A Labor Capital Asset Pricing Model

• Published date: 01 October 2017
• Date: 01 October 2017
• Author: MIKHAIL SIMUTIN,LARS‐ALEXANDER KUEHN,JESSIE JIAXU WANG
• DOI: http://doi.org/10.1111/jofi.12504

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 5 •OCTOBER 2017

A Labor Capital Asset Pricing Model

LARS-ALEXANDER KUEHN, MIKHAIL SIMUTIN, and JESSIE JIAXU WANG∗

ABSTRACT

We show that labor search frictions are an important determinant of the cross-section

of equity returns. Empirically, we find that firms with low loadings on labor market

tightness outperform firms with high loadings by 6% annually. We propose a partial

equilibrium labor market model in which heterogeneous firms make dynamic employ-

ment decisions under labor search frictions. In the model, loadings on labor market

tightness proxy for priced time-variation in the efficiency of the aggregate matching

technology. Firms with low loadingsare more exposed to adverse matching efficiency

shocks and require higher expected stock returns.

DYNAMICS IN THE LABOR MARKET are an integral component of business cycles.

More than 10% of U.S. workers separate from their employers each quarter.

Some move directly to a new job with a different employer, some become un-

employed, and some exit the labor force. These large flows are costly for firms,

because they need to spend resources to search for and train new employees.1

Building on the seminal contributions of Diamond (1982), Mortensen (1982),

and Pissarides (1985), we show that labor search frictions are an important

∗Lars-Alexander Kuehn is at the Tepper School of Business, Carnegie Mellon University;

Mikhail Simutin is at the Rotman School of Management, University of Toronto; Jessie Jiaxu

Wang is at the W. P.Carey School of Business, Arizona State University. We thank the Editor Ken

Singleton, two anonymous referees, Frederico Belo, Ilan Cooper, Andres Donangelo, Vito Gala,

Brent Glover, Bart Hobijn, Burton Hollifield, Finn Kydland, Christian Lundblad, Stefan Nagel,

Stavros Panageas, Dimitris Papanikolaou, Nicolas Petrosky-Nadeau, Chris Telmer, Lu Zhang, con-

ference participants of the 2012 Western Economic Association Annual Conference, 2012 Midwest

Macroeconomics Meeting, 2013 Midwest Finance Association Meeting, 2013 ASU Sonoran Winter

Finance Conference, 2013 SFS Finance Cavalcade, 2013 CAPR Workshop on Production Based

Asset Pricing at BI Norway, 2014 American Finance Association Meeting, 2016 CSEF-EIEF-SITE

Conference on Finance and Labor,and seminar participants at Carnegie Mellon University, Goethe

Universit¨

at Frankfurt, ESMT,Humboldt Universit ¨

at Berlin, University of Virginia (Darden), Uni-

versity of Michigan, Tsinghua University, University of Washington, Georgetown University, Vi-

enna University of Economics and Business, University of Oklahoma, and University of Texas at

Dallas for helpful comments. Mikhail Simutin gratefully acknowledges support from the Social

Sciences and Humanities Research Council (Grant 430-2013-0588). The authors have no conflicts

of interest, as identified in the Journal of Finance’s disclosure policy.

1According to the U.S. Department of Labor,the cost of replacing a worker amounts to one-third

of a new hire’s annual salary. Direct costs include advertising, sign-on bonuses, headhunter fees,

and overtime. Indirect costs include recruitment, selection, training, and decreased productivity

while current employees pick up the slack. Similar evidence is presented in Blatter, Muehlemann,

and Schenker (2012). Davis, Faberman, and Haltiwanger (2006) provide a review of aggregate

labor market statistics.

DOI: 10.1111/jofi.12504

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2132 The Journal of Finance R

determinant of the cross-section of equity returns. In search models, firms

post vacancies to attract workers, and unemployed workers look for jobs. The

likelihood of matching a worker with a vacant job is determined endogenously

and depends on the congestion of the labor market, which is measured as

the ratio of vacant positions to unemployed workers. This ratio, termed labor

market tightness, is the key variable of our analysis. Intuitively, a high ratio

implies that filling a vacancy is difficult because firms’ hiring activity is strong

and the pool of unemployed workers is shallow.

We begin by studying the empirical relation between labor market conditions

and the cross-section of equity returns. We measure aggregate labor market

tightness as the ratio of the monthly vacancy index published by the Confer-

ence Board to the unemployed population (see, for example, Shimer (2005)).

