Hours risk and wage risk: repercussions over the life cycle*

• Published date: 01 October 2023
• Author: Robin Jessen,Johannes König
• Date: 01 October 2023
• DOI: http://doi.org/10.1111/sjoe.12532

Scand. J. of Economics 125(4), 956–996, 2023

DOI: 10.1111/sjoe.12532

Hours risk and wage risk: repercussions

over the life cycle*

Robin Jessen

RWI, DE-10115 Berlin, Germany

robin.jessen@rwi-essen.de

Johannes K¨

onig

DIW Berlin, DE-10117 Berlin, Germany

jkoenig@diw.de

Abstract

We decompose earnings risk into contributions from hours and wage shocks. To distinguish

between hours shocks, modeled as innovations to the marginal disutility of work, and labor

supply reactions to wage shocks, we formulate a life-cycle model of consumption and labor

supply. For estimation, we use data on married American men from the Panel Study of

Income Dynamics. Permanent wage shocks explain 31 percent of total risk, permanent hours

shocks 21 percent. Progressive taxation attenuates cross-sectional earnings risk, but its life-cycle

insurance impact is much smaller. At the mean, a one-standard-deviation hours shock raises

lifetime income by 11 percent, a wage shock by 13 percent.

Keywords: Labor supply; earnings risk; structural estimation; progressive taxation;

consumption insurance

JEL classif‌ication:D31; J22; J31

1. Introduction

Earnings risk is a central determinant of individuals’ welfare. It can be

decomposed into wage risk and risk of hours of work. A f‌irst glance at the

data in Figure 1suggests that hours and wages contribute similarly to the

variance of earnings growth in the United States.1While variances give us

a f‌irst indication, the aim of this paper is to explain earnings risk – that is,

unexpected changes in earnings. Hours and wage risk are driven by many

*We thank Richard Blundell, Flora Budianto, Roland D¨

ohrn, Steffen Elstner, Giulio Fella,

Michael Graber, Thorben Korfhage, Maria Metzing, Ian Preston, Itay Saporta-Eksten, Carsten

Schr¨

oder, Viktor Steiner, Alexandros Theloudis, Guglielmo Weber, and seminar participants at

the Freie Universit¨

at Berlin, EALE 2018, ESWM 2018, and IAAE 2019 for valuable comments

and discussions. Open Access funding enabled and organized by Projekt DEAL.

1Studies using data from other countries, such as the Netherlands (De Nardi et al., 2021),

Norway (Halvorsen et al., 2020), and Germany (Pessoa, 2021), buttress this f‌inding.

c

2023 The Authors. The Scandinavian Journal of Economics published by John Wiley & Sons Ltd on behalf of F¨

oreningen

f¨

or utgivande av the SJE.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution

and reproduction in any medium, provided the original work is properly cited.

R. Jessen and J. K¨

onig 957

Figure 1. Components of annual earnings growth

Notes: Log densities of f‌irst f‌irst differences in log earnings, hours, and wages using main estimation sample of

prime-age males in the PSID, years 1970–1997 (see Section 3). Note that, as discussed in Section 3, the share

of measurement error in hours is larger than the share of measurement error in wages. Thus, the f‌igure tends to

understate the relative importance of hours for the variance in earnings growth.

ultimate sources, such as unexpected changes in remuneration, health, and

involuntary unemployment. Quantifying the contributions of wage and hours

risk to earnings risk is important not only for our understanding of the

common dynamics of these variables, but also to guide the evaluation of

policy measures aimed at reducing earnings risk. For instance, if earnings risk

was driven almost entirely by hours shocks, focusing on policies that reduce

the impact of wage shocks would not be expedient.

In this paper, we formulate a structural model of life-cycle labor supply

that features earnings risk from both wage and hours shocks, and we assess the

strength of their contributions to total earnings risk and lifetime earnings. We

f‌ind that both types of shocks are quantitatively important. Further, we evaluate

the insurance offered by progressive taxation, f‌inding that it strongly attenuates

cross-sectional earnings risk; transitory shocks more so than permanent ones.2

Besides the important implications for economic policy, explicitly accounting

for hours shocks also has relevant implications for economic modeling. In our

model, for example, we f‌ind that the estimate of the Marshallian labor supply

elasticity is sensitive to the inclusion of hours shocks.

2Our measure of insurance is the extent to which a mechanism reduces risk. Alternatively, one

could quantify individuals’ willingness to pay for the reduction of specif‌ic risks, distinguishing

between permanent and transitory shocks.

c

2023 The Authors. The Scandinavian Journal of Economics published by John Wiley & Sons Ltd on behalf of F¨

oreningen

f¨

or utgivande av the SJE.

958 Hours risk and wage risk: repercussions over the life cycle

In our model, individuals face idiosyncratic shocks to their productivity of

market work, captured as wage shocks. For instance, a promotion is a positive

permanent wage shock and loss of human capital a negative one. Our concise

extension of standard life-cycle models is to introduce hours shocks, which we

model as innovations to the disutility of work, which ultimately affect hours

of work. These shocks are conceptualized in an analogous fashion to wage

shocks. As an illustration, consider the case of one’s elderly parent falling ill

or being in need of around-the-clock care. This increases the opportunity cost

of market work sharply. Depending on the nature of the illness, the shock is

permanent or fades out. In terms of observed choices, one would then notice

a shock to hours of work. A positive hours shock could be a change in the

task content in one’s job, leading to increased job satisfaction and thus a

decrease in the marginal disutility of work. At f‌irst glance and considering

these illustrations, it might appear that hours shocks capture a lot of very

heterogeneous idiosyncratic variation and that, in contrast, wage shocks are

narrowly def‌ined and capture only variation in human capital. However, wage

shocks also capture more than what one might suspect at f‌irst. To name a few

examples, the wage shock variation can also come from changes in bargaining

power, on both the supply and demand side, and it can come from labor

demand shocks to production. In Section 5, we show that hours shocks, much

like wage shocks, are a pervasive phenomenon that cannot be pinned down to

one shock source. Our main goal is the assessment of the relative importance

of both channels for total risk; thus, pinning down the ultimate sources of the

shocks is not our primary concern.

In many models, wage shocks are the sole drivers of earnings risk.

Conveniently, the wage shock process can be estimated using only the

moments of wage residuals. This does not hold for the hours shock process.

In our setting, hours residuals contain hours shocks in addition to labor supply

reactions to wage shocks. These reactions are determined by a transmission

parameter, which measures the impact of permanent income shocks on the

marginal utility of wealth. Thus, without identifying this parameter, separating

the two shock types is impossible. We suggest a new method to estimate the

transmission parameter, which does not rely on the use of consumption data,

which are frequently employed for this purpose. The transmission parameter

is linked to consumption insurance. The larger it is, the larger is the impact

of permanent wage and hours shocks on consumption, and the lower is the

degree of insurance against risk. Thus, the parameter is a suff‌icient statistic for

all channels of consumption insurance other than progressive taxation. This

includes spousal labor supply, self-insurance through precautionary savings,

and formal and informal insurance (e.g., disability insurance). We show that

the comovement of consumption and earnings implied by our estimate is in

line with estimates in Blundell et al. (2008). The identif‌ication of the parameter

c

2023 The Authors. The Scandinavian Journal of Economics published by John Wiley & Sons Ltd on behalf of F¨

oreningen

f¨

or utgivande av the SJE.