Finance and Economics Discussion Series
Divisions of Research & Statistics and Monetary Affairs
Federal Reserve Board, Washington, D.C.
A Primer on the Economics and Time Series Econometrics
of Wealth Effects
Morris A. Davis and Michael G. Palumbo
2001-09
NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials
circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the
authors and do not indicate concurrence by other members of the research staff or the Board of Governors.
References in publications to the Finance and Economics Discussion Series (other than acknowledgement)
should be cleared with the author(s) to protect the tentative character of these papers.
A PRIMER ON THE ECONOMICS AND TIME SERIES
ECONOMETRICS OF WEALTH EFFECTS
Morris A. Davis and Michael G. Palumbo
*
Abstract
This paper reviews the statistical approach typically applied by macroeconomists to investigate the
empirical link between aggregate data on household consumption, income, and wealth. In particular, we
focus on studies determining whether and how much changes in net worth, such as those generated by the
stock-market boom in the U.S. over the latter 1990s, are responsible for subsequent swings in the growth
rate of consumer spending. We show how simple economic theory is used to motivate an econometric
strategy that consists of two stages of analysis. First, regressions are used to identify trend movements
shared by consumption, income, and wealth over the long run, then deviations of these series from their
common long-run trends are used to help forecast consumption growth over the short run. Our discussion
highlights the various judgments that researchers must make in the course of implementing this empirical
approach, and we detail how specific parameter estimates describing the magnitude of the wealth effect
on consumption--and even broad conclusions about its existence--are affected by making alternative
choices.
January 2001
* Davis: ReturnBuy, Inc., 21641 Beaumeade Circle, Suite 319, Ashburn, VA 20147;
mdavis@returnbuy.com; Palumbo: Division of Research and Statistics, Board of Governors of the
Federal Reserve System, Washington, DC 20551; mpalumbo@frb.gov
. We have benefitted from
discussions with many of our colleagues at the Federal Reserve Board. In particular, we appreciate
detailed comments and criticisms offered by Karen Dynan, Spencer Krane, David Reifschneider, and
Larry Slifman. The views expressed belong to the authors and should not be attributed to the Board of
Governors of the Federal Reserve System or its staff.
1
In the national accounts, the personal saving rate is defined as the percentage of after-tax
(disposable) income not spent by households on consumer goods and services or as interest payments to
businesses. Throughout this paper we use the term “personal saving rate” and “saving rate”
interchangably.
2
Both values are expressed at annual rates.
2
Introduction
The personal saving rate, as measured by the National Income and Product Accounts
(NIPA), dropped from 6.5 percent at the beginning of 1995 to 0.3 percent early in 2000.
1
To
give perspective on this decline, real (inflation adjusted) disposable personal income in the first
quarter of 2000 was $6.5 trillion while real personal consumption expenditures were $6.2
trillion:
2
All else equal, had households maintained their propensity to spend out of income at
the 1995 level, real purchases of goods and services would have been about $300 billion – nearly
5 percent – lower than reported in the first quarter of 2000.
Figure 1 shows that at the same time the personal saving rate fell the ratio of household
net worth to after-tax personal income increased dramatically. In this paper, we investigate
whether there is a direct economic relationship between the rise in the wealth-income ratio and
the decline in the personal saving rate. If so, then future movements in the wealth-income ratio
also have implications for future household expenditures. But, if the increase in the wealth-
income ratio and decline in the saving rate was mere coincidence, then the pace of household
spending may be immune to changes in wealth. Understanding the link between changes in
household wealth and spending – the so called “wealth effect” on consumption – is therefore
critical for interpreting the recent past and considering the future.
We first will discuss how the wealth-accumulation identity provides an accounting link
between wealth and consumption. The identity illustrates that wealth can increase through two
distinct channels: People can use some of their disposable income to invest in assets (tangible or
financial) instead of consuming; or, assets already owned by households (acquired through prior
investments) can appreciate in price. Evaluating this identity with the macroeconomic data, one
sees that the exceptional increase in wealth experienced by US households since the mid-1990s
has been, in very large part, due to the rapid appreciation of equity prices over this period.
