Endogeneity is a key issue in residential discrete choice modeling. It occurs because each dwelling unit is quasi-unique, making thus unavoidable the omission of attributes which would be correlated, particularly, with price. This problem causes an inconsistent and a severely upward biased estimation of the price coefficient in such type of models. The effect of thismodel mis-specification is indeed huge. Many empirical applications have reported statistically insignificant, small or even positive dwelling-unitprice coefficients. Furthermore, even residential choice models in which estimated price coefficients are negative and significant, are not necessarily consistently estimated. The case is that, even if it would be possible to account for all relevant attributes which are correlated with price, the quasi-uniqueness of the alternatives in the choice set faced by each individual would make necessary to estimate each coefficient in the model with a single observation. This would lead again to inconsistent estimatorsin what is known as the incidental parameters problem. The present article describes the derivation and application of a novel Lagrange Multiplier test for the validity of instrumental variables required to build control-functions to correct for endogenity in MNL models. The test proposed in this principally consists in the estimation of an auxiliary regression wherethe dependent variable is a weighed measure of the difference between fitted probabilities and actual choices, and where the independent variables correspond to weighed alternative variables and the instruments which exogeneity is to be tested. The intuition behind the test is that, if instruments are exogenous, the unadjusted multiple correlation coefficient of thatauxiliary regression should be nearly zero. Concordantly, a Lagrange Multiplier statistical test, based on this unadjusted multiple correlation coefficient but corrected for the degrees of freedom, is constructed. Finally, using McFadden (1987) and Engle (1984) asymptotics, it is claimed that the statistical is distributed chi-square with a number of degrees of freedom equal to number of independent variables. Test properties are studied using a Monte Carlo simulated database and residential data from Santiago, Chile. The empirical results show that endogeneity is relevant in the studied sample and that the average price of dwelling units in adjacent zones is a valid instrument for this experiment. Power properties and suitability of the proposed statistical test are also discussed, and suggestions forfurther research are drawn. For the covering abstract see ITRD E145999
Abstract