indices using ordinary least squares using fixed effects for each community. Another aspect of our research investigated the effects of different approaches for measuring the price indices. This analysis supported the use of the fixed effects and is summarized in Sieg, et al. (2002).

Two spatially delineated public goods, air quality and education, are considered in our model. Data for observed concentrations of ozone and particulate matter less than 10 microns in diameter (PM10) were obtained from the California Air Resources Board monitoring records. Southern California has one of the most extensive air quality monitoring systems in the world. In the five counties of interest, no fewer than 45 monitors were measuring ozone each year from 1987 to 1992 (after eliminating monitors active on less than 50 days). Beginning in 1987, less than 19 were measuring PM10.

There is not a one-to-one correspondence between air quality monitors and school districts. However, the large number of monitors enabled us to interpolate air quality measures for each school district. In Riverside County, for example, one-half of all houses are within 4.5 miles of at least one monitor, and 90 percent are within 9.9 miles. Air pollution is measured using a centered 3-year average (about the sales year) of pollution readings for the nearest monitor to each house in each year of the average. Our temporal window is 1989-1991. We computed the community estimate by using the Census owner weighted and unweighted averages for the houses sold in each community.

Three measures of air pollution, ozone concentration, ozone exceedences, and particulate matter (PM10), are considered for evaluating the effects of air quality. Ozone is measured in parts per million (ppm) as the average of the top 30 1-hour daily maximum readings at a given monitor during a year. The average of the 30 highest ozone readings was the most consistently important air pollution measurement in our estimates and the primary focus of the analysis.

To measure the quality of education, we constructed measures of performance from standardized test scores for each school district using the 1992-1993 California Learning Assessment System Grade Level Performance Assessment test. Each student taking this exam is assessed at one of six performance levels (with six being the highest level).

Table 2 summarizes a few key features of the data, price index estimates, ozone readings, as well as our estimates for the price and income elasticity demand for housing using the two different community definitions. Our estimation strategy assumes that housing can be “unbundled” into a set of structural characteristics of a house (including the lot size) and the site-specific public goods. Hedonic models construct a price index to account for the first influence and measure the residual due to community effects as the fixed effect. This process allows us to interpret our estimates for the housing demand parameters as relating to standardized units of housing. In the case of the 93 school districts version of the model, we reported both Census weighted and unweighted results for comparison. Asymptotic standard errors for the estimates are given in parentheses below the estimated elasticities.

Table 2. Summary of Key Features of Sieg, Smith, Banzhaf, and Walsh Model Results
Los Angeles (59,466 mi2)a
Orange (21,560)
Riverside (19,644)
San Bernadino (16,304)
Ventura (7,851)
93 to 103 school districts
Transactions Price 1989-1991
Price Index
Fixed Effects (unbundle community from structure)
1-6.672 (weighted)
1-7.010 (unweighted)
Average of 30 highest hourly readings
aThe numbers in parentheses are the number of observations for housing sales from each county used in our analysis.
bThis range is the average sales price range across counties in nominal dollars.
cThese numbers correspond to the number of communities used in the model. The values in parentheses below the estimated elasticities are the estimated asymptotic standard errors.

Evaluating Changes in Ozone

Two different policy analyses were conducted with the model. The first, reported along with the details of developing the estimates in Sieg, et al. (2003), considers the observed change in ozone conditions from the time period used to estimate the model 1990 to 1995. The second considers the U.S. Environmental Protection Agency's (EPA) policy evaluation of the impact of the Clean Air Act Amendments for Los Angeles as part of the First Prospective Analysis.

Table 3 summarizes a few of the findings from our analysis of the Hicksian WTP for the change in ozone from 1990 to 1995. Two features of this comparison are important. First, the price flexibility of income () varies with household and is larger than the income elasticities for housing reported in Table 2. Second, there are marked differences in what we have defined as partial and general equilibrium measures for the improvement in ozone. These estimates are reported as positive values. The minus sign in the table legend implies we are reporting the absolute magnitude of the proportionate reduction in ozone experienced by households in this area from 1990 to 1995.

Table 3. Some Illustrative Results for 1990 to 1995 Change in Ozonea


As the results in Table 3 suggest, there can be large differences in the partial equilibrium (PE) and general equilibrium (GE) measures of WTP. Moreover, the differences are not always in one direction. Households originally living in Ventura County experienced a gain measured with WTPGE for the smallest improvement in ozone conditions (about 6 percent reduction in the concentrations), but the overall adjustment also allowed them to realize a 1.2 percent reduction in their housing prices. Taken together, these changes imply a $561 difference per household between the WTPGE and WTPPE in Ventura County.

The reverse situation characterizes households in Riverside County. Although they had one of the largest improvements in ozone conditions (a 20.7 percent reduction), their WTPGE is less than the WTPPE measure. This outcome arises because their housing costs rose by nearly 6 percent.

We conducted two types of comparisons to benchmark our results with others to attempt to address these concerns. Our estimates of annual WTPGE for improved air quality (reduced ozone) fall between 1 and about 2.3 percent of annual income. These estimates would be low in comparison to the health-based assessments of the changes in all air pollutants in the Los Angeles area. However, this assessment is largely judgmental; we did not conduct a formal assessment. The EPA Retrospective and Prospective assessments offer benefit estimates for changes in these same pollutants based largely on their health impacts. We used them as a basis to form our evaluation.

