SAS/ETS 9.22 User''''s Guide 149 pdf

Output 21.3.1 Bivariate Probit Analysis ResultsEstimating a Tobit model The QLIM Procedure Model Fit Summary Number of Endogenous Variables 2 Maximum Absolute Gradient 3.23363E-7 Optimiz

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Output 21.3.1 Bivariate Probit Analysis Results

Estimating a Tobit model

The QLIM Procedure

Model Fit Summary

Number of Endogenous Variables 2

Maximum Absolute Gradient 3.23363E-7

Optimization Method Quasi-Newton

Parameter Estimates

Example 21.4: Sample Selection Model

This example illustrates the use of PROC QLIM for sample selection models The data set is the same one from Mroz (1987) The goal is to estimate a wage offer function for married women, accounting for potential selection bias Of the 753 women, the wage is observed for 428 working women The labor force participation equation estimated in the introductory example is used for selection The wage equation uses log wage (lwage) as the dependent variable The explanatory variables in the wage equation are the woman’s years of schooling (educ), wife’s labor experience (exper), and square of experience (expersq) The program is as follows:

/* Sample Selection */

proc qlim data=mroz;

model inlf = nwifeinc educ exper expersq

age kidslt6 kidsge6 /discrete;

model lwage = educ exper expersq / select(inlf=1);

run;

The output of the QLIM procedure is shown in Output 21.4.1

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Output 21.4.1 Sample Selection

Binary Data

Maximum Absolute Gradient 0.00502

Note the correlation estimate is insignificant This indicates that selection bias is not a big problem

in the estimation of wage equation.

Example 21.5: Sample Selection Model with Truncation and Censoring

In this example the data are generated such that the selection variable is discrete and the variable Y

is truncated from below by zero The program follows, with the results shown in Output 21.5.1 :

data trunc;

keep z y x1 x2;

do i = 1 to 500;

x1 = rannor( 19283 );

x2 = rannor( 19283 );

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u1 = rannor( 19283 );

u2 = rannor( 19283 );

zl = 1 + 2 * x1 + 3 * x2 + u1;

y = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;

if ( zl > 0 ) then z = 1;

else z = 0;

if y>=0 then output;

end;

run;

/* Sample Selection with Truncation */

proc qlim data=trunc method=qn;

model z = x1 x2 / discrete;

model y = x1 x2 / select(z=1) truncated(lb=0);

run;

Output 21.5.1 Sample Selection with Truncation

Binary Data The QLIM Procedure

In the following statements the data are generated such that the selection variable is discrete and the variable Y is censored from below by zero The results are shown in Output 21.5.2

data cens;

keep z y x1 x2;

do i = 1 to 500;

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x1 = rannor( 19283 );

x2 = rannor( 19283 );

u1 = rannor( 19283 );

u2 = rannor( 19283 );

zl = 1 + 2 * x1 + 3 * x2 + u1;

yl = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;

if ( zl > 0 ) then z = 1;

if ( yl > 0 ) then y = yl;

output;

end;

run;

/* Sample Selection with Censoring */

proc qlim data=cens method=qn;

model z = x1 x2 / discrete;

model y = x1 x2 / select(z=1) censored(lb=0);

run;

Output 21.5.2 Sample Selection with Censoring

Binary Data

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Example 21.6: Types of Tobit Models

The following five examples show how to estimate different types of Tobit models (see “ Types

of Tobit Models ” on page 1447) Output 21.6.1 through Output 21.6.5 show the results of the corresponding programs.

Type 1 Tobit

data a1;

keep y x;

do i = 1 to 500;

x = rannor( 19283 );

u = rannor( 19283 );

yl = 1 + 2 * x + u;

if ( yl > 0 ) then y = yl;

output;

end;

run;

/* Type 1 Tobit */

proc qlim data=a1 method=qn;

model y = x;

endogenous y ~ censored(lb=0);

run;

Output 21.6.1 Type 1 Tobit

Binary Data

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Type 2 Tobit

data a2;

keep y1 y2 x1 x2;

do i = 1 to 500;

x1 = rannor( 19283 );

x2 = rannor( 19283 );

u1 = rannor( 19283 );

u2 = rannor( 19283 );

y1l = 1 + 2 * x1 + 3 * x2 + u1;

y2l = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;

if ( y1l > 0 ) then y1 = 1;

if ( y1l > 0 ) then y2 = y2l;

output;

end;

run;

model y1 = x1 x2 / discrete;

model y2 = x1 x2 / select(y1=1);

run;

Binary Data

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Type 3 Tobit

data a3;

keep y1 y2 x1 x2;

do i = 1 to 500;

x1 = rannor( 19283 );

x2 = rannor( 19283 );

u1 = rannor( 19283 );

u2 = rannor( 19283 );

y1l = 1 + 2 * x1 + 3 * x2 + u1;

y2l = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;

if ( y1l > 0 ) then y1 = y1l;

if ( y1l > 0 ) then y2 = y2l;

output;

end;

run;

model y1 = x1 x2 / censored(lb=0);

model y2 = x1 x2 / select(y1>0);

run;

Binary Data

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Output 21.6.3 continued

Type 4 Tobit

data a4;

keep y1 y2 y3 x1 x2;

do i = 1 to 500;

x1 = rannor( 19283 );

x2 = rannor( 19283 );

u1 = rannor( 19283 );

u2 = rannor( 19283 );

u3 = rannor( 19283 );

y1l = 1 + 2 * x1 + 3 * x2 + u1;

y2l = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;

y3l = 0 - 1 * x1 + 1 * x2 + u1*.1 - u2*.5 + u3*.5;

if ( y1l > 0 ) then y1 = y1l;

if ( y1l > 0 ) then y2 = y2l;

if ( y1l <= 0 ) then y3 = y3l;

output;

end;

run;

model y1 = x1 x2 / censored(lb=0);

model y3 = x1 x2 / select(y1<=0);

run;

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Binary Data

Maximum Absolute Gradient 0.0000161

Type 5 Tobit

data a5;

keep y1 y2 y3 x1 x2;

do i = 1 to 500;

x1 = rannor( 19283 );

x2 = rannor( 19283 );

u1 = rannor( 19283 );

u2 = rannor( 19283 );

u3 = rannor( 19283 );

y1l = 1 + 2 * x1 + 3 * x2 + u1;

y2l = 3 + 4 * x1 - 2 * x2 + u1*.2 + u2;

y3l = 0 - 1 * x1 + 1 * x2 + u1*.1 - u2*.5 + u3*.5;

if ( y1l > 0 ) then y1 = 1;

if ( y1l > 0 ) then y2 = y2l;

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if ( y1l <= 0 ) then y3 = y3l;

output;

end;

run;

model y1 = x1 x2 / discrete;

model y3 = x1 x2 / select(y1<=0);

run;

Binary Data

Model Fit Summary Number of Endogenous Variables 3

Tiêu đề	The Qlim Procedure
Thể loại	Hướng dẫn sử dụng

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