Average and Quantile Effects in Nonseparable Panel Models

Abstract

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like "time is randomly assigned" or "time is an instrument."Partial identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T , the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds.Computationally-convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations. IntroductionInteresting empirical questions are often formulated in terms of the ceteris paribus effect of x on y, when observed x is an individual choice variable partly determined by preferences or technology.Panel data holds out the hope of controlling for individual preferences or technology by using multiple observations for a single economic agent. This hope is particularly difficult to realize with discrete or other nonseparable models and/or multidimensional individual effects. These models are, by nature, not additively separable in unobserved individual effects, making them challenging to identify and estimate. There are some simple solutions, such as the conditional MLE for the slope parameter of a binary-choice logit model with an individual location effect. However these are rare and dependent on specific models or distributions. For example, the slope parameter of the binary-choice model with a time dummy is identified only for logit as shown by Chamberlain (2010), and the average treatment effect is not identified even for logit without a time dummy, as shown below.A fundamental idea for using panel data to identify the ceteris paribus effect of x on y is to use changes in x over time to estimate the effect. In order for changes over time in x to correspond to ceteris paribus effects, the distribution of variables other than x must not vary over time. This condition is like "time being randomly assigned" or "time is an ...

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