NONPARAMETRIC INSTRUMENTAL REGRESSION WITH ERRORS IN VARIABLES
| Autor: | Karun Adusumilli, Taisuke Otsu |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
HB Economic Theory
H Social Sciences (General) Economics and Econometrics Observational error Actuarial science Mean squared error 05 social sciences Instrumental variable Nonparametric statistics Estimator Q Science (General) 01 natural sciences jel:C26 010104 statistics & probability 0502 economics and business Stein's unbiased risk estimate Applied mathematics Errors-in-variables models Endogeneity 0101 mathematics Nonparametric instrumental variable regression measurement error inverse problem deconvolution measurement error Social Sciences (miscellaneous) 050205 econometrics Mathematics |
| Zdroj: | Econometric Theory. 34:1256-1280 |
| ISSN: | 1469-4360 0266-4666 |
| DOI: | 10.1017/s0266466617000469 |
| Popis: | This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for the cases of mildly/severely ill-posed models and ordinary/super smooth measurement errors. We characterize how the presence of measurement error slows down the convergence rates of the estimator. We also study the case where the measurement error density is unknown and needs to be estimated, and show that the estimation error of the measurement error density is negligible under mild conditions as far as the measurement error density is symmetric. |
| Databáze: | OpenAIRE |
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