Qualitative and Limited Dependent Variable Exercises

Exercise 12.2

The SHAZAM commands to implement this exercise are as follows:

READ (DATA12-1) Accept GPA Bio Chem Phy Red Prb Qnt Age Gender 
OLS Accept GPA Bio Chem Phy Red Prb Qnt Age Gender /PREDICT=Yhat1
PRINT Yhat1
GENR D=(Yhat1.GT.0)*(Yhat1.LT.1)
GENR SigmaSq=Yhat1*(1-Yhat1)
GENR Wt=1/SigmaSq*D
OLS Accept GPA Bio Chem Phy Red Prb Qnt Age Gender /PREDICT=Yhat2 WEIGHT=Wt
PRINT Yhat1 D SigmaSq Wt Yhat2
PROBIT Accept GPA Bio Chem Phy Red Prb Qnt Age Gender

Both OLS and WLS/GLS (after setting the weights to zero for the inadmissible cases) give some predictions outside the range [0,1]. This demonstrates the uselessness of the linear probability model.

Exercise 12.4

The dependent variable is not binary here but is a fraction. Therefore the logit model is more appropriate. Compute Z = ln[K/(1-H)] and regress Z against a constant, Y, P, and R.

Exercise 12.7

This is an example of the Tobit model. Use the maximum likelihood procedure described in Section 12.4 of the textbook to estimate this model. SHAZAM will estimate a Tobit model through the TOBIT command.

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Updated March 24, 2000
noelroy@morgan.ucs.mun.ca