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Economics 310

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  1. Economics 310 Lecture 22 Limited Dependent Variables

  2. 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.

  3. 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).

  4. The statistical Model

  5. Simplest ModelLinear Probability Model

  6. Picture of LPM 1 0 X X0 X1

  7. 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.

  8. Probit Statistical Model • The probit model is a nonlinear (in the probability) statistical model that achieves the objective of relating the choice probability Pi 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

  9. Probit Model

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

  11. Interpreting the Probit Model

  12. Estimating Probit Parameters

  13. 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 $

  14. Results of probit estimationComputer 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

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