Cosine metric as a structural economic similarity measure

Structural similarity, the extent to which economic mechanisms respond alike to common shocks, matters for economic forecasting, policy transfer, and other decisions that rely on evidence from comparable settings. For mechanisms approximated by linear models, this idea has a simple geometric representation: The smaller the angle between their coefficient vectors, the more similarly they respond to the same shock. This paper introduces the cosine of this angle as a measure of structural similarity and develops the corresponding inference procedure. Applied to New Jersey's wage mechanism around the 1992 minimum-wage reform, the approach yields interesting evidence: Although the reform clearly affected the low-wage part of the wage distribution, the underlying mechanism linking worker characteristics to wages was no different from what would have prevailed without it.