Our interpretation of these results implies that a prudent assessment of our results would treat the effects attributed to the ozone measure as reflecting air pollutants that tend to be jointly present. For the case of our study area, this would likely include particulate matter. The second more specific comparison is discussed in the next section and relates to a comparison of the model's assessment of the benefits measured for the scenarios considered in the EPA's Prospective scenarios relative to the average benefit measures they report based on health effects.

One of the objectives of this research was to assess whether the locational equilibrium framework could be used to provide a localized assessment of large-scale policy effects. Such efforts would parallel the detailed regional and national ambient air quality assessments the EPA undertakes as part of its regulatory assessments. EPA's regional scale methodology relied on the Urban Airshed Model (UAM) and the variable grid-UAM (UAM-V) for ozone concentrations, which also were the primary focus of our policy analyses. UAM with higher resolution was applied to the Los Angeles area. EPA's Los Angeles modeling closely matched the area of our economic model. It is a 65 by 40 array of 5-kilometer resolution grid cells. The domain includes the South Coast Air Basin from Los Angeles to beyond Riverside.

EPA's analysis relates to the ambient concentrations of ozone that result from emissions in future years (2000 and 2010). EPA developed both a base year level of emissions and projected growth of polluting activities for 2000 and 2010 in the absence of Clean Air Act Amendments (CAAA) requirements. These projections were modified to reflect control assumptions in each of these two "future years." For volatile organic compounds (VOCs) and nitrogen oxide (NOx), both contributors to ambient ozone, the national assessment estimates a 27 percent reduction because of CAAA's effects on VOCs in 2000 and a 35 percent reduction in 2010. For NOx, the reduction is comparable for 2000 (i.e., 26 percent) and a little larger in 2010 (39 percent).

The EPA projections, with and without CAAA, considered the conditions for two separate 3-day periods (June 23-25, 1987, and August 26-28, 1987), with baseline conditions augmented by the emission profiles associated with each scenario.

Table 4 summarizes the VOC and NOx emission totals for each scenario in Los Angeles. With the assistance of the EPA staff and its contractors, the three analyses undertaken for Los Angeles were interpolated to a consistent 5-kilometer by 5-kilometer grid cell pattern for the study area included in our analysis.

Our analysis had access to the results of three sets of simulations from the air diffusion models: (1) baseline runs for ambient ozone concentrations in 1990; (2) ambient concentrations in 2000 and 2010, when air pollution regulations are "frozen" at federal, state, and local controls corresponding to their 1990 levels of stringency and effectiveness; and (3) concentrations in 2000 and 2010, when federal, state, and local rules promulgated under the 1990 CAAA are implemented (the ozone concentrations estimated to correspond to the reduced emission levels presented in Table 4).

Table 5 reports for each scenario the averages for the area as a whole (in the first row under each scenario), each county, and then for two of the school districts we profiled in describing the projected changes in ozone concentrations. Our policy comparison solves the locational equilibrium model under the 2000 and 2010 business-as-usual ozone levels (ba00 and ba10). Then, for comparison, the 2000 and 2010 equilibria are computed starting from the ba cases, under the assumption that the 1990 CAAA regulations are implemented in the years 2000 and 2010 (ct00 and ct10).

Table 4. EPA Projected VOC and NOx Emissions for Los Angeles (Tons Per Day)

The first column reports the average proportionate reduction in ozone implied by replacing the baseline 2000 (and 2010) "without CAAA" with the projected "with CAAA controls" for the initially assigned school district (delta2ozone). delta2p in column 2 (labeled "actual") corresponds to the proportionate changes in prices experienced by households whose initial assignment was the identified county or school district. Thus, they reflect the result of any movement between school districts. in the next column corresponds to a measure for what happened to prices in the original location, also reported as a proportionate change. The remaining statistics correspond to the average value for general equilibrium WTP, the WTPGE relative to income, and the WTPPE.

Averaged over all school districts, the discrepancy between the WTPGE and WTPPE measures is small, under $100 per household on average. This result is not surprising because the analysis holds the number of households constant. They resort among a finite set of alternatives under the changed conditions. Improvements in the amenity conditions at one location lead to movements to that area (adjustment is assumed costless), price adjustment results, and the balancing effect of the market reduces the gains available.

Table 5. Alternative Benefit Estimates With (ct) and Without (ba) CAAA Regulations for 2000 and 2010
   Los Angeles
   San Bernadino
Selected School Districts
   Long Beach (89)
   Claremont Unified (75)
Los Angeles
San Bernadino
Selected School Districts
Long Beach (89)
Claremont Unified (75)

All of these estimates were developed using the parameter estimates for the 103 school district models (with Census weights for the hedonic estimates of community specific prices). On average, they are comparable to the estimates derived in EPA's national assessment on a per household basis. Table 6 compares the per household health-related benefits for all criteria pollutants (in 1990 dollars) for 2000 and 2010, with the per household estimates from the Sieg, et al., model for Los Angeles using only the ozone improvements. This type of comparison is not intended to validate the locational model. Rather, it provides an order of magnitude comparison. Despite the parsimony in the parameterization of the Los Angeles analysis, it does appear to gauge the improvements in air quality conditions to be about the same level of importance as the EPA assessment.

