Hiroaki Kaido, Francesca Molinari, Jörg Stoye
arXiv 5 Jan 2016 · Mathematics — Statistics Theory · publishedEconometrica (2019) · 88 citations (OpenAlex)
arXiv:1601.00934 · PDF · DOI · OpenAlex · Extracted main text
We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the function of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the function of theta, not theta itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately, and we establish its rate of convergence. The algorithm is of independent interest for optimization problems with simple objectives and complicated constraints. An empirical application estimating an entry game illustrates the usefulness of the method. Monte Carlo simulations confirm the accuracy of the solution algorithm, the good statistical as well as computational performance of calibrated projection (including in comparison to other methods), and the algorithm's potential to greatly accelerate computation of other confidence intervals.
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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 | Chernozhukov, Hong, and Tamer (2007) Estimation and Confidence Regions for Parameter Sets In Econometric Models | 0.941 | 6 | 4 | 83% |
| 2 | Kaido, Molinari, Stoye, and Thirkettle (2017) Calibrated Projection in MATLAB | 0.928 | 4 | 3 | 100% |
| 3 | Jones, Schonlau, and Welch (1998) Efficient Global Optimization of Expensive Black-Box Functions | 0.928 | 4 | 3 | 100% |
| 4 | Bull (2011) Convergence rates of efficient global optimization algorithms | 0.894 | 14 | 5 | 71% |
| 5 | Kline and Tamer (2016) Bayesian inference in a class of partially identified models | 0.874 | 8 | 2 | 100% |
| 6 | Andrews and Soares (2010) Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection | 0.822 | 9 | 4 | 56% |
| 7 | Kaido, Molinari, and Stoye (2017) Confidence Intervals for Projections of Partially Identified Parameters self | 0.811 | 4 | 2 | 100% |
| 8 | Ciliberto and Tamer (2009) Market Structure and Multiple Equilibria in Airline Markets | 0.794 | 6 | 5 | 50% |
| 9 | Bugni, Canay, and Shi (2017) Inference for subvectors and other functions of partially identified parameters in moment inequality models | 0.693 | 6 | 3 | 33% |
| 10 | Magnac and Maurin (2008) Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data | 0.644 | 3 | 2 | 67% |
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