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1
Brian Motley
Ramon Moreno
and Norman-Yin
Adrian W Throop
Index Numbers and the Measurement of
Real GDP
Exchange Rate Policy and Shocks to Asset
_Markets: The Case of Taiwan in the 1980s
Consumer Sentiment: Its Causes and Effects
Table of Contents
Index Numbers and the Measurement of Meal GDP 0 „0s 00„e „<><,e „s 00„0000„9„ 3
Brian Motley
Exchange Rate Policy and Shocks to Asset Markets:
The Case of Taiwan in the 1980s 00„*„ 9009„*90„0909* 090«,09G9<>99„«„ 9099„ IS
Ramon Moreno and Norman Yin
Consumer Sentiment: Its Causes and Effects . . . . . . « „ . » . . . « G»»»»««. „. . . 9.. 3S
Adrian W. Throop
Federal Reserve Bank of San Francisco
1
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sarily reflect the views of the management of the Federal
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of the Federal Reserve System.
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2
E conom ic R eview / 1992, N um ber 1
Index Numbers and the Measurement of Real GDP
Brian Motley
The author would like to thank the members of the editorial
committee, Chan Huh and Bharat Trehan, and also Adrian
Throop for helpful comments. Robert Parker, of the Bureau
of Economic Analysis, U.S. Department of Commerce,
provided useful information on the recent rebenchmarking
of the national accounts and on the proposed alternative
indexes of real GDP and prices.
The measures ofreal GDP and inflation are aggregates
ofmany individual prices and quantities. These variables
are measured usingfixed-weight indexes, which can give a
misleading impression of price and output changes in a
particular year if the structures of output and relative
prices are different from those in the base year. This
measurement problem adds to the uncertainties facing
policymakers.
These ambiguities result from the definitions of output
and inflation in use. This article describes alternative measures ofgrowth and inflation that have a stronger theoretical
basis and avoid these ambiguities. Operational versions of
these measures will be introduced by the Bureau of Economic Analysis in 1992. These new measures will remove
one source of uncertainty facing policymakers.
Federal Reserve Bank of San Francisco
The Bureau of Economic Analysis (BEA), a division of
the Commerce Department, is responsible for preparing
and publishing estimates of the gross domestic product
(GDP), the most comprehensive measure of our economy's
total output. I Most commentators take it for granted that
these BEA estimates of GDP represent objective measures
of the nation's output. They assume, in other words, that
there is a "correct" measure of output that could be computed exactly if sufficient information were available and
that the GDP data issued by the BEA represent the best
available estimate of this "correct" measure. In fact, however, these measures of real GDP are subject to an inherent
arbitrariness known as the "index number problem."
This problem arises because the nation's total output
consists of a huge number of individual goods and services. Measures of real GDP are constructed as an aggregate of these separate components and so depend on the
method of aggregation used and the weights assigned to
the individual components. Last December, the BEA released revised GDP estimates that, among other changes,
altered these weights. These revised data suggest that the
cyclical downturn in the winter and spring of 1990~91 was
somewhat more severe than reported earlier.
Measures of the average price level encounter the same
problem. Price index numbers, such as the GDP fixedweight price index or the consumer price index, are weighted averages of the prices of individual goods and services.
When the prices of some items change more than those of
others, the value of such an index depends on the weights
attached to these prices. 2
This article discusses a number of issues raised by these
measurement problems. It examines the extent to which
existing methods of data construction might introduce
systematic biases into the numbers. Because of the arbitrariness inherent in existing measures of output and
prices, a number of alternative procedures are described
that have a stronger theoretical basis. The BEA plans to
introduce one such alternative approach to measuring
output and prices in 1992.
The plan of the paper is as follows. In Section I the index
number problem is described and illustrated. Sections II
and III explain two alternative approaches to measuring the
3
nation's output and price level that avoid the arbitrariness
ofthe existing measures. In the first of these, the focus is on
GDP as an indicator of the "standard of living" of the
typical consumer, while the second emphasizes the "productivity" of the representative firm in converting factors
of production ("inputs") into final products ("outputs").
Section IV discusses the recent benchmark revisions to the
national accounts and describes alternative measures of
GDP growth and inflation that the BEA plans to introduce
later in 1992. These alternative measures are based on the
theory of index numbers discussed in Sections II and III.
Since these alternative indexes will be forms of a "chain
index," this section also includes a brief discussion of this
type of index number. Section V concludes.
I.
This means that the growth rate of real GDP from date s
to date s + 1 is a weighted average of the growth rates of its
components:
REALGDP.+! - REALGDP.
REALGDP.
PITFALLS IN MEASURING THE NATION'S OUTPUT
The nation's total output includes a vast array of different goods and services. The nominal gross domestic
product (GDP) measures the aggregate of these individual
components, with each item valued at the price at which it
was sold to its final purchaser. 3 Thus, GDP may be viewed
as the weighted sum of its component commodities, with
their current prices serving as weights. Specifically, nominal GDP at date s may be written as:
(3)
N
(1)
N
GDPs
=
L Pnsqns
.
n=!
It is natural to use prices as weights since, in a competitive, private enterprise economy, the amounts paid for
commodities are good indicators of their usefulness (at the
margin) to their purchasers. However, if the average level
of prices increases (or decreases) over time, the change in
nominal GDP includes the effects of this price change and
so does not provide an accurate measure of the growth in
real output.
A measure of real output may be obtained by valuing the
output of each commodity at the price existing in some
(arbitrarily selected) base year rather than at the price
buyers actually paid. Operationally, the BEA calculates its
estimates of real GDP at date s in date t prices by deflating
each component of nominal GDP by the change in the price
of that component from date t to date s:
(2) REALGDP.
4
The weights, Pntqn/IPitqis, are given by the expenditure
shares of each comporient in GDP calculated at the baseyear prices. This means that if the base period is changed,
the weights, and hence the measured growth rate of real
GDP, also will change. Between 1985 and 1991, real GDP
was calculated with 1982 as the base year, but last December this was changed to 1987.
This procedure also means that real growth in a particular year is in many cases measured using relative prices
ruling in the distant future or past. The most recent
measures of real growth and inflation during the 1930s, for
example, use the relative prices ruling a half-century later.
The significant changes in relative prices over this period
may introduce large biases into the data.
In constructing its estimates of real GDP, BEA breaks
down nominal GDP (excluding the federal government)
into 811 components, each of which is deflated separately
by an appropriate price index (Young 1988, Table 5). Purchases of goods and services by the federal government are
divided into no fewer than 17,000 components! Equations
(2) and (3) show that not only the level but also the growth
rate of measured real GDP depend on which year's prices
are used in the process of aggregating the outputs of these
17,811 separate components.
As discussed in the accompanying Box, changing the
base to a later date usually reduces the estimate oflong-run
Economic Review / 1992, Number 1
BOX
An Example of the Index Number Problem
For a simple illustration of the effect of a change in the base date on the measurement of real GDP, consider a
hypothetical economy producing only two commodities, bread and wine. The top panel of the table shows the prices,
quantities produced, and current-dollar values of these two goods in four successive years. Nominal GDP in this
simple economy is the total value of the two goods. The middle panel of the table shows measures of real GDP in this
economy using each of the four years as a base year. These are calculated by multiplying the quantities of each good by
its price in the base year and summing the resulting values. Finally, the bottom panel shows the corresponding annual
growth rates of real GDP. Over the four years, real GDP increases 102.9 percent when the base is year 1, but 95.8
percent when the base is year 4.
In this example, selecting a later year as the base period produces a lower growth rate than selecting an earlier year.
