Consequences of Specification Error for Distributional Analysis with an Application to Intergenerational Mobility

In this paper we examine the properties of conditional distribution functions in the presence of several types of misspecification. We derive the properties of the cumulative conditional distribution function in the case of measurement error in the dependent variable, measurement error in the conditioning variables and omitted conditioning variables. Our focus on the conditional cumulative distribution is motivated by the fact that this distribution provides the natural starting point to investigate the direction and intensity of the effect of the variable a on the variable y. The results we present on measurement error have the character of dominance results: if the distribution of measurement error satisfies certain properties then we are able to sign the effect of specification error for a wide class of conditional CDF's. The effects are shown to depend on both the curvature of the true distribution and the properties of the error distribution. We illustrate our findings using a model of intergenerational mobility