A COMPANION TO Theoretical Econometrics

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.