Income Insurance and the Equilibrium Term Structure of Equity

• Author: ROBERTO MARFÈ
• Published date: 01 October 2017
• DOI: http://doi.org/10.1111/jofi.12508
• Date: 01 October 2017

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

Income Insurance and the Equilibrium Term

Structure of Equity

ROBERTO MARF `

E∗

ABSTRACT

Output, wages, and dividends feature term structures of variance ratios that are

respectively flat, increasing, and decreasing. Income insurance from shareholders

to workers explains these term structures. Risk-sharing smooths wages but only

concerns transitory risk and hence enhances short-run dividend risk. As a result,

actual labor-share variation largely forecasts the risk, premium, and slope of dividend

strips. A simple general equilibrium model in which labor rigidity affects dividend

dynamics and the price of short-run risk reconciles standard asset pricing facts with

the term structures of the equity premium, volatility, and macroeconomic variables,

which are at odds in leading models.

LEADING ASSET PRICING MODELS describe many characteristics of financial mar-

kets but fail to explain the timing of equity risk. These models have different

∗Roberto Marf`

e is at Collegio Carlo Alberto. I am grateful to Kenneth Singleton (the Editor), an

Associate Editor, and two referees for their comments and suggestions. I would like to thank my

supervisor Michael Rockinger and the members of my Ph.D. committee (Swiss Finance Institute),

Philippe Bacchetta, Pierre Collin-Dufresne, Bernard Dumas, and Lukas Schmid, for stimulat-

ing conversations and many insightful comments and advice. I would also like to acknowledge

comments from Hengjie Ai, Daniel Andrei, Marianne Andries (Stockholm discussant), Ainhoa

Aparicio-Fenoll, Ravi Bansal, Alessandro Barattieri, Cristian Bartolucci, Luca Benzoni, Jonathan

Berk, Harjoat Bhamra, Vincent Bogousslavsky,Maxime Bonelli, Andrea Buraschi, Gabriele Cam-

era, Gian Luca Clementi (EFA discussant), Stefano Colonnello, Giuliano Curatola, Marco Della

Seta, J´

erˆ

ome Detemple (Gerzensee and Paris discussant), Theodoros Diasakos, Jack Favilukis,

Jordi Gal´

ı, Christian Gollier, Edoardo Grillo, Campbell Harvey, Michael Hasler, Marit Hinnosaar,

Toomas Hinnosaar, Christian Julliard, Leonid Kogan, Kai Li, Jeremy Lise, Elisa Luciano, Sydney

Ludvigson, Loriano Mancini, Charles Manski, Guido Menzio, Antonio Merlo, Ignacio Monz´

on, Gio-

vanna Nicodano, Miguel Palacios (Rome discussant), Francisco Palomino, Julien Penasse, Ilaria Pi-

atti, Andrea Prat, Dan Quint, Jean Charles Rochet, Birgit Rudloff, YuliySannikov, Jantje S¨

onksen,

Raman Uppal, and Ernesto Villanueva,as well as from participants at the 2nd BI-SHoF Conference

in Asset Pricing and Financial Econometrics, the CSEF-EIEF-SITE Finance & Labor Conference

2015, the 32nd International Conference of the French Finance Association 2015, the 18th Annual

Conference of the Swiss Society for Financial Market Research 2015 (SGF), the 41st European

Finance Association Annual Meeting 2014 (EFA), the 11th International Paris Finance Meeting

2013 (AFFI/EUROFIDAI), the 12th Swiss Doctoral Workshop in Finance 2013, and seminars at

the Collegio Carlo Alberto, Essec Business School, and Laval University. All errors remain only

my responsibility. Part of this research was written when the author was a Ph.D. student at the

Swiss Finance Institute and at University of Lausanne, and a visiting scholar at Duke University.

Financial support by the NCCR FINRISK of the Swiss National Science Foundation and by the

Associazione per la Facolt`

a di Economia dell’ Universit`

a di Torino is gratefully acknowledged. The

usual disclaimer applies. The author has no conflict of interests and has nothing to disclose.

DOI: 10.1111/jofi.12508

2073

2074 The Journal of Finance R

rationales (e.g., habit formation, time-varying expected growth, disasters, and

prospect theory), but share an important feature: priced risk comes from vari-

ation in long-run discounted cash flows.1In contrast, van Binsbergen, Brandt,

and Koijen (2012), van Binsbergen et al. (2013), and van Binsbergen and Koijen

(2017) document that the term structures of equity volatility and premia are

downward-sloping, that is, markets compensate short-run risk. Moreover,stan-

dard models are usually based on assumptions concerning dividend dynamics

that imply an upward-sloping term structure of dividend risk (i.e., volatilities

or variance ratios (VRs) of dividends’ growth rates, which increase with the

horizon). Instead, and consistent with Belo, Collin-Dufresne, and Goldstein

(2015), this paper documents that dividend risk is strongly downward-sloping,

which implies that many models overestimate long-horizon dividend risk by an

order of magnitude.

