The QLIM Procedure

Example 22.2 Tobit Analysis

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.

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 .