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Unformatted text preview: Identification and Estimation of Marginal Effects in Nonlinear Panel Models 1 Victor Chernozhukov MIT Ivan Fern andezVal BU Jinyong Hahn UCLA Whitney Newey MIT February 4, 2009 1 First version of May 2007. We thank J. Angrist, B. Graham, and seminar participants of Brown Uni versity, CEMFI, CEMMAP Microeconometrics: Measurement Matters Conference, CEMMAP Inference in Partially Identified Models with Applications Conference, CIREQ Inference with Incomplete Models Conference, Georgetown, Harvard/MIT, MIT, UC Berkeley, USC, 2007 WISE Panel Data Conference, and 2009 Winter Econometric Society Meetings for helpful comments. Chernozhukov, Fern andezVal, and Newey gratefully acknowledge research support from the NSF. Abstract This paper gives identification and estimation results for marginal effects in nonlinear panel models. We find that linear fixed effects estimators are not consistent, due in part to marginal effects not being identified. We derive bounds for marginal effects and show that they can tighten rapidly as the number of time series observations grows. We also show in numerical calculations that the bounds may be very tight for small numbers of observations, suggesting they may be useful in practice. We propose two novel inference methods for parameters defined as solutions to linear and nonlinear programs such as marginal effects in multinomial choice models. We show that these methods produce uniformly valid confidence regions in large samples. We give an empirical illustration. 1 Introduction Marginal effects are commonly used in practice to quantify the effect of variables on an outcome of interest. They are known as average treatment effects, average partial effects, and average structural functions in different contexts (e.g., see Wooldridge, 2002, Blundell and Powell, 2003). In panel data marginal effects average over unobserved individual heterogeneity. Chamberlain (1984) gave important results on identification of marginal effects in nonlinear panel data using control variable. Our paper gives identification and estimation results for marginal effects in panel data under time stationarity and discrete regressors. It is sometimes thought that marginal effects can be estimated using linear fixed effects, as shown by Hahn (2001) in an example and Wooldridge (2005) under strong independence conditions. It turns out that the situation is more complicated. The marginal effect may not be identified. Furthermore, with a binary regressor, the linear fixed effects estimator uses the wrong weighting in estimation when the number of time periods T exceeds three. We show that correct weighting can be obtained by averaging individual regression coefficients, extending a result of Chamberlain (1982). We also derive nonparametric bounds for the marginal effect when it is not identified and when regressors are either exogenous or predetermined conditional on individual effects....
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