Nonlinear Models with Individual Effects

面板数据包括对单个经济因素的时间观察，它允许控制未被观察到的个体异质性的可能性。这种异质性可能是由于人们在品味或技术上未被察觉的差异造成的，也可能是一种重要的现象。在这种情况下，未能对其进行控制可能会导致误导性的推断。当未观察到的异质性影响解释变量时，这个问题尤其严重。当一些解释变量是决策变量时，自然会出现这种情况，例如，在动态面板数据模型中就是这种情况。很好地建立了控制线性模型中未观察到的异质性的模型和方法。然而，对于如何控制非线性模型中未观察到的异质性，人们知之甚少。适用于线性模型的方法不会以直接的方式应用于大多数非线性模型。除非在特殊情况下，否则不可能通过某些数据转换来消除个体影响，例如在线性模型中工作的时间序列观测的第一差分。此外，由于经济面板数据中典型时间序列的长度较短，将个体效应作为待估计参数的非线性模型的固定效应估计器也会遇到问题。本研究涉及控制面板数据非线性模型中未观察到的异质性的两个主题。第一个主题是以解释变量为条件，对个体效应的分布进行建模。这种模型可以用来指定随机效应有限因变量模型，该模型具有个体效应的非参数条件均值。第二个主题研究了应用于面板数据的时间序列维度的jacknife在减少非线性模型中固定效应估计量的偏差方面的应用。本研究将检验在不同的模型中，这种非参数偏差减少方法能在多大程度上缓解附带参数偏差。该项目的基本目标是评估要考虑的模型和方法的潜在经验影响，以及各种估计值的渐近分布的推导。

Panel data, consisting of observations across time for individual economic agents, allows the possibility of controlling for unobserved individual heterogeneity. Such heterogeneity can arise from unobserved differences in tastes or technology and can be an important phenomenon. In such instances failure to control for it can result in misleading inferences. This problem is particularly severe when the unobserved heterogeneity affects explanatory variables. Situations of this sort arise naturally when some of the explanatory variables are decision variables, as is the case, for example, in dynamic panel data models. Models and methods of controlling for unobserved heterogeneity in linear models are well established. However, less is known about how to control for unobserved heterogeneity in nonlinear models. The methods that work for linear models do not carry over in a straightforward way to most nonlinear models. Except in special circumstances, it is not possible to eliminate individual effects by some data transformation, such as first differencing of time series observations which works in linear models. Also, fixed effects estimators of nonlinear models, which treat the individual effects as parameters to be estimated, encounter problems because of the short length of the typical time series in economic panel data. This research concerns two topics in controlling for unobserved heterogeneity in nonlinear models of panel data. The first topic deals with modelling the distribution of the individual effects, conditional on the explanatory variables. Such models can be used to specify random effects limited dependent variable models with a nonparametric conditional mean for the individual effect. The second topic investigates the use of the jacknife, applied to the time series dimension of panel data, for reduction of the bias of fixed effects estimators in nonlinear models. The research will examine the extent to which this nonparametric bias reduction method can alleviate the incidental parameters bias, in different models. The basic goals of the project are to assess the potential empirical impact of the models and methods to be considered, as well as derivation of asymptotic distributions for the various estimators.