Closed-form estimation of nonparametric models with non-classical measurement errors

This paper proposes closed-form estimators for nonparametric regressions using two measurements with non-classical errors. One (administrative) measurement has location-/scale-normalized errors, but the other (survey) measurement has endogenous errors with arbitrary location and scale. For this setting of data combination, we derive closed-form identification of nonparametric regressions, and practical closed-form estimators that perform well with small samples. Applying this method to NHANES III, we study how obesity explains health care usage. Clinical measurements and self reports of BMI are used as two measurements with normalized errors and endogenous errors, respectively. We robustly find that health care usage increases with obesity.