Estimation of Average Derivatives of Latent Regressors: With an Application to Inference on Buffer-Stock Saving

TL;DR

This paper introduces a density-weighted average derivative estimator for latent regressors with measurement errors, enabling inference on economic models like buffer-stock saving, and demonstrates its effectiveness through simulations and real data application.

Contribution

It develops a root-n consistent estimator for derivatives of latent regressors with classical errors, with asymptotic normality and practical inference methods.

Findings

Estimator achieves root-n convergence rate.

Simulation studies confirm small-sample accuracy.

Empirical test supports buffer-stock saving model.

Abstract

This paper proposes a density-weighted average derivative estimator based on two noisy measures of a latent regressor. Both measures have classical errors with possibly asymmetric distributions. We show that the proposed estimator achieves the root-n rate of convergence, and derive its asymptotic normal distribution for statistical inference. Simulation studies demonstrate excellent small-sample performance supporting the root-n asymptotic normality. Based on the proposed estimator, we construct a formal test on the sub-unity of the marginal propensity to consume out of permanent income (MPCP) under a nonparametric consumption model and a permanent-transitory model of income dynamics with nonparametric distribution. Applying the test to four recent waves of U.S. Panel Study of Income Dynamics (PSID), we reject the null hypothesis of the unit MPCP in favor of a sub-unit MPCP, supporting the buffer-stock model of saving.