COLLABORATIVE RESEARCH: Identification, estimation and application of semiparametric panel data models

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)资助的。即获得面板数据，或同一样本单位(例如，个人、公司、州等)的多个观察结果。随着时间的推移，可以帮助控制未观察到的异质性的存在既是直观的，也是似是而非的。在线性回归模型中包含特定单元截距是控制经验工作中遗漏变量的最广泛的方法之一。这种建模策略的适当性要求任何时不变的相关异质性相加地进入结果方程。不幸的是，相加性虽然在统计上是方便的，但在经济上却很难激励。优化的经济模型表明，代理人的投入选择应该与其边际收益同步变化。此外，未观察到的异质性的非相加形式似乎与经验相关(例如，Browning和Carro，2007)。不幸的是，对于具有如此异质性的面板数据模型的识别和估计结果很少。面板数据越来越多的可获得性，这种数据允许削弱横断面案例中所要求的限制的假设，以及经验研究人员越来越多地认识到不可分离的异质性的重要性，这表明在半参数背景下对面板数据的识别能力进行全面分析将是有价值的。这个项目研究使用面板数据来识别和估计可能是承认不可分离的异质性的最简单的统计模型：静态相关随机系数(CRC)模型。在这个模型中，每个人的结果随着回归变量或输入的不同而线性变化。表征这种线性反应的系数因个体和时间的不同而不同。在这样一个模型的背景下，拟议的研究描述了投入的外生变化对结果的概率分布的影响。这类知识对于预测反事实政策的效果很重要。提出的方法是固定效应方法，即回归变量的联合分布和任何时不变的未观察到的异质性(即个体特有的效应)未被建模。建议活动的潜在智力优势包括增加我们对具有不可分离异质性的连续值结果的固定效应面板数据模型的理解。面板数据在实践中被广泛使用，然而，研究连续价值结果的经验研究人员可用的方法菜单仍然主要围绕张伯伦(1984)25年前调查的常系数线性模型进行组织。建议的项目代表了一种将固定效应面板数据方法扩展到具有不可分离异质性的模型的方法。虽然主要目的是为CRC面板数据模型提供有用的识别和估计结果，但这项工作也为半参数估计的理论文献做出了贡献。面板数据方法几乎应用于经验经济学和其他社会科学的所有领域。它们对于执行政策评估和生产函数估计的几种主要方法至关重要。CRC模型的一个优点是它的简单性和易解性。因此，拟议活动产生的更广泛影响包括广泛采用经济学和其他社会科学经验主义研究人员提出的方法的真正可能性。可公开获得的计算机软件和面向从业者的综合调查文件将促进这种采用。建议的方法将被用来研究卡路里需求相对于家庭总资源的弹性。这种弹性是食品政策分析的一个重要参数，在营养性贫困陷阱的理论模型中发挥着重要作用。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).That the availability of panel data, or multiple observations of the same sampling unit (e.g., individual, firm, state etc.) over time, can help to control for the presence of unobserved heterogeneity is both intuitive and plausible. The inclusion of unit-specific intercepts in linear regression models is among the most widespread methods of controlling for omitted variables in empirical work. The appropriateness of this modeling strategy requires that any time-invariant correlated heterogeneity enter the outcome equation additively. Unfortunately, additivity, while statistically convenient, is difficult to motivate economically. Economic models of optimization suggest than the input choice of an agent should covary with its marginal return. Furthermore, non-additive forms of unobserved heterogeneity appear to be empirically relevant (e.g., Browning and Carro, 2007). Unfortunately, few identification and estimation results for panel data models with such heterogeneity are available. The increasing availability of panel data, the presumption that such data allow for a weakening of restrictions required in the cross-section case, and a growing appreciation by empirical researchers of the importance of nonseparable heterogeneity, suggests that a comprehensive analysis of the identifying power of panel data in a semiparametric context would be valuable. This project studies the use of panel data for identifying and estimating what is perhaps the simplest statistical model admitting nonseparable heterogeneity: the static correlated random coefficients (CRC) model. In this model the outcome for each individual varies linearly with a regressor or input. The coefficients characterizing this linear response vary across individuals and over time. In the context of such a model the proposed research characterizes (features of) the effect on an exogenous change in the input on the probability distribution of the outcome. This type of knowledge is important for predicting the effects of counterfactual policies. The proposed approach is a fixed effects one, that is the joint distribution of the regressors and any time-invariant unobserved heterogeneity (i.e., the individual-specific effects) is left unmodeled.The potential intellectual merits of the proposed activity include increasing our understanding of fixed effect panel data models for continuously-valued outcomes with nonseparable heterogeneity. Panel data are widely-used in practice, yet the menu of methods available to empirical researchers studying continuously-valued outcomes is still heavily organized around the linear model with constant coefficients surveyed by Chamberlain (1984) twenty-five years ago. The proposed projects represent one approach to extending fixed effect panel data methods to models with non-separable heterogeneity. While the main goal is to provide usable identification and estimation results for CRC panel data models, the work also contributes to the theoretical literature on semiparametric estimation. Panel data methods are employed in virtually all fields of empirical economics and the other social sciences. They are essential to the implementation of several leading approaches to policy evaluation and production function estimation. A virtue of the CRC model is its simplicity and ease of interpretability. For this reason the broader impacts resulting from the proposed activities include the real possibility of widespread adoption of the methods developed by empirical researchers in economics and the other social sciences. Publicly available computer software and an integrative survey paper oriented toward practitioners will facilitate such adoption. The proposed methods will be used to study the elasticity of calorie demand with respect to total household resources. This elasticity is an important parameter for food policy analysis and plays a prominent role in theoretical models of nutritional poverty traps.