Equilibrium Sorting Research Articles

Efficiency and Equity Impacts of Urban Transportation Policies with Equilibrium Sorting

Efficiency and Equity Impacts of Urban Transportation Policies with Equilibrium Sorting

FRICTIONAL SORTING: THE IMPACTS OF DUAL CONSTRAINTS ON MOBILITY AND HOUSING SUPPLY IN CHINA

AbstractUsing an equilibrium sorting model and microdata from China, we evaluate the impacts of dual constraints on mobility and housing supply on workers’ sorting behavior, quantifying the welfare and distributional consequences. Counterfactual simulations show that lowering migration costs associated with institutional restrictions and migrant‐specific amenities would increase welfare and reduce inequality by moving workers from inland to coastal regions in China. These impacts depend on the housing supply elasticity in coastal regions. Similarly, the impacts of relaxing housing supply restrictions depend on mobility constraints. Results highlight the policy complementarities between reducing the two kinds of frictions.

Modeling Steady Grain Sorting in River Bifurcations

AbstractA striking feature of rivers is their ability to sort the sediments composing them. One of the chief causes for grain sorting consists in the selective transport of different sizes moving downstream. This process can be substantially influenced by the presence of lateral topographic variations, as those produced by channel bifurcations, in which water and sediment are diverted between two smaller anabranches. In particular, field and laboratory observations have shown that the asymmetric flux distribution commonly observed in actual bifurcations is associated with a coarsening of the most‐carrying branch. Here, equilibrium sorting in river bifurcations is addressed through a quasi‐2D model. Differently from previous works, a fully physically based description of the processes tied to a heterogeneous sediment mixture is introduced. The main mechanisms consist in the lateral pull of sediment due to a sloping bed upstream the bifurcation, and the variation of transport capacity in downstream branches. The model indicates that grain sorting tends to reduce the degree of flux asymmetry between branches for increasing heterogeneity of the mixture. Moreover, the uneven discharge distribution is associated with a different bed surface composition, with bed coarsening of the dominating channel and fining of the other branch. The reduced sediment transport asymmetry and bed surface fining enhance the transport of fine material in the less‐carrying branch, thus contributing to keep it morphologically active. Finally, the model predicts an overall fining of bed surface material with respect to the feeder channel.

Pricing group membership

We consider a model where agents differ in their ‘types’ which determines their contribution towards a club good (i.e public good within a group). We analyze what the equilibrium composition of groups are under mandated and voluntary choice. We show that there exists a top-down sorting equilibrium i.e. an equilibrium where there exists a set of prices which leads to groups that can be ordered by sets of types, with the highest types in the group paying the highest price and so on. This exists both under mandated and voluntary choosing. We also analyze the model with endogenous group size and examine under what conditions is top-down sorting socially efficient. We illustrate when integration (i.e. mixing types so that each group’s average type is the same) is socially better than top-down sorting.

Equilibrium sorting and moral hazard in residential energy contracts

This paper studies tenant behavior in rental housing when the landlord pays for heating. I develop a model in which renters have heterogeneous preferences for home size and indoor temperature. When energy is costly, renters choose smaller apartments and turn down the heat—or sort into apartments with landlord-pay energy bills. I estimate the model using exogenous variation in energy prices and use a machine-learning algorithm to explore preference heterogeneity. Surprisingly, I find that renters who prefer hotter temperatures do not systematically choose landlord-pay units, though I am unable to rule out sorting on preferences for unobserved home attributes. Eliminating moral hazard by forcing all renters to pay their own bill reduces energy consumption by 25% due to renters turning down the heat (21%) and choosing smaller units (4%). Moral hazard in residential energy contracts costs the United States $836 million per year in welfare losses including $246 million from carbon emissions.

Nash equilibrium sorting genetic algorithm for simultaneous competitive maximal covering location with multiple players

In this article, a new genetic algorithm (GA), called the Nash equilibrium sorting genetic algorithm (NESGA,) is introduced to identify Nash equilibria for the competitive maximal covering location problem with two and three competitors, which is a combinatorial game theory problem where it is computationally intractable to enumerate all decision options of the competitors. Although GAs are widely used in combinatorial optimization, their applications to non-cooperative, simultaneous games have been limited owing to challenges in guiding the evolutionary search to Nash equilibria, which are not necessarily on the Pareto front of the search space and cannot be found by current multi-objective GAs. A novel fitness assignment strategy is proposed to help the NESGA to converge to multiple Nash equilibria. Computational experiments show that the NESGA can discover multiple Nash equilibria in a single run and outperform other game-theoretic GAs.

