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How Important is the Stock Market Effect on Consumption?
Sydney Ludvigson and Charles Steindel*
Federal Reserve Bank of New York
August 1998
Preliminary
*Research and Market Analysis Group, 33 Liberty Street, New York, NY 10045. We thank Jordi
Galí for many valuable discussions, James Kahn and Kenneth Kuttner for helpful comments, and
Rita Chu and Beethika Khan for able research assistance. The views expressed in the paper are
those of the authors and are not necessarily reflective of views at the Federal Reserve Bank of
New York or the Federal Reserve System. Any errors or omissions are the responsibility of the
authors.
1
Abstract
The 1990s have seen astonishing growth in the stock market portfolios of Americans, which many
have argued has been a major force behind the growth of consumer spending. This paper reviews
the relationship between the stock market and the consumer. Using a variety of econometric
techniques and specifications, we fail to find evidence of a stable relationship between aggregate
consumer spending and changes in aggregate household wealth. While stock market gains have
surely provided some support for consumer spending, our hard knowledge is too limited to feel
comfortable relying on estimates of the stock market effect in macroeconomic forecasts.
2
How Important is the Stock Market Effect on Consumption?
The 1990s have seen astonishing growth in the stock market portfolios of Americans.
From 1991 through the middle of 1998, the aggregate value of household equity increased by
$9.45 trillion, or 260 percent. The ratio of household equity to disposable personal income grew
from a low of 0.83 in 1991 to 2.46 by mid-1998. The bulk of these gains occurred in the doubling
of the value of the market from the start of 1995 through the middle of 1997-- the value of the
market has been erratic since then.
The thrust of this paper is the examination of one of the possible consequences of the
market rise. Other things equal, an increase in the stock market makes people richer. In general,
the richer people are, the more they spend. Is it possible to quantify these banal truisms and come
up with some plausible estimates of the extent to which aggregate consumer spending in the
1990s has been supported by the stock market rise? Furthermore, how much would a market
correction take away from future spending?
This paper reviews the relationship between the stock market and the consumer. Our
conclusions are very modest: While stock market gains surely provide some support for consumer
spending, our knowledge is too limited to feel comfortable relying on estimates of the stock
market effect in forecasts.
The Stock Market and the Consumer: General Considerations and Preliminary Evidence
Traditionally the stock market effect has been viewed as an outgrowth of a more general
“wealth effect” on consumer spending. The wealth effect is the reaction of a consumer to an
3
unexpected increase in his or her wealth.1 A rational consumer--one who is concerned about
future as well as current well-being--will probably spend such a windfall gradually. The amount
that is spent in any time will depend upon such factors as the rate of return (the higher the rate of
return, the more that will be spent in any time period) and the length of the consumer’s planning
horizon (the longer the horizon, the less will be spent in any time period)2. Estimates of the stock
market effect have been determined by estimating aggregate time-series regressions of the form
Ct ' a%bWt%cYPt.
(1)
Where C=consumer spending
YP=A measure of permanent income (usually a distributed lag on realized after-tax income)
W=Consumer net worth.
Derivations of such estimating equations from the underlying theory of consumer behavior
may be found in Modigliani and Tarantelli (1975), Modigliani and Steindel (1977), and Steindel
(1977 and 1981). The estimated coefficient, b, on wealth, is described as the “marginal
propensity to consume out of wealth” and is interpreted as the increase in consumer spending that
1
The term “wealth effect” seems to be used for many different purposes. In a recent Wall
Street Journal article (Wysocki, [1998]) connections appeared to be drawn between stock market
movements and long-lived feelings of euphoria and despair in societies. In part, the analysts cited
in the piece were focusing on the after-effects of the spending shocks supposedly induced by
wealth changes, and including these in the concept of the “wealth effect.” Our definition is the
more modest one of the first-round consumer spending change.
2
The life cycle hypothesis of consumer spending asserts that a consumer’s planning
horizon is dominated by his or her life expectancy. The fact of retirement, and the subsequent
reduction in wage income, results in a sharp distinction between consumer reactions to increases
in wage income and nonwage income and wealth. “Time preference”--a general tendency to
prefer spending in the near term--can be viewed as a way of shortening the planning horizon or,
equivalently, creating an intrinsic return from consumption.
4
is associated with an increase in wealth. A widespread empirical practice is to differentiate wealth
into different categories, with the stock market wealth usually being one of them. A differential
coefficient on stock market wealth from other types is merely viewed as an artifact of
heterogeniety of consumers; stock market owners may be systematically older or younger than
other wealth owners or have other characteristics which lead to a different aggregate propensity
to consume out of this form of wealth. A common assumption is that b is on the order of .05 or
perhaps a bit smaller; in other words, roughly 5 cents on the dollar of an increase in wealth is
spent soon after it is earned. While this seems to be “small,” when we are looking at gains in
wealth from the stock market in the trillions of dollars, and increase in spending of 5 cents on the
dollar adds up to real money!
The perspective of modern dynamic economics is to be quite dubious about the value of
estimation of equations such as (1) using aggregate time series data. Aside from questions about
the appropriate estimation technique given the possible presence of aggregation and simultaneity
bias, and the use of largely untested simplifying assumptions to derive the estimating equation
from the theory, there is the more basic issue that the underlying theory applies to comparisons
across steady states--all else equal, how much more will a wealthy consumer spend than one who
is less wealthy but has the same permanent income? Aggregate time series data are not drawn
from steady states; they are taken from an environment where it should be assumed that
consumers are adjusting their behavior to new conditions. Recognizing this reality implies very
different ways to estimate the relationship between changes in wealth and changes in
consumption. This has been addressed in the literature on consumer spending since at least the
work of Hall (1978).
5
Despite the valid criticisms of equations such as (1), we begin as a reference point with the
estimation of this type of model. Equations of this sort have been very influential in the literature
on economic policy (for instance, Modigliani [1971]), and continue to be common in forecasting
exercises.3
We start with a traditional consumption function. Table 1 shows estimates of a regression
relating real per capita consumer spending to real per capita disposable personal income, and real
per capita net worth, with net worth split into stock market holdings and other. Four lags of each
of the right-hand side variables are included, in order to capture the adjustment process of
consumer spending to changes in fundamentals.4 Details about the data are provided in an
appendix. The estimation of the model includes a correction for first-order autocorrelation in the
error process.
Column (1) shows the estimated coefficients for the equation estimated over the 19531997 time period. The estimates include the sum of the lag coefficients on each of the right-hand
side variables, along with the estimated standard errors. This regression is more or less consistent
with traditional views of consumer behavior; the sum of the lag coefficients on income is about
.7, and those on the stock market and other forms of wealth is each about .04. Each of these
sums is more than twice as great as its computed standard error, which is normally interpreted as
3
For instance, both the Data Resources Incorporated (DRI) and Macroeconomic Advisors
econometric models use equations for consumption sectors very similar in form to (1). Mosser
(1992) provides some documentation of the evolution of wealth effects in the DRI model in the
1980s; a description of the model used by Macroeconomic Advisors can be found in Laurence H.
Meyer & Associates (1994).
4
A traditional interpretation of the lags on income in such an equation is to capture
expectations formation. We are uninterested in the specific interpretation of the lag.