Moreover, the remarkable performance of the stock market during much of the 1990s relative to
3
earlier periods of history suggests that in all likelihood the magnitude of the rise in equity prices
was not fully anticipated by most households before the fact. As discussed below, the
unanticipated nature of the increase in wealth turns out to have important macroeconomic
implications.
We next will discuss how economic theory links consumption and wealth. Our basic
analysis will rely on a simple benchmark model of consumer behavior known as the life cycle
model. According to the life cycle model, households accumulate and deplete their wealth to
keep their planned consumption spending roughly steady, even, for example, when their income
is expected to fall as it might during retirement. In the absence of wealth “surprises,” the life
cycle model predicts that wealth could vary substantially over time but that consumption
spending will be relatively stable. However, if households experience an unexpected increase in
their wealth, then households will formulate a new spending plan that involves a higher level of
outlays indefinitely into the future. Therefore, the life cycle model suggests that predictable
changes in household income and wealth (such as those reflecting new investments deliberately
generated by thrift) should not lead to changes in planned spending, while household spending
should respond to unexpected changes in wealth, such as from a stock-market surprise.
Economists have adapted the life cycle framework to build empirical models that
quantify the relationship between aggregate consumption, income, and wealth. In the third
section of the paper, we use these models to estimate the consumption response to changes in
wealth. Specifically, we estimate two sets of models of consumption behavior. The first
uncovers the long run relationship between consumption, income, and wealth. Under certain
assumptions about the behavior of the economy, these models predict the level of consumption
expected to persist after a few years in response to a change in wealth. Typical estimates of
these models suggest that consumption permanently increases approximately 4 cents for each
dollar that wealth increases. The dynamics of how consumption adjusts to changes in wealth is
described by a second set of models that explain quarter-to-quarter, short-run movements of
consumption. Estimates of these models show that, for example, in quarters when wealth
increases and consumption does not immediately jump to its new long run level, spending tends
to grow at an accelerated pace for several quarters in the future – until the level of consumption
is brought back into line with the new level of net worth.
3
The subscript t is used to reference the observation of a variable at a given point in time – such
as the value of household wealth at the end of a particular year or quarter or the average of income and
spending during the year or quarter; the subscript t-1 then refers to the observation in the preceding time
period. The variable W refers to household net worth; that is, the market value of all assets owned by
individuals minus the market value of all liabilities. The term
)
p
t
denotes the change in market prices for
assets between periods t-1 and t. The variable Y represents the sum of labor income, transfer income,
interest income less interest expenditures on debt, distributed capital gains from mutual funds, and
dividend income (all of which are net of tax payments). Expenditures on consumer goods and services
are denoted by the variable C.
4
(1)
In the final section of the paper, we examine the sensitivity of the long-run and short-run
consumption equations by examining a variety of alternative specifications. The long-run
equations we investigate always imply an economically and statistically significant role for
wealth in accounting for movements in consumption and saving. The estimated size of long-run
wealth effects vary, with the sets of models we examine showing consumption responses
between 3.0 cents and 6.5 cents for each dollar that wealth increases – suggesting that
consumption increased somewhere between $250 and $500 billion in response to the increase in
wealth from 1995 through the end of 1999. On the other hand, subtle differences in model
specification seem to have large effects on estimated short-run consumption dynamics. We
conclude by highlighting a few specific judgements made by different researchers that have led
them to different conclusions on the nature of short-run wealth effects.
I. Wealth, Income, and Consumption in the US since 1995
As a matter of accounting, household income, consumption, and wealth must be linked
together by the wealth- accumulation identity:
The identity states that the amount of wealth owned by a household at some date (W
t
) equals the
level of wealth owned at the end of the previous year (W
t-1
) plus the income saved during the
year (Y
t
- C
t
), plus any capital gains or losses that might have accrued due to changes in the price
of assets in the household’s portfolio over the year (
)
p
t
W
t-1
).
3
This accounting identity holds for
each household and for the aggregate across all households in the economy, as well.
