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Identification and Estimation of 'Irregular' Correlated Random Coefficient Models

  • Bryan S. Graham
  • James Powell

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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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
Note: HE LS PE TWP
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  1. David Card, 2000. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," NBER Working Papers 7769, National Bureau of Economic Research, Inc.
  2. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
  3. Esther Duflo, 2001. "Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment," American Economic Review, American Economic Association, vol. 91(4), pages 795-813, September.
  4. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366 Elsevier.
  5. Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
  6. Victor Chernozhukov & Ivan Fernandez-Val & Jinyong Hahn & Whitney Newey, 2009. "Identification and estimation of marginal effects in nonlinear panel models," CeMMAP working papers CWP05/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Honore, Bo E, 1992. "Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects," Econometrica, Econometric Society, vol. 60(3), pages 533-65, May.
  8. Anne Case & Christina Paxson, 2006. "Stature and Status: Height, Ability, and Labor Market Outcomes," NBER Working Papers 12466, National Bureau of Economic Research, Inc.
  9. Hahn, Jinyong, 2001. "Comment: Binary Regressors in Nonlinear Panel-Data Models with Fixed Effects," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 16-17, January.
  10. David Card, 1990. "The impact of the Mariel boatlift on the Miami labor market," Industrial and Labor Relations Review, ILR Review, Cornell University, ILR School, vol. 43(2), pages 245-257, January.
  11. Garen, John, 1984. "The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable," Econometrica, Econometric Society, vol. 52(5), pages 1199-1218, September.
  12. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
  13. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  14. Das, M., 2003. "Identification and sequential estimation of panel data models with insufficient exclusion restrictions," Journal of Econometrics, Elsevier, vol. 114(2), pages 297-328, June.
  15. Hoddinott, John & Skoufias, Emmanual, 2003. "The impact of Progresa on food consumption," FCND briefs 150, International Food Policy Research Institute (IFPRI).
  16. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc.
  17. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-96, May.
  18. Martin Browning & Jesus Carro, 2006. "Heterogeneity and Microeconometrics Modelling," CAM Working Papers 2006-03, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  19. Subramanian, S. & Deaton, A., 1994. "The Demand for Food and Calories," Papers 175, Princeton, Woodrow Wilson School - Development Studies.
  20. Abrevaya, Jason, 2000. "Rank estimation of a generalized fixed-effects regression model," Journal of Econometrics, Elsevier, vol. 95(1), pages 1-23, March.
  21. Bouis, Howarth E. & Haddad, Lawrence J., 1992. "Are estimates of calorie-income fxelasticities too high? : A recalibration of the plausible range," Journal of Development Economics, Elsevier, vol. 39(2), pages 333-364, October.
  22. Edmundson, W C & Sukhatme, P V, 1990. "Food and Work: Poverty and Hunger?," Economic Development and Cultural Change, University of Chicago Press, vol. 38(2), pages 263-80, January.
  23. Skoufias, Emmanuel, 2003. "Is the Calorie-Income Elasticity Sensitive to Price Changes? Evidence from Indonesia," World Development, Elsevier, vol. 31(7), pages 1291-1307, July.
  24. Angus Deaton & Salman Zaidi, 2002. "Guidelines for Constructing Consumption Aggregates for Welfare Analysis," World Bank Publications, The World Bank, number 14101.
  25. Card, David, 1996. "The Effect of Unions on the Structure of Wages: A Longitudinal Analysis," Econometrica, Econometric Society, vol. 64(4), pages 957-79, July.
  26. Janet Currie & Duncan Thomas, 1993. "Does Head Start Make a Difference?," NBER Working Papers 4406, National Bureau of Economic Research, Inc.
  27. Joseph G. Altonji & Thomas A. Dunn, . "Using Siblings to Estimate the Effect of School Quality on Wages," IPR working papers 96-10, Institute for Policy Resarch at Northwestern University.
  28. Wolfe, Barbara L & Behrman, Jere R, 1983. "Is Income Overrated in Determining Adequate Nutrition?," Economic Development and Cultural Change, University of Chicago Press, vol. 31(3), pages 525-49, April.
  29. Wooldridge, J.M., 1990. "Distribution-Free Estimation Of Some Nonlinear Panel Data Models," Working papers 564, Massachusetts Institute of Technology (MIT), Department of Economics.
  30. Behrman, Jere R & Deolalikar, Anil B, 1987. "Will Developing Country Nutrition Improve with Income? A Case Study for Rural South India," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 492-507, June.
  31. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, 09.
  32. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," NBER Working Papers 6699, National Bureau of Economic Research, Inc.
  33. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
  34. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07.
  35. Dasgupta, Partha & Ray, Debraj, 1986. "Inequality as a Determinant of Malnutrition and Unemployment: Theory," Economic Journal, Royal Economic Society, vol. 96(384), pages 1011-34, December.
  36. Arellano, Manuel & Carrasco, Raquel, 2003. "Binary choice panel data models with predetermined variables," Journal of Econometrics, Elsevier, vol. 115(1), pages 125-157, July.
  37. Gary Chamberlain, 1980. "Multivariate Refression Models for Paned Data," NBER Technical Working Papers 0008, National Bureau of Economic Research, Inc.
  38. Arellano, M., 2001. "Discrete Choices with Panel Data," Papers 0101, Centro de Estudios Monetarios Y Financieros-.
  39. Logan, Trevon D., 2006. "Nutrition and Well-Being in the Late Nineteenth Century," The Journal of Economic History, Cambridge University Press, vol. 66(02), pages 313-341, June.
  40. Wooldridge, Jeffrey M., 2003. "Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model," Economics Letters, Elsevier, vol. 79(2), pages 185-191, May.
  41. Bester, C. Alan & Hansen, Christian, 2009. "Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 235-250.
  42. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  43. Arellano, Manuel & Honore, Bo, 2001. "Panel data models: some recent developments," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 53, pages 3229-3296 Elsevier.
  44. Strauss, John & Thomas, Duncan, 1995. "Human resources: Empirical modeling of household and family decisions," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 3, chapter 34, pages 1883-2023 Elsevier.
  45. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
  46. James Heckman & Edward Vytlacil, 1998. "Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 974-987.
  47. Bliss, Christopher & Stern, Nicholas, 1978. "Productivity, wages and nutrition : Part I: the theory," Journal of Development Economics, Elsevier, vol. 5(4), pages 331-362, December.
  48. Griliches, Zvi, 1979. "Sibling Models and Data in Economics: Beginnings of a Survey," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages S37-64, October.
  49. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  50. Chamberlain, Gary, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 225-38, January.
  51. Ivan Fernandez-Val, 2005. "Bias Correction in Panel Data Models with Individual Specific Parameters," Boston University - Department of Economics - Working Papers Series WP2005-041, Boston University - Department of Economics.
  52. Dasgupta, Partha & Ray, Debraj, 1987. "Inequality as a Determinant of Malnutrition and Unemployment: Policy," Economic Journal, Royal Economic Society, vol. 97(385), pages 177-88, March.
  53. Bouis, Howarth E., 1994. "The effect of income on demand for food in poor countries: Are our food consumption databases giving us reliable estimates?," Journal of Development Economics, Elsevier, vol. 44(1), pages 199-226, June.
  54. Richard Blundell & James Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  55. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  56. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-62, March.
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