In this paper we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and NPIV models under two basic regularity conditions: the approximation number and the link condition. We show that both a simple projection estimator for the NPIR model and a sieve minimum distance estimator for the NPIV model can achieve the minimax risk lower bounds and are rate optimal uniformly over a large class of structure functions, allowing for mildly ill-posed and severely ill-posed cases.
Authors
Yale University
Markus Reiss
Journal article details
- DOI
- 10.1017/S0266466610000381
- Publisher
- Cambridge University Press
- Issue
- Volume 27, Issue 3, June 2011
Suggested citation
Chen, X and Reiss, M. (2011). 'On rate optimality for ill-posed inverse problems in econometrics' 27(3/2011)
More from IFS
Understand this issue
Empty defence spending promises are a shot in the dark
29 April 2024
Public investment: what you need to know
25 April 2024
The £600 billion problem awaiting the next government
25 April 2024
Policy analysis
Recent trends in and the outlook for health-related benefits
19 April 2024
4.2 million working-age people now claiming health-related benefits, could rise by 30% by the end of the decade
19 April 2024
Progression of nurses within the NHS
12 April 2024
Academic research
The employment and distributional impacts of nationwide minimum wage changes
10 April 2024
Willingness to pay for improved public education and public healthcare systems: the role of income mobility prospects
14 March 2024
Unfunded mandates and taxation
14 March 2024