Good‐Specific Habit Formation and the Cross‐Section of Expected Returns

• Published date: 01 August 2016
• Author: JULES H. VAN BINSBERGEN
• Date: 01 August 2016
• DOI: http://doi.org/10.1111/jofi.12397

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 4 •AUGUST 2016

Good-Specific Habit Formation and the

Cross-Section of Expected Returns

JULES H. VAN BINSBERGEN∗

ABSTRACT

I study asset prices in a general equilibrium framework in which agents form habits

over individual varieties of goods rather than over an aggregate consumption bun-

dle. Goods are produced by monopolistically competitive firms whose elasticities of

demand depend on consumers’ habit formation. Firms that produce goods with a high

habit level relative to consumption have low demand elasticities, set high prices for

their product, have low expected returns on their stock, and have low asset pricing

betas and stock return volatilities. I find supportive evidence for these predictions in

the data.

ASUBSTANTIAL PART of the empirical asset pricing literature attempts to explain

the cross-section of stock prices and returns. Habit formation models have suc-

cessfully explained some properties of the time series of stock prices.1Using

them to explain the cross-section, however, has been more challenging.2In

this paper, I present a model with good-specific habit formation that is capa-

ble of generating expected return spreads while matching important features

of prices and quantities in the data, both in the time series and in the cross-

section. The intuition is as follows. Monopolistically competitive firms offer

individual varieties of goods. The demand elasticities of each monopolist are

∗van Binsbergen is with the Wharton School, University of Pennsylvania. This paper was previ-

ously circulated under the title “Deep Habits and the Cross-Section of Expected Returns.” I would

like to thank the Editor, Associate Editor,and an anonymous referee for many useful and detailed

comments. I further wish to thank Hengjie Ai, Ravi Bansal, Jonathan Berk, Michael Brandt,

Alon Brav, Craig Burnside, John Campbell, V.V. Chari, George Constantinides, Larry Christiano,

John Cochrane, Darrell Duffie, Jesus Fernandez-Villaverde, Simon Gervais, John Graham, Cam

Harvey, John Heaton, Dirk Jenter, Ralph Koijen, Hanno Lustig, Rich Matthews, Juan Rubio

Ramirez, David Robinson, Tano Santos, Stephanie Schmitt-Grohe, Ken Singleton, Martin Uribe,

Stijn Van Nieuwerburg, Vish Viswanathan, seminar participants at Barclays Global Investors,

Berkeley Haas, Carnegie Mellon, Chicago GSB, Columbia, Duke, the Federal Reserve Board,

Harvard, MIT Sloan, Kellogg, NYU Stern, Princeton, Stanford GSB, UCLA, USC, Wharton, Yale

School of Management, the 5th Banco de Portugal Conference on Monetary Economics, the EFA

2008 meetings, the AFA 2009 meetings, and in particular Anamar´

ıa Pieschac´

on for helpful discus-

sions and comments. All remaining errors are my own. I have no relevant or muterial conflicts of

interest that relate to the research described in this paper.

1See Abel (1990), Constantinides (1990), Heaton (1995), Jermann (1998), Campbell and

Cochrane (1999), and Campbell and Cochrane (2000).

2See, for example, Lettau and Wachter (2007) and Santos and Veronesi (2006).

DOI: 10.1111/jofi.12397

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1700 The Journal of Finance R

time-varying and proportional to the consumption surplus ratio for the monop-

olist’s good. Firms that produce goods with a low consumption surplus ratio,

that is, a consumption level close to the habit level, have low demand elastic-

ities and set high prices for their products. As these low elasticities translate

into low sensitivities to shocks, they result in lower asset pricing betas, lower

return volatilities, and lower expected stock returns.

The main mechanism generating heterogeneity in expected stock returns in

the model is the representative consumer’s reluctance to scale back on goods

for which the consumption level is close to the habit level. Such reluctance re-

duces the demand elasticities for those goods, shielding the firm from negative

shocks. Put differently, the degree to which a good is necessary for consumers

varies over time and depends on habit formation. This intuition is independent

of whether (i) cross-sectional heterogeneity in consumption surplus ratios is

driven by idiosyncratic taste shocks or idiosyncratic productivity shocks, (ii)

aggregate shocks are permanent or transitory, and (iii) the distribution of the

aggregate shocks includes rare events and/or time-varying volatility.