This result arises because the good with the smaller increases in output over the four-year period (bread) was selected
as the one with the larger increases in price. This feature of the example corresponds to the observation that buyers tend
to substitute away from goods and services with the largest price increases and toward those with the smallest
increases. As a result, the sectors of the economy that experience the largest increase in prices tend to be those with the
smallest increases in real output. Since sectors are weighted by relative prices, moving to a later base date tends to
increase the weights given to sectors with below average increases in output and to decrease the weights given to those
with above average output growth. As a result, a later base date tends to produce lower estimates of average growth. a
The Index Number Problem in a Simple Economy
Data
Year
Price of
Bread
Price of
Wine
Quantity
of Bread
Quantity
of Wine
Value of
Bread
Value of
Wine
Nominal
GDP
Y1
Y2
Y3
Y4
7
8
10
13
6
6
7
9
15
17
18
19
23
35
50
60
105
136
180
247
138
210
350
540
243
346
530
787
Levels of Real GDP
Year
Year 1 Base
Year 2 Base
Year 3 Base
Year 4 Base
Y1
Y2
Y3
Y4
243
329
426
493
258
346
444
512
311
415
530
610
402
536
684
787
Growth Rates of Real GDP
Year
Year 1 Base
Year 2 Base
Year 3 Base
Year 4 Base
YI to Y2
Y2 to Y3
Y3 to Y4
Y4 to Y1
35.4
29.5
15.7
102.9
34.1
28.3
15.3
98.4
33.4
27.7
15.1
96.1
33.3
27.6
15.1
95.8
N
aIn terms of equation (3) in the text, components of GDP with weights, Pmqns/;'g"Pi,qiS that become larger when a later base date is
chosen tend also to be those with low growth rates (for which (qns + 1 - qns)/qns is small).
Federal Reserve Bank of San Francisco
5
real GDP growth. This is because buyers substitute away
from goods and services with larger than average price
increases in favor of items with smaller than average gains.
As a result, sectors of the economy that grow slowly tend
also to be those that have the largest price increases, and so
have larger weights in real GDP if a later base date is
chosen. Conversely, sectors that grow rapidly are generally
those with the smallest price increases and so have smaller
weights in real GDP if the base date is later.
The inverse relation between changes in sectoral prices
and outputs implies that most relative price changes are the
result of changes in costs on the supply side rather than of
taste changes on the demand side. If most relative price
changes were due to demand shifts, one would observe that
the sectors with the largest increases in prices also would
be those with the greatest increases in sales. Historically,
this has not been the case, implying that supply shifts were
more important than demand shifts in changing relative
prices.
An example of this effect is that between 1977 and 1990,
real GDP increased at an annual rate of 2.7 percent when
measured in 1982 dollars but only 2.5 percent in 1987
dollars (see Survey of Current Business 1991). A major
portion of the difference may be traced to the computer
industry. The output of computers increased very rapidly
during this period, while their prices fell sharply. As a
result of the price decline, the measured contribution of
this industry to overall growth is smaller if it is weighted by
1987 prices than if 1982 prices are used.
Similar revisions occurred on earlier occasions when the
base date was changed (see Survey of Current Business
1976 and 1985). When the base date was shifted from 1972
to 1982, the estimated average annual growth rate of real
GDP between 1972 and 1984 was reduced by 0.4 percentage points. This also was due largely to the changed
weighting of the computer industry. The change in the base
from 1958 to 1972 lowered the average annual growth rate
from 1958 to 1974 by 0.2 percentage points. In this case,
the main cause was the decreased weight assigned to the
auto industry. Auto prices rose less than average prices and
auto sales increased more than total GDP over this period.
Is There a "Correct" Measure of Real GDP?
The fact that a change in the base date produces a
different measure of real GDP growth suggests that there is
an arbitrary element to these measures that can never be
fully eliminated. Whereas nominal GDP is an aggregate of
transactions that actually occurred, real GDP is a statistical construct that represents the sum of a set of fictional
transactions. Hence, nominal GDP could, in principle, be
measured exactly if we had full and complete information
6
from the original transactors, but there may be no clearly
"correct" measure of real GDP, even with unlimited data.
For analogous reasons, there may be no measure of the
average level of prices that is obviously "correct".
A branch of microeconomic theory known as the economic theory of index numbers suggests that this conclusion may be too pessimistic. This theory indicates that if
we are prepared to define precisely what we mean by a
"correct" measure of GDP, it is possible to derive indexnumber formulae that measure the quantity and price of
GDP with no arbitrary element. Initially, this theory was
applied to the problem of defining a price index that would
measure the "cost of living." Later it was extended to the
definition of other price and quantity indexes.
II.
MEASURING THE "COST" AND "STANDARD"
OF LIVING
Consider first the problem of measuring changes in the
"cost of living." Suppose that in a particular base period,
the representative consumer faces a given set of prices and
buys a certain bundle of goods and services. In a subsequent period, she faces a different set of prices and chooses
a different bundle of commodities. The problem is to
determine how much the average price level (or "cost of
living") changed between the two periods. The corresponding "quantity" problem is to determine how much
larger (or smaller) the second commodity bundle is compared to the first (that is, how much her "standard of
living" changed).
One way to measure the change in the average price level
is to compute how much the base period commodity
bundle would cost at the second-period prices. This is the
procedure that underlies both the consumer price index and
the fixed-weight GDP price index. These types of measures are known as Laspeyres indexes. 4 The drawback of
this procedure is that it does not allow for the fact that the
consumer generally can reduce her expenditures in the
second period- with no reduction in her satisfaction-by
substituting away from commodities that have become
relatively dearer in favor of others that have become
relatively cheaper. 5 Because the Laspeyres index does not
allow for such substitutions, this type of fixed-weight price
index has an upward bias as a measure of the cost of
maintaining a given level of satisfaction.
Alternatively, one may evaluate how much the second
commodity bundle would have cost at base period prices
and compute the increase in the cost of this bundle.
However, an index number constructed this way, which is
known as a Paasche index, tends to understate the increase
in the cost of living. 6 This is because the second bundle
Economic Review /
was not the one that the consumer actually chose in the base
period, so computing its cost at the first set of prices
overstates the cost of living in that period.
If one knew the consumer's preferences, one could
predict what substitutions she would make in order to
maintain the same degree of satisfaction in response to any
given changes in relative prices. Thus, one could calculate
the minimum cost of attaining a particular level of satisfaction at any given set of prices. Changes in this minimum
cost over time would provide an exact measure of changes
in the "true cost of living," defined not as the cost of
buying a particular bundle of goods and services but as the
cost of obtaining a particular level of satisfaction. Although this approach has been attempted by some economists (for example, Klein and Rubin 1947-48), it has the
disadvantage of requiring a large body of data from which
to estimate consumers' responses to changes in the prices
they face. The economic theory of index numbers provides
an alternative and more economical approach. 7
The Economic Theory of Index
x
- 1
The Fisher Ideal price index exactly represents the consumer's true cost of living if the utility function that
describes her preferences at date s is a quadratic function of
the form: 9
N
N
E E Ctnmqnsqms' where Ctnm = Ctmn"
(5) U.
n=l m=l
The Tornqvist measure of the overall price increase is
the weighted geometric average of the increases in individual commodity prices, with weights equal to the average
expenditure shares in the base period t and the current
period s:
NlJmhpY'S
This theory begins with the assumption that the quantities of individual goods and services that we observe
consumers buying are those that maximize their satisfaction (or utility) given their incomes and the prices they face.
The theory then shows that by making certain mathematical assumptions about the form of consumer preferences,
one may derive index number formulae that measure
changes in the true cost of living (that is, the cost of
obtaining a certain level of satisfaction) in terms of the
observable prices and quantities of individual goods and
services. Index numbers that have this property are said to
be "exact."8 The appeal of this approach is that it is
necessary only to specify the form of the functions that
describe consumers' preferences and not necessary to
know the actual values of their parameters. This follows
from the assumption that if the consumer buys a particular
bundle of goods and services at a particular set of prices,
this means that this bundle maximizes her utility from a
given expenditure level (or minimizes the expenditure
required to obtain a given utility level). Hence, price and
quantity observations provide information about utility
levels.
Two exact index number formulae that have been derived
and used by advocates of this approach are the Fisher Ideal
index and the Tornqvist index. The Fisher ideal measure of
the increase in average prices from base period t to period s
is the geometric average of the Laspeyres and Paasche
price indexes:
Federal Reserve Bank of San Francisco
N
PT
=
II
n=l
Pns]
[ Pnl
T.,
where
(6)
+
The exact price index will be a Tornqvist one if preferences
may be described by a translog expenditure function (Diewert 1976). The translog unit expenditure function has the
form: 10
where Ctnm = Ct mn '
In this equation, es represents the minimum expenditure
that yields a unit level of utility at the prices ruling in period
s. This expenditure function imposes fewer restrictions on
the structure of consumer preferences than the quadratic
utility function.
At first sight, the assumptions on the forms of the utility
and· expenditure functions that underlie the Fisher and
Tornqvist price indexes appear to be rather restrictive.
