Nonparametric Identification and Estimation of Distributions of Unobserved Heterogeneity in Economic Choice Models using Mixtures

使用混合的经济选择模型中未观察到的异质性分布的非参数识别和估计

• 批准号: 0922046
• 负责人: Amit Kumar Gandhi
• 金额: $ 16万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-10-01 至 2010-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0922046&HistoricalAwards=false
• 关键词: Nonparametric; Identification; Estimation; Distributions; Unobserved

Structural economic choice models show how individual agents (firms, consumers, workers) make choices under different choice sets. There is no reason to believe that the parameters of these models are the same for all agents: agents will make different choices when faced with the same choice set. As the parameters vary across agents, the goal of empirical work with these models is to estimate the distribution of unobserved heterogeneity, or the distribution of random coefficients. This distribution is needed to calculate the welfare effects of a policy (say consumer surplus from a tax policy) or to compute demand for a new good, out of sample. In terms of statistical theory, a model with unobserved heterogeneity is called a mixtures model. The statistics literature has focused attention on mixtures of distributions in some parametric class, such as mixtures of normals. Much less attention has been paid to using the tools of mixtures to study more complex nonlinear statistical models, such as structural economic choice models. Nonparametric identification shows that one particular distribution of unobserved heterogeneity is consistent with limiting information on conditional outcome probabilities. We show identification using cross-sectional data on agents facing different choice sets. The statistics literature establishes that linear independence of the class of models being mixed over is necessary and sufficient for identification. This condition is difficult to algebraically verify for economic choice models. This project introduces a new condition, reducibility, that is sufficient for linear independence and hence identification. Reducibility is a property of economic models that can be easily verified, as is shown for a group of models of wide empirical use in economics. After showing identification, parametric or nonparametric distributions of unobserved Heterogeneity can be more confidently estimated. The most common tool for estimating mixtures models is the EM algorithm, which is certainly applicable. However, the EM algorithm has numerical issues and may be inappropriate for economic choice models that themselves require complex calculations, such as dynamic programming models. This project introduces a new, computationally simple mixtures estimator to resolve these issues. The estimator is nonparametric.BROADER IMPACT: The main broader impact will be to make the identification and estimation of distributions of unobserved heterogeneity (random coefficients) much simpler. This is done on two fronts: making the conditions for showing identification of new models easier to verify and introducing a computationally simple estimator. Models of choice by economic agents are used every day in thousands of empirical applications. For example, the decision of a married woman to participate in the labor market induces a selection problem: wages are observed only for the women who do work. The preferences and job opportunities of those observed to work are not representative of those who do not work. Jointly estimating the participation and wages decisions is necessary to resolve this selection problem. Understanding this process is necessary for understanding changes in the gender-wage gap over the last 30 years. For another example, consider the environmental economics problem of forecasting electricity use for appliances. The only data available on an appliance?s electricity use are for those consumers who buy the appliance, a selected sample. Changing the prices (say from a tax) of the appliances or of electricity itself will shift both the set of consumers who buy the appliance and electricity use conditional on buying. Estimating the distribution of heterogeneity is necessary for computing welfare measurements of the effect of the tax. One of the investigators has used these methods to estimate the consumer welfare implications of mergers of wireless carriers, the response of teacher attendance in India to financial incentives, and the job mobility response of experienced engineers to wage offers from competing firms. Overall, we see showing identification as making economists and statisticians more comfortable with estimating complex models. We hope to place these models on firm theoretical ground, so policymakers and other researchers treat results from these models with more confidence. We also expand the class of models that will be estimated. As parametric versions of some of these methods are in constant use in empirical work, we see this work as having tremendous impact of all areas of applied economics and related fields. One of the investigators has taught a mini course to graduate students and established researchers on these techniques at INSEE-CREST / ENSAE in Paris, France. Both investigators are teaching these techniques to PhD students at their home institutions and will do so more intensively for the undergraduate and graduate students funded by this grant.

结构经济选择模型展示了个体代理人（企业、消费者、工人）如何在不同的选择集下做出选择。没有理由相信这些模型的参数对所有代理人都是一样的：代理人在面对相同的选择集时会做出不同的选择。由于参数在不同的代理人，这些模型的实证工作的目标是估计未观察到的异质性的分布，或随机系数的分布。这种分布是计算政策的福利效应（例如税收政策的消费者剩余）或计算样本外对新商品的需求所必需的。 根据统计理论，具有不可观测异质性的模型称为混合模型。统计学文献集中注意一些参数类的混合分布，如混合正态分布。 很少有人注意到使用混合物的工具来研究更复杂的非线性统计模型，如结构经济选择模型。 非参数识别表明，一个特定的分布未观察到的异质性是一致的限制条件结果概率的信息。我们发现识别代理面临不同的选择集的横截面数据。统计学文献建立了被混合的模型类的线性独立性对于识别是必要和充分的。这个条件是很难代数验证的经济选择模型。这个项目引入了一个新的条件，reducibility，这是足够的线性独立性，因此识别。 约简性是经济模型的一个属性，它可以很容易地被验证，正如经济学中广泛使用的一组模型所示。 在显示识别后，可以更自信地估计未观察到的异质结的参数或非参数分布。估计混合模型的最常用工具是EM算法，它当然是适用的。然而，EM算法具有数值问题，并且可能不适合于本身需要复杂计算的经济选择模型，例如动态规划模型。这个项目引入了一个新的，计算简单的混合估计来解决这些问题。更广泛的影响：主要的更广泛的影响将是使未观察到的异质性（随机系数）的分布的识别和估计更加简单。这是在两个方面完成的：使新模型的识别条件更容易验证，并引入一个计算简单的估计。 经济行为人的选择模型每天都在成千上万的经验应用中使用。例如，一个已婚妇女决定参加劳动力市场会引起一个选择问题：只有工作的妇女才能得到工资。被观察到有工作的人的偏好和工作机会并不代表没有工作的人。联合估计参与和工资决定是必要的，以解决这个选择问题。了解这一过程对于了解过去30年来性别工资差距的变化是必要的。再举一个例子，考虑预测电器用电的环境经济学问题。设备上唯一可用的数据？的电力使用是为那些消费者谁购买的电器，一个选定的样本。改变电器或电力本身的价格（比如从税收角度）将改变购买电器的消费者群体和以购买为条件的电力使用。估计异质性的分布是必要的计算福利措施的影响，税收。其中一位研究人员使用这些方法来估计无线运营商合并对消费者福利的影响，印度教师出勤率对经济激励的反应，以及经验丰富的工程师对竞争公司工资的工作流动性反应。 总的来说，我们认为显示身份可以让经济学家和统计学家更轻松地估计复杂的模型。我们希望将这些模型建立在坚实的理论基础上，以便政策制定者和其他研究人员更有信心地对待这些模型的结果。我们还扩大了类的模型，将估计。 由于这些方法的参数版本在实证工作中不断使用，我们认为这项工作对应用经济学和相关领域的所有领域都有巨大的影响。 其中一名研究人员在法国巴黎的INSEE-CREST / ENSAE为研究生教授了一门迷你课程，并建立了这些技术的研究人员。两位研究人员都在他们的家乡机构向博士生教授这些技术，并将更深入地为该补助金资助的本科生和研究生教授这些技术。