Linear Probability Model Questions with Solutions

Linear Probability Model

Dummy Variables - answer Also known as a binary variable.

The coefficient on a variable take a value of 1 or 0 depending on whether a state exists.
An example is gender.

Can also be used for seasonal data, with a different dummy variable for each season.

Linear Probability Model - answerThe linear regression model when the dependent
variable (y) is a binary variable.

The error term in the LPM - answered y=1, then u = 1 - B0 - B1*Xi

if y=0. then u = -B0 - B1Xi

Variance of the error term in the LPM - answer Var( u I xi ) = (B0 +B1*Xi)(1 - B0 - B1Xi)

Problems with the LPM - answerThe fitted values (Y hat) will rarely be 1 or 0

Low R^2 values

Probabilities outside of the 0-1 range

MLR5 and MLR6 cannot be valid

The LPM Model - answer

Generalised Least Squares with the LPM - answerIf we knew the values of B0 and B1
we could calculate the weights of each variable in the form of weighted least squares.

Instead, we can only estimate using feasible least squares.

Can also use Robust Standard Errors. This has no effect on anything but the standard
errors.

The Logistic Function - answer