However, it can be shown that a wide range of alternative
7
utility and expenditure functions can be approximated
closely by either a quadratic or a translog function. 11
Diewert describes forms of the utility or expenditure
function that have this approximation characteristic as
"flexible forms" and the corresponding exactindex number formulae, such as the Fisher ideal or the Tornqvist, as
"superlative" indexes.
By construction, the Fisher ideal price index lies between the Laspeyres and Paasche indexes. It can be shown
that this also is true of the Tornqvist measure. For measuring changes in prices over time, there is little to choose
between these alternative measures, since in most cases
they give very similar results.
If the consumer's nominal income rises by the same
amount as the true cost of living, this means that her
satisfaction is unchanged. It is natural, therefore, to measure the change in the consumer's real income between two
dates by the extent to which the increase in her nominal
income exceeds the rise in the true cost of living, since
"real income" then will be an indicator of her utility level
or standard of living. If a measure of real GDP is constructed by deflating nominal GDP by a true cost of living
price index number, the result is a measure of the "quantity" of output that represents changes in the standard of
living enjoyed by the representative consumer. In other
words, with this definition, an increase in real GDP
represents a rise in consumer satisfaction or welfare. This
seems to be a sensible way of defining what is meant by the
quantity of output when the proportions of individual
commodities in the total change over time.
A drawback to defining and measuring real GDP in
terms of the standard of living of a representative consumer is that many of the commodities included in the
GDP are not consumer goods and do not directly contribute
to consumer welfare. An alternative approach that avoids
this drawback is to base the measure of real GDP on the
production capability of the representative firm rather than
the preferences of the representative household.
Ill.
PRODUCTION-BASED MEASURES
OFRi'-ALGDP
Suppose that, in the base period, a representative firmwith a given technology and set of inputs and facing a given
set of output prices-produces a certain bundle of outputs
with a certain dollar value. In a later period, facing a
different set of output prices, it produces a different bundle
of outputs, using a different technology and set of inputs.
The problem is to determine how much of the change in the
nominal value ofthe firm's output (that is, in its revenue) is
due to a change in the prices of its products and how much
8
toa change in the quantities produced. The rnicroeconornic
theory of production may be used to address this problem.
A rise in the firm's revenues represents an increase in the
quantity of its output if it may be attributed entirely to a
change in the inputs it uses or in its technology and not at
all to changes in the prices of any of its outputS. 12 Conversely, an increase in revenue that occurs with no change
eitherin the inputs used or in technology, must be due to a
change in the prices of its products and represents a rise in
the average price of its output. Put in more technical
terms, a revenue change is an increase in the quantity of the
firm's output if it represents an outward shift in its production possibility frontier, but is a price change if it represents a movement along the frontier. 13
In the same way as the consumption-based approach
relies on the assumption that consumers choose their
purchases so as to minimize the cost of obtaining any given
level of satisfaction, the production-based approach assumes that firms choose their outputs so as to maximize
their revenues given the technology and inputs they have
available. This assumption guarantees that the observed
quantities of output are those that maximize the firm's
revenues given its production possibilities and the prices
that it faces. As in the case of the consumption-based
approach, it is possible to derive exact output and price
indexes by suitably choosing the mathematical form of the
function that describes the firm's production possibilities.
Production possibilities may be described by either a
production function or a revenue function. 14 If the revenue
function is assumed to be translog, the corresponding
output price index will be a Tornqvist index. IS A similar
restriction on the production function implies a Tornqvist
output quantity index. 16 Somewhat stronger restrictions on
the production andrevenue functions imply that these price
and quantity measures will be Fisher ideal indexes.
If an exact price index is constructed, a measure of real
output is obtained by deflating the nominal value of output
using that index. Conversely, if an exact quantity index is
constructed, the corresponding price index is obtained by
dividing the nominal value ofoutput by this quantity index.
Fisher ideal indexes have the useful technical property that
if a Fisher price index is used to deflate nominal GDP, the
result is a Fisher index of the quantity of real GDP, and
conversely. I? Thus, a Fisher price index is an exact measure of the price level, and the corresponding real GDP
index is an exact measure of the quantity of output, but at
the same time their product is equal to nominal GDP.
Neither the Tornqvist index nor the measures that are
currently used by the BEA have this "factor reversal"
property. Real GDP currently is measured by a Laspeyres
fixed-weight output index and the preferred measure of
Economic Review / 1992, Number 1
inflation is the fixed-weight GDP price index, which also is
a Laspeyres index. The product of these measures of out
put and prices is not equal to nominal GDP. The measure of
prices obtained by dividing nominal by real GDP (the
implicit price deflator) is a poor indicator of inflation
because it reflects not only changes in prices but also
changes in the composition of GDP. Conversely, the meas
ure of output that would be obtained by dividing nominal
GDP by the fixed-weight price index (which might be
described as an “ implicit output measure” ) would be a
poor measure of real growth since it would reflect not only
changes in output but also changes in relative prices.
Adoption of Fisher ideal measures of prices and real GDP
would avoid these ambiguities.
IV. R e c e n t C h a n g e s
In c o m e A c c o u n ts
in th e
N a t io n a l
The Bureau of Economic Analysis issued revised GDP
estimates last December. In the course of this “ bench
mark” revision, the base date of the estimates was changed
from 1982 to 1987.18 As mentioned earlier, the average rate
of real GDP growth from 1977 to 1990 was 0.2 percentage
point lower in the revised data. However, in some periods
the rebasing caused much larger changes in measured
growth. For example, the growth of real GDP was reduced
by 0.5 percentage point in both 1987 and 1988 as a result of
rebasing, and the decline in real GDP in the cyclical
downturn in the winter and spring of 1990-91 appears to
have begun earlier and been somewhat more severe when
measured at 1987 prices than when measured at 1982
prices. Chart 1 compares the quarterly growth rates from
1975 to 1990 in the pre- and post-benchmark data.19
The BEA has indicated that, beginning sometime in
1992, two alternative measures of both real growth and
inflation will be published, using forms of the Fisher ideal
index. These alternative indexes will eliminate the periodic
revisions to measured growth resulting from the effects of
rebasing, and will remove the long-run bias in the current
measure of real output that results from the use of constant
relative prices. In addition, because the Fisher ideal index
is based on the economic theory of index numbers, these
alternative measures of the economy’s total production will
have a sounder theoretical basis.20
“Chain" Measures of GDP Growth
The planned alternative indexes will be forms of chain
indexes. A quarterly chain measure of GDP growth is
constructed by computing the real growth rate between
each successive pair of adjacent quarters, using current
relative prices as weights. For several years, the BEA has
published chain indexes of GNP growth, but these have
attracted little attention. In these indexes, real GNP
growth between each pair of adjacent quarters was meas
ured using the relative prices ruling in the first quarter.
Thus, these quarterly chain growth rates were Laspeyres
indexes. Average growth over longer periods could have
been computed by compounding these one-quarter chain
growth rates, but in the past the BEA did not do this.
To measure the growth of real GDP in a particular
quarter, it makes sense to weight its components by the
relative prices prevailing in that quarter rather than in the
distant past or future (see Moorsteen 1961). Measures of
average growth over longer periods constructed by com
pounding these chain growth rates would take account of
the changes in relative prices and the composition of output
that occurred. Hence the measurement bias that results
from the use of fixed-weight indexes would be reduced.
The measured average growth rate over a longer period
C hart 1
G ro ss Dom estic Product
P ercent
1982 an d 19 87 D o lla rs
A n n u a liz e d G ro w th R ates
P ercent
15
10
5
0
-5
-10
Federal Reserve Bank o f San Francisco
9
computed by compounding quarterly chain growth rates
would depend on the (changing) relative prices and composition of output throughout the period. This is because
the growth rate between each successive pair of quarters
depends on the relative prices and on the composition of
output in those quarters. By contrast, a measure of growth
calculated directly from the beginning to the end of the
period depends only on relative prices and on the composition of output at the beginning and the end. In other words,
a growth rate calculated by compounding quarterly chain
growth rates is "path-dependent."21 It represents the
average growth rate during the period rather than· the
average growth rate from the beginning to the end of the
period. In practice, however, the difference is likely to be
very smal};22
New Measures of Growth and Inflation
The new alternative measures of real GOP and the price
level to be introduced by BEA combine the features of the
Fisher ideal index and the chain approach. The BEA terms
these new measures time-series generalized Fisher ideal
(TGFI) indexes. 23 The TGFI index calculates real growth
between benchmark years using the standard Fisher ideal
formula. Growth rates in periods between the benchmarks
are calculated as the geometric average of the growth rates
calculated using the weights in the two benchmark years.