6
meaning that it is statistically greater than zero. The estimated coefficient of serial correlation,
while substantial, appears to be less than one, suggesting that the model is a valid statistical
construct.
The superficial view would be that this equation supports traditional views of the stock
market: Literally, the results suggest that approximately 4% of an increase in the stock market
enters the spending stream within a year of its being earned. However, this conclusion rests on
some very shaky grounds.
At the simplest level, the estimated stock market effect appears to be rather sensitive to
the period of estimation. Reestimating the equation over three different time periods (columns 2,
3, and 4 of Table 1) suggests that the stock market effect was larger in the late 1970s and early
1980s than either before or earlier.
Admittedly, columns 2-4 cook the books a bit to show this instability. If we split the
sample in thirds (columns 5-7) rather than picking 1975 and 1985 as the break points, the
coefficient estimates look stabler, though their standard errors vary. However, Chart 1
reinforces the view of a shifting model. It shows the estimated sum of the lag coefficients, along
with a one-standard error band, of the wealth and income terms from regressions of the form in
Table 1 estimated over 10-year periods. In particular, the remarkable thing about the chart on the
stock market variable is not so much the observation that such a parameter changes over time, but
that the change from year-to-year in the estimated effect can be rather large--recall that 10- year
regressions estimated ending in two consecutive years will have 80% of their observations in
common. Another thing to draw from the chart is that the point estimate of the sum of the lag
coefficients on the stock market for the most recent 10-year period is effectively zero. If all pre7
1988 data were destroyed we would be hard-pressed to conclude that there is a linkage between
the stock market and consumer spending, based on this model and estimation technique.
It is clear that the estimated marginal propensity to consume from stock market wealth is
not particularly stable 5 In principle, we could present conventional stability tests to see if we
could reject the hypothesis of stability in a statistical sense, or hone in on the precise break points
in the structure of the regression. Such exercises are not germane to this paper--from a
forecasting point of view awareness that this propensity can vary in a range from around 0 to .10
makes the wealth effect a very shaky reed to lean on . Also, as noted above, if we do not regard
equations of this type as valid approximations of consumer behavior then the standard statistical
tests of their structure are also not valid.
Chart 1 also shows us that the other coefficients shift over time. The observations we
make about an unstable stock market effect could be restated in terms of unstable effects from
income and other forms of wealth. We emphasize the stock market in the discussion mainly
because in the current environment scenarios for consumer spending are often in the form “if the
stock market does x, consumer spending will do y.” Our view is that we are not in a good
position to make such a statement; instability of the stock market effect is a good shorthand way
to state our ignorance, though instability of the other parameters would also contribute to these
5
Poterba and Samwick (1995), using somewhat different specifications than those used
here, and looking at cross-sectional and well as time-series evidence (as well as attempting to
correct for changing patterns of stock ownership) also failed to find evidence of a clear stable
stock market effect on consumption. Mankiw and Zeldes (1991) found that the growth rate of
spending on food by stockholders was sensitive to the excess return on the market, but this result
does not necessarily translate into a stable propensity to consume from a change in the value of
the market. Starr-McCluer (1998) found some modest evidence of life-cycle stock market wealth
effects on saving from analysis of responses to the University of Michigan survey of consumers,
but did not look into the issue of stability..
8
misgivings.
The Wealth Effect on Consumption: Updated Statistical Approaches
The empirical procedure above provides a descriptive summary of the relationship
between aggregate consumption and wealth. This approach is useful because it furnishes a basis of
comparison with earlier work by pioneers of the traditional life-cycle consumption literature.
Neveretheless, modern-day econometric theory points to a number of potential pitfalls with this
approach to estimating a wealth effect.
We now turn to updated statistical approaches to see if we can capture a stable wellestimated wealth effect which may be used for forecasting consumer behavior. One problem with
the traditional empirical approach used above concerns its failure to correct for the time-series
properties of C, W, and Y. At the least, each of these variables likely contains a stochastic trend,
and the conventional analysis performed above does not take into account the econometric
implications of this type of nonstationarity.
A second problem with the previous analysis pertains to the correlation between
consumption and current wealth. We seek, ideally, to identify the effect an increase in financial
wealth has on consumption. Yet the econometric techniques employed above ignore the
possibility that the consumption-wealth correlation found, at least partially, reflects the effect of
an increase in aggregate consumption on wealth. We refer to this “reverse causality” as
endogeneity bias.6 Failure to address either of these problems could skew statistical inference and
6
Of course, traditional “Cowles Commission” econometrics was fully aware of
simultaniety bias, but in practice there were few efforts to correct for it in the consumption
literature (an exception is the work of Mishkin (1976, 1977) on consumer durable spending),
probably because of the difficulties of finding suitable instrumental variables and perhaps a belief
that the problems were not severe.
9
lead to inconsistent estimates of how much an increase in wealth influences consumption.
In principle, econometric methodology can handle both nonstationary regressors and
endogeneity bias. In practice, addressing the range of potential problems presents a challenge
because the appropriate statistical tests often depend on what theoretical model researchers
assume. Thus theory plays an important role in selecting a suitable empirical specification; given a
specific null hypothesis, we can attempt to estimate the true structural affect of wealth on
consumption. On the other hand, theories, by construction, force us to look at a more limited set
of hypotheses and therefore fail to capture every aspect of reality. Theoretical models may imply
an empirical framework that is too restrictive to adequately fit the data.
To address these conflicting concerns, we make use of several empirical specifications
(described below) ranging from those that are primarily atheoretical to those that are primarily
theoretical. We discuss this next.
Estimating a Marginal Propensity to Consume Out of Wealth
To motivate our empirical approach, we begin by laying some theoretical ground work.
Much recent research on consumer behavior has focused on the dynamic optimization problem of
an infinitely-lived agent who faces an exogenous, stochastic labor-income process. Among the
most prominent of these paradigms is the so-called modern day permanent income hypothesis
(PIH), first formalized and tested by Hall (1978) and Flavin (1981). According to the PIH,
consumption of nondurable goods and services is chosen (via intertemporal optimization) to
match permanent income, defined as the annuity value of human and non-human wealth.7 In
7
Human wealth is defined as the present discounted value of expected future labor income
multiplied by the annuity factor r(1%r)&1 . See Flavin (1981).
10
addition, if preferences are intertemporally separable, felicity functions are quadratic, and there is
a constant real interest rate equal to the rate of time preference, the theory implies that
consumption follows a martingale, so that the first difference of consumption should be
unpredictable.
Galí (1990) extends this version of the permanent income hypothesis to allow for finite
horizons, and shows that the theory implies a linear relationship between aggregate consumption,
Ct, aggregate labor income, Yt, and aggregate non-human (financial) wealth, Wt
Ct ' "%$Wt%*Yt%ut.
(2)
The error term, ut, is a discounted value of expected future income increases (see Galí [1990]).8
Equation (2) establishes a linear relationship between aggregate consumption, labor
income and wealth that is derived from the theory of intertemporal choice. Since the theory
applies to total financial wealth, we focus our analysis in this section on total wealth, rather than
breaking it out into stock market and non-stock market wealth. If we take this version of the
permanent income hypothesis as our null hypothesis, then $ gives the true structural effect of
wealth on consumption and can be interpreted as the “marginal propensity to consume” out of
(financial) wealth.
This equation is almost identicle to equation (1), but there are some subtle differences.
