Xiaohong Chen, Timothy M. Christensen
arXiv 13 Aug 2015 · Statistics — Methodology · publishedQuantitative Economics (2018) · 75 citations (OpenAlex)
arXiv:1508.03365 · PDF · DOI · OpenAlex · Extracted main text
This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of $h_0$ and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating $h_0$ and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when $h_0$ is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean-squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence bands (UCBs) for collections of nonlinear functionals of $h_0$ under primitive conditions, allowing for mildly and severely ill-posed problems. Fourth, as applications, we obtain the first asymptotic pointwise and uniform inference results for plug-in sieve t-statistics of exact consumer surplus (CS) and deadweight loss (DL) welfare functionals under low-level conditions when demand is estimated via sieve NPIV. Empiricists could read our real data application of UCBs for exact CS and DL functionals of gasoline demand that reveals interesting patterns and is applicable to other markets.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Blundell, R., X. Chen, and D. Kristensen (2007) Semi-nonparametric iv estimation of shape-invariant engel curves | 1.000 | 15 | 4 | 100% |
| 2 | Horowitz, J. L (2011) Applied nonparametric instrumental variables estimation | 1.000 | 7 | 5 | 100% |
| 3 | Chen, X. and T. M. Christensen (2015) Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation self | 1.000 | 6 | 4 | 100% |
| 4 | Belloni, A., V. Chernozhukov, D. Chetverikov, and K. Kato (2015) Some new asymptotic theory for least squares series: Pointwise and uniform results | 1.000 | 6 | 3 | 100% |
| 5 | Newey, W. K. and J. L. Powell (2003) Instrumental variable estimation of nonparametric models | 1.000 | 6 | 3 | 100% |
| 6 | Chen, X. and D. Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals self | 1.000 | 5 | 3 | 100% |
| 7 | Newey, W. K (1997) Convergence rates and asymptotic normality for series estimators | 0.941 | 6 | 5 | 83% |
| 8 | Blundell, R., J. L. Horowitz, and M. Parey (2012) Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation | 0.928 | 4 | 3 | 100% |
| 9 | Chernozhukov, V., S. Lee, and A. M. Rosen (2013) Intersection bounds: Estimation and inference | 0.928 | 4 | 3 | 100% |
| 10 | Chen, X. and M. Reiss (2011) On rate optimality for ill-posed inverse problems in econometrics self | 0.874 | 9 | 5 | 67% |
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