Cultural Assimilation: Learning and Sorting

immigrants have greater exposure to co-ethnics, leading to fewer incentives to learn the local culture and assimilate. In this paper, the exposure channel through which source country richness affects assimilating immigration is modelled through neighbourhood location choices and incentives to learn the local culture in the host country. Two equilibrium outcomes are identified, in which, there is either only assimilating immigration in at least one neighbourhood of the host country (sorting equilibrium) when immigration is from a rich source country, or there is some non-assimilating immigration in all neighbourhoods (mixed equilibrium) when immigration is from a poor source country. The presence of this exposure channel is tested using data from the Longitudinal Survey of Immigrants in Canada: waves 1-3. Learning, rather than sorting into co-ethnic communities, is the main factor operating in the exposure channel between source country richness and assimilating immigration.

Patient selection in the presence of regulatory oversight based on healthcare report cards of providers: the case of organ transplantation.

Many healthcare report cards provide information to consumers but do not represent a constraint on the behavior of healthcare providers. This is not the case with the report cards utilized in kidney transplantation. These report cards became more salient and binding, with additional oversight, in 2007 under the Centers for Medicare and Medicaid Services Conditions of Participation. This research investigates whether the additional oversight based on report card outcomes influences patient selection via waiting-list registrations at transplant centers that meet regulatory standards. Using data from a national registry of kidney transplant candidates from 2003 through 2010, we apply a before-and-after estimation strategy that isolates the impact of a binding report card. A sorting equilibrium model is employed to account for center-level heterogeneity and the presence of congestion/agglomeration effects and the results are compared to a conditional logit specification. Our results indicate that patient waiting-list registrations change in response to the quality information similarly on average if there is additional regulation or not. We also find evidence of congestion effects when spatial choice sets are smaller: new patient registrations are less likely to occur at a center with a long waiting list when fewer options are available.

Efficiency and Equity Impacts of Urban Transportation Policies with Equilibrium Sorting

We estimate an equilibrium model of residential sorting with endogenous traffic congestion to evaluate the efficiency and equity impacts of urban transportation policies. Leveraging fine-scale data on household travel diaries and housing transactions with home and work locations in Beijing, we jointly estimate travel mode and residential location decisions. The estimation highlights the importance of incorporating work commute in housing decisions and features preference heterogeneity for the ease of work commute by gender. Counterfactual simulations show that while different policies can attain the same level of congestion reduction, their impacts on residential sorting and social welfare are drastically different. First, a driving restriction intensifies income-stratified urban structure where high-income households live closer to subway and work. Distance-based congestion pricing reduces the spatial separation between residence and workplace across income levels, while subway expansion does the opposite. Second, residential sorting strengthens the effectiveness of congestion pricing in improving traffic conditions but undermines that of the driving restriction and subway expansion. Third, the driving restriction is welfare reducing as it leads to large distortions on travel choices. Congestion pricing improves welfare but is regressive, highlighting the need to recycle revenue to address the associated equity concern. Finally, congestion pricing and subway expansion when combined deliver the largest congestion relief and efficiency gain and at the same time achieve self-financing, with revenue from congestion pricing fully covering the cost of subway expansion.

The Welfare Impacts of Large Urban Noise Reductions: Implications from Household Sorting in Vienna

We develop a pure characteristics equilibrium sorting model to recover estimates of willingness to pay (WTP) for both marginal and non-marginal changes in urban noise exposure. Using data from Vienna, Austria, we provide several new insights in the urban noise literature. First, we demonstrate the importance of considering general equilibrium feedback effects following large changes in noise levels. We document impacts to residents in policy targeted and non-targeted locations due to changes in both noise and equilibrium prices. Second, we confirm evidence of the importance of noise thresholds with significant and increasing negative impacts associated with increases in area covered by high levels of noise at 50 dB and 60 dB thresholds, respectively. Finally, we use an equilibrium sorting model to predict new price patterns and welfare implications following hypothetical policy changes that alter the distribution and intensity of nighttime noise in Vienna and are relevant to other urban settings seeking to reduce noise levels. Our work additionally provides a roadmap for conducting similar equilibrium sorting work in data limited settings outside the U.S.

