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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.

Suggested Citation

  • Bryan S. Graham & James Powell, 2008. "Identification and Estimation of 'Irregular' Correlated Random Coefficient Models," NBER Working Papers 14469, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14469
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    Cited by:

    1. Khan, Shakeeb & Ponomareva, Maria & Tamer, Elie, 2016. "Identification of panel data models with endogenous censoring," Journal of Econometrics, Elsevier, vol. 194(1), pages 57-75.
    2. Rosen, Adam M., 2012. "Set identification via quantile restrictions in short panels," Journal of Econometrics, Elsevier, vol. 166(1), pages 127-137.
    3. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    4. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 987-1020.
    5. 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.
    6. Victor Chernozhukov & Ivan Fernandez-Val & Jinyong Hahn & Whitney K. 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.
    7. Hoderlein, Stefan & Sherman, Robert, 2015. "Identification and estimation in a correlated random coefficients binary response model," Journal of Econometrics, Elsevier, vol. 188(1), pages 135-149.
    8. repec:ran:wpaper:710-1 is not listed on IDEAS
    9. David Powell, 2010. "Unconditional Quantile Treatment Effects in the Presence of Covariates," Working Papers 816, RAND Corporation.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • I1 - Health, Education, and Welfare - - Health
    • O1 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

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