Correcting for truncation bias caused by a latent truncation variable
We discuss estimation of the model Y[sub i] = X[sub i]b[sub y] + e[sub Yi] and T[sub i] =X[sub i]b[sub T] + e[sub Ti] when data on the continuous dependent variable Y and on the independent variables X are observed if the "truncation variable" T > 0 and when T is latent. This case is distinct from both (i) the "censored sample" case, in which Y data are available if T > 0, T is latent and X data are available for all observations, and (ii) the "observed truncation variable" case, in which both Y and X are observed if T > 0 and in which the actual value of T is observed whenever T > O. We derive a maximum-likelihood procedure for estimating this model and discuss identification and estimation.
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- Heckman, James J, 1979.
"Sample Selection Bias as a Specification Error,"
Econometric Society, vol. 47(1), pages 153-61, January.
- Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
- Wales, T J & Woodland, A D, 1980. "Sample Selectivity and the Estimation of Labor Supply Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 437-68, June.
- Jerry A. Hausman & David A. Wise, 1976. "The Evaluation of Results from Truncated Samples: The New Jersey Income Maintenance Experiment," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 421-445 National Bureau of Economic Research, Inc.
- Olsen, Randall J, 1982. "Distributional Tests for Selectivity Bias and a More Robust Likelihood Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(1), pages 223-40, February.
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