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Quantile Effects Nonseparable Panel

Quantile Effects Nonseparable Panel - Quantile and Average...

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Quantile and Average E ff ects in Nonseparable Panel Models 1 V. Chernozhukov, I. Fernandez-Val, W. Newey MIT, Boston University, MIT First Version, July 2009 Revised, October 2009 1 We thank seminar participants at Stanford and Harvard-MIT econometrics workshops, B. Graham, and J. Hausman for comments. We gratefully acknowledge research support from the NSF.
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Abstract This paper gives identi fi cation and estimation results for quantile and average e ff ects in nonsep- arable panel models, when the distribution of period speci fi c disturbances does not vary over time. Bounds are given for interesting e ff ects with discrete regressors that are strictly exogenous or predetermined. We allow for location and scale time e ff ects and show how monotonicity can be used to shrink the bounds. We derive rates at which the bounds tighten as the number T of time series observations grows and give an empirical illustration.
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1 Introduction This paper gives identi fi cation and estimation results for quantile and average e ff ects in nonsep- arable panel models, when the distribution of period speci fi c disturbances does not vary over time. Bounds are given for interesting e ff ects with discrete regressors that are strictly exogenous or predetermined. We allow for location and scale time e ff ects and show how monotonicity can be used to shrink the bounds. We derive rates at which the bounds tighten as the number T of time series observations grows and give an empirical illustration. Nonseparable models are often needed to model important features of economic problems as discussed by Altonji and Matzkin (2005) and others. Also, Browning and Carro (2007) showed that economics motivates multiple sources of heterogeneity (not just an additive e ff ect), and showed their importance in an application. Recently Hoderlein and White (2009) have considered a nonseparable panel data model that is close to the one we study. Much of the work on nonseparable models in panel data (and other settings) has relied on control variables that arise from restricting the correlation between regressors and individual e ff ects. Control variables are functions of observables such that the regressors and individual e ff ects are independent conditional on those variables. Results on control variables for panel data are given by Chamberlain (1984), Altonji and Matzkin (2005), and Bester and Hansen (2009). We consider a di ff erent source of potential identi fi cation, time homogeneity. Similar conditions have been used for identi fi cation by Chamberlain (1982), Manski (1987), Honore (1992), Hahn (2001), Wooldridge (2005), Chernozhukov, Fernandez-Val, Hahn, and Newey (2007), Graham and Powell (2008), and Hoderlein and White (2009), among others. This paper is the fi rst to consider identi fi cation of the quantile structural function (QSF) of Imbens and Newey (2009) and the average structural function (ASF) of Blundell and Powell (2003) under time homogeneity. We fi nd that it is not possible to identify the QSF and ASF in panel data with discrete regressors though certain conditional e ff ects may be identi fi ed. We give easily computed bounds for the QSF and ASF. We show that these bounds can be quite tight and
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