Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911847975747584 |
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| author | Wu, Shaomin |
| author_facet | Wu, Shaomin |
| contents | In this paper, I study the nonparametric identification and estimation of the marginal effect of an endogenous variable $X$ on the outcome variable $Y$, given a potentially mismeasured instrument variable $W^*$, without assuming linearity or separability of the functions governing the relationship between observables and unobservables. To address the challenges arising from the co-existence of measurement error and nonseparability, I first employ the deconvolution technique from the measurement error literature to identify the joint distribution of $Y, X, W^*$ using two error-laden measurements of $W^*$. I then recover the structural derivative of the function of interest and the "Local Average Response" (LAR) from the joint distribution via the "unobserved instrument" approach in Matzkin (2016). I also propose nonparametric estimators for these parameters and derive their uniform rates of convergence. Monte Carlo exercises show evidence that the estimators I propose have good finite sample performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments Wu, Shaomin Econometrics In this paper, I study the nonparametric identification and estimation of the marginal effect of an endogenous variable $X$ on the outcome variable $Y$, given a potentially mismeasured instrument variable $W^*$, without assuming linearity or separability of the functions governing the relationship between observables and unobservables. To address the challenges arising from the co-existence of measurement error and nonseparability, I first employ the deconvolution technique from the measurement error literature to identify the joint distribution of $Y, X, W^*$ using two error-laden measurements of $W^*$. I then recover the structural derivative of the function of interest and the "Local Average Response" (LAR) from the joint distribution via the "unobserved instrument" approach in Matzkin (2016). I also propose nonparametric estimators for these parameters and derive their uniform rates of convergence. Monte Carlo exercises show evidence that the estimators I propose have good finite sample performance. |
| title | Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments |
| topic | Econometrics |
| url | https://arxiv.org/abs/2404.13735 |