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Extra resources for Analysis of Panels and Limited Dependent Variable Models
Arellano, O. M. Labeaga Appendix B Type I Tobit with symmetric trimming Assuming that y*it | xi(tϪ1) has a symmetric distribution with heteroskedasticity of unknown form, we can estimate consistently the t using Powell’s (1986) symmetrically censored least squares method (SCLS). 1) iϭ1 where it(˜ rt ) ϭ1(xЈi (tϪ1)˜ rt Ͼ0) for rՆ1 and it(˜ 0t )ϭ1 (that is, the initial value is the OLS estimator). In this case, since the SCLS estimation criterion is not diﬀerentiable we cannot use the argument of section 3 for normal Tobit or Heckman’s estimator in order to obtain the asymptotic covariance matrix of ˜ ϭ (˜Ј2 … ˜ TЈ )Ј.
2) and (3) use Heckman’s estimates of the reduced form. 3. 2. 38 M. Arellano, O. M. Labeaga these estimates do not correct for selectivity, but given the low conditional non-participation rates in the samples we would not expect them to diﬀer substantially from those with selectivity corrections. The estimates shown in the remaining two columns are based on Heckman’s estimates of the reduced-form coeﬃcients. 3 use the same moments as the ones in the ﬁrst columns, and as expected the diﬀerences between the two sets of estimates are small.
Manski and D. : MIT Press. J. E. MaCurdy (1980), “A Life-Cycle Model of Female Labour Supply,” Review of Economic Studies, 47: 47–74. , W. Newey, and H. Rosen (1988), “Estimating Vector Autoregressions with Panel Data”, Econometrica, 56: 1371–1395. Honoré, B. (1992), “Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Eﬀects,” Econometrica, 60: 533–565. (1993), “Orthogonality Conditions for Tobit Models with Fixed Eﬀects and Lagged Dependent Variables,” Journal of Econometrics, 59: 35–61.