International Evidence On
Sticky Consumption Growth
July 1, 2010
Christopher D. Carroll1 |
. |
Jiri Slacalek2 |
. |
Martin Sommer3 |
. |
_____________________________________________________________________________________
Abstract
This paper estimates the degree of ‘stickiness’ in aggregate consumption
growth (sometimes interpreted as reflecting consumption habits) for thirteen
advanced economies. We find that, after controlling for measurement
error, consumption growth has a high degree of autocorrelation, with
a stickiness parameter of about 0.7 on average across countries. The
sticky-consumption-growth model outperforms the random walk model of
Hall (1978), and typically fits the data better than the popular Campbell and
Mankiw (1989) model, though in a few countries the sticky-consumption-growth
and Campbell–Mankiw models work about equally well.
Consumption, Sticky Expectations, Habits
E21, F41
PDF: | http://www.econ2.jhu.edu/people/ccarroll/papers/cssIntlStickyC.pdf |
Web: | http://www.econ2.jhu.edu/people/ccarroll/papers/cssIntlStickyC/ |
Archive: | http://www.econ2.jhu.edu/people/ccarroll/papers/cssIntlStickyC.zip |
(Contains data and estimation software producing paper’s results) |
1Carroll: Department of Economics, Johns Hopkins University, Baltimore, MD, http://www.econ2.jhu.edu/people/ccarroll/, ccarroll@jhu.edu, Phone: (410) 516 7602 2Slacalek: European Central Bank, Frankfurt am Main, Germany, http://www.slacalek.com/, jiri.slacalek@ecb.europa.eu, Phone: +49 69 1344 5047 3Sommer: International Monetary Fund, Washington, DC, http://martinsommeronline.googlepages.com/, msommer@imf.org, Phone: (202) 623 9998
A large literature ranging across macroeconomics, finance, and international economics has argued that ‘habit formation’ can explain many empirical facts related to consumption dynamics.2 The core empirical pattern driving all these findings appears to be that aggregate consumption growth is too ‘sticky’ to be explained with standard models. Other explanations for the persistence of aggregate spending growth, or ‘excess smoothness’ (in Campbell and Deaton (1989)’s terminology), include consumers’ inattentiveness to macroeconomic news (Sims (2003); Reis (2006); Carroll and Slacalek (2007)), or their inability to distinguish micro- from macro-economic shocks (Pischke (1995)). Further explanations could undoubtedly be imagined.
But a full consensus has not emerged on whether empirical data are irreconcilable with Hall (1978)’s benchmark random walk model of consumption. Hall’s model implies that consumption growth is unpredictable (excess smoothness is zero). However, standard extensions of the Hall model can generate some degree of stickiness in consumption growth. For example, excess smoothness might merely reflect the fact that spending decisions are made more frequently than consumption data are measured (Working (1960); this viewpoint has recently been advocated in papers by Ludvigson and Lettau (2001); Lettau and Ludvigson (2004)). Also, in the presence of uncertainty, the precautionary motive slows down consumers’ response to shocks, which could also explain part (though not all) of the excess smoothness (Ludvigson and Michaelides (2001)). Another possibility, not often mentioned but nevertheless worth serious consideration, is that the smoothness of measured spending reflects data construction methods (e.g. for components of spending for which quarterly observations are imputed using annual data sources). Finally, many of the papers in the habit formation literature have not carefully examined the possibility that their results might reflect the presence of some ‘rule-of-thumb’ consumers, who simply set consumption equal to income in each period, as proposed in influential papers by Campbell and Mankiw (1989, 1991).
Motivated by this debate and by the fact that much of the empirical evidence on excess smoothness has come from a single country (the U.S.), this paper provides systematic estimates of three simple canonical models of consumption dynamics using data for all advanced economies for which we were able to construct appropriate datasets (thirteen countries in all). We compare the random walk model of Hall (1978) with two alternatives: the Campbell and Mankiw (1989) model, and a model that permits (but does not require) excess smoothness. We remain deliberately agnostic (in this paper) about whether such smoothness reflects habits, inattention, or other factors; our aim is simply to document the key stylized facts that should be matched by any model of aggregate consumption dynamics.
Using both instrumental variables (IV) (section 3.1) and Kalman filter structural (section 3.2) estimation methods, we find strong evidence of excess smoothness (‘stickiness’) in consumption growth in every country in our sample.3 Although there is some variation across countries in the estimated degree of stickiness, in every country we can reject the hypothesis that the stickiness coefficient is zero (the random walk theory), while in no country can we reject the hypothesis that it is 0.7 in quarterly data. Furthermore, wherever there is a clear distinction between the two non-random-walk models, the sticky consumption growth model outperforms the rule-of-thumb model, usually by a decisive statistical margin. (In a few cases, the two non-random-walk models are not statistically distinguishable from each other.)4
The large size of our estimated stickiness parameter may come as a surprise to some readers, because the serial correlation coefficient for spending growth in the raw data is much lower than 0.7 (for instance, in U.S. data the OLS estimate of the AR(1) coefficient for nondurables and services consumption growth is about 0.35). The discrepancy reflects our use of econometric methods that are robust to the presence of measurement error. Consistent with Sommer (2007)’s findings for the United States, our estimates suggest that in most countries at least half of the quarterly variation in consumption growth can be interpreted either as measurement error or as truly transitory spending disturbances unrelated to the theoretical consumption model (caused, for example, by unseasonal weather, which can have a nontrivial effect at the quarterly frequency in most countries).5
The remainder of the paper is organized as follows. Section 2 outlines two theoretical frameworks that generate sticky consumption growth and provide the conceptual framework for our estimation strategy. Section 3 presents the main empirical results and Section 4 concludes.
This section sketches the two most popular theoretical frameworks—habit
formation and sticky expectations—that can generate serial correlation in
aggregate consumption growth. In the habit formation model, the serial
correlation coefficient reflects the strength of habits (if
, the model
collapses to the Hall random walk model); in the sticky information model,
is the fraction of aggregate expenditure by households that have
not fully updated their information set about the latest macroeconomic
developments (and again,
corresponds to the Hall model).
Because the implications of the two frameworks are indistinguishable
in aggregate data, our empirical evidence is consistent with either
model.6
Muellbauer (1988) proposed a simple model of habit persistence, in which the representative consumer maximizes time-nonseparable utility
![]() | (1) |
subject to the usual transversality condition and the dynamic budget constraint:
![]() | (2) |
where is the discount factor,
is the consumption level,
is market
resources (net worth plus current income),
is the constant interest factor,
and
is noncapital income.
in (1) represents the ‘habit stock,’ i.e., the
reference level of consumption to which the consumer compares the current
consumption level. The parameter
captures the strength of habits. After
rewriting the utility function as
, one
can see that, for
, the consumer derives utility from both the level
and the change in consumption.
Dynan (2000) shows that for a habit-forming consumer with Constant
Relative Risk Aversion (CRRA) outer utility and
, a first order approximation to the Euler equation leads to
consumption dynamics that satisfy:
![]() | (3) |
where mainly reflects innovations to lifetime
resources.7
Hence, in contrast to the standard intertemporally separable utility specification,
some of period
’s consumption growth is predictable at time
, and the
strength of habits
can be measured directly by estimating an AR(1)
regression like (3) on aggregate consumption data.
Carroll and Slacalek (2007) present an alternative model that also generates sticky aggregate consumption growth, but without departing from the conventional intertemporally separable utility specification. The key assumption is that consumers are mildly inattentive to macro developments—for example, some households do not immediately notice shocks to aggregate macroeconomic indicators such as productivity growth or the unemployment rate.8
Assume that consumers maximize the discounted sum of time separable utility
subject to the budget constraint (2). In a Hall (1978) model
with quadratic utility, in which households use all available information, the
optimal consumption level follows a random walk:
. Numerical
simulations in Carroll and Slacalek (2007) show that when quadratic utility is
replaced with CRRA utility and the model is solved with realistic calibrations of
idiosyncratic and aggregate uncertainty, the log of aggregate consumption is close
to a random walk with drift (the drift reflects the precautionary motive and the
attendant nonlinearities):
.
Suppose now that the economy consists of a continuum of inattentive but
otherwise-standard CRRA-utility consumers, each of whom updates the
information about his permanent income with probability in each period. For
each consumer, this probability is assumed to be independent of the date when
he last updated his information set (and independent of his income, wealth,
or other characteristics). This assumption resembles firm behavior in
Calvo (1983)’s model of price setting, which is commonly used in the monetary
economics literature. Carroll and Slacalek (2007) show that the change in
the log of aggregate consumption,
, approximately follows an
AR(1) process, whose autocorrelation coefficient approximates the share
of consumers (
) who do not have up-to-date information about
macroeconomic developments. That is, consumption growth is well approximated
by:9
![]() | (4) |
In addition, in the spirit of Akerlof and Yellen (1985) and Cochrane (1991), Carroll
and Slacalek (2007) show that the utility loss from the infrequent updating of
expectations is very small under standard calibrations of the model with per
quarter.10
This section tests the model of sticky consumption growth (3) and (4) against the alternatives of rule-of-thumb behavior and the random walk hypothesis. The organizing framework for our empirical analysis is a specification for consumption growth from the excess sensitivity literature,11 which has been expanded here to include a term capturing stickiness of consumption growth:
![]() | (5) |
where is household income and
denotes the ratio of household (net)
assets to permanent income. The first two right-hand side regressors correspond
to two of the tested theories of consumption behavior: inattentiveness or habit
formation (
) and rule-of-thumb consumers (
). Under the
third tested theory—the random walk hypothesis—the coefficients
and
should both be zero. The third term in the equation above (
) is included
as a control—any of the three theories allow for some direct effect of
asset holdings on consumption growth, either due to effects related to
uncertainty (which induces a precautionary saving motive) or due to time
variation in interest rates (which we assume is captured by time variation in
).12
There are at least three reasons to expect the OLS estimates of coefficients in (5) to be biased and inconsistent. First, as argued by Wilcox (1992) and Sommer (2007), quarterly consumption data may be contaminated with substantial measurement error. Second is the undoubted existence of transitory spending disturbances such as those related to weather (or even, for some smaller countries, one-time events like the hosting of the Olympics). Standard theoretical models ignore these kinds of shocks, yet back-of-the-envelope calculations suggest their effects could be substantial in quarterly data. Our final reason for expecting OLS to be biased is the well-known problem of time aggregation.13
We develop the points about importance of measurement error and transitory spending fluctuations using the United States as an example. The Bureau of Economic Analysis (2006) describes the methodology by which aggregate expenditures on nondurable goods are estimated using data on retail sales at a sample of retail outlets; since only a subset of retail stores are surveyed, the retail sales figures must contain sampling error. As an example of a “transitory disturbance,” under some plausible assumptions, Hurricane Katrina may have reduced quarterly personal consumption expenditure (PCE) growth by about 1 percentage point on an annualized basis in Q3:2005.14 However, even a much more benign event such as mild winter can reduce annualized quarterly consumption growth significantly—for instance, by about 1/4 percentage point in the United States in Q1:2006—through lower outlays on energy.
To address these three estimation issues (measurement error, transitory consumption, and time aggregation) in quarterly consumption data, we use two econometric methods. The first technique attempts to overcome these problems using instrumental variables estimation. As with any IV method, validity of the results depends on our ability to find suitable instruments (though the extensive literature on the predictability of consumption growth provides good candidates). As an alternative for those who dislike IV regressions, our second technique uses the Kalman filter and structural modeling assumptions to separate ‘true’ consumption growth from its transitory components and measurement error.15 In this case, the usual caveat applies: The validity of this maximum likelihood method hinges on the assumed structure of the stochastic processes for measurement error and ‘true’ consumption dynamics.16 We view the similarity between the results obtained from these two different methods, along with the coherence of our results with the large literature on habit formation in macroeconomics, as persuasive evidence that stickiness in consumption growth is a robust phenomenon.
Equation (5) is estimated using aggregate quarterly data for thirteen advanced
economies ranging roughly over the past forty years (table 5 provides data details).
Our preferred measure of consumption is the sum of expenditures on nondurable
goods and services. However, this measure is available only for six countries in
our sample (Canada, France, Germany, Italy, the U.K. and the U.S.); total
personal consumption expenditures are therefore used for the other sample
countries.17
Finally, and
are measured as household disposable
income and the ratio of financial wealth to disposable income,
respectively.18
The main advantage of IV estimation is that with appropriate instruments, there is no need to make assumptions about the stochastic structure of measurement error and other transitory fluctuations in quarterly consumption growth. The only requirements are that the instruments are uncorrelated with measurement error and temporary consumption fluctuations, but correlated with the instrumented variables.
Under habit formation or sticky expectations, Sommer (2007) shows that time
aggregation makes “true” consumption growth (i.e., consumption
growth without measurement error and transitory consumption) follow an
ARMA(1,2) process:
![]() | (6) |
where the s are complicated functions of
. In addition, the
MA(2) coefficient
is close to zero for all reasonable values of
, so that
is approximately ARMA(1,1). Given these
considerations, equation (5) can be estimated using the IV estimator
with instruments lagged at least twice (e.g., dated as of time
and
earlier).19
The baseline instrument set for the IV regressions consists of variables that are strongly correlated with consumption growth and yet unlikely to be correlated with measurement error: the unemployment rate, a long-term interest rate, and an index of price volatility.20 Consumer sentiment is also used as an instrument whenever available (the G-7 countries and Australia), as in Carroll, Fuhrer, and Wilcox (1994) and others.
Table 1 summarizes the baseline estimation results for four
alternative econometric specifications nested in equation
(5).21
The left panel reports the results from univariate regressions in which
each right-hand side variable enters the estimated specification as
the only regressor. The first column presents the IV estimates of
consumption persistence , which are for all countries much higher
than the (unreported) OLS estimates and are always highly statistically
significant.22
The IV estimates of consumption persistence in table 1 are on average about
0.7—a strong rejection of the random walk proposition which implies a
coefficient of zero. The second column reports p values of the null hypothesis
implied by the heteroscedasticity and autocorrelation robust version of
the conditional likelihood ratio (HAR-CLR) test of Andrews, Moreira, and
Stock (2004). The test is robust to potentially weak instruments and is
effectively uniformly most powerful among tests invariant to rotations of the
instruments. The
values indicate that the zero restriction on
is soundly
rejected in almost all countries.
The third column estimates the Campbell–Mankiw model. Our results
are broadly consistent with the evidence presented in Campbell and
Mankiw (1991): Rule-of-thumb consumers (for whom, by assumption,
consumption equals current income) are on average estimated to earn about
of aggregate income. Interestingly, the estimates of
in the left
panel are often less significant than those of consumption persistence
and are in three or four cases insignificant (depending on whether the
standard or HAR-CLR p values are used). This means that—aside from the
question of how the Campbell–Mankiw model stands up against the
alternative of habit formation or sticky expectations—rule-of-thumb spending
behavior cannot be reliably detected in about a third of our sample
countries.
The fifth column investigates the relative importance of wealth (expressed as
the ratio of net financial assets to income) in aggregate consumption dynamics.
The coefficient on the wealth–to–income ratio, , turns out to be statistically
significant only in four countries, although the HAR-CLR
values suggest
more often that
is not zero. In addition, the coefficient
has in most
countries the opposite sign to that predicted by either precautionary saving
theory or intertemporal substitution as channelled through the interest rate.
This is unsurprising for at least two reasons. First, the overwhelming significance
of consumption (and also income) in the previous regressions implies a severe
omitted-variable bias problem with the univariate regression that only includes
wealth. Second, the previous literature generally finds little evidence of interest
rate or precautionary saving effects in aggregate consumption growth
data.23
The last column of the left panel displays the adjusted s from the
first-stage regressions of consumption growth on instruments (denoted
).
This measure of the strength of instruments ranges between 0.1 and 0.2 for most
countries.24
25
The right panel of table 1 reports estimation results when all three regressors
are included in equation (5). The results strongly suggest that past consumption
growth is by far the strongest predictor of current consumption growth. The
average persistence parameter in the country regressions falls only very slightly
compared with the average estimates from univariate regressions reported in the
left panel (from to
) and remains statistically significant at
the five percent level in ten of our thirteen countries. The predicted income
growth term dominates the lagged consumption term only in one country,
Germany.26
The last column of the right panel reports the p-values of the Hansen’s
overidentification test—results of which imply that the null of instrument
exogeneity cannot be rejected.
Table 2 averages the coefficient estimates from table 1 across various country
groups. As in table 1, while the average consumption persistence falls
relatively little after income and wealth are added to the estimated equations
(compare the right and left panels of the table), the income and wealth
coefficients become essentially zero. The result holds for all five groups of
countries reported in the table which suggests considerable homogeneity in
among advanced economies, a fact already apparent in the previous table with
the results for individual countries.
Table 3, whose format is identical to table 1, estimates aggregate consumption dynamics with an alternative instrument set, in which long-run interest rates and price volatility have been replaced with income growth and the interest-rate spread.27
The estimation results are broadly consistent with our baseline: (i) the coefficient on lagged consumption growth in univariate regressions is large and significant for ten countries, (ii) in the regressions that include all three regressors, the coefficients on instrumented income growth and wealth tend to be small and less often statistically significant compared with univariate regressions, and (iii) lagged consumption growth beats lagged income in nine horse-race regressions (but gets badly beaten in German data).
As a more efficient alternative to IV, we also estimate the dynamics of
consumption growth using the Kalman filter. To proceed, it is necessary
to specify an assumption about the stochastic process of measurement
error. We follow the methodology of Sommer (2007) and assume that
measurement error in the log-level of consumption follows an MA(1)
process.28
Observed consumption growth, , can be written as the sum of ‘true’
consumption growth,
, and a measurement error,
, as follows:
As noted above, s are not free parameters but are complicated functions of
. The Kalman filter jointly estimates the sticky expectations coefficient
and the degree of the first autocorrelation in measurement errors,
. The filter
also generates separate estimates of ‘true’ consumption growth,
, and
the measurement error component,
. For the purposes of this subsection, we
assume that the correlation structure of measurement error remains unchanged
over the sample period.
The model described in equations (7) and (8) has been rewritten in a
state-space form (see appendix B) and estimated using consumption data for the
countries in our dataset (listed in table 5). Table 4 presents the estimation
results. As in the case of the IV estimation, the coefficient reflecting consumption
growth stickiness, , is large and highly statistically significant in almost
all sample countries. The value of
typically ranges between 0.6 and
0.8, with only Denmark and the United Kingdom having coefficients
estimated below 0.4. For the United States, the estimated consumption
persistence is about 0.7, which is consistent with previous studies (e.g.
Fuhrer (2000)).
It is encouraging that the Kalman filter estimates of consumption persistence tend to be close to the IV estimates. This suggests that stickiness of consumption growth is a robust feature of the data that appears similarly even when viewed through quite different lenses.
The estimation results also suggest that measurement error in the level of consumption is positively and significantly autocorrelated in about half of our sample countries—a fact that is not surprising given the interpolation techniques that are often used by statistical agencies when constructing quarterly consumption data.
The Kalman filter’s estimate of “true” consumption growth, , is presented,
along with the raw data, in figures 1 and 2. The Kalman filter estimation suggests
that the share of transitory components in published quarterly consumption data
is large (about 50 percent for the United States and even more for some
countries).29
To see how the restrictions on
s imposed by the theoretical model with habits
affect estimates of
, we have also experimented with several versions of model
(7)–(8) in which
s are free parameters (rather than known functions of
). In
such models, consumption sluggishness
robustly turns out to be similar to
the values shown in Table 4. However, the fact that in a few cases
s appear
unrealistic (greater than one or smaller than minus one) suggests that
imposing theoretical restrictions is helpful in identifying them (rather than
).
The state-space representation (7)–(8) fits nicely into the structural DSGE
framework recently proposed by Ireland (2004), who estimates a small
log-linearized model with the Kalman filter. Control variables in
his model can be solved in terms of state variables
and residuals
:
![]() | (9) |
Ireland, p. 1210 views the disturbances as follows: “the residuals [
] may
… soak up both measurement errors, but they can be interpreted more liberally
as capturing all of the movements and co-movements in the data that
the real business cycle model, because of its elegance and simplicity,
cannot explain.” Once we plug our transition equation for consumption
growth (8) into the measurement equation (7), the Kalman filter model
we estimate above has exactly the structure (9) with
,
,
and
.
Thus the state-space representation (7)–(8) can be interpreted as a
stripped-down version of Ireland’s model with consumption habits in which
measured consumption is affected by a combination of measurement errors
and shocks
to “true” consumption
. As our main goal is to estimate
consumption stickiness
, we do not take a stand on where the consumption
shocks
come from (be it news about income, wealth, interest rates, fiscal
policy or something else). Our model is simple enough to be estimable using
classical techniques, including the maximum likelihood estimator, so that data
have complete control over the estimates of
, in contrast to larger-scale DSGE
models, which are often inevitably estimated with Bayesian methods with
informative priors.
Hall (1978) provided macroeconomists with a clean theoretical benchmark to which actual consumption data could be compared: Consumption growth should be essentially unpredictable. In contrast with this benchmark, we find that, when econometric techniques that account for measurement error are used, consumption growth exhibits a high degree of persistence or “momentum.” The stickiness of aggregate consumption growth can be interpreted as reflecting the behavior of fully informed households with a strong consumption habit, or the behavior of an aggregate economy in which households are not always perfectly up to date in their knowledge of macroeconomic developments. Fitting the model to data from thirteen countries, we estimate that consumption growth persistence is always significantly above the random-walk benchmark of 0 and is never robustly different from about 0.7. Our analysis also suggests that, on balance, the model of sticky consumption growth describes aggregate consumption data better than the rule-of-thumb model of Campbell and Mankiw (1989), although our point estimates do typically indicate that a modest proportion of aggregate income (in the range of 10–20 percent) may be received by households who consume their current income every quarter.30
Our findings imply that the large literature claiming to find evidence of sticky consumption growth in the U.S. probably cannot be explained away as reflecting time aggregation problems or other mistreatment of the data, suggesting that many of the insights gleaned from that literature are likely applicable to other countries as well. (However, it is worth bearing in mind that analyses that rely heavily on the literal interpretation of the habits-in-the-utility-function framework, such as calculations of the welfare cost of aggregate fluctuations, may not hold up under alternative interpretations of consumption growth stickiness.)
Our analysis also strengthens a key policy message about the sluggish average response of consumption to monetary and fiscal policy innovations highlighted earlier in the context of the habit formation literature—an important policy consideration at the current cyclical juncture in many countries, including in the United States.
Estimation with | Estimation with | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
one regressor only | all three regressors
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
![]() | CLR p val ![]() | ![]() | CLR p val ![]() | ![]() | CLR p val ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Country | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | OID
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Canada![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | France![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Germany![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Italy![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
United Kingdom![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
United States![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Mean G7 | ![]() ![]() | – | ![]() ![]() | – | ![]() ![]() | – | – | ![]() ![]() | ![]() ![]() | ![]() ![]() | –
| ||||||||||||
Australia![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Belgium![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Denmark![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Finland![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Netherlands![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Spain![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Sweden![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Mean Other | ![]() ![]() | – | ![]() ![]() | – | ![]() ![]() | – | – | ![]() ![]() | ![]() ![]() | ![]() ![]() | –
|
Notes: Left Panel: Regressions were estimated with one regressor only. Right Panel: Regressions were estimated with all three
regressors. : p value of the null hypothesis that the parameter equals 0 tested using the HAC robust version of the conditional
likelihood ratio (HAR-CLR) test of Andrews, Moreira, and Stock (2004), window: 4 lags. Consumption variable:
: nondurables,
semidurables and services consumption,
: total personal consumption expenditure,
: ratio of household financial wealth to
income.
Statistical significance at
percent (using robust standard errors).
: Adjusted
from
the first-stage regression of consumption growth on instruments. OID: p-value from the Hansen’s
statistic for
overidentification.
![]() | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Estimation with | Estimation with | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
one regressor only | all three regressors
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Country | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
All Countries | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
G7 Countries | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Anglo–Saxon | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Euro Area | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
European Union | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Notes: Instruments: Lags and
of the unemployment rate, long-run interest rate, price volatility and consumer
sentiment. Left Panel: Regressions were estimated with one regressor only. Right Panel: Regressions were estimated with all three
regressors. Robust standard errors are in parentheses.
Statistical significance at
percent. Standard errors
are simple averages of individual countries in a given group.
All countries: Canada, France, Germany, Italy, the United Kingdom, the United States, Australia, Belgium, Denmark, Finland, the
Netherlands, Spain, Sweden. G7 countries: Canada, France, Germany, Italy, the United Kingdom, the United States. Anglo–Saxon
Countries: Australia, Canada, the United Kingdom, the United States. Euro Area Countries: France, Germany, Italy, Belgium,
Finland, the Netherlands, Spain. European Union: France, Germany, Italy, the United Kingdom, Belgium, Denmark, Finland, the
Netherlands, Spain, Sweden.
Estimation with | Estimation with | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
one regressor only | all three regressors
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
![]() | CLR p val ![]() | ![]() | CLR p val ![]() | ![]() | CLR p val ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Country | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | OID
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Canada![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | France![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Germany![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Italy![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
United Kingdom![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
United States![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Mean G7 | ![]() ![]() | – | ![]() ![]() | – | ![]() ![]() | – | – | ![]() ![]() | ![]() ![]() | ![]() ![]() | –
| ||||||||||||
Australia![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Belgium![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Denmark![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Finland![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Netherlands![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Spain![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Sweden![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Mean Other | ![]() ![]() | – | ![]() ![]() | – | ![]() ![]() | – | – | ![]() ![]() | ![]() ![]() | ![]() ![]() | –
|
Notes: Left Panel: Regressions were estimated with one regressor only. Right Panel: Regressions were estimated with all three
regressors. : p value of the null hypothesis that the parameter equals 0 tested using the HAC robust version of the conditional
likelihood ratio (HAR-CLR) test of Andrews, Moreira, and Stock (2004), window: 4 lags. Consumption variable:
: nondurables,
semidurables and services consumption,
: total personal consumption expenditure,
: ratio of household financial wealth to
income.
Statistical significance at
percent (using robust standard errors).
: Adjusted
from
the first-stage regression of consumption growth on instruments. OID: p-value from the Hansen’s
statistic for
overidentification.
Parameter Estimates
| ||||||||||||||||||||||||||||||||||||||||||
Country | ![]() | ![]() | ![]() | ![]() | ![]() | |||||||||||||||||||||||||||||||||||||
G7 Countries | ||||||||||||||||||||||||||||||||||||||||||
Canada![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
France![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Germany![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Italy![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
United Kingdom![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
United States![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
|||||||
Australia![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Belgium![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Denmark![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Finland![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Netherlands![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Spain![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Sweden![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Notes: Consumption variable: : nondurables, semidurables and services consumption,
: total personal consumption
expenditure.
Statistical significance at
percent.
Data for the G-7 economies are from the Haver Analytics database. Data for other countries are from the database of the NiGEM model of the NIESR Institute, London. The original sources for most of these data are OECD, Eurostat, national statistical offices and central banks. Income is measured as personal disposable income. Wealth is approximated using data on the net financial wealth. All series were deflated with consumption deflators and expressed in per capita terms. The population series are from DRI International and were interpolated from annual data to quarterly observations. Japan is not included in our sample as creating a quarterly dataset with consumption data going prior to 1980 would involve splicing consumption series based on three very different methodologies. Adjustments to the Japanese national accounts methodology in 2002 and 2004 have significantly improved the reliability of quarterly consumption series but the current-methodology data are only available since Q1:1994 (International Monetary Fund (2006)).
We thank Roberto Golinelli for consumer sentiment series for G7 countries and Australia used (and described in detail) in Golinelli and Parigi (2004). (We have not used consumer sentiment series for the remaining countries, because the data are not available before 1985.) We are grateful to Carol Bertaut and Nathalie Girouard for providing us with the data used in Bertaut (2002) and Catte, Girouard, Price, and Andre (2004), respectively. Ray Barrell, Amanda Choy and Robert Metz answered our questions about the NiGEM’s database.
Country | Time Frame | Consumption/Source | Income/Source | Wealth/Source |
G7 Countries
| ||||
Canada | Q4:1970–Q3:2002 | NDS/Haver | PDI/Haver | NFW/NiGEM |
France | Q1:1985–Q4:2003 | NDS/Haver | PDI/Haver | NFW/NiGEM |
Germany![]() | Q4:1975–Q4:2002 | NDS/Haver | PDI/Haver | NFW/NiGEM |
Italy | Q1:1981–Q4:2003 | NDS/Haver | PDI/Haver | NFW/NiGEM |
United Kingdom | Q1:1974–Q4:2003 | NDS/Haver | PDI/Haver | NFW/NiGEM |
United States | Q3:1962–Q2:2004 | NDS/Haver | PDI/Haver | NFW/NiGEM |
Other Countries
| ||||
Australia | Q4:1975–Q4:1999 | PCE/Haver | PDI/Haver | NFW/NiGEM |
Belgium | Q2:1980–Q4:2002 | PCE/NiGEM&MEI | PDI/NiGEM&MEI | NFW/NiGEM |
Denmark | Q1:1977–Q2:2003 | PCE/NiGEM&MEI | PDI/NiGEM&MEI | NFW/NiGEM |
Finland | Q3:1973–Q2:2003 | PCE/NiGEM&MEI | PDI/NiGEM&MEI | NFW/NiGEM |
Netherlands | Q1:1975–Q4:2002 | PCE/NiGEM&MEI | PDI/NiGEM&MEI | NFW/NiGEM |
Spain | Q1:1978–Q4:1999 | PCE/NiGEM&MEI | PDI/NiGEM&MEI | NFW/NiGEM |
Sweden | Q1:1977–Q4:2002 | PCE/NiGEM&MEI | PDI/NiGEM&MEI | NFW/NiGEM |
Notes: PCETotal personal consumption expenditures, NDS
Nondurables and services, PDI
Personal disposable
income, NFW
Net financial wealth,
: Regressions for Germany were estimated with a reunification dummy in Q1:1991;
Source: Haver—Haver Analytics, NiGEM—Database of the NiGEM model of the NIESR Institute, London, MEI—Main Economic
Indicators of OECD.
Following Sommer (2007), equations (7) and (8) can be rewritten in the state-space form with the measurement equation:
![]() |
and the state-evolution equation:
![]() |
and with the associated covariance matrices and
![]() |
respectively.
The state-space form is estimated with the Kalman filter using the consumption series described in
table 5. The coefficients and
are not free parameters but instead depend on the consumption
persistence coefficient
:
. Our Kalman filter estimation incorporates this
relationship between
,
, and
.
Figures 1 and 2 display the measured consumption growth and true consumption
estimated using the Kalman smoother based on the above state-space model.
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