Teacher Compensation and Structural Inequality: Evidence from Centralized Teacher School Choice in Peru

This paper studies how increasing teacher compensation at hard-to-staff schools can reduce inequality in access to qualified teachers. Leveraging an unconditional change in the teacher compensation structure in Peru, we first show causal evidence that increasing salaries at less desirable locations attracts better quality applicants and improves student test scores. We then estimate a model of teacher preferences over local amenities, school characteristics, and wages using geocoded job postings and rich application data from the nationwide centralized teacher assignment system. Our estimated model suggests that the current policy is helpful but both inefficient and not large enough to effectively undo the inequality of initial conditions that hard-to-staff schools and their communities face. Counterfactual analyses that incorporate equilibrium sorting effects characterize alternative wage schedules and quantify the cost of reducing structural inequality in the allocation of teacher talent across schools. Overall our results show that a policy that sets compensation at each job posting using the information generated by the matching platform is more efficient and can help reduce structural inequality in access to learning opportunities. In comparison, a rigid system that ignores teacher preferences will indirectly reinforce such inequalities.

Accounting for Tuition Increases Across U.S. Colleges

This paper sheds light on the persistent rise in college tuition between the late 1980s and the Great Recession using a combination of detailed micro data and a newly developed dynamic equilibrium model of the higher education, student loan, and labor markets. The model features equilibrium sorting between heterogeneous students and imperfectly competitive colleges that gives rise to rich tuition pricing patterns within and across institutions. The integration of this framework into a full life cycle model with income risk, student loan borrowing, and default makes it possible to disentangle the contribution of several different economic forces to increasing college prices. The quantitative analysis successfully accounts for the entire growth in net tuition during this period and identifies demand-side factors--particularly expansions in federal student aid and rising parental transfers--as the primary culprits, followed by more modest supply-side contributions from lagging public funding and Baumol's cost disease.

Within-Job Wage Inequality: Performance Pay and Job Relatedness

Over the past few decades, we find that about 80% of the widening residual wage inequality to be within jobs. We propose performance-pay incidence and job relatedness as two primary factors driving within-job inequality and embed them into a sorting equilibrium framework. We show that equilibrium sorting is positive assortative both within-job and across jobs. While performance-pay position amplifies within-job wage inequality through self-selection, the overall relationship between job relatedness and within-job wage inequality is found generally ambiguous. To quantify the role played by these factors, we calibrate the model to the US economy in 2000, where the model can account around 92% of the changes in within-job inequality among the highly educated from 1990 to 2000. Counterfactual analysis shows the contributions of performance-pay incidence and job relatedness are about 42% and 26%, respectively, both higher than that of job-specific productivity. While performance-pay incidence is particularly crucial for within-job wage dispersion in business/professional industry and professional occupation, job relatedness is the most important for mining/goods/construction industry and sales occupation.

Willingness to pay for clean air in China

We use a residential sorting model incorporating migration disutility to recover the implicit value of clean air in China. The model is estimated using China Population Census Data along with PM2.5 satellite data. Our study provides new evidence on the willingness to pay for air quality improvements in developing countries and is the first application of an equilibrium sorting model to the valuation of non-market amenities in China. We employ two instrumental variables based on coal-fired electricity generation and wind direction to address the endogeneity of local air pollution. Results suggest important differences between the residential sorting model and a conventional hedonic model, highlighting the role of moving costs and the discreteness of the choice set. Our sorting results indicate that the economic value of air quality improvement associated with a one-unit decline in PM2.5 concentration is up to $8.83 billion for all Chinese households in 2005.

Sorting into Contests: Evidence from Production Contracts

Abstract In this paper, we investigate sorting patterns among chicken producers who are offered a menu of contracts to choose from. We show that the sorting equilibrium reveals a positive sorting where higher ability producers self-select themselves into contracts to grow larger chickens and lower ability types self-select themselves into contracts to grow smaller birds. We also show that eliciting this type of sorting behavior is profit maximizing for the principal. In the empirical part of the paper, we first estimate growers’ abilities using a two-way fixed effects model and subsequently use these estimated abilities to estimate a random utility model of contract choice. Our empirical results are supportive of the developed theory.

