INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 135
5.2.3.0 MAIN CONTENTS 5.2.3.1 The Linear Probability Model The simplest binary choice model is the linear probability model whereas the name implies, the probability
of the event occurring,
p, is assumed to be a linear function of a set of descriptive variables. That is
(
)
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For one descriptive variable, the relationship is as shown in Figure 5.1. Of course,
p is unobservable, and as expected
there is only one data Y, on the outcome. In the linear probability model, this is used as a dummy variable for the dependent variable.
Figure 5.1. Linear Probability Model Regrettably, the linear probability model though simple still has some serious defects. First, there are problems with the disturbance term. As usual, the value
of the dependent variable in observation
i,has a nonstochastic component and a random component. The nonstochastic
component depends on and the parameters and is the expected value of
given
(
|
). The random component is the disturbance term.
(
|
)
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