Heterogeneity, individual decision making and matching equilibria under uncertainty

本项目分为两部分；这两项研究都在先前资助的研究范围内。-第一部分将扩展使用偏微分方程的连续和离散选择模型的非参数识别的结果，并提供在不确定性下由异构代理决策的应用。我们将从一般的理论角度考虑非参数识别问题，特别强调识别条件在一个未知函数中产生（至少两个）一阶偏微分方程系统的背景-这是几种经济模型中常见的结构，包括家庭行为的“集体”模型。这些理论思想可以应用于具体的问题，特别是关于离散选择模型的非参数识别。特别是，我们计划分析具有异构代理和未观察到的产品特性的（多重）离散选择模型，这些模型经常用于实证IO文献（所谓的“BLP”模型）。然后将这些理论工具应用于涉及不确定性下决策的具体问题。虽然决策理论在过去几十年里取得了巨大的进步，但许多（如果不是大多数）实证研究仍然指的是依赖于预期效用、真实概率和代表性消费者的标准框架。我们的目标是测试和非参数估计不确定性下决策的经验模型，包括非预期效用、概率变形（或“风险感知”）和不可观察的异质性。第二部分是匹配理论。同样，它将包括理论和实证工作。在理论方面，我们计划分析标准匹配理论的几个扩展，包括多维匹配、没有可转移效用的匹配、独特群体内的匹配（所谓的“室友问题”）、匹配的动态等。在经验方面，我们将首先仔细地重新考虑与匹配模型的经验估计有关的问题；特别是，如何在匹配模型中引入（合理的）随机结构。然后，我们计划将这些模型应用于实证问题，特别强调两个主题：风险分担和婚姻市场上的匹配。虽然该项目的一些成果将相当技术性，但利害关系显然是普遍的。第一部分的最终目的是提高我们对不确定性下决策的理解。现代决策理论强调了几个以前被忽视的模式。一个是风险感知的重要性（正式地说，就是通常所说的概率变形）。标准理论假定一个完全透明的感知过程——即，人们只是使用“真实”的概率，至少当它们是已知的。实际上，事情要复杂得多，风险评估是一种复杂的（部分或大部分）主观操作，可能反映决策者的特质。虽然相应的理论现在已经很发达，但对这些问题的实证分析主要集中在实验室实验上。我们的目标是超越实验，这些实验不可避免地有其局限性（特定人群，小赌注，实验条件……），并尝试将这些概念应用于“现实生活”情境。实现这一目标的第一个要求是认真地重新考虑经验方法，我们计划在今后几年中进行这一工作。另一方面，匹配模型越来越广泛地应用于许多主题的研究。我们自己的调查从根本上是由一个基本信念驱动的——即，家庭内部的权力分配对家庭决策很重要。例如，我们认为，当某项福利支付给妻子而不是丈夫时，可能不会产生同样的行为结果（比如，在孩子身上的投资）。尽管这种说法听起来很明显，而且可能得到许多实证结果的支持，但值得注意的是，至少在上世纪90年代之前存在的标准消费者理论，只是假设了这种差异影响。事实上，基于预算约束下独特的家庭效用最大化的主导模型暗示了一种收入汇集属性，即只有总收入，而不是其不同组成部分可能重要。过去的研究，部分由以前的国家科学基金会资助，为一个更一般的概念框架提供了理论基础和实证支持，在这个框架中，配偶各自的决策权确实影响结果。我们当前的主题是更好地理解这种力量的产生。特别是，我们计划调查婚姻市场上的法律和人口条件如何影响家庭内部决策权的分配，并最终影响家庭行为。这些条件包括有关离婚和赡养费的法律，也包括男女之间的性别比例、收入分配和教育。举两个例子：在过去的几十年里，男女对高等教育需求的巨大差异可以用教育对婚姻市场不断变化的影响来解释。具体来说，Chiappori， Iyigun和Weiss （AER 2009， nsf资助）已经校准了一个模型，表明观察到的结果的符号和大小都可以用这种类型的模型来解释。我们计划将这一理论应用到美国过去50年的婚姻模式数据中，看看观察到的经验模式是否支持或证伪我们的方法。-一些婚姻市场的一个显著特征，特别是在中国和印度，是最近出现的严重不平衡的性别比例（在一些邦，男女比例高达125比100）。这种不平衡将对家庭内部资源配置产生强烈影响；我们计划对这些影响进行建模和量化。更重要的是，我们将研究由此产生的再分配将如何改变个人获取和维持人力资本的动机；特别是，人们是否可以预期女性对人力资本的需求会显著增加，这可能会进一步加剧不平衡。最后，有一个主题是前面两个主题的交集，即风险分担。我们计划更好地了解一般家庭和社区如何应对收入冲击，特别是风险补偿转移和劳动力供给调整的各自作用和相互作用。同样，重点将放在性别问题（男性和女性各自决策权的差异是否影响家庭对冲击的反应？）和匹配问题（如何开始形成风险分担网络？）

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?).