HPQLIM Procedure

(View the complete code for this example.)

This example illustrates the use of the HPQLIM procedure. The data were originally published by Mroz (1987), and the following statements show a subset of that data set:

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
;

In these data, Hours is the number of hours that 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.

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 outside the home at all ( is observed). This yields the following model:

where and the set of explanatory variables is denoted by . The following statements fit a Tobit model to the hours worked with years of education and years of work experience as covariates:

/*-- Tobit Model --*/
proc hpqlim data=subset;
   model hours = yrs_ed yrs_exp;
   endogenous hours ~ censored(lb=0);
   performance nthreads=2 details;
run;

The output of the HPQLIM procedure is shown in Figure 1.

The “Parameter Estimates” table contains four rows. The first three rows correspond to the vector estimate of the regression coefficients . The last row is called _Sigma, which corresponds to the estimate of the error variance .