Unobserved Binary Random Factors and the Returns to Lying

Unobserved Binary Random Factors Abstract :
Suppose V and U are two independent mean zero random variables, where V
has an asymmetric distribution with two mass points and U has a
symmetric distribution. We show that the distributions of V and U are
nonparametrically identified just from observing the sum V +U, and
provide a rate root n estimator. We illustrate the results with an
empirical example looking at possible convergence over time in the world
income distribution. We also extend our results to include covariates X,
showing that we can nonparametrically identify and estimate cross
section regression models of the form Y = g(X,D*)+U, where D* is an
unobserved binary regressor.
Returns to Lying Abstract:
Consider an observed binary regressor D and an unobserved binary
variable D*, both of which affect some other variable Y . This paper
considers nonparametric identication and estimation of the effect of D
on Y, conditioning on D*=0. For example, suppose Y is a person’s wage,
the unobserved D* indicates if the person has been to college, and the
observed D indicates whether the individual claims to have been to
college. This paper then identifies and estimates the difference in
average wages between those who falsely claim college experience versus
those who tell the truth about not having college. We estimate this
average effect of lying to be about 6% to 20%. Nonparametric
identification without observing D* is obtained either by observing a
variable V that is roughly analogous to an instrument for ordinary
measurement error, or by imposing restrictions on model error moments.