STATISTICAL DISCRIMINATION AND DURATION DEPENDENCE IN A SEMISTRUCTURAL MODEL

• Published date: 01 August 2024
• Author: Ismail Baydur,Jianhuan Xu
• Date: 01 August 2024
• DOI: http://doi.org/10.1111/iere.12696

INTERNATIONALECONOMIC REVIEW

Vol. 65, No. 3, August 2024 DOI: 10.1111/iere.12696

STATISTICAL DISCRIMINATION AND DURATION DEPENDENCE IN A

SEMISTRUCTURAL MODEL∗

By Ismail Baydur and Jianhuan Xu

Singapore Management University, Singapore

This article develops a job-search model with unobserved worker heterogeneity and learning about worker

types from unemployment duration. The model features negative duration dependence that stems from unob-

served heterogeneity, skill depreciation, and statistical discrimination. We estimate job-finding rates implied by

our model using microlevel data from the Current Population Survey. We find that removing interview costs

counterfactually, thereby eliminating statistical discrimination, substantially increases the job-finding rates of

the long-term unemployed. The performance of low-skill workers at the interview stage with discriminating

firms plays a key role in explaining our counterfactual result.

1. introduction

The fraction of the unemployed who find a job within a month falls dramatically by unem-

ployment duration. This feature of the U.S. labor market, which is referred to as negative du-

ration dependence, has been studied by a large body of literature. More recently, Kroft et al.

(2013) show in an experimental study with fictitious resumes that the callback rates to an in-

terview decline with unemployment duration. This phenomenon, called statistical discrimina-

tion, could be an important source in explaining the large difference between short- and long-

term job-finding rates.

In this article, our goal is to study statistical discrimination in a job-search model and quan-

tify its contribution to the negative duration dependence for the U.S. economy. To this end, we

develop a job-search model where workers randomly meet with vacancies at an exogenously

given rate. However, matching does not guarantee hiring. Firms matched with a worker de-

cides whether to go through an interview process, and hiring occurs only if the outcome of

the interview is successful. The outcome of the interview is a random event. At the interview

stage, the matched pair randomly draws match-specific productivity and the firm hires the

worker only if this random draw is above a minimum productivity level required for a match

to be viable.

There are two worker types, which we call high-skill and low-skill. A high-skill worker

draws match-specific productivity from a distribution that first-order stochastically dominates

that of a low-skill worker so that he is better at turning interviews into job offers. Worker

types are not constant over time. High-skill workers lose their abilities and become low-skill

at a constant rate as they remain in the unemployment pool; that is, they experience skill

∗Manuscript received July 2022; revised December 2023.

We are grateful to the editor, Iourii Manovskii, for comments and guidance, as well as to three anonymous refer-

ees. We also thank Nicolas Jacquet, Thomas Sargent, Sephorah Mangin, Costas Meghir, Gueorgui Kambourov,Dirk

Krueger, Jeremy Greenwood, Toshihiko Mukoyama, Wouter den Haan, and Russell Cooper for their comments and

suggestions. We also thank seminar and conference participants at City University of Hong Kong, GRIPS, Kyushu

University, National University of Singapore, Singapore Management University, Econometric Society conferences

in Seoul and Auckland, and Midwest Macro Meetings in Michigan State University. Qiugu He provided valuable re-

search assistance. This study is funded through a research grant (Fund No: C244/MSS18E001) from Singapore Man-

agement University. All errors are our own. Please address correspondence to: Ismail Baydur, Singapore Manage-

ment University, 90Stamford Road, Singapore, 178903. E-mail: ismailb@smu.edu.sg.

1357

© 2024 the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association.

1358 baydur and xu

depreciation. Similarly, low-skill workers become high-skill at a constant rate while employed;

that is, they experience on-the-job learning.

A key feature of our model is hiring firms do not observe a worker’s true type, but they

can infer the probability that the worker is high-skill from his most recent unemployment

duration. We call this probability the resume of the worker. Firms update these resume values

based on the differences between the job-finding rates of the high- and low-skill workers and

interview applicants only if the prospects are favorable relative to the cost of the interview.

There are two types of firms: discriminating and nondiscriminating. A discriminating firm

draws a random interview cost and selectively interviews the applicants, whereas a nondis-

criminating firm interviews every applicant at zero cost.1Because more low-skill workers are

present at longer durations, discriminating firms are less likely to interview the long-term

unemployed, which leads to statistical discrimination in our model.

To measure the importance of statistical discrimination, we consider the counterfactual job-

finding rates after removing the interview costs so that every firm indiscriminately interviews

every applicant. We calculate the percentage increase in the long-term job-finding rates rel-

ative to the baseline equilibrium with statistical discrimination and use this metric to assess

the importance of statistical discrimination. We show this metric is the product of two ratios:

(i) the share of discriminating firms relative to that of nondiscriminating firms, and (ii) the

interview success probability of a low-skill worker with a discriminating firm relative to that

with a nondiscriminating firm. Intuitively, discriminating firms very rarely interview the long-

term unemployed workers in the baseline equilibrium, because these workers are mostly low-

skilled. The first ratio determines the percentage increase in the probability of getting an in-

terview for a long-term unemployed worker after removing the interview costs. However, the

overall increase in the long-term job-finding rates also depends on how the low-skill workers

perform at these interviews with the discriminating firms, which is not possible in the baseline

equilibrium due to statistical discrimination. The second ratio captures this second effect. For

statistical discrimination to have a big impact on the long-term job-finding rates, our metric

requires both a large share of discriminating firms and a high success probability for the low-

skill workers with these firms.

Our model delivers a parametric hazard model for job-finding rates. We obtain a reduced-

form representation of these job-finding rates and estimate its parameters via maximum like-

lihood using individual-level data from the Current Population Survey (CPS). An advantage

of our reduced-form approach is that one of the reduced-form parameters corresponds to the

metric we defined in the previous paragraph to measure the importance of statistical discrimi-

nation. This feature allows us to estimate the impact of removing interview costs without hav-

ing to identify the underlying structural model parameters. We provide a formal discussion

about identification of this parameter. Our key insight is that the higher the job-finding rate

of a medium-term unemployed worker relative to that of a long-term unemployed worker, the

higher the value of this parameter.

Intuitively, both the medium- and long-term unemployed workers are predominantly low-

skill workers, and in either case, most of the hired workers are low-skill workers.2There-

fore, the difference between their job-finding rates is largely driven by the type of the hir-

ing firm. Nondiscriminating firms interview everyone, but a medium-term unemployed worker

has a greater chance of being interviewed by a discriminating firm, because this group has rel-

atively more high-skill workers. If a large difference exists between the medium- and long-

term job-finding rates, a sizable amount of discriminating firms must be present. This require-

ment alone is not sufficient, because the job-finding rates also depend on the outcome of these

interviews. Recalling that medium-term unemployed workers are mostly low-skill workers, a

1In the data, the job-finding rates approach a value that is significantly greater than zero. Wecapture this feature of

the data in our model with the nondiscriminating firms.

2As a point of reference, we consider six months as medium term. Based on our estimates, the share of high-

skill workers at this unemployment duration is only about 10%. The longest reported unemployment duration is

24 months (104 weeks) in our sample.