Thus, if A and B are benchmark years and t and t+ I are
years between A and B, the TGFI real growth rate from t to
t + I is:
(8)
nA
Lq.nt+lP
n
LqntPnA
n
[Eqnt+lPnB
x_n
_
~
1 .
LqntPnB
n
Similarly, the TGFI increase in prices between t and t + I
is given by
Direct computation shows that the cumulation of the
TGFI growth rates for the periods between A and B is equal
to the Fisher ideal measure of growth calculated directly
from year A to year B. As a result, the TGFI measure of
10
growth between benchmark years is not path-dependent.24
The TGFI index also has the factor reversal property that
the growth rates of real GOP and the price level from one
benchmark year to the next sum to the growth rate of
nominal GOP.
An attractive property of chain Fisher ideal indexes is
that the measures of real growth and inflation in each
quarter incorporate the structure of the economy and
relative prices in that quarter and so should give a more
accurate indication of current developments. For this reason, these measures might be more valuable topolicymakers. We have found, for example, that the chain measure of
real GNP growth is a slightly better predictor of changes in
the unemployment· rate than the standard measure. The
TGFI indexes will have similar advantages, since the real
growth and inflation measures for each quarter will be
based on the relative prices and the structure of output in
nearby benchmark years.
BEA plans to construct two alternative TGFI indexes.
The first alternative index will use as weights the relative
prices and composition of output in the preceding and
current years. In terms of equations (8) and (9), years A
and B refer to the previous and current years. 25 The
BEA describes this index as a "chain-type annual
weights" index. The second index, which will be termed a
"benchmark-years weights" index will use as weights the
relative prices and composition of output in benchmark
years five years apart. 26
A disadvantage of the chain approach (including the
TGFI measures) is that it provides a measure of the growth
rate of real GOP in a given quarter or year, but no unique
measure of its dollar level. A measure of the level of real
GOP can be constructed by multiplying nominal GOP in
an· arbitrary base year by the compounded chain growth
rates. However, the resulting measure of real GOP does not
have the easily understood interpretation of the fixedweight measure now in use. Specifically, it does not
measure what the GOP would be if all prices had remained
constant since the base year.
A related disadvantage of a GOP measure computed by
cumulating a chain index such as the TGFI is that the level
of real GOP constructed in this way is not equal to the
simple sum of its components (consumption, investment,
etc.). Instead,. it is a weighted sum of these components
with weights that change as relative prices vary. Over short
periods this might not cause problems, but it could be
inconvenient for studying the sources of growth over longer
periods. 27 The BEA will avoid this aggregation problem by
publishing only index numbers of real GOP and its principal components rather than dollar values. Hence it will not
be possible to study the decomposition of GOP growth over
time using these new measures.
Economic Review /
Number ].
V
CONCLUSION
The measures of real GDP and inflation to which
policymakers respond are aggregates of vast numbers of
individual prices and quantities. Measuring these macroeconomic variables using fixed-weight indexes adds to
the uncertainties facing policymakers, since changes in the
base date used in constructing measures of output and
prices sometimes alter our perceptions both of the economy's long-run real growth and inflation rates and of its
short-run cyclical behavior.
This article has shown that these ambiguities are the
result of the particular definitions of output and inflation
that are currently in use. The economic theory of index
numbers shows that if an increase in total output were
defined as a change in the bundle of goods and services
produced that either raises the utility level of the representative consumer or increases the revenue ofthe representative firm with no change in the prices of its outputs, the
ambiguities could, in principle, be resolved. These definitions may be made operational by specifying the mathematical form either of the household's utility function or of'
the firm's production function.
The alternative measures of real GDP and inflation that
the BEA soon willintroduce appear to be a sharp improvement over those that have been in use since the Census
Bureau began constructing national product data on a regular basis in 1947. These new indexes of real GDP and infla~
tion will make use of the economic theory of index nUInbers
discussed in this paper, and so will have a sounder theoretical basis than the current measures. In addition, the alternative data will avoid much of the ambiguity associated with
fixed-weight aggregates and will more closely reflect the
current structure of the economy, because the price and
quantity weights used will be based on conditions in nearby
benchmark years. These improvements will remove at least
one source of uncertainty facing policymakers.
ENDNOTES
1. Until last December, the BEA focused on gross national product
rather than gross domestic product. GNP measures the outputof
resources owned by U.S. residents (including output produced abroad
using American-owned labor and capital), whereas GDP measures the
output produced within the borders of the U. S ..(including the output of
foreign-owned labor and capital). For purposes of the issues discussed
in this article, this distinction is not an important one.
2. It also depends on the type of average used. The existing official price
indexes are constructed as weighted arithmetic averages of the prices
of their components, but index numbers also could be constructed
as weighted geometric averages. The Tornqvist index discussed below is an example of one constructed as a geometric average of its
components.
3. Measuring the prices of individual items correctly involves a host of
difficult problems. For example, when the amount spent on an item
increases at the same time as its quality improves, it may be difficult to
determine whether its true price has risen or declined. The rising cost of
medical care is an example of this problem. To keep its length
manageable, this paper will ignore these issues and assume that the price
and quantity produced of each individual commodity are measured
without error.
4. The Laspeyres measure of the increase in prices from base period t to
period sis:
N
p
L
=
L,pnsq.,
.-1
N
-I
L,P.,q.,
11=1
5. If, for example, chicken has risen in price more than fish, she may
obtain the same satisfaction at less cost by consuming less chicken and
more fish.
6. The Paasche measure of the increase in prices from base period t to
period sis:
N
L,Pnsqns
Pp=
'~I
-I
L,P.,qns
.=1
7. For a useful survey of the literature on index numbers, see W.E.
Diewert (1987). Diewert has been responsible for much of the recent
theoretical development of this branch of economics.
8. In technical terms, the theory requires the mathematical form of the
utility function or the expenditure function to be specified. The utility
function assigns a utility value to each commodity bundle, such that if
the consumer prefers one bundle to another, it will have a higher utility
value. The expenditure function specifies the minimum cost of attaining
a given utility level as a function of the commodity prices that the
consumer faces. It can be shown that either of these functions may be
used to represent the consumer's preferences.
9. This was first proved in Koniis and Byushgens (1926).
10. The expenditure function defines the minimum expenditure required
to obtain a given level of utility and hence depends on the specified
utility level as well as on prices. However, since the measurement of
utility is arbitrary, it is convenient to set the reference level of utility at
Federal ReseJrVc Bank of San Francisco
11
unity. This causes the terms involving the utility level to drop out of
equation (7) since the logarithm of one is zero.
11. Specifically, either of these forms can provide a second order
approximation to any twice continuously differentiable linearly homogeneous function.
12. In addition, an increase in the quantity of output that occurs with no
increase in the amounts of inputs used must be attributed to a change in
technology, and hence represents a rise in productivity. The index
number methodology discussed in this section also may be used to
define exact measures of productivity growth.
13. For more detailed discussions ofthis issue, see Moorsteen (1961) and
Fisher and Shell (1972).
14. The production function describes the combinations of outputs and
inputs that are feasible for the firm with its given technology. The
revenuefunction defines the maximum revenue the firm can obtain from
selling (at the output prices it faces) the outputs it can produce with a
given set of inputs and a given technology. It can be shown that the firm's
production possibilities may be fully described by either a production
function or a revenue function.
15. The maximum revenue that the firm can obtain depends on the prices
of its outputs and the quantities of inputs it has available. If the firm
producesN outputs with prices PI . • . PN usingM inputs VI' .• VM , the
translog revenue function is
This form is "flexible" since it can approximate any arbitrary linearly
homogeneous twice-differentiable function.
16. Proofs of these results are given in Diewert (1983). The result with
regard to the output deflator requires that the output distance function be
translog in form. The distance function, which may be derived from the
production function, measures the distance of the firm's present production possibilities frontier from some base frontier.
