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。面板数据的可用性，或同一抽样单位（例如，个人、公司、国家等）随时间的多次观察，可以帮助控制未观察到的异质性的存在，这既直观又合理。在线性回归模型中包含单位特定截距是控制实证工作中省略变量的最广泛方法之一。这种建模策略的适当性要求任何时不变的相关异质性加性地进入结果方程。不幸的是，可加性虽然在统计上很方便，但在经济上很难激发。最优化的经济模型表明，一个主体的投入选择应该与其边际收益协变。此外，未观察到的异质性的非加性形式似乎与经验相关（例如，Browning和Carro， 2007）。不幸的是，对具有这种异质性的面板数据模型的识别和估计结果很少。面板数据的可用性越来越高，假设这些数据允许削弱横截面情况下所需的限制，以及经验研究人员对不可分离异质性重要性的日益认识，表明对半参数背景下面板数据识别能力的全面分析将是有价值的。本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，每个个体的结果随回归量或输入呈线性变化。表征这种线性反应的系数因个体和时间而异。在这样一个模型的背景下，提出的研究描述了输入对结果概率分布的外生变化的影响（特征）。这类知识对于预测反事实政策的影响非常重要。所提出的方法是固定效应方法，即回归量的联合分布和任何时不变的未观察到的异质性（即个体特定效应）都未建模。所提出的活动的潜在智力优点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，但可供实证研究人员研究连续值结果的方法菜单仍然围绕25年前Chamberlain（1984）调查的常系数线性模型进行大量组织。提出的项目是将固定效应面板数据方法扩展到不可分异质性模型的一种方法。虽然主要目标是为CRC面板数据模型提供可用的识别和估计结果，但这项工作也有助于半参数估计的理论文献。面板数据方法几乎应用于实证经济学和其他社会科学的所有领域。它们对于执行若干主要的政策评价和生产函数估计方法至关重要。CRC模型的优点是它的简单性和易于解释性。由于这个原因，拟议的活动所产生的更广泛的影响包括广泛采用经济学和其他社会科学的实证研究人员开发的方法的真正可能性。公开可用的计算机软件和面向从业者的综合调查报告将促进这种采用。所提出的方法将用于研究卡路里需求相对于家庭总资源的弹性。这种弹性是粮食政策分析的一个重要参数，在营养贫困陷阱的理论模型中发挥着突出作用。

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.