# 15-061/III (2015-05-22)

Author(s)
Giuseppe De Luca, University of Palermo, Italy; Jan Magnus, VU University Amsterdam, the Netherlands; Franco Peracchi, University of Tor Vergata, Rome, Italy
Keywords:
Omitted variables, Misspecification, Least-squares estimators, Bias, Mean squared error
JEL codes:
C13, C51, C52

This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.