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The Linear Probability Model (LPM) is one of the simplest approaches used to model binary outcome variables in econometrics. It applies ordinary least squares (OLS) regression to a dependent variable that takes values 0 or 1, representing two mutually exclusive outcomes. While the LPM is intuitive and easy to implement, it has several notable limitations that restrict its applicability in practical research contexts. One of the most fundamental limitations of the LPM is that it can produce predicted probabilities that fall outside the logical range of 0 and 1. Since the model is linear in parameters, there is no inherent constraint ensuring that the predicted values remain within the permissible probability interval. For instance, a combination of explanatory variables with certain coefficient estimates may yield a predicted probability of 1.2 or -0.3, which are clearly nonsensical in a probabilistic context. This limitation undermines the interpretability and reliability of the model, particularly when making forecasts or policy evaluations based on predicted probabilities. Another significant limitation of the LPM is the assumption of constant variance, also known as homoscedasticity, which is a core assumption in OLS regression. In the context of a binary dependent variable, the variance of the error term is inherently heteroskedastic because it depends _______ ___ ____ _______ _________ ____ _____ _____ __________.
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