Table 6. Comparing the Average Household Gains Estimated in U.S. EPA's Analysis with the Los Angeles Model
1. U.S. EPA Prospective Analysis Health Benefits
   Aggregate (billion)
   Per household (dollars)
2. GE Benefits for Los Angeles Area
   Area Wide Average per household
-47 to 6,136
-118 to 7,347

The last row in Table 6 also highlights a point illustrated at the school district level in Table 7. It reports the range of estimates for the WTPGE across households in these school districts. Households in the lowest income districts do experience losses, despite the fact that the air quality in these communities does improve. The losses stem from increases in their housing costs.

There is an important caveat to this conclusion. The locational equilibrium model requires that we define a finite and fixed set of alternatives. The lowest income households have "nowhere to go" in the model. In a real world setting, there may be areas outside the domain defined by the market area that would provide locations they could "adjust to." Of course, this outcome is not guaranteed. The model assumes costless adjustment, and the low-income households may well be most sensitive to this assumption. Thus, it is not certain that adjustment to areas outside the assumed "market" would mitigate or eliminate these estimated losses.

Overall, these analyses demonstrate that it is feasible to develop models of household preferences for housing and site-specific amenities at a level of spatial resolution that is consistent with the EPA's air quality assessments for policy. Thus, it would be possible in principle to develop micro-consistent models of household behavior at the urban scale level that would be consistent with the more detailed urban scale assessments undertaken for the analysis of air quality.

This research demonstrated that it is possible to estimate household preferences for site-specific air quality conditions that are based on the aggregate predictions implied by a locational equilibrium model. Moreover, it is illustrated how to address questions about the implications of the equilibrium effects on benefit measures derived from property values for changes in spatially delineated public goods. To illustrate how the framework could be used in a specific policy, estimates were developed for the average household's annual WTPGE for the reductions in ozone concentrations in Los Angeles between 1990 and 1995. The measure considered both the ozone improvement and the changes in prices and other exogenous public goods households would make through relocation. They were estimated at about 2 percent of a household's annual income.

It is important to note that the models developed are not full-scale GE models. They do not consider adjustment in factor markets along with commodity markets as is done in the national computable GE models. Nonetheless, they do offer the ability to link economic adjustment to spatial features of economic activities and, as such, to consider one aspect of household adjustment to spatially differentiated amenities. The Los Angeles analysis is the first large-scale application, and considerable additional research would be needed before economic urban scale models, consistent with policy needs, would be available. Specific attention would need to be given to the effects of employment opportunities in locational choice and to evaluate the importance of transactions costs for general equilibrium adjustments. Although these are important issues, the information necessary to address these questions can be assembled. Moreover, some independent research by Bayer, et al. (2003), has suggested related modeling structures that may help to resolve some of the methodological issues associated with implementing the models.

Publications and Presentations:
Journal ArticleSmith VK, Banzhaf HS. A diagrammatic exposition of weak complementarity and the Willig condition. American Journal of Agricultural Economics.
Journal ArticleSieg H, Smith VK, Banzhaf HS, Walsh R. Estimating the general equilibrium benefits of large changes in spatially delineated public goods. International Economic Review.
Journal ArticleSieg H, Smith VK, Banzhaf HS, Walsh R. General equilibrium benefit estimates for environmental improvements: projected ozone reductions for the Los Angeles air basin. Journal of Environmental Economics and Management.
Journal ArticleSieg H, Smith VK, Banzhaf HS, Walsh R. Interjurisdictional housing prices in locational equilibrium. Journal of Urban Economics 2002;52(1):131-153.
Journal ArticleSmith VK, Pattanayak S. Is meta-analysis a Noah's ark for non-market valuation? Environmental and Resource Economics 2002, Volume: 22, Number: 1-2 (JUN), Page: 271-296.
Journal ArticleBanzhaf HS, Smith VK. Meta analysis in model implementation: choice sets and the valuation of air quality improvements. Journal of Applied Econometrics.
Journal ArticleSmith VK, Banzhaf HS. Quality adjusted price indexes and the Willig Condition in one graph. Journal of Economic Theory.
Journal ArticleSieg H, Smith VK, Banzhaf HS, Walsh R. The role of optimizing behavior in willingness to pay estimates for air quality. American Journal of Agricultural Economics 1999;81(5):1112-1117.
Supplemental Keywords:
air pollution benefits, environmental equity, benefit transfer practices, locational equilibrium, ozone improvement, household adjustment, general equilibrium benefit measures, nonmarket valuation of public goods, spatially delineated public goods, optimizing behavior. , Economic, Social, & Behavioral Science Research Program, RFA, Scientific Discipline, Ecology and Ecosystems, Economics, Economics & Decision Making, Social Science, decision-making, air pollution policy, behavior model, collective choice process, ecosystem valuation, locational equilibria

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