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

We analyze the consequences of three types of specification error for conditional distribution functions F (y|a): measurement error in y, measurement error in a and omitted conditioning variables. The paper uses exact results to obtain conditions under which the effect of the misspecification on the computed distribution function can be signed. The effects are shown to depend on both the curvature of the true distribution and the properties of the error distribution. The consequences of misspecification are illustrated using a model of intergenerational mobility.