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1. Linear Probability Model vs. Logit (or Probit)

EEP/IAS 118 Andrew Dustan Section Handout 13 1. Linear Probability Model vs. Logit (or probit ) We have often used binary ("dummy") variables as explanatory variables in regressions. What about when we want to use binary variables as the dependent variable? It's possible to use OLS: = + + + + where y is the dummy variable. This is called the Linear Probability Model . Estimating the equation: = 1| = = + + + is the predicted Probability of having = 1 for the given values of .. Problems with the Linear Probability Model (LPM): 1. Heteroskedasticity: can be fixed by using the "robust" option in Stata. Not a big deal. 2. Possible to get < 0 or > 1. This makes no sense you can't have a Probability below 0 or above 1. This is a fundamental problem with the LPM that we can't patch up. Solution: Use the Logit or probit Model . These models are specifically made for binary dependent variables and always result in 0 < < 1.

Linear Probability Model Logit (probit looks similar) This is the main feature of a logit/probit that distinguishes it from the LPM – predicted probability of =1 is never below 0 or above 1, and the shape is always like the one on the right rather than a straight line.

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