Asset Pricing without Garbage

• Published date: 01 February 2017
• DOI: http://doi.org/10.1111/jofi.12438
• Date: 01 February 2017

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 1 •FEBRUARY 2017

Asset Pricing without Garbage

TIM A. KROENCKE∗

ABSTRACT

This paper provides an explanation for why garbage implies a much lower relative

risk aversion in the consumption-based asset pricing model than National Income

and Product Accounts (NIPA) consumption expenditure: Unlike garbage, NIPA con-

sumption is filtered to mitigate measurement error. I apply a simple model of the

filtering process that allows one to undo the filtering inherent in NIPA consumption.

“Unfiltered NIPA consumption” well explains the equity premium and is priced in

the cross-section of stock returns. I discuss the likely properties of true consumption

(i.e., without measurement error and filtering) and quantify implications for habit

and long-run risk models.

IN RESPONSE TO THE FAILURE of the classic consumption-based capital asset

pricing model to explain the equity premium, the risk-free rate, and return

predictability, recent literature has largely focused on developing alternative

models of investor behavior.However, the deficiencies of the classic model might

be attributed, at least in part, to a failure to measure consumption correctly.

In a seminal contribution, Savov (2011) finds that using garbage to capture

consumption, the classic model matches the equity premium and risk-free rate

with a coefficient of relative risk aversion that is several times lower compared

to using any other consumption measure based on National Income and Product

Accounts (NIPA). A possible explanation for the relative success of garbage is

that NIPA consumption fails to measure consumption properly (Savov (2011,

p. 200)). Yet dozens of statisticians have tried to estimate NIPA consumption

∗Tim A. Kroencke is at University of Basel. This paper is a revised version of the first chapter

of my PhD thesis at the University of Mannheim. I am grateful for invaluable discussions and

advice to my dissertation committee, Erik Theissen and Stefan Ruenzi. I would like to give special

thanks to Kenneth Singleton (the Editor) and two anonymous referees for comments that sub-

stantially improved the paper. I have also benefited from suggestions by Yakov Amihud, Nicole

Branger, Michael Burda, John Cochrane, Patrick Gruening, Lena Jaroszek, Paolo Maio, Frieder

Mokinski, Stig Møller, Jonathan Parker,Marco Poltera, Felix Schindler, Andreas Schrimpf, Chris-

tian Walksh¨

ausl, Paul Whelan, participants at conferences of the European Finance Association

Lugano 2014, Financial Management Association Maastricht 2014, Swiss Finance Association

(SGF) Zurich 2014, the German Finance Association (DGF) Wuppertal 2013, and seminar partici-

pants at Aarhus University, Humboldt University Berlin, University of Mannheim, University of

Muenster, and the ZEW Mannheim Brownbag. I also thank Alexi Savov for sharing his data. I

have no relevant or material financial interests that relate to the research described in this paper.

An Internet Appendix and the unfiltered NIPA consumption series can be found on the Journal of

Finance website.

DOI: 10.1111/jofi.12438

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48 The Journal of Finance R

as precisely as possible. It is therefore highly unlikely that NIPA consumption

is simply a poor proxy for consumption and that the story ends here.

This paper offers an alternative explanation for the dismal performance of

NIPA consumption. Observable consumption is subject to measurement er-

ror, which is uncorrelated with stock market returns. From an asset pricing

perspective, observable consumption growth would be eligible to measure the

consumption risk of stock returns, that is, should produce unbiased estimates

of consumption covariances. However, NIPA statisticians do not attempt to pro-

vide a consumption series to measure stock market consumption risk. Instead,

they try to estimate the level of consumption as precisely as possible. As a

result, they optimally filter observable consumption to generate their series of

reported NIPA consumption. Concerning asset pricing, however, filtered con-

sumption leads to disastrous results when the consumption risk of stocks is

estimated. The simpler measure of garbage, in contrast, is not subject to fil-

tering; garbage covariances are accordingly not “distorted.” On top, filtering is

intensified by the well-known bias stemming from time-aggregation: While re-

ported consumption is an estimate of consumption flow during a specific period,

the consumption-based asset pricing model relates asset returns to consump-

tion at a specific point in time (Breeden, Gibbons, and Litzenberger (1989)).

I find that a simple model of the filter process involved in the estimation of

reported NIPA consumption is surprisingly effective at explaining the charac-

teristics of alternative consumption measures sampled at the annual frequency.

Importantly,the filter model allows the effects of the filtering that are inherent

in NIPA consumption to be stripped out using a simple backward recursion.