To measure the sensitivity of firm value to labor market conditions, we esti-

mate loadings of equity returns on the log changes in labor market tightness

controlling for the market return. We use rolling firm-level regressions based

on three years of monthly data to allow for time-variation in the loadings. Us-

ing the panel of U.S. stock returns from 1951 to 2014, we show that loadings

on the changes in labor market tightness robustly and negatively predict future

stock returns in the cross-section. Sorting stocks into deciles on the estimated

loadings, we find an average spread in future returns of firms in the low- and

high-loading portfolios of 6% per year. We emphasize that this return differ-

ential is not due to mispricing. While it cannot be attributed to differences

in loadings on common risk factors, such as those of the CAPM or the Fama-

French (1993) three-factor model, it arises rationally in our model due to risk

associated with labor market frictions as we describe in detail below.

To ensure that the relation between labor search frictions and future stock

returns is not driven by firm characteristics known to relate to future returns,

we run Fama-MacBeth (1973) regressions of stock returns on lagged estimated

loadings and other firm-level attributes. We include conventionally used con-

trol variables such as a firm’s market capitalization and book-to-market ratio

as well as recently documented determinants of the cross-section of stock re-

turns that may potentially correlate with labor market tightness loadings, such

as asset growth (Cooper, Gulen, and Schill (2008)) and hiring rates (Belo, Lin,

and Bazdresch (2014)). The Fama-MacBeth (1973) analysis confirms the ro-

bustness of results obtained in portfolio sorts. In particular, the coefficients on

labor market tightness loadings are negative and statistically significant in

all regression specifications. Moreover, the magnitude of the coefficients sug-

gests that the relation is economically important: for a one-standard-deviation

increase in loadings, future annual returns decline by approximately 1.5%.

Our main results hold not only when controlling for firm-level characteris-

tics as in Fama-MacBeth (1973) regressions but also after accounting for macro

variables. For example, labor market tightness and industrial production are

correlated and highly procyclical. However, we show that loadings on labor

market tightness contain information about future returns, while loadings on

industrial production do not. We also find that, unlike many cross-sectional

predictors of equity returns that are priced mainly within industries, labor

A Labor Capital Asset Pricing Model 2133

market tightness loadings contain information about future returns when con-

sidered both within and across industries. Numerous robustness tests confirm

our results. For example, excluding micro stocks has little effect on the return

spread across labor market tightness portfolios.

To interpret the empirical findings, we propose a labor-market-augmented

capital asset pricing model. Building on the search and matching framework

pioneered by Diamond-Mortensen-Pissarides, we develop a partial equilibrium

labor search model and study its implications for firm employment policies and

stock returns. For tractability, we do not model the supply of labor as an opti-

mal household decision; instead we assume an exogenous pricing kernel. Our

model features a cross-section of firms with heterogeneity in their idiosyn-

cratic profitability shocks and employment levels. Given the pricing kernel,

firms maximize their value by posting vacancies to recruit workers or by firing

workers to downsize. Both firm policies are costly at proportional rates.

In the model, the fraction of successfully filled vacancies depends on labor

market conditions as measured by labor market tightness (the ratio of vacant

positions to unemployed workers). As more firms post vacancies, the likelihood

that vacant positions are filled declines, thereby increasing the costs to hire new

workers. Since labor market tightness is a function of all firms’ vacancy policies,

it has to be consistent with individual firm’s policies and is thus determined as

an equilibrium outcome. In equilibrium, the matching of unemployed workers

and firms is imperfect, which results in both equilibrium unemployment and

rents. These rents are shared between each firm and its workforce according

to a Nash bargaining wage rate.

Our model is driven by two aggregate shocks, both of which are priced: a pro-

ductivity shock and a shock to the efficiency of the matching technology, which

was first studied by Andolfatto (1996). The literature has shown that varia-

tion in matching efficiency can arise for many reasons, and we are agnostic

about the exact source. For example, Pissarides (2011) emphasizes that match-

ing efficiency captures the mismatch between the skill requirements of jobs

and the skill mix of the unemployed, the differences in geographical location

between jobs and unemployed, and the institutional structure of an economy

with regard to the transmission of information about jobs.

Aggregate productivity and matching efficiency are not directly observable

in the data. To quantitatively compare the model with the data, we map the

aggregate productivity and matching efficiency shocks onto the market return

and labor market tightness, which are observable. As a result, we show that

expected excess returns obey a two-factor structure in the market return and

labor market tightness. We call the resulting model the Labor Capital Asset

Pricing Model. Importantly, a one-factor CAPM does not span all risks and

thus implies mispricing, in line with the data.

Our model replicates the negative relation between loadings on labor market

tightness and expected returns. Intuitively, firm policies are driven by oppos-

ing cash flow and discount rate effects. On the one hand, positive shocks to

matching efficiency decrease marginal hiring costs. This cash flow channel

implies an increase in optimal vacancy postings. On the other hand, positive