Heterogeneity Individual Decision Making and Matching Equilibria Under Uncertainty

National Science Foundation, SES-1124277
Principal Investigator: Pierre AndrĂ© Chiappori

Abstract

The project is in two parts; both are in the line of previously funded research.

The first part will extend results obtained on non-parametric identification of continuous and discrete choice models using partial differential equations, and provide an application to decision under uncertainty by heterogeneous agents. We shall consider the issue of non-parametric identification from a general, theoretical perspective, a particular emphasis being put on contexts in which identification conditions generate systems of (at least two) first order PDEs in one unknown function - a structure common in several economic models, including 'collective' models of household behavior. These theoretical ideas can then be applied to specific questions, regarding in particular non-parametric identification of discrete choice models. Particularly, we plan to analyze models of (multiple) discrete choice with heterogeneous agents and unobserved product characteristics, frequently used in the empirical IO literature (the so-called 'BLP' models). These theoretical tools will then be applied to specific issues involving decision under uncertainty. While decision theory has made dramatic progresses in the last decades, many (if not most) empirical studies still refer to a standard framework that relies on expected utility, true probabilities and a representative consumer. Our goal is to test and non-parametrically estimate empirical models of decisions under uncertainty involving non-expected utility, probability deformation (or 'risk perception') and unobservable heterogeneity.

The second part is devoted to matching theory. Again, it will include theoretical and empirical work. On the theory front, we plan to analyze several extensions of standard matching theory, including multidimensional matching, matching without transferable utility, matching within a unique population (the so-called 'roommates problem'), dynamics of matching and others. On the empirical front, we shall first carefully reconsider issues linked to the empirical estimation of matching models; in particular, how can a (reasonable) stochastic structure be introduced within a matching model. We then plan to apply these models to empirical issues, with a particular emphasis on two topics: risk sharing and matching on the marriage market.

While some outcomes of the project will be fairly technical, the stakes are clearly general. The first part is ultimately aimed at improving our understanding of decision-making under uncertainty. Modern decision theory has emphasized several patterns that had been previously neglected. One is the importance of risk perception (which, formally, translates into what is often called probability deformation). Standard theory used to assume a fully transparent perception process - i.e., people simply use 'true' probabilities, at least when they are known. In reality, matters are much more complex, and risk assessment is a sophisticated and (partly or largely) subjective operation that may reflect the decision-maker's idiosyncrasies. While the corresponding theory is by now well developed, empirical analysis of these issues has largely concentrated on laboratory experiments. Our goal is to go beyond experiments, which unavoidably come with their limitations (selected populations, small stakes, experimental conditions ...), and try to apply these notions to 'real life' situations. The first requirement to achieve this goal is a serious reconsideration of empirical methods, which we plan to undertake in the coming years.

Matching models, on the other hand, are more and more widely used to study many topics. Our own investigation is fundamentally motivated by one basic belief - namely, that the intrahousehold distribution of power matters for household decision making. We believe, for instance, that a given benefit may not have the same behavioral outcomes (in terms of, say, investment on children) when paid to the wife instead of the husband. Obvious as this claim may sound - and supported as it may be by a number of empirical results - it is worth noting that standard consumer theory, at least as it existed until the 90s, was simply assuming away such a differential impact. Indeed, the dominant model, based on the maximization under budget constraint of a unique, household utility, implied an income pooling property, whereby only aggregate income, not its different component, may matter. Past research, funded in part by previous NSF grants, has provided both theoretical foundations and empirical support for a more general conceptual framework, in which the spouses' respective decision powers do influence outcomes. Our current topic is to better understand the generation of such powers. In particular, we plan to investigate how the legal and demographic conditions on the marriage market influence the allocation of decision power within the household - and, ultimately, household behavior. These conditions include laws governing divorce and alimony, but also the sex ratio and the distribution of earnings and education among men and among women. Two examples can be mentioned:

- The spectacular discrepancy between male and female demand for higher education over the last decades can be explained by the changing impact of education on marriage markets. Specifically, Chiappori, Iyigun and Weiss (AER 2009, NSF-funded) have calibrated a model showing that both the sign and the magnitude of the observed outcomes could be explained by a model of this type. We plan to take this theory to data on marital patterns in the US over the last 50 years, to see whether observed empirical patterns support or falsify our approach.

- A striking feature of some marriage markets, particularly in China and India, is the recent emergence of hugely imbalanced sex ratios (up to 125 men for 100 women in some states). Such disequilibria will have strong effects on intrahousehold allocation of resources; we plan to model and quantify these effects. More importantly, we shall investigate how the resulting reallocations will alter individual incentives to acquire and maintain human capital; in particular, whether one can expect a significant increase in female demand for human capital, which could further exacerbate the disequilibrium.

Finally, a topic lies at the intersection of the previous two themes, namely risk sharing. We plan to better understand how households and communities in general cope with income shocks, especially the respective roles of and the interactions between risk-compensating transfers and labor supply adjustments. Again, emphasis will be put on gender issues (do variations in male and female respective decision powers influence the household's reactions to shocks?) and on matching (how are risk sharing networks formed to start with?).

http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=1124277