Inference Based on Conditional Moment Inequalities

Andrews, Donald W.K.; Shi, Xun

doi:10.2139/ssrn.1625890

Cited by 138 publications

(285 citation statements)

References 35 publications

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“…The model (4.11) appears almost the same as the conditional moment inequality model discussed extensively in, e.g., Andrews and Shi (2013) and Chernozhukov, Lee, and Rosen (2008). However there is one essential difference that we need now address.…”

Section: Aggregating Moment Inequalities To the Market Levelmentioning

confidence: 91%

“…This procedure makes it feasible in practice to perform inference in moment inequality models with many parameters and is critically needed for our demand estimation problem. The existing approach to inference in a moment inequality setting such as ours -for example, Andrews and Shi (2013) -requires exhaustive grid search over the parameter space to compute confidence sets. However, such computation is infeasible for demand studies because at least a moderate number of control variables are needed to ensure validity of the instrument for price, resulting in a moderate to large dimensional parameter space.…”

Section: Introductionmentioning

confidence: 99%

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Estimating demand for differentiated products with error in market shares

Gandhi¹,

Lu²,

Shi³

2013

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In this paper we introduce a new approach to estimating differentiated product demand system that allows for error in market shares as measures of choice probabilities. In particular, our approach allows for products with zero sales in the data, which is a frequent phenomenon that arises in product differentiated markets but lies outside the scope of existing demand estimation techniques. Although we find that error in market shares generally undermine the standard point identification of discrete choice models of demand, we exploit shape restrictions on demand implied by discrete choice to generate a system of moment inequalities that partially identify demand parameters. These moment inequalities are fully robust to the variability in market shares yet are also adaptive to the information revealed by market shares in a way that allows for informative inferences. In addition, we construct a profiling approach for parameter inference with moment inequalities, making it feasible to study models with a large number of parameters (as typically required in demand applications) by focusing attention on a profile of the parameters, such as the price coefficient. We use our approach to study consumer demand from scanner data using the Dominick's Finer Foods database, and find that even for the baseline logit model, demand elasticities nearly double when the full error in market shares is taken into account.

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Section: Aggregating Moment Inequalities To the Market Levelmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Estimating demand for differentiated products with error in market shares

Gandhi¹,

Lu²,

Shi³

2013

Self Cite

View full text Add to dashboard Cite

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“…However, we show that this computational hardship can be avoided, and the sharp identi…cation region can be characterized as the set of parameter values for which the maximum of an easy-to-compute superlinear (hence concave) function over the unit ball is equal to zero. We show that …nite sample inference can be carried out adopting the generalized moment selection procedure with in…nitely many conditional moment inequalities recently proposed by Andrews and Shi (2009). We exemplify our methodology by applying it to empirically relevant models, for which a feasible characterization of I was absent in the literature.…”

Section: Discussionmentioning

confidence: 94%

“…Remark 2.1 Using the method proposed by Andrews and Shi (2009), expression (2.4) can be transformed, using appropriate instruments, into a set of unconditional moment inequalities indexed by the instruments and by u 2 B; even when the conditioning variables have a continuous distribution. Equations (2.2)-(2.3) can be modi…ed accordingly, to yield straightforward criterion functions which are minimized by every parameter in the sharp identi…cation region.…”

Section: Representation Through Random Sets Theorymentioning

confidence: 99%

“…This sample analog is given by the set of minimizers of a sample criterion function. We establish that the methodology of Andrews and Shi (2009) can be applied in our context, to obtain con…dence sets that uniformly cover each element of the sharp identi…cation region with a prespeci…ed asymptotic probability. Related methods for statistical inference in partially identi…ed models include, among others, Chernozhukov, Hong, andTamer (2004, 2007), Pakes, Porter, Ho, and Ishii (2006), Molinari (2008), Rosen (2008), Chernozhukov, Lee, and Rosen (2009), Galichon and Henry (2009b), Kim (2009), Andrews andSoares (2010), Bugni (2010), Canay (2010), and Romano and Shaikh (2010).…”

Section: Introductionmentioning

confidence: 99%

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Sharp identification regions in models with convex moment predictions

Beresteanu¹,

Molchanov²,

Molinari³

2010

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We provide a tractable characterization of the sharp identi…cation region of the parameters in a broad class of incomplete econometric models. Models in this class have set valued predictions that yield a convex set of conditional or unconditional moments for the observable model variables. In short, we call these models with convex moment predictions. Examples include static, simultaneous move …nite games of complete and incomplete information in the presence of multiple equilibria; best linear predictors with interval outcome and covariate data; and random utility models of multinomial choice in the presence of interval regressors data. Given a candidate value for ; we establish that the convex set of moments yielded by the model predictions can be represented as the Aumann expectation of a properly de…ned random set. The sharp identi…cation region of ; denoted I ; can then be obtained as the set of minimizers of the distance from a properly speci…ed vector of moments of random variables to this Aumann expectation. Algorithms in convex programming can be exploited to e¢ ciently verify whether a candidate is in I : We use examples analyzed in the literature to illustrate the gains in identi…cation and computational tractability a¤orded by our method.

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Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance

Szydlowski

2019

J of Applied Econometrics

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In economic duration analysis, it is routinely assumed that the process which led to censoring of the observed duration is independent of unobserved characteristics. The objective of this paper is to examine the sensitivity of parameter estimates to this independence assumption in the context of an economic model of optimal unemployment insurance. We assume a parametric model for the duration of interest and leave the distribution of censoring unrestricted, allowing it to be correlated with both observed and unobserved characteristics. This leads to loss of point-identification. We provide a practical characterization of the identified set with moment inequalities and suggest methods for estimating this set. In particular, we propose a profiled procedure that allows us to build a confidence set for a subvector of the model parameters. We apply this approach to estimate the elasticity of exit rate from unemployment with respect to unemployment benefit and find that both positive and negative values of this elasticity are supported by the data. When combined with the welfare formula in Chetty (2008), these estimates do not permit us to put an upper bound on the size of the welfare * I would like to thank Elie Tamer, Ivan Canay, Alex Torgovitsky for their guidance and support. I am grateful to Joel Horowitz for useful suggestions and discussions at the early stage of this project. I also benefited from comments by Agnieszka Szydłowska, Ryan Marsh, Shruti Sinha, Florian Hoffman, seminar participants at CERGE-EI and conversations with Tiago Pires. I would like to thank Raj Chetty for sharing his dataset and codes. This research used the ALICE High Performance Computing Facility at the University of Leicester and the Social Sciences Computing Cluster (SSCC) at Northwestern University. 1 change due to an increase in the unemployment benefit. We conclude that given the available data alone, one cannot credibly judge if the unemployment benefits in the US are close to the optimal level.

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Inference Based on Conditional Moment Inequalities

Cited by 138 publications

References 35 publications

Estimating demand for differentiated products with error in market shares

Estimating demand for differentiated products with error in market shares

Sharp identification regions in models with convex moment predictions

Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance

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