The major discrepancy concerns the income and error terms. Equation (2) uses current income,
8
Other work attempting to combine the traditional life-cycle views with modern timeseries econometrics are Blinder and Deaton (1985) and Campbell and Mankiw (1990).
11
while equation (1) uses permanent income.9 Like equation (1), however, equation (2) relates
consumption to permanent income (where in this case permanent labor income is defined
explicitly as the annuity value of human wealth). In equation (2), permanent labor income has
simply been split into current labor income, which appears as a regressor, and the present
discounted value of expected future labor income increases, which appears in the disturbance
term, ut. The error term in equation (2) is specifically related to the consumer spending decision;
the error term in equation (1) is an empirical “add-on.”
Econometric Considerations
In order to confront the potential empirical pitfalls discussed above, several econometric
considerations must be taken into account when estimating equation (2).
First notice that (2) implies the existence of at least one cointegrating relationship among
consumption, labor income and nonhuman wealth, as long as at least two of the three variables
are nonstationary and contain a unit root. (We refer to variables that contain a unit root as first
order integrated, or I(1).) If there is at least one cointegrating relation among the variables in (1),
consistent estimates of the parameters can be obtained by estimating the equation with variables in
levels. By contrast, if C, Y, and W are each I(1) but the variables are not cointegrated, the
equation must be estimated with variables in first differences to avoid spurious regression (see
Campbell and Perron [1991]).
A second econometric consideration concerns the error term, ut. As mentioned,
9
There’s also a distinction between the overall income measure used in (1) and the labor
income measure used in (2). . See Modigliani and Tarantelli (1975), Modigliani and Steindel
(1977), and Steindel (1977 and 1981) for discussions of the conceptual issues involved in using a
total income measure in a consumption model including wealth.
12
according to the PIH, ut is the discounted value of expected future labor income increases,
implying that the error term will typically be serially correlated and correlated with Wt and Yt.
This endogeneity--or correlation between ut and included variables--can lead to biased estimates
of the parameters ", $ and *. However, under the maintained hypothesis that C, W, and Y are I(1)
with a single cointegrating relationship among them, ", $ and * can be estimated
“superconsistently” by OLS, implying that point estimates will be robust to the presence of
endogeneity of the regressors (see Hamilton [1994], ch. 19). In this case, the permanent income
model can be estimated without requiring a measure of expected future income. By contrast, if
there is not a single cointegrating relationship among C, W, and Y, OLS estimation of ", $, and *
is no longer robust to the presence of regressor endogeneity, and the standard errors-in-variables
procedure calls for the use of instrumental variable (IV) estimation. If, additionally, C, W, and Y
are all I(1), IV estimation must be applied to the first-differenced values to avoid spurious
regression.
A third consideration concerns hypothesis tests about the cointegrating relation in (1).
Even if ", $, and * can be estimated superconsistently by OLS, the resulting point estimates will
typically have non-standard distributions.10 Stock and Watson (1993) suggest a simple method for
correcting the standard errors by augmenting the cointegrating regression with leads and lags of
the first difference of each right-hand-side variable. This “dynamic” OLS procedure yields the
same estimates of $ asymptotically, as does standard OLS. We use this procedure below.
Finally, because the theory used to derive (2) assumes that C consists of goods which
10
These non-standard distributions for the coefficient estimates arise from the possibility of
nonzero correlations between {)Wt, )Yt} and the error term ut (see Hamilton [1994], ch. 19).
13
depreciate entirely within the period, we use as our measure of consumption, personal
consumption expenditures on nondurables and services, excluding shoes and clothing.11 This
consumption series is scaled up so that its sample mean matches the sample mean of total
consumption.12
Taken together, these econometric considerations suggest the following empirical
approach. We begin with diagnostic tests of the time series properties of C, Y, and W. This
preliminary analysis includes unit root tests to determine whether each variable may be
characterized as first-order integrated. If unit root tests indicate that these variables may be I(1),
we can then perform tests for cointegration among the three variables. Tests for cointegration
include both residual based tests (designed to distinguish a system without cointegration from a
system with at least one cointegrating relationship), and tests for cointegrating rank (designed to
estimate the number of cointegrating relationships). If evidence supports the hypothesis that C, Y,
and W are all I(1) with a single cointegrating relationship, then the specification in (1) can be used
to obtain a consistent estimate of $ by OLS. If, instead, C, Y, and W are all I(1) but the variables
are not cointegrated, consistent estimates of $ require first differencing the variables and using IV
estimation.
In the next section we discuss diagnostic tests on the order of integration of each variable,
and on the degree of cointegration among the variables. We find that the results of some of these
11
The older literature referenced also often drew this distinction as well. Our estimation
used total consumer spending since that may be more directly related to forecasting and policy
concerns.
12
The ratio of nondurables and services to total personal consumption expenditure has
experienced very little change over the last forty five years, declining only slightly from about 92
percent of total in 1947 to about 88 percent of total in 1998.
14
tests--particularly the cointegration tests--are inconclusive. Instead of taking a firm stand on the
degree of cointegration among the variables, we employ several specifications for estimating the
relationship between consumption and wealth that would be appropriate under alternative
assumptions about the extent of cointegration. Using each of these specifications, we investigate
whether a reasonable empirical relationship between consumption and wealth can be found.
Empirical Results
We begin with tests designed to determine whether each variable contains a unit root.
Table 2 presents Dicky-Fuller tests for the presence of a unit root in C, Y, and W. The DickyFuller procedure tests the null hypothesis of a unit root against the alternative hypothesis that the
series is stationary around a trend. Although standard Dicky-Fuller tests presume a first order
autoregressive (AR(1)) structure, some allowance may be needed for possible additional serial
correlation in the time series. Thus, the table presents “Augmented” Dicky-Fuller test statistics
which allow for higher-order autoregressive structures in addition to the standard tests based on a
first order lag structure.
As the table shows, the tests statistics for C, Y, and W fall within the 95 percent
confidence region are therefore consistent with the hypothesis of a unit root in those series.13 The
evidence suggests that C, Y, and W are well characterized as I(1) processes. The second panel of
Table 2 shows that the log values of these variables can also be well characterized as I(1)
processes.
13
There is one case for which the test statistic for consumption is right on the boarder of
the 5% significance level. This occurs for the level of consumption, when we assume four lags; in
this case the critical value is -3.45, less in absolute terms than the value of the test statistic, equal
to -3.478. By contrast, we never reject the null hypothesis of a unit root for the log of
consumption.
15
Since the results in Table 2 suggest that each variable follows an I(1) process, we can now
carry out tests for cointegration. Table 3 reports statistics corresponding to the Phillips-Ouliaris
(1990) residual based cointegration tests. This test is designed to distinguish a system without
cointegration from a system with at least one cointegrating relationship.14 The approach applies
the augmented Dicky-Fuller unit root test to the residuals of (2).15 If the variables in (2) are
cointegrated, the error term is stationary, and we may reject the hypothesis of a unit root in ut.
The table shows both the Dicky-Fuller t-statistic from the residual based unit root test, and the
relevant 5 and 10 percent critical values. As the table shows, these tests do not reject the null
hypothesis of a unit root in ut, and therefore do not establish evidence in favor of cointegration.
