Assessment of Two Tests for the Validity Instruments in Logit Models
C Guevara, M Ben-Akiva, Universidad de los Andes, CL
A new test for the validity of instruments in Logit is compared with a previous regression-based test. Experiments show that both tests have similar properties, making the new and simpler test an attractive tool for practitioners
Endogeneity is a prevalent problem in diverse applications of Logit models. Methods to address endogeneity rely on the availability of instrumental variabkes. Instruments have to be correlated with the endogenous variable but, at the same time, uncorrelated with the error term, which is not observable and makes its validation cumbersome.
This paper deeps and extends the analysis of the novel test for the validity of instrumental variables in Logit models proposed by Guevara and Ben-Akiva (2008). This test relies in over-identification (more instruments than endogenous variables) and uses a generalized definition of residuals in Logt that was proposed by McFadden (1987). Additionally, the paper proposes an alternative test that is easier to implement with standard estimation packages. This simpler version relies also in over-identification and consists in the inclusion of one of the instruments as an additional variable of an auxiliary Logit model.
Both tests were compared using Monte Carlo experimentation. The experiments consisted in a binary choice model that suffered endogeneity of and was latter corrected using subsequently: two good instruments; one good and one bad instrument; and two bad instruments. Experiments show that the power and size properties of both tests are equivalent, what makes the simpler version an attractive alternative for practitioners. Experiments also show that the power of both tests may be importantly reduced when the instruments are highly correlated.
The paper additionally includes applications with real data on residential location for the cities of Lisbon, Portugal and Santiago, Chile. The hypothesis is that both models suffer of price endogeneity due to the omission of quality attributes that can not be measured by the analyst. In both cases the instruments were built using the price of nearby dwellings outside certain vicinity. For Santiago and for Lisbon, the correction for endogeneity resulted in estimates more concordant with economic theory. However, both tests for the validity of instruments resulted in a rejection for the Portuguese data. This is arguably the result of specification problems of that database, beyond price endogeneity problem.
The paper finishes with an analysis of the impacts, limitations and extension of this research.
Association for European Transport