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

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  • Hao Dong
  • Yuya Sasaki
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.

Suggested Citation

  • Hao Dong & Yuya Sasaki, 2022. "Estimation of Average Derivatives of Latent Regressors: With an Application to Inference on Buffer-Stock Saving," Papers 2209.05914, arXiv.org.
    • Handle: RePEc:arx:papers:2209.05914
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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