Racial Residential Segregation: Measuring Location Choice Attributes of Environmental Quality and Self-Segregation

Both sorting on public goods and tastes for segregation contribute to the persistence of segregation in America. Incorporating Schelling’s (1969, 1971) concept of “neighborhood tipping” into a two-stage equilibrium sorting model, in which both neighborhood demographic composition and public goods (e.g., environmental quality) affect households’ residential location choice, this study investigates how preferences for neighborhood demographic composition could obscure the role of exogenous public goods on segregation. The results reveal that non-white households face higher level of exposure to air pollution, suggesting the presence of environmental injustice in Franklin County, OH. Using a counterfactual scenario of switching off heterogeneous taste for environmental quality, this study identifies that sorting on Toxic Release Inventory (TRI) emissions drives little correlations between emissions and demographics. However, when taste parameters of the interactions between neighborhood demographic composition and household race are eliminated, segregation (as measured by over-exposure to households of the same race) of black and white households decreases by 7.63% and 16.36%, respectively, and own-race neighbor preferences contribute to segregation differently according to household income. These results may help explain some recent puzzles in the relationship between environmental quality and demographics.

Can Understanding Spatial Equilibria Enhance Benefit Transfers for Environmental Policy Evaluation?

A conceptual model of consumer sorting in markets for housing, labor and health care is outlined and used to make three points about how benefit transfers are used for environmental policy evaluation. First, the standard approach to assessing benefits of air quality improvements by transferring the value of a statistical life from labor market studies embeds several untested (but testable) assumptions. Second, if the cost of an environmental policy exceeds its capitalized effect on housing prices, then the capitalization effect is an insufficient statistic for determining whether benefits exceed costs. Third, there are several ways in which equilibrium sorting models may be usefully extended to assess distributional welfare effects of environmental policies.

Town mouse and country mouse: Effects of urban growth controls on equilibrium sorting and land prices

Urban growth controls can preserve open space and other amenities, but may come at the expense of higher land and housing prices. Previous studies quantify the benefits and costs of land-use regulations by comparing properties subject to differing degrees of regulatory intensity. A separate, but related, issue is how housing and land markets will evolve over time when a set of regulations remains in place. We examine how the value of developed land changes over time in cities that have adopted urban growth boundaries (UGBs). We present a theoretical model that combines equilibrium sorting, spatially-varying amenities, and urban growth controls. The model is used to examine how prices for developed lands inside and outside the UGB change with growth in the city's population. The UGB is shown to increase relative prices of exurban lands outside the UGB if new residents prefer the amenities in this area. The UGB also affects relative prices by influencing the quality of developed lands. We use a parcel-level panel data set on developed land values to quantify the scarcity and quality effects of UGBs in Oregon. Our results suggest that, overall, UGBs have prevented the development of exurban lands that residents would have preferred over lands closer to the urban center.

Policy Analysis in Matching Markets

Price and quantity interventions intended to affect assignments are common in many labor and education markets (e.g., financial aid, quotas). This article discusses an empirical framework, based on the theory of stable matching, that is suitable for policy analysis while accounting for the presence of equilibrium sorting. It then compares financial incentives and supply interventions for encouraging the training of family medicine residents in rural America. Due to equilibrium effects, the primary effect of financial incentives is to increase the quality, not numbers, of residents in rural programs, while quantity regulations directly affect numbers without adversely affecting quality.

How Property Markets Determine Welfare Outcomes: An Equilibrium Sorting Model Analysis of Local Environmental Interventions

This paper examines the pivotal role played by property markets in determining the magnitude and distribution of welfare changes resulting from localised environmental change. We address that issue using an equilibrium sorting model (ESM) calibrated, by way of example, to the circumstances of a road infrastructure project in the English town of Polegate. Previous ESM research has tended to assume that all households rent property from a fixed property stock. The narrative that arises from those models concerns environmental gentrification, wherein access to environmentally improved locations is appropriated by the relatively wealthy through their ability to out-compete the less wealthy in the rental property market. Our research shows that to be only part of a much more complex story. We develop a model that extends the sophistication with which ESMs replicate property market dynamics, allowing for households to choose whether to rent or purchase their home and introducing greater realism into housing supply responses to changing market conditions. Our research shows that property markets redistribute welfare gains across the population in complex ways in which tenure choice and housing supply constraints play central roles.