17. This can be shown by direct computation. For simplicity, consider
the two-commodity case. The increase in nominal GDP from period 0 to
period 1 divided by the Fisher ideal measure of the increase in prices is:
19. The benchmark revisions also incorporate new sources of data and
some methodological changes. However, in most quarters,' the change of
base from 1982 to 1987 is the largest source of revisions in the measured
GDP growth rate.
20. Since many commentators take it for granted that there is only one
"correct" measure of real GDP, the publication of alternative measures
of real output may create uncertainty at first.
21. This was first pointed out by Triplett (1988). Note that path
dependence occurs even if growth in each individual quarter is measured by an exact index such as a Fisher ideal or Tornqvist index.
22. Between 1982 and 1987, for example, real GNP increased at an
average annual rate of 3.76 percent in 1982 prices and 3.54 percent in
1987 prices. Since these are the Laspeyres and Paasche measures ofreal
growth, respectively, the Fisher ideal measure of average growth between these two dates is equal to their geometric mean, or 3.65 percent.
The average growth rate calculated by compounding quarterly Fisher
ideal chain measures is 3.64 percent.
23. This index was introduced in Young (1988).
24. However, measured growth over shorter or longer periods will be
path dependent. For example, if A, B, and C are benchmark years, the
direct Fisher ideal measure of growth fromA to C will not be equal to the
product of growth from A to B and that from B to C.
25. For measuring quarterly real GDP and inflation during the current
year, the previous year's weights will be used until the current year is
complete.
26. For example, 1982 and 1987 are benchmark years, Quarterly growth
and inflation rates between the third quarter of 1982 and the second
quarter of 1987 will be calculated using the relative prices and composition of output in 1982 and 1987. Thus, in future benchmark revisions,
these data will be unaffected by base-date changes. For quarters after
1987.Q2, the calculations will use weights for 1987 and the most recent
complete year. After complete data for 1992 are available, growth
between 1987.Q3 and 1992.Q2 will be measured using weights for 1987
and 1992.
27. In the case of a TGFI measure, the weights would remain constant
between benchmark years, but would change when moving from one
inter-benchmark period to the next.
(Pllqll) +(PZI%I)
(PlOqIC) + (PzoqzJ
(PllqlJ + (PzlqzJ (Pl1qll) +(PZlq21)
(PlOqlJ + (PzoqzJ . PlOql1) + (Pzoqzl)
This expression may be simplified to:
(P1O%1)+(Pzoqzl) (Pl1ql1)+(P21q21)
(PlOqIJ+(PzoqzJ· (Pl1qIJ+(PZI%J
This is the Fisher ideal measure ofthe increase in real output from period
o to period I.
18. In addition to altering the base date for measuring constant dollar
quantities, this benchmark revision incorporated a number of other
procedural changes, including the replacement of GNP by GDP as the
primary measure of U.S. output.
12
Economic Review I 1992, Number 1
REFERENCES
Diewert, W.E.1976. "Exact and Superlative Index Numbers." Journal
of Econometrics 4, pp. 115-145.
_ _ _ _ . 1983. "The Theory of the Output Price Index and the
Measurement of Real Output Change." In Price Level Measurement, ed. W.E. Diewert and C. Montmarquette, Ottawa: Statistics
Canada.
. 1987. "Index Numbers." In The New Palgrave: A
Dictionary ofEconomics Vol. 2. London: MacMillan.
Fisher, Franklin M., and Karl Shell. 1972. "The Pure Theory of the
National Output Deflator." In The Economic Theory of Price
Indices, ed EM. Fisher and K. Shell. New York: Academic Press.
Klein, L. R., and H. Rubin. 1947-1948. "A Constant-Utility Index of
the Cost of Living." Review of Economic Studies 15, pp. 84-87.
KonUs, A. A., and S. S. Byushgens. 1926. "K Probleme Pokupatelnoi
cm Deneg." Voprosi Konyunkturi 2.
Moorsteen, Richard H. 1961. "On Measuring Productive Potential and
Relative Efficiency." Quarterly Journal of Economics 75 (August).
Survey ofCurrent Business. 1976. "Alternative Measures of ConstantDollar GNP" (December).
Survey of Current Business. 1985. "Revised Estimates of the National
Income and Product Accounts of the United States: An Introduction," Table 19 (December).
Triplett, Jack E. 1988. "Price Index Research and Its Influence on Data:
A Historical Review." Presented at 50th Anniversary Conference
on Researchon Income and Wealth sponsored by the NBER, May
12-14, Washington, DC.
Young, Allan H. 1988. "Alternative Measures of Real GNP." Survey of
Current Business 69, Table 5.
Federal Reserve Bank of San Francisco
13
Exchange Rate Policy and ~hocJ(sto .i\sset
Markets: The Case of Taiwan in the 1980s
Ramon Moreno and Nonnan Yin
Economist, Federal Reserve Bank of San Francisco and
Professor and Chairman, Banking Department, National
Chengchi University, Taipei, Taiwan. The authors thank
the Editorial Committee, Mark Levonian, Reuven Glick,
and Fred Furlong for helpful comments that led to significant .improvements 'in the paper. Ramon Moreno thanks
Mary Linda Chan for assistance in translation. Research
assistance by Mary Linda Chan, Judy H. Wallen, and Sean
Kelly is gratefully acknowledged.
This paper uses a simple theoretical model to show how
the credibility of unsterilized intervention policy may
affect the pattern of adjustment in the exchange rate,
velocity, and asset prices. When the outcome of unsterilized intervention is credible, any degree ofexchange rate
stability can be achieved at the cost ofa sufficiently large,
one·time change in the money supply. When the outcome of
intervention is not credible, intervention can lead to persistent, and possibly accelerating, changes in exchange
rates, the money supply, velocity, and asset prices. Under
certain conditions, intervention may even amplify the
cumulative' change in the exchange rate, rather than reduce it. The model is used to interpret Taiwan's experience
with unsterilized exchange rate intervention in the second
half of the 1980s.
14
Over the past decade, internation~l capital mobility in
many Pacific Basin econol1lies has increasedconsiderabl~
ThisJrendhasmade it more difficult forpolicymakers to
stabilize the foreign value of their currencies. The greater
ability of speculators to buy and selldOlnesticcurrencyin
foreign exchange markets has in some cases resulted in
unwelcome fluctuations in currency values, in spite of
governmeritefforts to limit such fluctuations.
Some progress has been made inunderstandingt?e
problems of stabilizing" the exch'l11ge ,rate jneco~?mies
wi
0bile international capitaL Re~.~ar~h inope~ economy macroeco~omicssince the 1960s de.~cri?~sho\V, disturbances to foreign exchange ,.markets, and government
policies affect exchange rate behaviorgiven certain institutional features ofthe economy, such as the degree ofcapital
mobility. or asset •substitutabilit~
More, recentl)', research has c1arifiedhowcredibility
affects the abilityofthegovernmen~ to enforceane~change
rate target. For example, Krugman(1979) shows how government attempts to peg the exchange rate with limited
foreign exchange reserves may lead to speculative attack
and an abandonment of the peg. Another literature (see
Lessard and Williamson 1987) analyzes capital flight in
economies that are forced to deal with serious macroeconomic imbalances or that are saddled with large external
debt burdens. Such capital flight may impair the government's ability to stabilize the exchange rate. However,
these approaches do not necessarily highlight the difficulties that may arise when a well-managed economy (one
that faces no foreign exchange reserve constraints, maintains a largely balanced government budget, and has no
external debt burden) attempts to stabilize its currency.
This paper draws on the experience of Taiwan in the
1980s to shed some light on these potential difficulties.
Due to certain asymmetries in foreign exchange controls,
Taiwan had' a relatively high degree of capital mobility up
to 1987, while it maintained a policy of lil1liting movements in the exchange rate. Taiwan's relative openness
exposed it to disturbances to its foreign exchange markets
in the second half of the 1980s that illustrate the difficulties
that may arise when a country attempts to stabilize its
exchange rate.
tllll1
Economic Review ,/,1992, Number 1
Two features of Taiwan's experience in the 1980sare of
particular interest.. First, following a period of tranquility
i.n foreign exchange markets in the first half of 1980s, the
New Taiwan (NT) dollar appreciated at an acceleratin~ rate
against the U.S. dollar from late 1985 through 1987, in
spite of increasing intervention in· exchange markets designed tolimit such appreciation} Second, in spite of the
steep acceleration in money growth associated with intervention after 1985, there was relatively little inflationinthe
goods market. Rapidmoneygrowthwas associated in§tead
with a persistent decline intheincome velocity of money
and a boom in asset prices. Neither the persistent acceleration. in exchange rate •appreciation, .·nor .the relationship
between money growth and domestic goods and asset
pnceshav~been fully explailled. 2
.
