Linear probability model: Difference between revisions

Revision as of 14:23, 20 August 2023

Revision as of 14:25, 20 August 2023

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: <math>y^* = b_0+ \mathbf x'\mathbf b + \varepsilon,\;\; \varepsilon\mid \mathbf x\sim U(-a,a).</math>

The critical assumption here is that the error term of this regression is a symmetric around zero Uniform[[Continuous uniform distribution|uniform]] random variable, and hence, of mean zero. The cumulative distribution function of <math>\varepsilon</math> here is <math>F_{\varepsilon|\mathbf x}(\varepsilon\mid \mathbf x) = \frac {\varepsilon + a}{2a}.</math>

Define the indicator variable <math> y = 1</math> if <math> y^* >0</math>, and zero otherwise, and consider the conditional probability