Monte Carlo Confidence Sets for Identified Sets

Chen, Xiaohong; Christensen, Timothy; Tamer, Elie

doi:10.3982/ecta14525

Cited by 72 publications

(42 citation statements)

References 69 publications

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“…In this section, we aim to discuss how our method practically compares to more standard methods using data from the Santa Clara study. In our comparison we include Bayesian methods, a classical likelihood ratio-based test, and the Monte Carlo-based approach to partial identification proposed by Chen et al (2018). 8…”

Section: Santa Clara Study: Comparison To Other Methodsmentioning

confidence: 99%

“…The parameter of interest in our application could only be the disease prevalence, whereas the true/false positive rates of the antibody test may be considered "nuisance". In this paper, we directly project Θ 1−α (or Θ alt 1−α ) on a single dimension to perform marginal inference (see Section 4), but this is generally conservative, especially at the boundary of the parameter space (Stoye, 2009;Kaido et al, 2019;Chen et al, 2018). A sharper way to do marginal inference with our procedures is an interesting direction for future work.…”

Section: Reject All Valuesmentioning

confidence: 99%

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Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach

Toulis

2020

SSRN Journal

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We propose a partial identification method for estimating disease prevalence from serology studies. Our data are results from antibody tests in some population sample, where the test parameters, such as the true/false positive rates, are unknown. Our method scans the entire parameter space, and rejects parameter values using the joint data density as the test statistic.The proposed method is conservative for marginal inference, in general, but its key advantage over more standard approaches is that it is valid in finite samples even when the underlying model is not point identified. Moreover, our method requires only independence of serology test results, and does not rely on asymptotic arguments, normality assumptions, or other approximations.We use recent Covid-19 serology studies in the US, and show that the parameter confidence set is generally wide, and cannot support definite conclusions. Specifically, recent serology studies from California suggest a prevalence anywhere in the range 0%-2% (at the time of study), and are therefore inconclusive. However, this range could be narrowed down to 0.7%-1.5% if the actual false positive rate of the antibody test was indeed near its empirical estimate (∼0.5%).In another study from New York state, Covid-19 prevalence is confidently estimated in the range 13%-17% in mid-April of 2020, which also suggests significant geographic variation in Covid-19 exposure across the US. Combining all datasets yields a 5%-8% prevalence range. Our results overall suggest that serology testing on a massive scale can give crucial information for future policy design, even when such tests are imperfect and their parameters unknown.

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Section: Santa Clara Study: Comparison To Other Methodsmentioning

confidence: 99%

Section: Reject All Valuesmentioning

confidence: 99%

Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach

Toulis

2020

SSRN Journal

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“…None of these establish uniform validity of confidence sets. Chen, Christensen, and Tamer () established uniform validity of MCMC‐based confidence intervals for projections, but aimed at covering the projection of the entire identified region

Θ_{I} false(P false)

(defined later) and not just of the true θ . Gafarov, Meier, and Montiel‐Olea () used our insight in the context of set identified spatial VARs.…”

Section: Introductionmentioning

confidence: 99%

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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“…For more discussion of the comparison among these options, see Kaido et al (2019a) and Gafarov (2019). Other alternatives include the procedures discussed by Romano & Shaikh (2008) and Chen et al (2018).…”

Section: Methodsmentioning

confidence: 99%

“…Romano & Shaikh (2008) discuss subvector inference based on subsampling. Chen et al (2018) discuss confidence sets for the identified set for subvectors based on a quasi-posterior Monte Carlo approach.…”

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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Monte Carlo Confidence Sets for Identified Sets

Cited by 72 publications

References 69 publications

Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach

Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach

Confidence Intervals for Projections of Partially Identified Parameters

Inference for Linear Conditional Moment Inequalities

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