Inference for subvectors and other functions of partially identified parameters in moment inequality models

Bugni, Federico A.; Canay, Ivan A.; Shi, Xun

doi:10.3982/qe490

Cited by 86 publications

(127 citation statements)

References 42 publications

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“…where c MR n is the critical value proposed in Bugni, Canay, and Shi (2017) and T n is any test statistic that they allowed for. The E-A-M algorithm can be used to compute the endpoints of this set so that the researcher may report an interval.…”

Section: Appendix B: Applying the E-a-m Algorithm To Profilingmentioning

confidence: 99%

“…This brings us to our second contribution, namely, a general method to accurately and rapidly compute confidence intervals whose construction resembles (). Additional applications within partial identification include projection of confidence regions defined in Chernozhukov, Hong, and Tamer (), Andrews and Soares (), or Andrews and Shi (), as well as (with minor tweaking; see Appendix B) the confidence interval proposed in Bugni, Canay, and Shi (, BCS henceforth) and further discussed later. In an application to a point identified setting, Freyberger and Reeves (, Supplement Section S.3) used our method to construct uniform confidence bands for an unknown function of interest under (nonparametric) shape restrictions.…”

Section: Introductionmentioning

confidence: 99%

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Confidence Intervals for Projections of Partially Identified Parameters

Kaido

Molinari

Stoye

2019

ECTA

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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 θ, not θ 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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Section: Appendix B: Applying the E-a-m Algorithm To Profilingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Confidence Intervals for Projections of Partially Identified Parameters

Kaido

Molinari

Stoye

2019

ECTA

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“… Inference procedures for subvectors have been further developed by Chaudhuri and Zivot (), Kaido, Molinari, and Stoye (), Andrews (), and Bugni, Canay, and Shi (). …”

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confidence: 99%

Inference for VARs identified with sign restrictions

Granziera¹,

Moon²,

Schorfheide³

2018

Quantitative Economics

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There is a fast growing literature that set‐identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign‐restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign‐restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for sign‐restricted SVARs within a moment‐inequality framework. In particular, it develops methods of constructing confidence bands for impulse response functions of sign‐restricted SVARs that are valid from a frequentist perspective. The paper also provides a comparison of frequentist and Bayesian coverage bands in the context of an empirical application—the former can be substantially wider than the latter.

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“…Finally, there is a large literature on techniques which seek to reduce sensitivity to the inclusion of slack moments in settings without nuisance parameters, including D. Andrews & Soares (2010), D. Andrews & Barwick (2012), Romano et al (2014a), and Cox & Shi (2019). , Bugni et al (2017), Belloni et al (2018), and Kaido et al (2019a) build on related ideas to reduce sensitivity to slack moments in models with nuisance parameters. If applied in our setting, however, these techniques would eliminate the linear structure which simplifies computation.…”

Section: Introductionmentioning

confidence: 99%

Inference for Linear Conditional Moment Inequalities

Andrews¹,

Roth²,

Pakes³

2019

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We consider inference based on linear conditional moment inequalities, which arise in a wide variety of economic applications, including many structural models. We show that linear conditional structure greatly simplifies confidence set construction, allowing for computationally tractable projection inference in settings with nuisance parameters. Next, we derive least favorable critical values that avoid conservativeness due to projection. Finally, we introduce a conditional inference approach which ensures a strong form of insensitivity to slack moments, as well as a hybrid technique which combines the least favorable and conditional methods. Our conditional and hybrid approaches are new even in settings without nuisance parameters. We find good performance in simulations based on Wollmann (2018), especially for the hybrid approach.Example 2 Katz (2007) studies the impact of travel time on supermarket choice.Katz assumes that agent utilities are additively separable in utility from the basket of goods bought (B i ), the travel time to the supermarkets chosen (T i,s ), and the cost of the basket (π(B i , s)). Normalizing coefficient on cost to one, agent i's realized utility is assumed to bewhere C s are observed characteristics of the supermarket, T i,s is the travel time for i going to s, and β +ν i is its impact on utility, where ν i has mean zero given supermarket characteristics and travel times.Katz assumes travel times and store characteristics are known to the shopper. Fors a supermarket with T i,s > T i,s that also marketed B i , he divides the difference s and notes that a combination of expected utility maximization and revealed preference impliesOur approach to this application relies on the conditional moment restriction E P [ε i |Z i ] = 0. As discussed by Ponomareva & Tamer (2011), this means that the identified set may be empty if the linear model is incorrect. For Z i = (T i , V i ) , Beresteanu & Molinari (2008) assume only that E[ε i Z i ] = 0, and their approach yields inference on the (necessarily nonempty) set of best linear predictors. Bontemps et al. (2012) study identification and inference, including specification tests, for a class of linear models with unconditional moment restrictions.If the observed data result from a Nash equilibrium then E m l (θ) j,f,i,t |V f,i,t ≤ 0 for l ∈ {1, 2, 3, 4} and all variables V f,i,t in the firm's information set at the time of the decision. We obtain two further conditional moment inequalities by considering heavier and lighter models than the firm actually marketed. To state them formally, define

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Inference for subvectors and other functions of partially identified parameters in moment inequality models

Cited by 86 publications

References 42 publications

Confidence Intervals for Projections of Partially Identified Parameters

Confidence Intervals for Projections of Partially Identified Parameters

Inference for VARs identified with sign restrictions

Inference for Linear Conditional Moment Inequalities

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