Next we consider testing procedures suggested by Johansen (1988, 1991) that allow the
researcher to estimate the number of cointegrating relationships. This procedure presumes a pdimensional vector autoregressive model with k lags and Gaussian errors, where p corresponds to
the number of stochastic variables among which the investigator wishes to test for cointegration.
For the application above, p = 3. The procedure allows one to test the null hypothesis of one
cointegrating relationship against the alternative that there are two or three cointegrating
relationships, the latter conforming to the hypothesis that all series are trend-stationary. The
critical values obtained using the Johansen approach depend on the trend characteristics of the
data.
14
Phillips and Ouliaris (1990) tabulate critical values for the augmented Dickey-Fuller t test
applied to residuals of a cointegrating equation with up to five variables.
15
When unit root tests are applied to the estimated residuals of a cointegrating
relationship, the critical values depend on whether a constant and/or a time trend are included in
the regression; Table 3 reports results assuming there is both a constant and a linear time trend
present.
16
The Johansen procedure provides two tests for cointegration: under the null hypothesis,
H0, that there are exactly r cointegrating relations, the ‘Trace’ statistic supplies a likelihood ratio
test of H0 against the alternative, HA, that there are p cointegrating relations, where p is the total
number of variables in the model. We report this test-statistic under the columns headed <Trace’ in
the tables below. A second approach tests the null hypothesis of r cointegrating relations against
the alternative of r+1 cointegrating relations. We report this test-statistic under the columns
headed ‘L-max’.
The Johansen procedure applies maximum likelihood to an vectorautoregressive (VAR)
representation for the series being investigated, hence the test procedure depends the number of
lags assumed in the VAR structure. Since it is difficult to determine the appropriate lag structure
for this procedure, the table presents the test results obtained under a number of lag
assumptions.16
Like the residual based tests for cointegration, the Johansen tests fail to establish evidence
of a single cointegrating relationship among the variables in (2). Moreover, the results are not
sensitive to the lag specification in the model. Table 4 shows that, although we cannot reject the
null hypothesis of one cointegrating relationship against the alternative that all variables are trend
stationary (Trace statistic, middle row of each panel), or against the alternative that there are two
cointegrating vectors (L-Max statistic, middle row of each panel), we also cannot reject the null
16
Tests for the appropriate lag length in this case require estimation of the autoregressive
model in its vector error correction form. This in turn requires the researcher to specify the
number of cointegrating relationships in the error correction model. Since the number of
cointegrating relationships cannot be determined without first using the Johansen procedure
(which itself requires an assumption about lag length), we therefore perform the Johansen
procedure under several assumptions about the number of lags in the VAR.
17
hypothesis that there is no cointegration against the alternative that all variables are trend
stationary, or against the alternative that there is a single cointegrating relation (top row of each
panel) Similarly, we cannot reject the hypothesis that there are two cointegrating vectors against
the alternative that there are three (bottom row of each panel). Thus, the data do not provide
evidence of a single cointegrating relation among C, W, and Y.
The cointegration test results weaken the evidence in favor of the permanent income
hypothesis since the model implies the existence of a single cointegrating relationship.17 Although
the test results do not provide evidence in favor of cointegration, they also do not provide
evidence against cointegration, and so the findings do not imply a formal rejection of the model.
In practice, cointegration may be very difficult to formally establish simply because, in finite
samples, every cointegrated process can be arbitrarily well approximated by a non-cointegrated
process (Campbell and Perron [1991]).
In summary, preliminary diagnostic tests suggest that each variable in (2) can be
characterized as nonstationary, and first order integrated, or I(1). Diagnostic tests about the order
of cointegration, however, are less conclusive. Since the appropriate empirical procedure
depends, not only upon whether the variables are nonstationary, but also upon whether the
variables contain a single cointegrating relationship, we employ empirical specifications that
would be suitable under a variety of assumptions.
We begin by estimating equation (2) using OLS with the variables in either first differences
or in log first differences. Recall that unit root tests suggest each variable is nonstationary and
integrated of order one. If the variables are not cointegrated, then first differencing eliminates the
17
This statement assumes that labor income is I(1).
18
possibility of finding a purely spurious correlation between wealth and consumption. Tables 5 and
6 present the results for specifications that use the first difference of variables, and the log first
difference, respectively.18
We then move on to take into account the possibility of endogenous regressors: we
estimate equation (2) on the first differenced variables using IV estimation. This specification
would be appropriate in the presence of endogenous regressors if the variables are not be
cointegrated. These results are given in Tables 7 through 10.
Finally, our most theoretical specification assumes that the PIH is correct, so that there is
one cointegrating vector describing the relationship among C, Y, and W given in equation (2).
Note that if the PIH is true, ut is a present discounted value of future labor income growth--and
will therefore be correlated with the right hand side variables--but in this case, the parameter
vector can be estimated superconsistently by OLS. As already noted, even though this procedure
yields consistent point estimates, statistical inference cannot be carried out using the conventional
standard errors since the resulting parameter estimates have non-standard distributions. Thus, we
instead use the Stock and Watson (1993) dynamic OLS which includes leads and lags of the right
hand side variables as additional regressors.19 This output is contained in Table 11.
18
In Table 5, we perform OLS regressions in first differences to provide a basis of
comparison with earlier literature. In most of our analysis, however, we use log first differences
instead of level first differences. Aggregate time series on consumption and income appear to
follow loglinear processes since the mean change of the series and the variance of the innovation
of the first difference grow with the level of the series. See Campbell and Mankiw (1989). Note
however, when variables are expressed in logs, the coefficient on wealth no longer can be
interpreted as the marginal propensity to consume out of wealth, as defined above.
19
The Stock-Watson dynamic OLS procedure for estimating the coefficients in (2) gives
the same parameter estimates, asymptotically, as conventional OLS. In finite samples, however,
the two procedures could produce different estimates. In the Table, we report the point estimates
19
Table 5 shows the results of estimating equation (2) with the variables in first differences.
Although each table reports the estimate of both $, the coefficient on Wt, and *, the coefficient on
Yt, we focus our discussion on $, the parameter of interest.
As panel A of Table 5 shows, the parameter, $, is estimated to be around 0.01 in the full
sample, a small magnitude but statistically significant. The coefficient is about the same in the
earlier two subsamples, but drops to essentially zero in the later subperiod and is not statistically
different from zero.
Although equation (2) establishes the formal relationship linking contemporaneous values
of C, Y, and W that is implied by the PIH, this specification may be too restrictive to be useful as a
description of actual consumption dynamics. The series on personal consumption expenditure is
quite persistent and may display much richer dynamics than that implied the model’s solution
given in (2). A straightforward extension of the model that has become common for providing a
better fit with the data, assumes that consumption is partially adjusted in each period to eliminate
a fraction of the gap between last period’s consumption and its current optimal level.20 This
extension requires that we include the one-period lagged value of the dependent variable on the
right hand side of the estimating equation. Panel B of Table 5 therefore includes the lagged
dependent variable on the right-hand side as an additional regressor. This inclusion has only one
obtained using dynamic OLS since we also use this output to correct the standard errors. See
Hamilton (1994, ch. 19).
20
See Clarida, Galí, and Gertler (1997). We follow these authors by assuming that there
are costs to adjusting the level (or log level) of consumption. This assumption implies that the
lagged level (log level) of consumption should appear on the right hand side when the regression
in equation (2) is run in levels (logs), or that the lagged first difference (log difference) of
consumption should appear as an additional explanatory variable when the regression is run in
first (log) differences.
