2. Economics 310 Lecture 22 Limited Dependent Variables

3. Examples of limited dependent variables Decision to go to graduate school or not. Decision to get married or not. Decision to have a child or not. Decision to vote for a proposition or not. Decision to send child to private school or not.

4. Modeling Decision This yes or no type decision leads to a dummy variable. The dependent variable of our model is a dummy variable. We will be modeling the probability function, P(Y=1).

5. The statistical Model

6. Simplest Model Linear Probability Model

7. Picture of LPM X 1 0 X0X0 X1X1

8. Problems of LPM Predictions outside 0-1 range. Heteroscedasticity This can be solved and a estimated GLS estimator developed. Coefficient Determination has little meaning. Constant marginal effect.

9. Probit Statistical Model The probit model is a nonlinear (in the probability) statistical model that achieves the objective of relating the choice probability P i to explanatory factors in such a way that the probability remains in the (0,1] interval. Model can be developed from several theories. Threshold theory Utility theory

10. Probit Model

11. Interpreting the Probit Model I 0 1 0 F(I)

12. Interpreting the Probit Model

13. Estimating Probit Parameters

14. Estimating Probit Model using LIMDEP read; nobs=13081; nvar=5;names=1;file=wlottq07205.asc $CREATE; COMPUTER=HESCU1A=1 $CREATE; AGE=PRTAGE $CREATE; AGESQ=AGE*AGE $CREATE; NONWHITE=PERACE>1 $CREATE; FEMALE=PESEX=2 $CREATE; EARNING=PTERNWA $PROBIT; LHS=COMPUTER; RHS=ONE,AGE,AGESQ,NONWHITE,FEMALE,EARNING $STOP $

15. Results of probit estimation Computer ownership model Variable Coefficient Standard Error b/St.Er. P¢¦Z¦>z| Mean of X --------------------------------------------------------------------- Index function for probability Constant -.1504969.91575E-01 -1.643.10029 AGE.8665748E-03.49262E-02.176.86036 38.79 AGESQ -.1163434E-03.59141E-04 -1.967.04916 1669. NONWHITE -.4021405.31576E-01 -12.736.00000.1499 FEMALE.1392186.23382E-01 5.954.00000.4955 EARNING.7477787E-03.31510E-04 23.732.00000 573.2