The following statements show a subset of the Mroz (1987) data set. In these data, Hours
is the number of hours the wife worked outside the household in a given year, Yrs_Ed
is the years of education, and Yrs_Exp
is the years of work experience. A Tobit model will be fit to the hours worked with years of education and experience as
covariates.
By the nature of the data it is clear that there are a number of women who committed some positive number of hours to outside work ( is observed). There are also a number of women who did not work at all ( is observed). This gives us the following model:
where . The set of explanatory variables is denoted by .
title1 'Estimating a Tobit model'; data subset; input Hours Yrs_Ed Yrs_Exp @@; if Hours eq 0 then Lower=.; else Lower=Hours; datalines; 0 8 9 0 8 12 0 9 10 0 10 15 0 11 4 0 11 6 1000 12 1 1960 12 29 0 13 3 2100 13 36 3686 14 11 1920 14 38 0 15 14 1728 16 3 1568 16 19 1316 17 7 0 17 15 ;
/*-- Tobit Model --*/ proc qlim data=subset; model hours = yrs_ed yrs_exp; endogenous hours ~ censored(lb=0); run;
The output of the QLIM procedure is shown in Output 22.2.1.
Output 22.2.1: Tobit Analysis Results
Estimating a Tobit model |
Model Fit Summary | |
---|---|
Number of Endogenous Variables | 1 |
Endogenous Variable | Hours |
Number of Observations | 17 |
Log Likelihood | -74.93700 |
Maximum Absolute Gradient | 1.18953E-6 |
Number of Iterations | 23 |
Optimization Method | Quasi-Newton |
AIC | 157.87400 |
Schwarz Criterion | 161.20685 |
In the “Parameter Estimates” table there are four rows. The first three of these rows correspond to the vector estimate of the regression coefficients . The last one is called _Sigma, which corresponds to the estimate of the error variance .