. . . •• • . .
•.
This paper suggests that the .persistent and accelerating
appreciation of the NT dollar may haVe been related to
government efforts to limit such appr~ciation. Some.simpIe examples are offeredto illustrate how such a situation
may arise if the government's exchange rate. policy loses
credibility. Using a conventional small open economy
model, it is also shown that intervention in response to
disturbances in Taiwan's foreign exchange markets may
have contributed to persistent declines in the income
velocityof money and to the boom in Taiw~'s asset prices.
It is .suggested that weak international arbitrage links,
which are at least partiy attributable to Taiwan's relatively
undeveloped domestic financial markets, facilitated the
sharp changesin asset prices. While the paper uses conv~nti()nal analytical tools, it offers a new way of thinking
about the interaction between exchange market intervention and exchange rate expectations and about the potential
effects of such interaction.
The paper is organized as follows. Section I provides
some background on Taiwan's exchange rate policy, capital
mobility, and the domestic financial sector. Section II
describes a simple theoretical model . that can be used to
examine the likely effects of Taiwan's exchange rate policy
on the persistence of shocks to exchange rate expectations
and the behavior of money, velocity, and asset prices.
Section III interprets Taiwan's experience using the framework developed earlier. Section IV sums up some· of the
lessons of Taiwan's experience.
/. EXCHANGE RATE POLICY, CAPITAL CONTROLS
AND THE DOMESTIC FINANCIAL SECTOR3
To set the context for the theoretical analysis that follows, we review the characteristics of Taiwan's exchange
rate policy, capital cOl}trols, and financial markets. Table!
summarizes the evolution of Taiwan's external and domestic financial sector policies in the 1980s.
Federal Reserve Bank of San Francisco
Exchange Rate Policy
The government's exchange rate policy in the .198Qs
reflectedtwo basic criteria. BeginninginSeptember 1982,.
dailyfluc.tUations in the currency were limited by a policy
rule requiring that the daily.adjustment (upward or downward) of the spot rate not exceed 2.25 percent of the central
rate on the previous business day. This rule was in effect
ulltil April 1<)89, when the cUrrency .was tIoat~d.Policy
makers also sought to prevent cUrrency movements from
excessively . impairing the competitiveness of Taiwan's
export sector by limiting the rate. of appreciation of the
currency.
Controls on Capital Outflows, Notlnfl()ws
The implementation of exchange rate policy.alsowas
influenced by the nature of capital controls. Until 1987
capital controls in Taiwan focused on preventing capital
outflows. For example, the government required that all
foreign exchange be sold to the central·batik in exchange
for local currency. (Authorized foreign currency depositsin
local batiks were exempt.) In contrast. to the stringent
controls on outflows, Taiwan his~orically had no effective
controls on capital inflows. In particular, foreign asset
holders could easily acquire NT dollar assets through the
banking segtor.
The aSYnllnetry in Taiwan's capital controls was.reduced
in 1987 when the governmentsignificantly tightened restrictions on capital·inflows.while liberalizing capital outflmvs. (These measures were in. response to a surge in
short-term capital inflows discussed later;) In May 1987,
the government froze the outstanding amount ofcommercialbanks' foreign liabilities at US$13.8 billion (the level
of May 31,1987) and in July 1987restricte4 inward remittances for each person to US$50 1000 per year. ~strictions
on capital inflows were.liberalizedin 1989 when the limit
on individual remittances was raised to US$200,OOO in
July,·toU~$500,OOOin September,and to US$lmillion in
November 1989.
At ~bout the same time asrestrictions on capital inflows
were being imposed, restriction~ on capital ()utflows were
liberalized. Current account transactions were completely
liberalized on July 15,1987, and individuals or companies
were allowed to purchase and remit outward up to an
annual limit of US$5 million.
Thin and Underdeveloped Markets
'i'
As is the case in many developillgeconomies, Taiwan's
domestic financial markets are relatively underdeveloped.
15
Table 1
Financial Sector Policies
pre-1979
External
N~wTaiwan
(NT) dollar pegged to the U.S; dollar.
All foreign exchange transactions require governmentapproval. Current account transactions and capital outflows
restricted. Exporters required to surrender their foreign currency eamings to the government.
Moderate restrictions on foreign bOrrowing by financial institutions, and on certain capital inflows.
Domestic
Government determines interest rates set by banks.and in money and capital markets.
External
February
The foreign ex:change.rnarket is established and a managed float is adopted.
1979
The spot central rate ofthe U.S.dollar against the NT dollar henceforth to be setdaily by 5 major authorized banks
on the basis of the weighted average of interbank transaction rates on the previous business day.
The buying and selling rates for the U.S. dollar between the bank and the customer are set within the limit of
NT$O.05 above or below the central rate for transactions up to US$30,OOO. For larger transactions, the correspoIlding limit is NT$O.lO.
1980
External
January
Privately held foreign currency deposits in authorized banks. permitted.
March
Daily exchange rate ceiling abandoned by Central Bank.
Domestic
November
Banks allowed to set their own interest rates on NCDs and debentures, as well as on bill discounts.
A committee of the Bankers' Association is authorized to set, on a monthly basis, actualdeposit and loan rates
within ceilings determined by the Central Bank. The Central Bank sets maximum depositrates and maximumand
minimum loan rates.
Interest rates on· commercial paper, bankers' acceptances and Treasury bills·are fully liberalized.
1982
External
External
September
Central rate trading system established in the foreign exchange market with the exchange rate to be based on the
daily weighted average exchange rate of interbank trading.
1983
December
Offshore Banking Statutes established allowing local banks to engage in offshore banking. business.
1984
External
August
Bank restrictions on the holding of long positions in foreign currencies removed.
Domestic
November
Range of maximum and minimum loan rates widened by the Central Bank. The base loan rate lowered
Y2 percentage point.
(continued)
16
Economic Review .j 1992, Number 1
Table 1 -Financial Sector Policies (continued)
Domestic
1985
March
BanJ(s allowed to set prime rate. according to market conditions.
August
Banks allowed to set own rates on foreign currency deposits.
Banker's association to set the range of maximum and tninimUIn lending rates while the individual banks allowed
to charge customer rates based on credit rating and loan maturity date.
External
1986
October
Allowedforeigri banks to set up second branches in Taiwan.
Domestic
March
...
.....
..
.....
... .. ...
. ....
. ..
Limitation on the holding position and underwriting of short-term bills issued by any single firm removed .
. Upp~r lill1it~nc~rnll1e~cialp~perllnderwriting··forthebr~~ches~f· fo;eig~ banks raised.
External
May
1987
The Central~ank freezes the outstanding amount ofcommercial.banks' foreign liabilities at US$ 13.8 billion, the
level of May 31, 1987.
June
Foreign banks permitted to join the local inter-bank remittance system and the interbank ATM sharing. system.
July
Current account transactions are completely liberalized on July 15. Requiremynts to surrender export proceeds,
advanced import deposits and restrictions on payments for invisiblesare lifted.
An individual or a company is allowed to purchase and remit outward up. to an annual· limit of US$5 million.
Aceiiing on inward remittances for each person set at US$50,OOO per year.
October
The Central Bank lifts.the freeze on baIlks'. foreign liabilities on October 1, 1987. Following capital inflowof $3
billion, the Central Bank reimposes a freeze at $16.2 billion on October 2.
Borrowing of·foreign exchange by nonbanks is not subject to the freeze.
1989
External
April.
... .
.
A new system offoreign exchange trading is established,based on bid-ask quotations. The new system appliesto
interbank trading and retail trading over US$lO,OOO. The previous limits on daily fluctuations of the interbank
rate are rescinded.
July
The ceiling for banks' foreign liability is raised to 30% of the average daily balance during the 45-dayperiod
ended July 15, 1989.
The ceiling for inward remittances for each person is raised to US$200,000 on July 20.
i}.ugust
Foreign exchange interbank call loan market established.
September
Annual capital inflow increased from US$200,OOO to US$500,000perperson.
November
Capital inflow limitation increased to US$1 million per individual.