20
notable impact on the results reported in panel A: the marginal propensity to consume out of
wealth is no longer significant at the five percent level in the middle subperiod.
Table 6 gives results analogous to those in Table 5, but uses log differences instead of first
differences in levels. For the full sample period, the estimate of $ is about 0.05, while for the
subperiod extending from the first quarter of 1968 to the fourth quarter of 1982, the coefficient
estimate is about 0.06. These are the only periods of estimation for which the estimate is
statistically significant at the five percent level. Results do not vary much in panel B of Table 5
where the lagged value of the dependent variable is included as an additional regressor; in either
panel, there does not appear to be a stable relationship between consumption and wealth over
subsamples of the data.
As already noted, if the variables in (2) are not cointegrated but each variable is
individually I(1), OLS is not consistent and IV estimation must be applied with variables in first
differences. In performing instrumental variable estimation, we must first decide on appropriate
instruments. Appropriate instruments are those that are both correlated with the explanatory
variables and uncorrelated with the error term. To begin, we use lags of the right-hand-side
variables as instruments. These variables would be appropriate as instruments if we interpret the
error term, ut, as a “consumption innovation”, where consumption depends only on fundamentals
and a shock, so that the error term is uncorrelated with any variable dated at t-1 or before.21 As an
alternate instrument, we compute an average corporate tax rate variable (TAX), and include its
21
This assumption is not consistent with the PIH, since that model implies that the error
term consists of expected future income growth, and is therefore stationary, but serially
correlated. Thus, this specification only provides an atheoretical benchmark. We relax this
assumption below.
21
current and past values in the set of instruments. This variable may be reasonable instrument
because corporate tax rates directly affect the profitability of firms (and therefore the value of
equity), but are less likely to influence the consumption decisions of households. Thus, the
instrument is likely to be correlated with Wt (and possibly Yt) but uncorrelated with ut.22 We show
below that both Yt and Wt are well forecast by TAX in the full sample.23 The results in Tables 7
and 8 were obtained using lagged values of the right hand side variables and TAX as instruments;
output presented in tables 9 and 10 were obtained from regressions using only TAX and its lags
as instruments.
Compared to the results obtained with OLS estimation in Tables 5 and 6, the results in
Table 7 displays less evidence of a significant wealth effect. In only one subperiod do we find the
point estimate of $ significant at the five percent level (panel A). Moreover this period is not one
of those subperiods for which we previously found a consistently significant wealth effect over
several specifications using OLS estimation: in Table 7, $ is statistically significant at the 5 percent
level in the period from the first quarter of 1953 to the fourth quarter of 1967, but not in the full
sample or in the other subsamples. Note also that the overall magnitude of the point estimates is
not robust across the two forms of estimation; estimates presented in Table 7 indicate that $ may
be as high as 0.09, whereas the analogous point estimate given in Table 5 is around 0.01.
One possible reason the estimates obtained with the OLS procedure diverge from those
22
We also considered government expenditures as an instrument for aggregate output, but
found that it had virtually no explanatory power in the first stage regressions.
23
In fact, lagged values of the right hand side variables have far less predictive power for
either the first difference, or the log first difference, in wealth than does TAX; thus we always
include TAX in the instrument set. Tables 9 and 10 show the results when the lagged explanatory
variables are eliminated from the instrument set.
22
obtained with the IV procedure is that the instruments could have weak predictive power for the
right-hand-side variables. Panel B of Table 7 gives some indication of how well the instruments
predict the right hand side variables in each subperiod. As the table shows, the instruments are
jointly significant at better than the five percent level over the full sample, and at better than the
10 percent level in the last two of the three subsamples. By contrast, the instruments have very
weak predictive power for the right-hand-side variables over the subperiod 1953 first quarter to
1967 fourth quarter--the only subsample for which we obtain a significant wealth effect. Thus, the
bulk of the predictive power displayed by the instruments is derived from subsamples of the data
for which wealth shows no significant relation to consumption. Since instrumental variable
estimates can be very misleading when the instruments have weak forecasting power for the righthand-side variables, the significant wealth effect found in the first subsample must be viewed with
skepticism.24
Table 8 shows results obtained using the same instruments as in Table 7, but including the
one-period lagged dependent variable as an explanatory variable.25 The resulting estimate of $ in
the first subperiod is similar to that obtained in Table 7, when the lagged dependent variable was
excluded from the equation, but it is no longer statistically significant at the 5 percent level.
24
We also conducted tests of the over-identifying restrictions implied by each IV
regression. An LM test statistic is formed by regressing the residual from the IV regression on the
instruments, and taking T times R2 from this regression, where T is the sample size. This statistic
is distributed P2 with K - N degrees of freedom, where K is the number of instruments and N is the
number of independent variables. The overidentifying restrictions were not rejected at the 5
percent critical level any subperiods for any IV specification, though this acceptance of the
restrictions was marginal in the results presented in Table 8 when using the full sample, and the
subsample from 1968 first quarter to 1982 fourth quarter.
25
The lagged dependent variable is included as both a regressor and an instrument.
23
Unlike the results presented in Table 7 there are no estimation periods for which the wealth
coefficient is statistically significant at the five percent level. In the full sample, the point estimate
of $ is now statistically significant at the ten percent level, equal to about 0.07. Note, however,
the first stage results in panel B indicate that the instruments only have significant predictive
power for the explanatory variables in the full sample.
The procedure used to obtain the results in Tables 7 and 8 required the assumption that
consumption is solely a function of fundamentals and a shock, implying that the error term is
uncorrelated with explanatory variables dated at t-1 or before. Nevertheless, there are plausible
circumstances under which this assumption would not be reasonable. As a notable example, ut will
likely be correlated with the included variables if the PIH is true, since in that case the error term
consists of expected future income growth. If income growth is serially correlated, lagged values
of income and wealth will be correlated with ut.
We next present results from IV estimation when we include only the average corporate
tax rate variable (TAX) and its lags in the instrument list. Even if the PIH is true, this instrument
may be correlated with Wt (and possibly Yt) but is less likely to be correlated with ut than are
lagged explanatory variables.26 Tables 9 and 10 present these results (with variables in log first
differences) using current and lagged values of TAX as instruments.
The table shows that the coefficient on wealth, $, is not statistically significantly different
from zero in the full sample estimation, or in the subperiods 1968 first quarter to 1982 fourth
quarter, and 1983 first quarter to 1997 fourth quarter. Note that the instruments have significant
26
We also considered government expenditures as an instrument for aggregate output, but
found that it had virtually no explanatory power in the first stage regressions. Thus, we dropped it
from the instrument list.
24
predictive power for wealth in each of these periods. By contrast, estimation over the first
subperiod, extending from the first quarter of 1953 to the last quarter of 1967, yields a significant
coefficient on wealth, but the first stage results do not reveal a significant correlation between the
instruments wealth. The results are very similar in Table 10 where we include the lagged
dependent variable as an additional explanatory variable. In short, the IV results do not yield a
significant wealth effect over any subperiod of the data for which the instruments have significant
predictive power for the right hand side variables.
We now turn to estimating our most theoretical specification, that which would be
appropriate if the PIH were valid. Given that the evidence in Table 2 supports an I(1)
characterization for C, W, and Y, the PIH implies that the variables also have a cointegrating
relationship given by equation (2). As already noted, OLS estimation can then be applied with
variables in levels yielding consistent estimates of $. Table 11 presents the results of estimating
(1) using the dynamic OLS procedure discussed above, with the variables in levels, over the full
sample period.27
The point estimate of the marginal propensity to consume out of wealth, $, is about 0.03
and statistically significant at the ten percent level. This figure is slightly smaller than found in the
early life cycle literature. Note also that Tables 5 through 10 show that estimates of $ obtained
27
We apply the dynamic OLS to equation (2) in order to correct the standard errors for a
possible correlation between the error term and the first difference of the right hand side variables
(See Hamilton [1994]). This procedure is only valid asymptotically, however, so that reliable
estimates of the marginal propensity to consume, or its standard error, cannot be obtained over
small subsamples of the data. Consequently, we only perform dynamic OLS over the full sample
period. Moreover, no theory has currently been developed to asymptotically correct the standard
errors when there are lagged dependent variables appearing as right hand side variables; thus we
do not include Ct&1 as an additional explanatory variable when performing this form of estimation.
25
from other empirical specifications are smaller in the last subperiod than they are in the first
subperiod, suggesting that the marginal propensity to consume out of wealth may be declining in
recent years. We investigated this possibility more formally by plotting estimates of $ taken from
a rolling regression over the period extending from the first quarter of 1987 to the fourth quarter
of 1997.28 The results are similar to those presented in Chart 1 regardless of whether dynamic
OLS or standard OLS estimation is used: the marginal propensity to consume out of wealth rose
from a low of about 0.02 in the beginning of 1987, to about .034 in the early 1990s, but has
declined precipitously since 1995 and has fallen back to 0.02 in 1997. Thus, the most recent
period of rapid growth in stock market wealth is also a period during which households appear to
be consuming a declining amount out of any given increase in wealth.
In summary, the results presented above do not uncover a robust wealth effect on
consumption. The degree to which financial wealth is correlated with consumer expenditure varies
according to what estimation technique is employed, what instruments are used, and what
variables are included on the right hand side of our estimating equation. Results using OLS
estimation generally suggest that the wealth effect is small, not stable across subperiods of the
data, and declining in recent years. Indeed, in all of our OLS regressions, the correlation between
financial wealth and consumer expenditure is not statistically different from zero in data after the
first quarter of 1983. Instrumental variables estimation does not produce dramatically different
results. In particular, IV estimation typically does not reveal a robust wealth effect in any
subperiod of the data for which the instruments have significant predictive power for the right
Estimates of $ in the figure are obtained by first estimating equation (2) over the period
1953 first quarter to 1987 first quarter, and then incrementally adding one data point on the end
of the sample and reestimating.
28
26
hand side variables.
Conclusion
This paper investigates the relationship between aggregate consumer expenditure and financial
wealth. Our results show that the correlation between wealth and consumption appears to be
declining in recent years, and is not stable across subsamples of the data.
The question of how much a large movement in financial wealth would affect consumer
expenditure is an important policy issue. This issue has become one of immediate concern due to
the widespread belief that U.S. stock markets have recently surged to levels that may be
inconsistent with market fundamentals, and therefore unsustainable over the long run. Monetary
policy makers who seek to dampen large fluctuations in output and consumer prices need to be
informed about how much a significant swing in the value of financial wealth could influence real
variables. At one extreme, some commentators have suggested that a prolonged downturn in
stock prices could so depress consumer spending as to result in a recession (for example, The
Economist [1998]).
Despite the pressing importance of these issues, and despite the fact that practitioners and
forecasters continue to base their predictions on a presumed correlation between wealth and
consumption, virtually no work has set out to quantify the relationship between wealth and
consumer expenditure since several authors undertook this task in early life-cycle consumption
research. In this paper, we provide an updated estimate of how much a change in the value of
wealth might affect consumer expenditure.
The evidence presented here provides little support for the hypothesis that we have a good
27
idea of the effect of any given change in wealth on consumer demand-- the relationship between
wealth and consumer expenditure is not stable over time.
Why have we failed to uncover a stable wealth effect? One distinct possibility is that we
have not taken into account all the major factors impacting the interaction between consumer
spending and the stock market. For instance, one important missing factor is uncertainty about
the market’s rate of return. Merton (1971) described the theoretical relationship between the
levels of consumer spending and wealth in the presence of uncertainty about the rate of return on
one asset; while the analytical formula he derived is quite complex and not susceptible to a simple
interpretation, his work does suggest that the marginal propensity to consume from wealth is
sensitive to changes in perceptions of the volatility of the market. It is, of course, very reasonable
to believe that market valuation is also sensitive to volatility. Failing to correct for changes in
volatility could lead to fluctuating estimates of the marginal propensity to consume out of market
changes. Unfortunately, it is not clear how Merton’s steady-state model could be extended to a
dynamic framework (including uncertainty about future labor income as in the PIH) nor how
precisely perceived market volatility would be measured, though data from derivatives markets is
an obvious possibility.29
We also would like to note that we are addressing the pure wealth effect--the effect of any
given or observed change in the value of the stock market on consumer spending. Much of the
29
Another missing factor which may suggest itself are changes in the structure of stock
market holdings from direct household ownership to pension fund and mutual fund holdings.
Poterba and Samwick (1995) found that such corrections were of little help in isolating a clear
wealth effect. Our view is that the change in ownership patterns has been rather gradual (see
Steindel (1993) as well as Poterba and Samwick ), suggesting that this mechanism--however,
specifically, it may affect consumer behavior--is unlikely to account for the sometimes abrupt
changes we have observed in the estimated marginal propensities.
28
earlier literature on the wealth effect dealt with changes in the stock market as a transmission
mechanism for monetary policy (most notably, Modigliani [1971]). In that literature, the
assumption is that the force moving the stock market are changes in the rate of return induced by
monetary policy. The theoretical and empirical implications of such changes on consumer
spending are different than the generic stock market change we examined in our empirical work.
While our purely technical critique of the earlier consumption literature also applies to the policy
literature, our empirical results do not necessarily suggest that the consumption effect of a policyinduced change in the value of the stock market is volatile or even different than the earlier
results--we simply didn’t address that point.
How important is the stock market effect on consumption? Our results suggest that this
question is very difficult to answer. Although existing consumer theory provides a framework for
estimating the structural relationship between wealth and consumption, our estimates reveal no
stable association between these variables. The instability in our parameter estimates suggests that
forecasts of consumer spending which rely on wealth effects are likely to be unreliable. One
possible reason for the instability we find is that existing theory provides us with the wrong null
hypothesis. In particular, because existing theory provides us with no well developed explanation
of stock market behavior, we may not be able to capture truly structural effects of a “wealth
shock” on consumption. Rather than answering the question posed above, our findings bring into
question the notion that observations of aggregate stock market movements--independent of any
informed view of the causes of the market’s move--can provide reliable information about the
current and future course of consumer spending.
29
Data Appendix
This appendix provides a description of the data used in the empirical analysis.
Consumption
Consumption is measured as either total personal consumption expenditure, or expenditure on
nondurables and services excluding shoes and clothing. The quarterly data seasonally adjusted at
annual rates (SAAR), in billions of chain-weighted 1992 dollars.
Source: Bureau of Economic Analysis (BEA).
Labor Income
Labor income is defined as wages and salaries plus transfers minus personal contributions for
social insurance. The quarterly data are in current dollars. The nominal data is deflated by the
PCE chain-type price deflator. The components are from the National Income and Product
Accounts.
Price Deflator
PCE chain-type price deflator (1992=100), seasonally adjusted (SA)
Source: BEA.
Population
A measure of population is created by dividing real total disposable income by real per capita
disposable income. Both measures of income is in SAAR and chain-weighted 1992 dollars (total
income is in billions of chain-weighted $1992).
Source: BEA
30
Wealth
Total wealth is household net wealth in billions of current dollars.
Source: The quarterly data is provided by the Board of Governors of the Federal Reserve.
Tax
Tax is the tax liability of corporations as a share of their profits (profits tax liability/corporate
profits). Profits tax liability is SAAR, in billions of current dollars. Corporate profits is defined as
profits with inventory valuation and capital consumption adjustment. The quarterly data is SAAR
and billions of current dollars.
Source: BEA.
31
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August 10, p.1
34
Table 1: OLS Estimation
Model: Ct = ' *iYt-i + ' >i SWt-i + ' µ i NWt-i + ,t
3
4
i=0
i=1
4
i=1
Estimation Period
1
1953:1-1997:4
2
1953:1-1975:4
3
1976:1-1985:4
4
1986:1-1997:4
5
1953:1-1967:4
6
1968:1-1982:4
7
1983:1-1997:4
Income*
0.731
(0.067)
0.711
(0.059)
0.568
(0.195)
1.015
(0.077)
0.684
(0.091)
0.832
(0.141)
0.822
(0.074)
Stock Wealth*
0.040
(0.009)
0.026
(0.010)
0.106
(0.041)
0.021
(0.011)
0.030
(0.018)
0.023
(0.019)
0.042
(0.010)
Non-Stock
Wealth*
0.038
(0.017)
0.043
(0.015)
0.069
(0.048)
-0.027
(0.017)
0.049
(0.020)
0.012
(0.036)
0.016
(0.018)
Serial Correlation
Coefficient
0.937
(0.030)
0.781
(0.090)
0.937
(0.069)
0.755
(0.097)
0.800
(0.094)
0.886
(0.069)
0.809
(0.091)
Standard Error
of Regression
70.7
59.8
86.7
65.7
41.4
84.7
76.2
Sum of Squared
Residuals of
Regression
830835
279012
202961
150994
78739
336836
272807
* Real per-capita terms.
Notes: Standard errors in parentheses. Y is personal income, SW is stock market wealth, NW is non-stock market wealth.
35
Table 2: Dickey-Fuller Test for Unit Roots
Dickey-Fuller t-Statistic
Lag=1
Lag=2
Lag=3
Lag=4
Total Wealth*
0.082
-0.697
-0.617
-0.779
Labor Income*
-1.564
-1.588
-1.906
-2.184
Consumption (excl
shoe & clothes)*
-1.939
-2.572
-2.718
-3.478
Dickey-Fuller t-Statistic
Lag=1
Lag=2
Lag=3
Lag=4
Log (Total Wealth*)
-2.417
-3.067
-2.880
-3.077
Log (Labor Income*)
-0.889
-1.183
-1.330
-1.290
Log (Consumption excl shoe &clothes*)
-0.363
-0.812
-0.944
-1.280
*Real, per-capita terms. The model includes a time trend.
Table 3: Phillips-Ouliaris Test for Cointegration
Dickey-Fuller t-Statistic
Critical Values
Lag=1
Lag=2
Lag=3
Lag=4
5% Level
10% Level
No Trend
-1.019
-0.969
-1.242
-1.491
-3.77
-3.45
Trend
-0.837
-0.719
-0.957
-1.203
-4.16
-3.84
Note: Dickey-Fuller test statistic applied to the fitted residuals from the cointegrating regression.
Using consumption for nondurables and services, excluding shoes and clothes, as the dependent
variable.
36
Table 4A: Cointegration Test: I(1) Analysis with Unrestricted Constant and
Trend in Cointegration Space
Endogenous Variable: Total Wealth, Labor Income, Consumption
(Nondurables and Services, excl. Shoes & Clothing)
Lag in VAR-model=1
L-max
Trace
H0 = r
14.52
22.68
0
5.69
8.16
1
2.47
2.47
2
L-max
Trace
H0 = r
8.56
17.10
0
4.84
8.53
1
3.69
3.69
2
L-max
Trace
H0 = r
8.70
15.16
0
3.92
6.46
1
2.54
2.54
2
L-max
Trace
H0 = r
10.89
18.19
0
4.86
7.30
1
2.44
2.44
2
Lag in VAR-model=2
Lag in VAR-model=3
Lag in VAR-model=4
37
Table 4B: Cointegration Test: I(1) Analysis with Unrestricted Constant
Endogenous Variable: Total Wealth, Labor Income, Consumption
(Nondurables and Services, excl. Shoes & Clothing)
Lag in VAR-model=1
L-max
Trace
H0 = r
8.03
14.46
0
4.05
6.42
1
2.37
2.37
2
L-max
Trace
H0 = r
4.92
8.97
0
3.91
4.05
1
0.14
0.14
2
L-max
Trace
H0 = r
4.27
6.90
0
2.61
2.63
1
0.02
0.02
2
L-max
Trace
H0 = r
5.03
7.71
0
2.44
2.68
1
0.24
0.24
2
Lag in VAR-model=2
Lag in VAR-model=3
Lag in VAR-model=4
38
Table 5A: Effect of Wealth on Consumption, OLS
Model: ÎCt = " + $ÎWt + *ÎYt + ,t
Sample Period
$
*
1953:1-1997:4
0.009*
(2.484)
0.300*
(3.027)
1953:1-1967:4
0.009*
(2.120)
0.394*
(6.916)
1968:1-1982:4
0.014*
(2.873)
0.407*
(3.859)
1983:1-1997:4
0.003
(0.743)
0.192
(1.595)
Table 5B: Effect of Wealth on Consumption, OLS
Model: ÎCt = " + $ÎWt + *ÎYt + (ÎCt-1 + ,t
Sample Period
$
*
1953:1-1997:4
0.009*
(2.794)
0.267*
(3.202)
1953:1-1967:4
0.009**
(1.717)
0.395*
(5.182)
1968:1-1982:4
0.014*
(3.076)
0.355*
(3.078)
1983:1-1997:4
0.002
(0.808)
0.199**
(1.879)
*Coefficients significant at the 5% or better level.
**Coefficients significant at the 10% or better level.
39
Table 6A: Effect of Wealth on Consumption, OLS
Model: ÎlnCt = " + $Î lnWt + *Î lnYt + ,t
Sample Period
$
*
1953:1-1997:4
0.051*
(3.290)
0.291*
(4.650)
1953:1-1967:4
0.051**
(1.891)
0.305*
(6.755)
1968:1-1982:4
0.066*
(3.030)
0.372*
(3.812)
1983:1-1997:4
0.018
(0.912)
0.173
(1.618)
Table 6B: Effect of Wealth on Consumption, OLS
Model: ÎlnCt = " + $Î lnWt + *ÎlnYt + (Î lnCt-1 + ,t
Sample Period
$
*
1953:1-1997:4
0.055*
(3.551)
0.256*
(4.392)
1953:1-1967:4
0.047
(1.512)
0.321*
(5.047)
1968:1-1982:4
0.068*
(3.012)
0.318*
(3.001)
1983:1-1997:4
0.015
(0.968)
0.180**
(1.953)
*Coefficients significant at the 5% or better level.
