  Kotlarski's identity has been widely used in applied economic research.
However, how to conduct inference based on this popular identification approach
has been an open question for two decades. This paper addresses this open
problem by constructing a novel confidence band for the density function of a
latent variable in repeated measurement error model. The confidence band builds
on our finding that we can rewrite Kotlarski's identity as a system of linear
moment restrictions. The confidence band controls the asymptotic size uniformly
over a class of data generating processes, and it is consistent against all
fixed alternatives. Simulation studies support our theoretical results.
