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Identification and Estimation of 'Irregular' Correlated Random Coefficient Models

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  • Bryan S. Graham
  • James Powell

Abstract

In this paper we study identification and estimation of a correlated random coefficients (CRC) panel data model. The outcome of interest varies linearly with a vector of endogenous regressors. The coefficients on these regressors are heterogenous across units and may covary with them. We consider the average partial effect (APE) of a small change in the regressor vector on the outcome (cf., Chamberlain, 1984; Wooldridge, 2005a). Chamberlain (1992) calculates the semiparametric efficiency bound for the APE in our model and proposes a √ N consistent estimator. Nonsingularity of the APE’s information bound, and hence the appropriateness of Chamberlain’s (1992) estimator, requires (i) the time dimension of the panel ( T) to strictly exceed the number of random coefficients ( p) and (ii) strong conditions on the time series properties of the regressor vector. We demonstrate irregular identification of the APE when T = p and for more persistent regressor processes. Our approach exploits the different identifying information in the subpopulations of ‘stayers’ — or units whose regressor values change little across periods — and ‘movers’ — or units whose regressor values change substantially across periods. We propose a feasible estimator based on our identification result and characterize its large sample properties. While irregularity precludes our estimator from attaining parametric rates of convergence, it limiting distribution is normal and inference is straightforward to conduct. Standard software may be used to compute point estimates and standard errors. We use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor Nicaraguan households.

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Bibliographic Info

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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Publication status: published as Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models Bryan S. Graham1, James L. Powell2,† Article first published online: 25 SEP 2012 DOI: 10.3982/ECTA8220 © 2012 The Econometric Society Issue Econometrica Econometrica Volume 80, Issue 5, pages 2105–2152, September 2012
Handle: RePEc:nbr:nberwo:14469

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Cited by:
  1. Stefan Hoderlein & Halbert White, 2009. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," CeMMAP working papers CWP33/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Rosen, Adam M., 2012. "Set identification via quantile restrictions in short panels," Journal of Econometrics, Elsevier, vol. 166(1), pages 127-137.
  3. Victor Chernozhukov & Ivan Fernandez-Val & Jinyong Hahn & Whitney Newey, 2008. "Identification and estimation of marginal effects in nonlinear panel models," CeMMAP working papers CWP25/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Shakeeb Khan & Maria Ponomareva & Elie Tamer, 2011. "Identification of Panel Data Models with Endogenous Censoring," Working Papers 11-07, Duke University, Department of Economics.
  5. Manuel Arellano & Stéphane Bonhomme, 2009. "Identifying Distributional Characteristics In Random Coefficients Panel Data Models," Working Papers wp2009_0904, CEMFI.
  6. Stefan Hoderlein & Robert Sherman, 2012. "Identification And Estimation In A Correlated Random Coefficients Binary Response Model," Boston College Working Papers in Economics 837, Boston College Department of Economics.
  7. David Powell, 2010. "Unconditional Quantile Regression for Panel Data with Exogenous or Endogenous Regressors," Working Papers 710-1, RAND Corporation Publications Department.
  8. Stefan Hoderlein & Yuya Sasaki, 2011. "On the role of time in nonseparable panel data models," CeMMAP working papers CWP15/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. David Powell, 2010. "Unconditional Quantile Treatment Effects in the Presence of Covariates," Working Papers 816, RAND Corporation Publications Department.

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