Constraint Qualifications in Partial Identification

Kaido, Hiroaki; Molinari, Francesca; Stoye, Jörg

doi:10.1017/s0266466621000207

Cited by 11 publications

(6 citation statements)

References 27 publications

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“…It is worth highlighting that Assumption 4 places restrictions on the variance of Y n,0 but not on its mean µ n,0 . This contrasts with linear independence constraint qualification (LICQ) assumptions that have been considered in other work (e.g., Cho & Russell 2021, Gafarov 2019, which restrict the set of moments that can be binding in population and thus the value of µ n,0 (see Kaido et al (2021) for discussion). In the simplest case without nuisance parameters (X n,0 =0), for example, Assumption 4 holds if all of the elements of Y n,0 have positive variance and are not perfectly correlated, whereas a standard LICQ condition would impose that µ n,0 has a unique maximum element.…”

Section: Structure Of the Formmentioning

confidence: 97%

“…We now briefly discuss the connections and differences between Assumption 4 and linear independence constraint qualification (LICQ) conditions that have been imposed in the literature. We refer the reader to Kaido et al (2021) for detailed discussion of constraint qualifications in the moment inequality literature, and Appendix A.2 of Rambachan & Roth (2021) for additional results for our conditional test under LICQ.…”

Section: Starting From {Nmentioning

confidence: 99%

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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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Section: Structure Of the Formmentioning

confidence: 97%

Section: Starting From {Nmentioning

confidence: 99%

Inference for Linear Conditional Moment Inequalities

Andrews¹,

Roth²,

Pakes³

2019

View full text Add to dashboard Cite

show abstract

“…It is worth highlighting that Assumption 4 involves the variance of Y n,0 but not its mean µ n,0 . This contrasts with linear independence constraint qualification (LICQ) assumptions that have been considered in other work (e.g., Cho & Russell 2021, Gafarov 2019), which restrict the set of moments that can bind in population and thus the value of µ n,0 (see Kaido et al (2021) for discussion). In the simplest case without nuisance parameters (X n,0 = 0), for example, Assumption 4 holds if all of the elements of Y n,0 have positive variance and are not perfectly correlated, whereas a standard LICQ condition would impose that µ n,0 has a unique maximum element.…”

Section: Let ⌥mentioning

confidence: 99%

“…We now briefly discuss the connections and differences between Assumption 4 and linear independence constraint qualification (LICQ) conditions that have been imposed in the literature. We refer the reader to Kaido et al (2021) for detailed discussion of constraint qualifications in the moment inequality literature, and Section 3 of Rambachan & Roth (2022) for additional results for our conditional test under LICQ.…”

mentioning

confidence: 99%

Inference for Linear Conditional Moment Inequalities

Andrews

Pakes

2023

Review of Economic Studies

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We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in settings with nuisance parameters. We first introduce least favorable critical values which deliver non-conservative tests if all moments are binding. Next, we introduce a novel conditional inference approach which ensures a strong form of insensitivity to slack moments. Our recommended approach is a hybrid technique which combines desirable aspects of the least favorable and conditional methods. The hybrid approach performs well in simulations calibrated to Wollmann (2018), with favorable power and computational time comparisons relative to existing alternatives.

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“…(2) The assumption on λ ∈ Λ is a type of Mangasarian-Fromowitz constraint qualification. See Kaido et al (2022) for a discussion of constraint qualifications in partially identified models.…”

Section: Parameter On the Boundarymentioning

confidence: 99%

A Generalized Argmax Theorem with Applications

Cox¹

2022

Preprint

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The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to the argmax of a limiting stochastic process. This paper generalizes the argmax theorem to allow the maximization to take place over a sequence of subsets of the domain. If the sequence of subsets converges to a limiting subset, then the conclusion of the argmax theorem continues to hold. We demonstrate the usefulness of this generalization in three applications: estimating a structural break, estimating a parameter on the boundary of the parameter space, and estimating a weakly identified parameter. The generalized argmax theorem simplifies the proofs for existing results and can be used to prove new results in these literatures.

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Constraint Qualifications in Partial Identification

Cited by 11 publications

References 27 publications

Inference for Linear Conditional Moment Inequalities

Inference for Linear Conditional Moment Inequalities

Inference for Linear Conditional Moment Inequalities

A Generalized Argmax Theorem with Applications

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