Domestic
July
All •remaining· regulations controlling maximum deposit rates and • maximum and· minimum loan rates are
eliminated.
Federal Reserve Bank of San Francisco
17
Although interest rate restrictions were gradually liberalized in the 1980s and a 1989bankihg law significantly
liberalized entry by allowing foreign banks to offer a full
range' of banking serVices, restrictions on the financial
sector had an important effect on financial market behavior
for intichof the decade. Financial policies have traditionally guaranteed a dominant role for government-owned
domestic banks. These policies included entry restrictions
(particularly" branching and operational restrictions' that
have limited the activities of foreign banks) and restrictions on deposit and loan interest rates that tended to limit
competitive pressures. 4
Financial sector restrictions tended to segment financial
m.atketsluid reduced the allocation of funds outside the
regulated financial sector. Flow offunds .data reported by
the Central Bank.of China (1989) indicate that up to the
lllid-1980s, more than 50 percent of the financial uses of
fllndsofhouseholds and non-profit institutions were channeledt6 regulated finanCial market intermediaries, notably
banks.
.
Outside of regulated financial intermediaries, the bulk
of household funds was channeled to two sectors. First,
households placed funds in the unregulated"curb" market. On average, this sector accounted for less than 8
percent of household uses of funds, and its share tended to
decline in the 1980s. Second, households invested between
}Is and Y3 of their funds in capital markets. Tne bulk of such
investment was in the dit:ect acquisition of shares in enterprises or in the stock market.
Stock market shares were the only tradable securities
readily available to household investors. By all accounts,
this market was quite thin, and a relatively limited amount
of capital was raised in this market. In the period 1980-85,
companies listed in the stock market accounted for only
about 16 percentofthe total capital of Taiwan enterprises,
s6that households may have allocated as little as 3 percent
(the 20 percent total·flow allocated to capital markets times
the 16 percent share of listed firms in the capital of
registered enterprises) of their funds to the stock market in
the 1980s.
The allocation of household funds to long-term bonds,
or to'money markets was negligible. The holding of longterm bonds (mainly central bank securities) and money
market, instruments (negotiable certificates of deposit,
bankers acceptances, and commercial paper) was dominated by financial intermediaries.
To sum up, three features characterize the maCJ:'oeconp!Aicahd financial environment in the 1980s. First,
exchange rate policy was influenced by the desire of
poiicymakers to preserve the competitiveness of the export
seCtor and by a policy rule that limited fluctuations in the
18
exchange rate. Second, until 1987, capital controls curbed
capital outflows but did not effectively restrict capital
inflows.~ubsequent1y, capital outflows were liberalized,
while, inflowswererestrlcted. Third,Taiwan's secondary
financial markets were thin and underdeveloped.
fl. A
SMALL OPEN ECONOMY MODEL
To assess the implications of the institutional characteristics of Taiwan's economy, consider static, small open
economy model with flexible prices. There are three assets:
40mestic money (m), a domestic financial asset earning
nonzero returns (h) which will be called a bond, and a
foreign ,asset if) denominated in foreign currency.
FOfconvel1ience, the return on the foreign asset is fixed
at zero. Real money demand is theil a function of the
nominal return on the domestic asset (i), the expected rate
of appreciation of the domestic currency (x), real wealth
(w), and real income (y). In what follows variables in lower
case, except for i and.x, are in logs. To simplify the discussion, which is mainly concerned with the effects of shocks
to exchange rate expectations, we assume inflationary
expectations are exogenous and set them to zero.
In. equilibrium real money supply equals real money
demand:
a
wherep is the domestic price and mj<O; mx,my, mw>O.
In equation (1), i reflects the opportunity cost of holding
money rather than the domestic bond, while x is the cost of
holding the foreign asset.
The equilibrium in the market for the foreign asset may
be expressed as follows:
where St denotes the nominal exchange rate (foreign currency/NT$). Itis assumed thath, fx<O,/x' fw>O. Since
real money and foreign asset and domestic bond holdings
comprise total wealth, equilibrium in the domestic bond
(h) market follows from the wealth constraint and equations (1) and (2).
The .economy produces a single internationally traded
good. Domestic demand (at) depends on wealth, while net
exports (l?t) are determined by wealth and the re,al exchange rate rt = St +Pt - p/, where p/ denotes th€t (exogenous) foreign price. Equilibrium In the goodS. market
re9uires ,that the sum of domestic and net export demand
equal an exogenously determined national income: 5
Ecoilomic Review / 1992, Number 1
where aw,bw>O; br<O. In th~ model, s, p,andr are endogenous and can be solved using equations (I), (2); and
(3).As shown in Appendix A, the model yieldsthefollowing reduced form responses to shocks to the exogenous
variabl~s:6
(4)
~1=s.lu,+snAm/ +sf·il
Its,
\
s"YO,sm< 0, sf> 0
where A is the first difference operator,so ASt = St- S, ~ t.
We focus on~.e effects of disturbances to exchange rate
exwctations,the money supply, and foreign assets because
they are particularly. relevant for Taiwan's case over the
time period b¢ing discussed.
Underplau~ibleassumptions,.an expected. appreciation
(a ris~in x) increases the demand for domestic assets,
resulting incutrency appreciation,alower price level, and
a.declineintbe domestic interest rate. An increasein the
money supply creates an excess supply of money, resulting
ill. the depreciation of thedomestic currency, anincr~ase in
thedomestic·price level,and a lower domestic interest rate.
An increase in the supply of the foreign asset creates an
excess demand for domestic assets, resulting in currency
appreciation, a lower price leveLand. a decline in the
domestic interest rate. (qualitatively the same as. an expectedappreciation). These effects conform to what might
be expected from intuition.
Implications of Institutional Characteristics
Tlie institutional characteristics of Taiwan's economy
described in Section I affect tbe. specification of the model
or the model's parametersin a number of ways. In Taiw~,
th~ absen~eof • restrictions on capital inflows .• allowed
speclliators ·to arbitra~e between .domestic and foreign assets (it is assumed that.speculators who use. foreign assets
to acquire· domestic assets can reverse such transactions
with .• relative. ease,.. as. seems· to h~lVe been the. case in
Taiwan). This·is reflected in tbe assumption that exchange
Federal Reserve Bank ofBan Francisco
rate expecta,tions affect the d~mand for domestic assets. If
capital controls were effective, speculators would be una~le tp exchange their foreign assets for domestic assets il,l
r~sponse to.changes in exChange rateexpectations~andthe
terms$x, Px' lx in equations (4) to (6) would equal zero.
.In small open economy models that assume perfect
substitutability between domestic and foreign.assets, the
domestic interest rate is determined by the interest parity
condition i. =. x. However, the thin and relatively less
developed financial markets of Taiwan suggest that domestic and foreign assets. are imperfect substitutes. As a result,.
the domestic interest rate i, and exchange rate .exwctations
x enter s~paratelyin the model rather than being direc.tly
lirikedbyan .arbitrage condition. 7 Thin and undeveloped
finan(:ialmarkets.alsoreducetheinteresl seqsitivity.ofthe
demand for money and foreign assets'(mi andft).•·InsWCtion ofAppendix A'shows that this increases.therespollse
of interest rates (or asset prices) to shocks to exchange rate
expectations ortochanges in the supply of domestic money
or foreign assets (ix' im,. ~ increase in equation (6».
Relatively weak arbitrage liriks may partly explain why
(:ertain ass~t.prices in Taiwan-notably the stock pricechanged much more sharply than did comparable asset
prices in the U.S. arid Japan in the later part of the 1980s.
Implications of Exchange Rate Policy
Adjustment when the intervention outcome is credible. To
highlight' the consequences of central barik intervention
m<:>re fully, ·it.is useful to recall that the central barik can
change the money supply in two ways. First, it.can intervene in the foreign exchange market, which will. be reflected il,l changes. in the. net foreign assets held by the
central barik,labeled.f,"b; Second, it can undertake open
rnarketpurchases or sales of domestic bonds that change
tbe supply of domesticcredit, dt .. These implications of the
central. bank balance sheet are approximated by:
where W, 1- W are respectively the average weights of net
foreign arid domestic assets in the central barik balance
sheet.S We assume for now that the government changes the
money supply only by intervening in foreign exchange mar~
ketsand. thatthere are no domestic open market operations,
so Adt=O. This is known as "unsterilized" intervention.
