Economics 310 Lecture 22 Limited Dependent Variables.

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Presentation transcript:

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. Decision to send child to private school or not.

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).

The statistical Model

Simplest Model Linear Probability Model

Picture of LPM X 1 0 X0X0 X1X1

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.

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

Probit Model

Interpreting the Probit Model I F(I)

Interpreting the Probit Model

Estimating Probit Parameters

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 $

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 E AGE E E AGESQ E E NONWHITE E FEMALE E EARNING E E