We consider a simultaneous equation model with two equations whose dependent variables (individual wage and reservation wage taken from a cross-sectional survey sample) are both partially observed, or "limited", as a consequence of a selection mechanism that doesn’t allow to observe them together. In particular, the observation of each of the two dependent variables doesn’t permit us to observe the other. The selection mechanism may be specified by a third equation represented by a participation function, whose dependent variable is a binary dummy “indicator” that produces, alternatively, two different regimes given by the working status of the subject. Furthermore, we can consider that the choice of a subject to work or not is influenced by both wage and reservation wage with opposite effects. The two-regimes characteristic suggests to specify the model as an endogenous two-regimes “switching” regression model (Maddala and Nelson, 1975; Poirier and Ruud, 1981 inter alia). We assume, in particular, that the specification of both the individual wage equation and the reservation wage equation is related to the expected value of the two dependent variables in each of two regimes. We compare a Maximum Likelihood (FIML) estimator similar to the estimator proposed by Poirier-Ruud (1981) and Powers (1993), but quite rarely adopted in practical applications for its computational complexity, with the well-known Two-Stage procedure (Heckman, 1976 and 1978; Lee, 1978, inter alia), widely adopted by practitioners for its simplicity and still dominant in applied works on the evaluation of causal effects (Heckman, Tobias and Vytlacil, 2003). An accurate Monte Carlo experiment shows that the relative efficiency of the FIML estimator over to the Two-Stage procedure is remarkably high in presence of a high degree of endogeneity in the selection equation.

Individual Wage and Reservation Wage: Efficient Estimation of a Simultaneous Equation Model with Endogenous Limited Dependent Variables

CALZOLARI, Giorgio;DI PINO INCOGNITO, Antonino
2009-01-01

Abstract

We consider a simultaneous equation model with two equations whose dependent variables (individual wage and reservation wage taken from a cross-sectional survey sample) are both partially observed, or "limited", as a consequence of a selection mechanism that doesn’t allow to observe them together. In particular, the observation of each of the two dependent variables doesn’t permit us to observe the other. The selection mechanism may be specified by a third equation represented by a participation function, whose dependent variable is a binary dummy “indicator” that produces, alternatively, two different regimes given by the working status of the subject. Furthermore, we can consider that the choice of a subject to work or not is influenced by both wage and reservation wage with opposite effects. The two-regimes characteristic suggests to specify the model as an endogenous two-regimes “switching” regression model (Maddala and Nelson, 1975; Poirier and Ruud, 1981 inter alia). We assume, in particular, that the specification of both the individual wage equation and the reservation wage equation is related to the expected value of the two dependent variables in each of two regimes. We compare a Maximum Likelihood (FIML) estimator similar to the estimator proposed by Poirier-Ruud (1981) and Powers (1993), but quite rarely adopted in practical applications for its computational complexity, with the well-known Two-Stage procedure (Heckman, 1976 and 1978; Lee, 1978, inter alia), widely adopted by practitioners for its simplicity and still dominant in applied works on the evaluation of causal effects (Heckman, Tobias and Vytlacil, 2003). An accurate Monte Carlo experiment shows that the relative efficiency of the FIML estimator over to the Two-Stage procedure is remarkably high in presence of a high degree of endogeneity in the selection equation.
2009
9788861294257
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1886433
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