The Consumption Euler Equation or the Keynesian Consumption Function?*

Date01 February 2021
AuthorPål Boug,Anders Rygh Swensen,Eilev S. Jansen,Ådne Cappelen
DOIhttp://doi.org/10.1111/obes.12394
Published date01 February 2021
252
©2020 TheAuthors. OxfordBulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
Thisis an open access article under the ter ms of the CreativeCommons Attribution License, which permits use, distribution and reproduction in any medium, provided
the original work is properlycited.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 83, 1 (2021) 0305–9049
doi: 10.1111/obes.12394
The Consumption Euler Equation or the Keynesian
Consumption Function?*
P˚
al Boug,Ådne Cappelen,Eilev S. Jansen,† and Anders Rygh
Swensen
Research Department, Statistics Norway, PB 2633, 0131 Oslo, Norway (e-mails:
pal.boug@ssb.no, adne.cappelen@ssb.no and eilev.jansen@ssb.no)
Department of Mathematics, University of Oslo, PB 1072 Blindern, 0316 Oslo, Norway
(e-mail: swensen@math.uio.no)
Abstract
Wefor mulate a general cointegrated vectorautoregressive (CVAR) model that nests both a
class of consumption Euler equations and various Keynesian-type consumption functions.
Using likelihood-based methods and Norwegian data, we f‌ind support for cointegration
between consumption, income and wealth once a structural break around the time of the
f‌inancial crisis is allowed for. The fact that consumption cointegrates with both income and
wealth and not only with income points to the empirical irrelevance of an Euler equation.
Moreover, wef‌ind that consumption equilibrium cor rects to changes in income and wealth,
but not that income equilibrium corrects to changes in consumption, which would follow
from an Euler equation. We also f‌ind that most of the parameters stemming from the
class of Euler equations are not corroborated by the data when conditional expectations
of future consumption and income in CVAR models are considered. Only habit formation
seems important in explaining Norwegian consumer behaviour. Our estimated conditional
Keynesian-type consumption function implies a f‌irst year marginal propensity to consume
(MPC) out of income of close to 40%.
I. Introduction
Economists have long been concerned with how households react to changes in f‌iscal
policy. The f‌inancial crisis in 2008 led to renewed interest in how household asset com-
position, liquidity and credit market conditions may affect consumption; see for instance
Muellbauer (2016) and Kaplan et al. (2018). The effects of f‌iscal policy depend on the
marginal propensity to consume (MPC) out of shocks to income. A new consensus seems
JEL Classif‌ication numbers: C51, C52, E21
*We are grateful to seminar and conference participants at Statistics Norway, Nuff‌ieldCollege at Oxford University
and the 2018 IAAEAnnual Conference in Montr ´eal (Canada), Jennifer Castle, JurgenDoor nik, Sophocles Mavroeidis,
John Muellbauer, Bent Nielsen and Takamitsu Kurita, in particular, for helpful discussions, and to Thomas von
Brasch, H˚avard Hungnes, Ragnar Nymoen and TerjeSkjer pen for comments and suggestions on earlier drafts. Last,
but not least, we thank the editor and two anonymousreferees for useful advice and constructive criticism. The usual
disclaimer applies.
Euler equation or Keynesian consumption? 253
to be emerging on the size of the MPC that is much larger than what used to be common
in many DSGE models. For instance, the heterogeneity-augmented model by Carroll et al.
(2017) predicts an aggregate MPC of around 20% compared to roughly 5% implied by
macroeconomic models with representative agents.
In contrast to the Keynesian consumption function, which maintains that changes in
current household income affect consumption markedly, both the permanent income hy-
pothesis of Friedman (1957) and the life-cycle hypothesis ofAndo and Modigliano (1963)
imply that consumption depends on unanticipated and not on anticipated income shocks
with a much stronger response to permanent than transitory shocks. These hypotheses are
typically formulated as consumption Euler equations, where consumption of a represen-
tative agent does not respond much to transitory income changes. However, consumption
Euler equations have found little support in aggregate data; see Flavin (1981), Campbell
and Deaton (1989), Muellbauer and Lattimore (1995), Yogo (2004), Palumbo et al. (2006)
and Canzoneri et al. (2007). Recent microeconometric studies also f‌ind that households
react much more strongly to transitory income shocks than is predicted by the standard
forward-looking theory of consumption. For instance, Jappelli and Pistaferri (2014) esti-
mate an average MPC of 48% using Italian data, and Fagerenget al. (2019) f‌ind an a MPC
that ranges between 35 and 70% using Norwegian data.
Extended versions of the standard forward-looking theory that allow for precautionary
saving, liquidity constraints and habit formation can explain some of the empirical results
found in the literature. Campbell and Mankiw (1991) among others account for precau-
tionary saving and liquidity constraints in a model for aggregate consumption assuming
constant relative risk aversion (CRRA) utility preferences and that some of the households
are current income consumers. Deaton (1991) explains consumer behaviour by means
of the so-called buffer-stock model, in which households facing liquidity constraints use
liquid assets to buffer against temporary income shocks. Kaplan and Violante (2014) in-
troduce trading costs to explain evidence of current income consumers even for those who
are wealthy due to illiquid assets and credit constraints. The consumption model of Smets
and Wouters (2003), which many DSGE models are typically based upon, includes habit
formation in that current consumption is proportional to past consumption.
The contributions of the present paper are threefold. First, we formulate a general
cointegrated vector autoregressive (CVAR) model that nests both a class of consumption
Euler equations and various Keynesian-type consumption functions. The former includes
a version of the martingale hypothesis of Hall (1978) and the precautionary saving and
liquidity constraints equations as in Campbell and Mankiw (1991) and of habit forma-
tion as in Smets and Wouters (2003). Using likelihood methods, one can test the prop-
erties of cointegration between consumption and income and of equilibrium correction
in the nested CVAR. Drawing upon Eitrheim et al. (2002), the former property repre-
sents the common ground for a Keynesian-type consumption function and a consump-
tion Euler equation while the latter represents the discriminating feature between them.1
The joint implication of a consumption Euler equation and existence of cointegration
between consumption and income is that saving todaypredicts income declines tomor row,
the so-called ‘saving for a rainy day’hypothesis of Campbell (1987).
1See also Anundsen and Nymoen (2019) for a recent application toAmerican data.
©2020 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and JohnWiley & Sons Ltd.

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT