Least squares estimation

When attention is focused on modeling just the conditional mean, least squares methods are inferior to the approach of the previous subsection.

Linear least squares regression of V on x leads to consistent parameter esti­mates if the conditional mean is linear in x. But for count data the specification E [ y|x] = x’P is inadequate as it permits negative values of E [ y|x]. For similar reasons the linear probability model is inadequate for binary data.

Transformations of V may be considered. In particular the logarithmic transforma­tion regresses ln V on x. This transformation is problematic if the data contain zeros, as is often the case. One standard solution is to add a constant term, such as 0.5, and to model ln(y + .5) by OLS. This method often produces unsatisfactory
results, and complicates the interpretation of coefficients. It is also unnecessary as software to estimate basic count models is widely available.

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