I refer to this backward recursion as the “unfilter method” and call the mea-

sure resulting from this process “unfiltered NIPA consumption.” I can also

substantially mitigate time-aggregation bias by adding a correction factor to

the unfilter recursion and applying a time-aggregation timing adjustment to

stock returns, similar to Cochrane (1996).

More specifically, I first find that unfiltered NIPA consumption is able to ex-

plain the equity premium together with constant relative risk aversion (CRRA)

preferences with a coefficient of relative risk aversion between 19 and 23 in the

postwar period (1960–2014), which is close to the coefficient of 16 for garbage.

A coefficient below 10 is well within two standard errors. A feature of unfil-

tered NIPA consumption is a sample covering a longer period. When including

the prewar observations in the sample (1928–2014), I find a point estimate

for the coefficient of relative risk aversion as low as 10 for unfiltered NIPA

consumption.

Second, I find that the proposed filter model of NIPA consumption provides a

unifying explanation for the success of three-year consumption (Parker and Jul-

liard (2005)) and fourth-quarter to fourth-quarter consumption (Jagannathan

and Wang (2007)). These alternative NIPA-based consumption measures have

been shown in previous research to be priced in the cross-section of stock re-

turns. In support of my hypothesis, this implies that there is valuable latent

information in NIPA consumption. A simulation experiment using the filter

model shows that fourth-quarter to fourth-quarter consumption is effective in

Asset Pricing without Garbage 49

removing time-aggregation bias, while the three-year consumption measure is

effective in removing filtering. In this sense, both can be viewed as simple ad

hoc unfilter rules.

Third, I find that unfiltered NIPAconsumption can explain a substantial frac-

tion of the average returns of decile portfolios sorted by size, book-to-market,

and investment growth. Pricing errors are low and R2s are above 60%. At the

same time, cross-sectional slope coefficients imply a coefficient of relative risk

aversion of around 30. Three-year and fourth-quarter consumption produce

similar low pricing errors, but only with a substantially larger coefficient of

relative risk aversion. However, these pricing results do not hold for profitabil-

ity portfolios. On the contrary, highly profitable stocks have low consumption

risk despite earning high average returns. Put differently, (unfiltered) con-

sumption risk fails to explain the profitability premium, just as the market

return factor fails to explain the value premium (Fama and French (1993)).

Fourth, I find that unfiltered NIPA consumption together with CRRA pref-

erences cannot account for stock return predictability. In view of this result,

I investigate the implications of unfiltered NIPA consumption for asset pric-

ing models that are able to generate time-varying risk premia, particularly

the external habit model developed by Campbell and Cochrane (1999)andthe

long-run risk model of Bansal and Yaron (2004).1Reported NIPA consumption

has a substantially lower one-year standard deviation than true consumption

and has a persistent component due to the filtering. In contrast, observed

consumption growth has a higher standard deviation than true consumption

and is mean-reverting due to measurement error. Hence, a researcher cali-

brating consumption growth to reported NIPA consumption, and as a result

not accounting for the evidence provided by observed consumption (unfiltered

NIPA consumption or garbage), may (i) underestimate the one-year consump-

tion standard deviation and the contemporaneous stock market covariance, or

(ii) overstate the predictability of future consumption growth and future stock

market covariances.

I show that the filter model is in line with the postwar data when true

consumption growth has no persistent component and its one-year standard

deviation is equal to its long-run standard deviation of 2.5%.2Regarding the

habit model, this implies that relative risk aversion is reduced and the fit of

the model to the data can be considerably improved. In the long-run risk model,

the filter model strengthens the role of short-run consumption risk at the ex-

pense of long-run consumption risk. At the same time, there remains the pos-

sibility of consumption volatility risk having a significant role. These results

1In principle, the proposed filter model of reported consumption is complementary to virtually

any consumption-based asset pricing model, for example, models that include reduced-form vari-

ants of time-varying price of consumption risk, income from labor, complementary goods, housing,

time-varying disasters, or small departures from rationality (Lettau and Ludvigson (2001), Santos

and Veronesi (2006), Yogo (2006), Piazzesi, Schneider, and Tuzel (2007), Wachter (2013), Adam,

Marcet, and Nicolini (2016)). Ludvigson (2013) provides an overview.

2I obtain a long-run standard deviation of 2.5% from calibrating the filter model to postwar

consumption data. Interestingly,Dew-Becker (2016) reports a benchmark estimate of 2.5% as well.