Segregation in networks

Schelling [Schelling, T., 1969. Models of segregation. American Economic Review 59, 488–493; Schelling, T., 1971a. Dynamic models of segregation. Journal of Mathematical Sociology 1, 143–186; Schelling, T., 1971b. On the ecology of micromotives. The Public Interest 25, 61–98; Schelling, T., 1978. Micromotives and Macrobehavior. W.W. Norton and Company, New York] considered a model with individual agents who only care about the types of people living in their own local neighborhood. The spatial structure was represented by a one- or two-dimensional lattice. Schelling showed that an integrated society will generally unravel into a rather segregated one even though no individual agent strictly prefers this. We generalize this spatial proximity model to a proximity model of segregation, examining models with individual agents who interact ‘locally’ in a range of more general social network structures. The levels of segregation attained are in line with those reached in the lattice-based spatial proximity model.     

Aumann's and Schelling's Game Theory: The Nobel Prize in Economic Science, 2005

Abstract

Robert Aumann and Thomas Schelling won the Nobel Prize in Economic Science in 2005. Their work in game theory shows two different approaches to understanding strategic interaction. Schelling's work on the strategic aspects of negotiations, focal points, and self-command is mathematically informal and is based on experimental and inductive knowledge of players' capabilities. Aumann's work on repeated games and common knowledge is mathematically deductive, and assumes highly rational agents. An exploration of their work allows for a comparison of these two approaches.     

Racial segregation and the black–white test score gap

Racial segregation is often blamed for some of the achievement gap between blacks and whites. We study the effects of school and neighborhood segregation on the relative SAT scores of black students across different metropolitan areas, using large microdata samples for the 1998–2001 test cohorts. Our models include detailed controls for the family background of individual test-takers, school-level controls for selective participation in the test, and city-level controls for racial composition, income, and region. We find robust evidence that the black–white test score gap is higher in more segregated cities. Holding constant family background and other factors, a shift from a highly segregated city to a nearly integrated city closes about one-quarter of the raw black–white gap in SAT scores. Specifications that distinguish between school and neighborhood segregation suggest that neighborhood segregation has a consistently negative impact while school segregation has no independent effect, though we cannot reject equality of the two effects. Additional tests indicate that much of the effect of neighborhood segregation operates through neighbors' incomes, not through race per se. Data on enrollment in honors courses suggest that within-school segregation increases when schools are more highly integrated, potentially offsetting the benefits of school desegregation and accounting for our findings.     

Tax evasion and social interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's [Manski, C.F. (1993). Identification of Endogenous Social Effects: The Reflection Problem. Review of Economic Studies 60(3), 531–542.] nomenclature, our model takes into account endogenous interactions, i.e., social conformity effects, exogenous interactions, i.e., fairness effects, and correlated effects. Our model is tested using experimental data. Participants must decide how much income to report given individual and group tax rates and audit probabilities, and given a feedback on the other members' reporting behavior. Myopic and self-consistent expectations are considered in the analysis. In the latter case, the estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf [Brock, W.A., Durlauf, S.N. (2001b). Interactions-Based Models, in J. Heckman and E. Leamer, eds., Handbook of Econometrics 5, Elsevier Science B.V., 3297–380.], the intrinsic nonlinearity between individual and group responses helps identify the model. Our results provide evidence of fairness effects but reject social conformity.     

“From warfare to welfare”: Contextualising Arrow and Schelling's models of racial inequalities (1968–1972)*

ABSTRACT

This paper focuses on Arrow and Schelling's contributions to the study of racial inequality in the late 1960s. We start from the authors’ account of the origin of their work. Then, we locate the “material origin” of the models at the RAND Corporation in the late 1960s and show how it relates to the transfer of the RAND tool-box to the study of welfare issues. Finally, we describe how Arrow's and Schelling's modelling strategies relate to their conception of “science for action,” inherited from their “warfare” work.     

The α-beauty contest: Choosing numbers,thinking intervals

We present a model for the α-beauty contest that explains common patterns in experimental data of one-shot and iterative games. The approach is based on two basic assumptions. First, players iteratively update their recent guesses. Second, players estimate intervals rather than exact numbers to cope with incomplete knowledge of other players' rationality. Under these assumptions we extend the cognitive hierarchy model of Camerer et al. [Camerer, C., Ho, T., Chong, J., 2003b. A cognitive hierarchy model of one-shot games. Quart. J. Econ. 119, 861–898]. The extended model is estimated on experimental data from a newspaper experiment.     

