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Identification and Estimation of 'Irregular' Correlated Random Coefficient Models

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Bryan S. Graham
James Powell

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Abstract

In this paper we study identification and estimation of the causal effect of a small change in an endogenous regressor on a continuously-valued outcome of interest using panel data. We focus on the average partial effect (APE) over the full population distribution of unobserved heterogeneity (e.g., Chamberlain, 1984; Blundell and Powell, 2003; Wooldridge, 2005a). In our basic model the outcome of interest varies linearly with a (scalar) regressor, but with an intercept and slope coefficient that may vary across units and over time in a way which depends on the regressor. This model is a special case of Chamberlain's (1980b, 1982, 1992a) correlated random coefficients (CRC) model, but not does not satisfy the regularity conditions he imposes. Irregularity, while precluding estimation at parametric rates, does not result in a loss of identification under mild smoothness conditions. We show how two measures of the outcome and regressor for each unit are sufficient for identification of the APE as well as aggregate time trends. We identify aggregate trends using units with a zero first difference in the regressor or, in the language of Chamberlain (1980b, 1982), 'stayers' and the average partial effect using units with non-zero first differences or 'movers'. We discuss extensions of our approach to models with multiple regressors and more than two time 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). Our CRC average elasticity estimate declines with total outlay more sharply than its parametric counterpart.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14469.

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Date of creation: Nov 2008
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Handle: RePEc:nbr:nberwo:14469

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data
I1 - Health, Education, and Welfare - - Health
O1 - Economic Development, Technological Change, and Growth - - Economic Development
O15 - Economic Development, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Manuel Arellano & Stéphane Bonhomme, 2009. "Identifying distributional characteristics in random coefficients panel data models," CeMMAP working papers CWP22/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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