I focus on a parsimonious version of the model in which the only firm decision

is to set prices, and thereby choose quantities to be produced. This provides the

firm with a type of operating flexibility that is different from what is usually

studied in the production-based asset pricing literature.3That literature gen-

erally focuses on the investment problem of the firm and does not have firms

operate at less than full capacity.4

The model yields several predictions that I explore in the data. First, it

predicts that product prices can be used to generate expected return spreads in

the data. Decreasing product prices are a symptom of increasing competitive

pressure and higher demand elasticities. This makes firms more sensitive to

aggregate shocks, leading investors to demand higher expected stock returns.

Using data from the producer price index program, in each period, I sort firms

into deciles based on their cumulative product price changes to date since the

industry entered the PPI database. I show that firms that have decreased their

prices earn higher average stock returns compared to firms that increase their

prices. The return spread appears to be best explained by the Capital Asset

Pricing Model (CAPM). However, the return spread becomes more puzzling

when commonly used multifactor models are the benchmark. The alpha relative

to the Fama French four-factor model equals 6% to 8.5%. When I use the

product-price-sorted return factor as the asset pricing model, I find that this

factor prices part of the aggregate market (and explains one third of the equity

risk premium), fully prices the size premium, and correlates negatively with

the value-minus-growth (HML) factor.Therefore, the return premium I uncover

seems to be negatively related to the value premium puzzle.

Second, the model predicts that the return volatility of a portfolio of firms

that have decreased their prices is higher than that of a portfolio of firms that

3For other work on operating flexibility, see Garlappi and Song (2013).

4A version of the model that includes production input decisions was included in an earlier

version of this paper.

Good-Specific Habits and the Cross-Section of Returns 1701

have increased their prices. When sorting firms into deciles in the model (data),

I find that the volatility is monotonically decreasing across deciles, and that the

tenth decile has a volatility that is a third (quarter) lower than the volatility

of the first decile. Finally, the model predicts that conditional factor loadings

are a function of product prices, where higher product prices lead to lower

factor loadings. I show in a panel regression that this negative relationship

does indeed hold, both for the beta on the market portfolio (CAPM), and for the

beta on the size factor.5

To my knowledge, this is the first paper to explore the implications of good-

specific habits and producer prices on the cross-section of expected stock re-

turns. The idea that households form their habits over individual varieties of

goods goes (at least) as far back as Pollak (1970) and Pollak (1976). It has re-

cently been explored in the macroeconomic literature by Ravn, Schmitt-Grohe,

and Uribe (2006), who propose to call this type of habit formation “deep habits.”

They show that expansions in output driven by preference shocks, government-

spending shocks, or productivity shocks are accompanied by declines in

markups. This implication of the model is in line with the extant empirical lit-

erature, which finds markups to be counter-cyclical (Rotemberg and Woodford

(1999)). The preferences I consider in this paper are a generalization of Ravn,

Schmitt-Grohe, and Uribe (2006), whose preferences have the undesirable prop-

erty that, without additional assumptions, the optimal price level for the mo-

nopolists is infinity, making the global price optimization problem ill-defined.

The generalization that I propose resolves this infinite price-setting problem.

Product-specific habit formation is also studied in the marketing literature;

see, for example, Guadagni and Little (1983). This literature uses the term

“loyalty variable.” This variable measures how “hooked” consumers are on a

given firm’s product, and it is measured as a weighted average of past sales. It

therefore resembles the notion of habits in the economics and finance literature.

That literature also discusses the importance of brand and product loyalty for

firm valuation. The results in this paper suggest that habit formation may not

only increase firm value due to higher future profitability, but also due to lower

discount rates.

One obvious question that comes to mind is how coarse should the classi-

fication of varieties be. I have in mind an environment in which consumers

form habits over narrow categories of goods (Ravn, Schmitt-Grohe, and Uribe

(2006)). The advantage of defining habits over categories of goods, as opposed to

over specific goods within categories, is that in the data household expenditures

on categories of goods generally go up as income increases, that is, categories of

goods behave as normal goods. Individual goods within categories, in contrast,

may be inferior goods.

A recent important literature argues that, when the same data are repeatedly

used to sort stocks, data mining issues should be taken seriously and multiple

testing corrections need to be applied. In particular,Harvey, Liu, and Zhu (2013)

5Motivated by Berk (1995), I interpret the size factor as a noisy proxy for the difference between

the true (in this case habit-based) stochastic discount factor and the market portfolio.