Optimum commodity taxation in pooling equilibria

This paper extends the standard model of optimum commodity taxation (Ramsey, F., 1927. A Contribution to the Theory of Taxation. Economic Journal 37, 47–61; Diamond, P., Mirrlees, J., 1971. Optimal Taxation and Public Production, II: "Tax Rules". American Economic Review 61, 261–278) to a competitive economy in which markets are inefficient due to asymmetric information. Insurance markets are prime examples: consumers impose varying costs on suppliers but firms cannot associate costs with individual customers and consequently all are charged equal prices. In such a competitive pooling equilibrium, the price of each good is equal to the average of individual marginal costs weighted by equilibrium quantities. We derive modified Ramsey–Boiteux Conditions for optimum taxes in such an economy and show that, in addition to the standard formula, they include first-order effects which reflect the deviations of prices from marginal costs and the response of equilibrium quantities to the taxes levied. An explanation of the additional terms is provided. It is shown that a condition on the monotonicity of demand elasticities enables to sign the direction of the deviations from the standard case.     

Preference Evolution,Two-Speed Dynamics,and Rapid Social Change

We present a dynamic analysis of the evolution of preferences in a strategic environment. In our model, each player's behavior depends on both the game's payoffs and his idiosyncratic biases, but only the game's payoffs determine his evolutionary success. Dynamics run at two speeds at once; while natural selection slowly reshapes the distribution of preferences, players quickly learn to behave as their preferences dictate. We establish the existence and uniqueness of the paired trajectories of society's preferences and behavior. While aggregate behavior adjusts smoothly in equilibration games, in coordination games aggregate behavior can jump discretely in an instant of evolutionary time. Journal of Economic Literature Classification Numbers: C72, C73.     

Social preferences and moral biases

An emerging consensus in economics is that three motives are at work in strategic decisions: distributive preferences, reciprocal preferences and self-interest. An important obstacle, however, has been moral biases: distortions created by self-interest can obscure our measures of social preferences. This paper describes a simple experiment to address this. We compare the decisions of implicated “stakeholders” with those of impartial “spectators.” We find that stakeholders are less inclined to respond to the generosity of others than are spectators. We also clarify a result in previous research [e.g., Offerman, T., 2002. Hurting hurts more than helping helps. European Economic Review 46, 1423–1437] that stakeholders punish unkindness more than they reward kindness. We find that this asymmetry in reciprocity has two sources: an asymmetry in the underlying preference that even impartial spectators display and a moral bias; stakeholders punish more and reward less than spectators. In sum, we find that all three motives have important and significant effects on final allocations.     

Mutual Insurance,Individual Savings,and Limited Commitment

We examine a dynamic model of mutual insurance when households can also engage in self-insurance by storage. We assume that there is no enforcement mechanism, so that any insurance is informal and must be self-enforcing. We show that consumption allocations satisfy a modified Euler condition and that an enhanced storage technology can either improve or diminish welfare. Furthermore we show that the ex ante transfers introduced into dynamic informal insurance models recently by Gauthier et al. (Gauthier, C., Poitevin, M., and González, P. (1997). Journal of Economic Theory76, 106–144) are only used here in the first period, with the role of ex ante transfers being replaced by differential individual storage. Journal of Economic Literature Classification Numbers: C61, C73, D90, E21.     

In search of stars: Network formation among heterogeneous agents

This paper reports results from a laboratory experiment on network formation among heterogeneous agents. The experimental design extends the Bala–Goyal [Bala, V., Goyal, S., 2000. A non-cooperative model of network formation, Econometrica 68, 1131–1230] model of network formation with decay and two-way flow of benefits by introducing agents with lower linking costs or higher benefits to others. Furthermore, agents' types may be common knowledge or private information. In all treatments, the (efficient) equilibrium network has a “star” structure. While equilibrium predictions fail completely with homogeneous agents, star networks frequently occur with heterogeneous agents. Stars are not born but rather develop: with a high-value agent, the network's centrality, stability, and efficiency all increase over time. A structural econometric model based on best response dynamics and other-regarding preferences is used to analyze individual linking behavior. Maximum-likelihood estimates of the underlying structural parameters, obtained by pooling data from several treatments, allow us to explain the main treatment effects.     

Temporal risk and the nature of induced preferences

It has been known since the work of H. Markowitz (“Portfolio Selection: Efficient Diversification of Investments,” Yale Univ. Press, 1959) and J. Mossin (Amer. Econ. Rev.59 (1969), 172–174) that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms will not choose over delayed (i.e., “temporal”) risky prospects in a manner which can be modelled as expected utility maximizing. Since most economically important instances of risk taking (insurance, real investment, agriculture, career training) involve delayed as opposed to immediately resolved risk, the standard use of expected utility theory to model such decisions must be questioned. In this paper the technique of “generalized expected utility analysis” (M. J. Machina, Econometrica50 (1982), 277–323) and the theory of support functions (R. T. Rockafellar, “Convex Analysis,” Princeton Univ. Press, 1970) are applied to exactly model and hence determine the nature of preferences over temporal risky prospects.     

