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Economics 310

Economics 310. Lecture 22 Limited Dependent Variables. 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.

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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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