Why is dividend risk downward-sloping? Under which conditions does

downward-sloping dividend risk transmit to equity risk and premia? And what

macroeconomic channel explains short-term equity returns? This paper empiri-

cally and theoretically addresses these questions by providing a macroeconomic

foundation of the timing of risk and by reconciling, in equilibrium, standard

asset pricing facts with new evidence about term structures. This is important

because the term structures of both fundamentals and equity provide informa-

tion about how prices are determined in equilibrium. Hence, a term structure

perspective offers additional testable implications for asset pricing frameworks

and can help us understand the macroeconomic determinants of asset prices.

In this paper,I argue that labor rigidity is at the heart of the timing of macroe-

conomic risk. Danthine and Donaldson (1992,2002), among others, show that

a mechanism of income insurance from shareholders to workers, which takes

place within the firm, leads to volatile and procyclical dividends. This mecha-

nism explains why equity commands high compensation.2Beyond such a cycli-

cality effect of income insurance, however,I show that a term structure effect also

takes place. Since output, wages, and dividends are cointegrated (Lettau and

Ludvigson (2005)), income insurance implies that the transitory component of

aggregate risk is shared asymmetrically between workers and shareholders,

whereas the permanent component is faced by both. In particular, wages are

partially insured with respect to transitory risk, whereas dividends load more

on transitory risk as a result of operating leverage. Thus, wage (dividend)

risks shift toward the long (short) horizon, and workers (shareholders) bear

more long-run (short-run) risk. I embed this mechanism of income insurance

in an otherwise standard closed-form general equilibrium model and show that,

1Examples are the seminal works of Campbell and Cochrane (1999), Barberis, Huang, and

Santos (2001), Bansal and Yaron (2004), and Gabaix (2012), among others.

2The idea that the firm’s verypurpose is to function as an insurance provider has a long tradition

since Knight (1921), Baily (1974), Azariadis (1978), Boldrin and Horvath (1995), and Gomme and

Greenwood (1995). These works suggest that worker remuneration is partially fixed in advance

and hence shareholders bear most of the aggregate risk but, in exchange for income insurance,

gain flexibility in labor supply. In recent work, Guiso, Pistaferri, and Schivardi (2005), Shimer

(2005), and R´

ıos-Rull and Santaeul`

alia-Llopis (2010) provide empirical support for this idea.

Income Insurance and the Equilibrium Term Structure of Equity 2075

under standard preferences, the term structure effect of income insurance is

inherited by financial markets, leading to downward-sloping term structures

of equity risk and premia. As a result, actual labor-share variation largely

predicts short-term equity risk, premium, and slope.

Empirical analysis supports the main model mechanism. First, I document

that the timing of risk is heterogeneous across macroeconomic variables. The

term structures of risk of output, wage, and dividend risk are, respectively,flat,

increasing, and decreasing. In line with the model, these term structures—and

the cointegrated relationships among the levels of these variables—support

the idea that while workers and shareholders are both subject to permanent

shocks, they share transitory shocks asymmetrically as a result of income insur-

ance. Similarly, Gamber (1988) and Menzio (2005) show that implicit contracts

and labor market search frictions lead to wage rigidity over transitory risk

only, Guiso, Pistaferri, and Schivardi (2005) and Ellul, Pagano, and Schivardi

(2014) provide evidence that insurance does not concern permanent shocks,

and R´

ıos-Rull and Santaeul`

alia-Llopis (2010) document that the wage-share is

stationary and countercyclical.

Second, I find further support for the term structure effect of income insur-

ance by investigating the model predictions that the VRs of dividends should

be decreasing with the labor-share and the gap between the VRs of wages and

dividends should be increasing with the labor-share. The model predicts that,

after a negative transitory shock, wages are partially insured, whereas divi-

dends are more exposed. This implies that wages are high relative to dividends

(the cyclicality effect) and that wages load less than dividends on transitory risk

(the term structure effect). Therefore, the distance between the upward-sloping

VRs of wages and the downward-sloping VRs of dividends should increase when

the labor-share is high. The opposite holds after a positive transitory shock. I

provide robust empirical evidence that such a relation obtains in the data.

Third, I document a strong connection between labor-share variation and

short-term equity returns. The correlations between the labor-share and one-

year-ahead dividend strip volatility (risk), excess return over the risk-free rate

(premium), and excess return over the market return (slope) are 86%, 57%, and

52%, respectively.

Fourth, I show that the remainder of output minus wages features a term

structure of risk that is markedly downward-sloping and essentially recov-

ers the negative slope of dividend risk. This implies that the bulk of the gap

between the approximatively flat VRs of output and the decreasing VRs of div-

idends should be imputed to labor. Consistent with this idea, I document that

the transitory component of dividends that should not be imputed to income

insurance does not help explain the negative slope of dividend risk or dividend

strip returns. Finally, I find that the term structure effect of income insurance

implies that the labor-share positively forecasts dividend and consumption

growth, which I show to be a robust feature of the data.

The model consists of a few simple ingredients and is similar to Greenwald,

Lettau, and Ludvigson (2014). Investment is not directly modeled and total re-

sources are shared by workers and shareholders. The former do not invest but