An empirical comparison of implied tree models for KOSPI 200 index options

This paper compares implied tree models for KOSPI 200 index options with regards to the pricing and hedging performance. With Cox, Ross, and Rubinstein's [Cox, J., Ross, S., & Rubinsteinm, M., 1979. Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263] standard binomial tree (SBT) model as a benchmark, we analyzed three models: Rubinstein's [Rubinstein, M., 1994. Implied binomial trees. Journal of Finance, 49, 771–818] implied binomial tree (IBT), Jackwerth's [Jackwerth, J. C., 1997. Generalized binomial trees. Journal of Derivatives, 5, 7–17] generalized binomial tree (GBT), and Derman and Kani's [Derman, E., & Kani, I., 1994. Riding on a smile. Risk, 7, 32–39] implied volatility tree (IVT) models. The SBT model, the simplest, shows the best performance. Moreover, the delta-hedged strategy in all of the binomial models generates, on average, negative gains. This finding, consistent with the findings by Bakshi and Kapadia [Bakshi, G., & Kapadia, N., 2003. Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies, 16, 527–566], indicates the existence of a negative market volatility risk premium.     

A note on optimal income taxation,public goods provision and robust mechanism design

This paper extends the model of optimal income taxation due to Mirrlees (Mirrlees, J., 1971. An exploration in the theory of optimum income taxation. Review of Economic Studies 38, 175–208) and includes private information on public goods preferences. A mechanism design approach is used to establish the following result: If policies are required to be robustly implementable in the sense of Bergemann and Morris (Bergemann, D., Morris, S., 2005. Robust mechanism design. Econometrica 73, 1771–1813), then the optimality conditions in the extended model with uncertainty about tax and expenditure policies are the same as in the standard model of optimal income taxation. The paper provides a foundation for a widely-used assumption in public finance, namely that individuals optimize their behavior subject to a predetermined and commonly known tax system.     

Politicians and Preferences of the Voter Majority: Does Gender Matter?

Does the gender of political representatives affect the extent to which they adhere to the voter majority's preferences? By matching individual male and female representatives' votes on legislative proposals with real referendum outcomes on the same issues, we obtain a direct measure of divergence. We find that female and male representatives adhere equally close to the majority's preferences if party affiliations are taken into account. This suggests that observed gender differences with respect to the national majority of voters may be reduced to an ideological left–right dimension.     

Market access for sale

This paper focuses on the links between foreign lobbying and preferential market access granted by the United States' government to exporters in the rest of the Americas. We first develop a simple framework based on Grossman and Helpman [Grossman, G., Helpman, E., 1994. Protection for sale. American Economic Review 84 (4) 833–850.] to explain how lobbying by foreign firms affects their preferential access to the United States market. We then estimate the model using data on tariff preferences and lobby contributions for the 34 countries in the region. Empirical results suggest that foreign lobbying is an important force behind preferential market access to the United States. The structural estimates indicate that the weight given to foreign lobby contributions in the United States' government objective function is five times higher than the weight granted to tariff revenue forgone due to preferences. Thus, our results indicate that market access is up for sale and foreign lobbies are buying it.     

Racial Preferences in Dating

We examine racial preferences in dating. We employ a Speed Dating experiment that allows us to directly observe individual decisions and thus infer whose preferences lead to racial segregation in romantic relationships. Females exhibit stronger racial preferences than males. The richness of our data further allows us to identify many determinants of same-race preferences. Subjects' backgrounds, including the racial composition of the ZIP code where a subject grew up and the prevailing racial attitudes in a subject's state or country of origin, strongly influence same-race preferences. Older subjects and more physically attractive subjects exhibit weaker same-race preferences.     

Wealth effects and agency costs

We analyze how the agent's initial wealth affects the principal's expected profits in the standard principal–agent model with moral hazard.We show that if the principal prefers a poorer agent for all specifications of action sets, probability distributions, and disutility of effort, then the agent's utility of income must exhibit a coefficient of absolute prudence less than three times the coefficient of absolute risk aversion for all levels of income, thus strengthening the sufficiency result of Thiele and Wambach (1999). Also, we prove that there is no condition on the agent's utility of income alone that will make the principal prefer richer agents. Moreover, we show that, for an interesting class of problems, the principal prefers a relatively poorer agent if agent's wealth is sufficiently large. Finally, we discuss how alternative ways of modeling the agent's outside option affects the principal's preferences for agent's wealth.     

Bargaining and Boldness

We study a multiperson bargaining problem with general risk preferences through the use of Shaked's game of cycling offers with exogenous breakdown. If preferences are “smooth,” then as the risk of breakdown vanishes, the limiting outcome is one in which bargainers are equally marginally bold; where a bargainer's marginal boldness measures his willingness to risk disagreement in return for a marginal improvement in his position. Under smoothness, any (ordinal-)Nash solution is an equally marginally bold outcome. However, unlike the concept of the (ordinal-)Nash solution, a unique equally marginally bold outcome exists in natural cases—in particular, if all bargainers have risk-averse preferences of the rank-dependent expected utility type. For these preferences, the equally marginally bold outcome maximizes a “bargaining power”-adjusted (asymmetric) Nash product where the degree of asymmetry is determined by the disparity in the marginal valuation of certainty among bargainers. Journal of Economic Literature Classification Numbers: C72, C78, D81.