The Econometrics of Shape Restrictions

Chetverikov, Denis; Santos, Andrés; Shaikh, Azeem M.

doi:10.1146/annurev-economics-080217-053417

Cited by 51 publications

(35 citation statements)

References 161 publications

(178 reference statements)

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“…First, we need the moment estimates to be rationalizable by some

G \in scriptG

in order to subsequently use them as constraints when estimating bounds via our linear programming method. Second, imposing valid shape constraints in estimation typically improves accuracy and precision (see Chetverikov, Santos, and Shaikh (2018) for a review). Details of the SCGMM estimation procedure, which involves solving a quadratic programming (QP) problem, appear in Appendix D of the Supplemental Material.…”

Section: Moment and Posterior Estimatesmentioning

confidence: 99%

Reasonable Doubt: Experimental Detection of Job‐Level Employment Discrimination

Kline

Walters

2021

ECTA

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This paper develops methods for detecting discrimination by individual employers using correspondence experiments that send fictitious resumes to real job openings. We establish identification of higher moments of the distribution of job‐level callback rates as a function of the number of resumes sent to each job and propose shape‐constrained estimators of these moments. Applying our methods to three experimental data sets, we find striking job‐level heterogeneity in the extent to which callback probabilities differ by race or sex. Estimates of higher moments reveal that while most jobs barely discriminate, a few discriminate heavily. These moment estimates are then used to bound the share of jobs that discriminate and the posterior probability that each individual job is engaged in discrimination. In a recent experiment manipulating racially distinctive names, we find that at least 85% of jobs that contact both of two white applications and neither of two black applications are engaged in discrimination. To assess the potential value of our methods for regulators, we consider the accuracy of decision rules for investigating suspicious callback behavior in various experimental designs under a simple two‐type model that rationalizes the experimental data. Though we estimate that only 17% of employers discriminate on the basis of race, we find that an experiment sending 10 applications to each job would enable detection of 7–10% of discriminatory jobs while yielding Type I error rates below 0.2%. A minimax decision rule acknowledging partial identification of the distribution of callback rates yields only slightly fewer investigations than a Bayes decision rule based on the two‐type model. These findings suggest illegal labor market discrimination can be reliably monitored with relatively small modifications to existing correspondence designs.

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“…First, we need the moment estimates to be rationalizable by some

G \in scriptG

Section: Moment and Posterior Estimatesmentioning

confidence: 99%

Reasonable Doubt: Experimental Detection of Job‐Level Employment Discrimination

Kline

Walters

2021

ECTA

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“…Allowing for measurement error, we obtain bounds on the elements of P 0;1 , given in (5). 11 We consider the following misclassi…cation assumptions. Q:…”

Section: Assumptionsmentioning

confidence: 99%

Partial Identification of Economic Mobility: With an Application to the United States

Millimet

Roychowdhury

2019

Journal of Business & Economic Statistics

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Any opinions expressed in this paper are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but IZA takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The IZA Institute of Labor Economics is an independent economic research institute that conducts research in labor economics and offers evidence-based policy advice on labor market issues. Supported by the Deutsche Post Foundation, IZA runs the world's largest network of economists, whose research aims to provide answers to the global labor market challenges of our time. Our key objective is to build bridges between academic research, policymakers and society. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author.

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“…Our proofs that combine empirical process theory and the characterization of the (smoothed) NPMLE for the monotone hazard are also of independent interest. The shape restricted estimation and inference constitute a rich and evolving literature in econometrics and statistics, as reviewed by and Chetverikov et al (2018). The rest of the paper is organized as follows: Section 2 discusses the log-concavity restriction.…”

Section: Introductionmentioning

confidence: 99%

Accelerated failure time models with log-concave errors

Liu

2019

The Econometrics Journal

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We study accelerated failure time (AFT) models in which the survivor function of the additive error term is log-concave. The log-concavity assumption covers large families of commonly-used distributions and also represents the aging or wear-out phenomenon of the baseline duration. For right-censored failure time data, we construct semi-parametric maximum likelihood estimates of the finite dimensional parameter and establish the large sample properties. The shape restriction is incorporated via a nonparametric maximum likelihood estimator (NPMLE) of the hazard function. Our approach guarantees the uniqueness of a global solution for the estimating equations and delivers semiparametric efficient estimates. Simulation studies and empirical applications demonstrate the usefulness of our method.

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The Econometrics of Shape Restrictions

Cited by 51 publications

References 161 publications

Reasonable Doubt: Experimental Detection of Job‐Level Employment Discrimination

Reasonable Doubt: Experimental Detection of Job‐Level Employment Discrimination

Partial Identification of Economic Mobility: With an Application to the United States

Accelerated failure time models with log-concave errors

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