Author(s): Jacob Hutchings
Mentor(s):
Institution BYU
We examine the effect of multicollinearity on Generalized Method of Moments (GMM) overidentification tests in the Instrumental Variables (IV) setting. Specifically, we consider the case of valid instruments and simulate rejection rates for the Hausman and Hansen tests given various levels of multicollinearity in Z'X and Z'Z, two matrices which appear in the test statistic formulas. Little research has been done into these specific cases despite both of them having intuitive and practical significance for modern research. We construct two novel data-generating processes which provide an environment where IV is necessary and successfully generate multicollinearity as measured by the condition number and variance-inflation factor. We show that our sample moment conditions hold for all levels of multicollinearity. Using this simulated data, we compute rejection rates of the Hausman and Hansen test for given levels of multicollinearity. We find that multicollinearity in Z'Z has no effect on Hansen test rejection rates and has a surprising but explainable effect on Hausman rejection rates. Multicollinearity in Z'X positively effects rejection rates for both tests. We continue this analysis of rejection rates and multicollinearity by also considering how these rates change for different degrees of overidentification in the model. In both cases, the degree of overidentification is positively correlated with rejection rates. Lastly, we use our simulated data to show that the tests remain consistent even in the face of fairly extreme multicollinearity by running our Monte Carlo simulation with different numbers of observations. Together, these results all show that multicollinearity does have an effect on overidentification tests in all cases except Z'Z and the Hansen test.