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Irregular Correlated Random Coefficient

Irregular Correlated Random Coefficient - Identication and...

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Identi fi cation and estimation of ‘irregular’ correlated random coe cient models 1 Bryan S. Graham and James L. Powell Initial Draft: December 2007 This Draft: July 3, 2008 Preliminary and Incomplete Abstract In this paper we study identi fi cation and estimation of the causal e ff ect of a small change in an endogenous regressor on a continuously-valued outcome of interest using panel data. We focus on average e ff ects, over either the full population distribution of unobserved heterogeneity (the average partial e ff ect, APE), or over subpopulations de fi ned by their regressor values (local average responses, LARs). In our primary model the outcome of interest varies linearly with a (scalar) regressor, but with an intercept and slope coe cient that may vary across units and over time in a way which depends on the regressor. Our model is a special case of Chamberlain’s (1992a) correlated random coe cients (CRC) model, but not does not satisfy the regularity conditions he imposes. We show how two measures of the outcome and regressor for each unit are su cient for identi fi cation of the APE and LAR, as well as aggregate trends that are mean-independent of the regressors. We identify aggregate trends using units with a zero fi rst di ff erence in the regressor, in the language of Chamberlain (1980b, 1982) ‘stayers’, and the average partial e ff ect using units with non-zero fi rst di ff erences or ‘movers’. We discuss extensions of our approach to models with multiple regressors and more than two time periods, periods. We use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor Nicaraguan households (cf., Strauss and Thomas, 1995, Subramanian and Deaton, 1996). JEL Classification: C14, C23, C33 Key Words: Panel Data, Correlated Random Coefficients, Control Function, Average Partial Effects, Local Average Response, Kernel Regression, Calorie De- mand 1 We would like to thank seminar participants at UC - Berkeley, UCLA, USC and Harvard, members of the Berkeley Econometrics Reading Group and participants in the Conference in Economics and Statistics in honor of Theodore W. Anderson’s 90th Birthday (Stanford University) and the JAE Conference on Distributional Dynamics (CEMFI, Madrid) for comments and feedback. Discussions with Manuel Arellano, Stéphane Bonhomme, Gary Chamberlain, Michael Jansson and Edward Vytlacil were helpful in numerous ways. Max Kasy provided excellent research assistance. All the usual disclaimers apply. Department of Economics, University of California - Berkeley, 508-1 Evans Hall #3880, Berkeley, CA 94720 and National Bureau of Economic Research. E-mail: [email protected] . Web: http://www.econ.berkeley.edu/~bgraham/. Department of Economics, University of California - Berkeley, 508-1 Evans Hall #3880, Berkeley, CA 94720.
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