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This paper proposes a density-weighted average derivative estimator based ontwo noisy measures of a latent regressor. Both measures have classical errorswith possibly asymmetric distributions. We show that the proposed estimatorachieves the root-n rate of convergence, and derive its asymptotic normaldistribution for statistical inference. Simulation studies demonstrateexcellent small-sample performance supporting the root-n asymptotic normality.Based on the proposed estimator, we construct a formal test on the sub-unity ofthe marginal propensity to consume out of permanent income (MPCP) under anonparametric consumption model and a permanent-transitory model of incomedynamics with nonparametric distribution. Applying the test to four recentwaves of U.S. Panel Study of Income Dynamics (PSID), we reject the nullhypothesis of the unit MPCP in favor of a sub-unit MPCP, supporting thebuffer-stock model of saving.

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