Nonparametric Gini-Frisch bounds

Abstract

The Gini-Frisch bounds partially identify the constant slope coefficient in a linear equation when the explanatory variable suffers from classical measurement error. This paper generalizes these quintessential bounds to accommodate nonparametric heterogeneous effects. It provides suitable conditions under which the main insights that underlie the Gini-Frisch bounds apply to partially identify the average marginal effect of an error-laden variable in a nonparametric nonseparable equation. To this end, the paper puts forward a nonparametric analogue to the standard “forward” and “reverse” linear regression bounds. The nonparametric forward regression bound generalizes the linear regression “attenuation bias” due to classical measurement error.