**Coefficients significant at the 10% or better level.
40
Table 7A: Effect of Wealth on Consumption from Instrumental Variable
Regressions
Model: )lnCt = " + $ )lnWt + * )lnYt + ,t
Sample Period of IV
Regression
$
*
1953:1-1997:4
0.061
(1.399)
0.442*
(4.703)
1953:1-1967:4
0.095*
(2.107)
0.455*
(5.317)
1968:1-1982:4
0.037
(1.049)
0.496*
(5.627)
1983:1-1997:4
0.069**
(1.866)
-0.015
(-0.265)
Notes: t-statistic in parentheses. Instruments: Constant, )lnWt{1 to 3}, Tax{0 to 3} and )lnYt{1
to 3}
Table 7B: First Stage Regressions of Included Variables on Instruments
Sample Period of IV
Regression
Adjusted R2 from regressing
total wealth on instruments
Adjusted R2 from regressing
labor income on instruments
1953:1-1997:4
0.100*
0.128*
1953:1-1967:4
0.025
0.351*
1968:1-1982:4
0.122**
0.373*
1983:1-1997:4
0.136**
0.135**
*Instruments jointly significant at the 5% or better level.
41
Table 8A: Effect of Wealth on Consumption from Instrumental Variable
Regressions
Model: )lnCt = " + $ )lnWt + * )lnYt + ( )lnCt-1 + ,t
Sample Period of IV
Regression
$
*
1953:1-1997:4
0.072**
(1.794)
0.332*
(3.390)
1953:1-1967:4
0.094**
(1.832)
0.509*
(4.912)
1968:1-1982:4
0.046**
(1.934)
0.370*
(4.648)
1983:1-1997:4
0.041
(1.272)
0.021
(0.386)
Notes: t-statistic in parentheses. Instruments: Constant, )lnWt{1 to 3}, Tax{0 to 3}, )lnYt{1 to
3} and )lnCt-1{1}.
Table 8B: First Stage Regressions of Included Variables on Instruments
Sample Period of IV
Regression
Adjusted R2 from regressing
total wealth on instruments
Adjusted R2 from regressing
labor income on instruments
1953:1-1997:4
0.095*
0.156*
1953:1-1967:4
0.021
0.356*
1968:1-1982:4
0.110
0.386*
1983:1-1997:4
0.119**
0.117**
*Instruments jointly significant at the 5% or better level.
42
Table 9A: Effect of Wealth on Consumption from Instrumental Variable
Regressions
Model: )lnCt = " + $ )lnWt + * )lnYt + ,t
Sample Period of IV
Regression
$
*
1953:1-1997:4
0.009
(0.173)
0.439*
(3.294)
1953:1-1967:4
0.478*
(2.341)
0.206
(1.261)
1968:1-1982:4
0.049
(1.060)
0.589*
(4.277)
1983:1-1997:4
-0.029
(-0.269)
0.339
(0.789)
Notes: t-statistic in parentheses. Instruments: Constant and Tax{0 to 3}.
Table 9B: First Stage Regressions of Included Variables on Instruments
Sample Period of IV
Regression
Adjusted R2 from regressing
total wealth on instruments
Adjusted R2 from regressing
labor income on instruments
1953:1-1997:4
0.108*
0.064*
1953:1-1967:4
-0.011
0.233*
1968:1-1982:4
0.174*
0.206*
1983:1-1997:4
0.200*
0.014
*Instruments jointly significant at the 5% or better level.
43
Table 10A: Effect of Wealth on Consumption from Instrumental Variable
Regressions
Model: )lnCt = " + $ )lnWt + * )lnYt + ( )lnCt-1 + ,t
Sample Period of IV
Regression
$
*
1953:1-1997:4
0.016
(0.339)
0.381*
(2.709)
1953:1-1967:4
0.421*
(2.228)
0.151
(0.700)
1968:1-1982:4
0.045
(1.019)
0.571*
(4.076)
1983:1-1997:4
0.072
(0.738)
-0.067
(-0.219)
Notes: t-statistic in parentheses. Instruments: Constant, Tax{0 to 3} and )lnCt-1{1} .
Table 10B: First Stage Regressions of Included Variables on Instruments
Sample Period of IV
Regression
Adjusted R2 from regressing
total wealth on instruments
Adjusted R2 from regressing
labor income on instruments
1953:1-1997:4
0.103*
0.141*
1953:1-1967:4
0.008
0.327*
1968:1-1982:4
0.159*
0.253*
1983:1-1997:4
0.187*
0.001
*Instruments jointly significant at the 5% or better level.
44
Table 11: Dynamic OLS Estimates of MPC out of Wealth and Labor Income
Model: Ct = " + $1 Wt + $2 )Wt-1 + $3 )Wt + $4 )Wt+1 + *1Yt + *2 )Yt-1 + *3 )Yt +
*4 )Yt+1 + 81T + ,t
Sample Period
$1
*1
1953:1-1997:4
0.029**
(1.893)
0.516*
(3.923)
*Significant at the 5% or better level; **Significant at the 10% or better level.
Notes: T denotes a linear time trend. The t-statistics reported in parenthesis have been corrected
for the possibility of nonzero correlations between ut and {)Wt, )Yt }.
45
Chart 1
Marginal Propensity to Consume
From Disposable Income
Ten Year Samples
1.4
1.4
1.2
1.2
..'
.... ...
'•
1
! \._
0.8
......... -· -··············
··---- .... -··
0.6
1
\ ...................
·······--
!
·-------·
..
,.-----
0.8
······....................•
....
,·
0.6
.....
•
0.4
0.2
0
·- -..... ·········
/·····...
0.4
0.2
...
1953
1957
1961
1965
1969
1973
Starting Quarter
Dotted lines indicate one-standard error band.
1977
1981
1985
0
Marginal Propensity to Consume
From Stock Market Wealth
Ten Year Samples
0.15
0.15
.... ..
,/.
·-------.___
..
.
f
0.1
'.
0.1
. ........
..
...............
0.05
0.05
-···
.,
................... .
.. •
,,,,·····•• .......... :
' .... , ....
,.
0
.. '.
·.:.,
.·
..
0
.......
....,,'.
-0.05
-0.05
'i
1953
1957
1961
1965
1969
1973
Starting Quarter
Dotted lines indicate one-standard error band.
1977
1981
1985
Marginal Propensity to Consume
From Non-Stock Market Wealth
Ten Year Samples
....
0.2
" . ,.,_
0.15
0.2
0.15
....................
0.1
----··"
0.05
0
\.'
\\
····....
0.1
0.05
.. -------·
.•
~·
0
.......\
-0.05
-0.05
...
-0.1
-0.1
/\
-0.15
-0.2
,,,
....
1953
1957
1961
-0.15
1965
1969
1973
1977
1981
1985
-0.2
Starting Quarter
Dotted lines indicate one-standard error band.
@FedFRASER