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Suppose that y is a dummy variable, and is determined by the linear probability model below:

= + +

or

Pr( = 1|) = +

Further suppose that the parameters (a and b) and the range that x can take ensures that these probabilities are between 0 and 1.

This is a problem on my homework, does this have to do with IID?

jgriff
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  • IID or normality? Also, kindly add the self-study tag and read its wiki. – Dave Mar 29 '20 at 23:06
  • A normal distribution has domain $(-\infty, +\infty)$. Clearly there are values $u$ is not allowed to take because they would make the probability outside $[0,1]$. So $u$ cannot follow a normal distribution. – Noah Mar 30 '20 at 17:25
  • See also https://stats.stackexchange.com/questions/144092/linear-probability-model, https://stats.stackexchange.com/questions/19797/likelihood-function-of-a-linear-probability-model, https://stats.stackexchange.com/questions/207625/how-to-choose-between-logit-probit-or-linear-probability-model – kjetil b halvorsen Aug 01 '23 at 02:23

1 Answers1

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Since the response $y$ is binary, that is, 0 or 1, the error term $u$ can clearly not have a normal distribution, since that has as range the full real line. But, when the name Linear Probability Model is used, estimation is usually done using least squares, which is the same as using the normal-based likelihood.

That can clearly only be an approximation.

kjetil b halvorsen
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