Suppose a shockraises the expected rate ofappreciation
inthecurrencyfrom 0 in period 0 to Xl in period I. The net
change in the exchange rate in response to this shock is the
sum ofthe changes inthe. exchange rate attributable to the
private sector and the government,
19
(13' ),
(8)
-asxAx
1\ Feb _
1
W~Jl - .
Snja
wl1erethentlmer~l subscripts refer to the titne IJe~()d. ,The
change in the exchange rate attributable to the private
sectorfollows from equation (4): '
The change in the exchange rate attributable to the government depends on the government's exchange rate policy.
Suppose that. the government has a policy of reducing, the
rate ofchange iothe. exchange, rate ,that would otherwise
resllit from private sector actions by a proportion O~a<l.
This policy ,can he described by the"following equation:
(1,0)'
~S 1g =
-a& 1P= -asx
Axl '
Thefirsfequality in equation (10) is thegoverntnent's
exchange rate rule. The, second equality follows from
equation (9). Eqtlations (8), (9), and (10) thenimplythat
the, one~period change in the exchange raJein response toa
shock to exchange rate expectati()ns is:
~ \'~; ~ . . ' .
.
".
'Wecan)use the. preceding' framework to. assess the
itnplicationsof policy and behavioral parameters. Equation{ll) implies that the government can limit exchange
rate changes to any degree desired by increasing the
intervention parameter ex. However, greater exchange rate
stability will be associated with a larger change in the
money. supply 'and in the net foreign 'assets held by the
central bank (equations (12), and (13». This is a familiar
tradeoff.
Equations (12) and (13)al§0 indicate that the volume of
. intervention required to satisfythe exchange rate objective
(10) is afunction of institutional and behavioral parameters. 'The required, intervention is larger, the larger the
impact of expectations on the exchange rate sX' As discllssed in Section I, if capital were not mobile, Sx = 0 and
no intervention would be required forthe government to
achieve its exchange rate target. Tlie required intervention
is smaller, the larger the impact of such intervention on the
exchange rate (snja)'
Adjusttnerttwhen the intervention outcome is notcredible.
The" central bank can. implementthe exchange rate rule
(lO)by increasing thetnoney supply in order to purchase
foreign "bonds in the foreign exchange' market.-In the
absence of offsetting domestic open market operations,
this will be reflected in an increase inthe money supply and
a>tnatching reductionin the supply offoreign assets held by
domestic residents (~mf= '--~fn. Equations (4) and(9)
imply that in order'to meet the central bank's foreign
exchange target, the money supply must adjust to a shock
to exchange rate expectations according to the following: 9
(12)
where we define the coefficient Snja=sm ~sl<:O. In the
absence of domestic open market operations, the central
bank balance sheet relationship (7) implies that ~mf =
W~!Icb. (The reader may recallthat w, the average share of
foreign assets held by the central bank, appears in this
expression because we are using a logapproximation tothe
central' bank balance sheet.) Using this last equality to
substitute for ~mf in equation (12), we find the increase in
the foreign assets held by the central bankthat is consistent
with the exchange rate target,given an initial shock to
exchange rate expectations:
20
The discUssion up to this point has focused on the oneperio<i response to a shockto exchange rate expectations.
The total change in the exchange rate in the long run will
depend on how expectations, so far treated as exogenous,
areaffectedbyintetvention. Supposethatthe outcome of
intervention is credible, in the.sensethat speculators believethat there wilFbeno further change in the exchange
rate. Then agents will make no further effort to acquire
domestic assets. Equation(ll) then describes the total
change in the exchange rate that will occur in response to
the initialshocktoexchange rate expectations.
To see/how the pattern of adjustment differs when the
outcome of intervention is notcredible, assume that speculatorsbelieve that the exchange rate must ultimately
adjustto Some target exchange tate s*, regardless ofthe
short-runattempts of policymakers to prevent such adjustment. We can think of s *as thelevelof the exchange rate
that will satisfy some long-run equilibrium condition (for
example, the value of the exchangerate thatwill guarantee
that {he net present·· value.' of an economy's external liabilities is zero). Alterriatively, we can think of s* as the
level()f the exchange rate that is seen as acceptable by a
country's major trading partners or a country's creditors.
Consider noW- a shockto exchange rate expectations in
period 1, caused by a one-time increase ins* above the spot
exchangetate,or (s* :"-so»O. Speculators acquire domestic assets onthe expectationthat the gap between the target
exchange rate s* and the spot rate So will be eliminated.
Economic Review / 1992, Number 1
When.markets.·reopen in the next period, the government
has prevented full adjustment in the spot rate to s* by the
proportion (l=.a.) (as in equation (11», and speculators
again acquire domestic assets on the expectation thatthe
remaining •. gap .between. s* and the··.• spot rate will be
eliminated. This process of repeated domesticassetacquisition and. intervention will continue in subsequent
periods, producingfurther changes in the. exchange rate. In
effect,we cansay thatintervention spreads the initialshock
to exchange rate expectations over several periods. In each
period, the shock to expectations is measured by the gap
between the target rate and the spot rate:
(14)&:1 =S*- SI_I;t= 1,2,3,... ,
wherelixl.is now. the shock to exchange.rate expectations
that?ccurs in each period as a resultof the initial increase
ins* above so'
In equation (14), the path oflixtdependsonthepath of
St. We can solve for the path ofst by using equations (4)
and (14), which yield the· following difference equation:
where the coefficientsx is implied by eqllation (4). 10
As discussed in Appendix B, t.l}e solution to equation
(15) is:
where
O~I3==1-sX<1~a)~1;Equation(16)·shows that.
th~rateof change intheexchangerate ineachperiod after
tile initial shock depends on the rate of intervention a and
the magnitude oftheinitial shocktoexchange rate expecta-'
tions. The term W- 1 impliesthat the rate of change in the
exchange rate declines asymptotically towards zero. In the
absence. of intervention (a= O),thefull impact ofthe shock
to expectations is felt in the first period;·· and· according to
equation (4)the exchange rate changes by ~Sl==sx(S*-so)'
From equation (16), the cumulative changein.theexchange rate overTperiods that is.associated withtheinitial
shockis:
T
(17)
T
L Lls1=(l-a)sxL (jt-l(s* -so),
1=1
1=1·
Chartl illustrates. the path of exchange rate changes
implied. by equation (16). The area under the curve is
measllredby equation (17); The chartassumes a ·100
percent appreciation in the. target . exchange rates;!, ,and
sx==1 .. 'rhepathsofexchange ratecl1anges areillllstrated
for the cases in which the rate of appreciation in each
periodis limited to 2.5 percent (a =.0.975)andlOpercent
(a = 0.9).
Inspection of the chart and the equations suggests that
Chart
Response to Appreciation in Target. Exchange Rate
under Alternative Rates of Intervention
Billions US$
15.0
12.5
Changes in
Reserves
10.0
~
7.5
I
,-\
I
I
I
5.0
Current Account
I
J
J
./I
2.5
O.O+·~=7~F---=:"~~··:--~·-~o--O'ir--"~·-:-~~-;~-o~""'."~;""'\.. ~-/":'---------=.......:j~i-\ -toTf-~
Capital Flows
-2.5
\\1
"t
-5.0 +--..,...-----..,...-.--..,...--..,...--..----..-----=,.---'-.-------.------,
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
Federal Reserve Bank ofSan Francisco
21
the expectation that the spot exchange rate in any.given
period will tend to some target s* affects thepattem of
exchangerate adjustment in anumber of ways.
First,·. intervention.. can distribute the impact. of a·.one-
time shock to expectations over time under certainassumptionsabout the adjustment ofexpectations. The reason is
that speculators seek to acquire domestic currency-·.and
create. upward pressure on> the currency-in every period
solong as the exchange rate is below s*. In contrast,. when
the.outcome ofintervention.isctedible (as in equation
(11»,· the exchange rate change lasts only one period.
Second, intervention is effective in the short run, but not
.initheilongrun.In the absence ofinterventi()n .(a:=::O), the
spot exchange rate would appreciate 100 percentin one
period~andthere would be no further . changes·· in•.·the
exchangerate. In contrast, in Chart I, for the case a =0.9,
the cumulative change in theexchangerateislimited to 10
percent in the first period. and 65 percent after 10 periods.
While intervention does stabilize the exchange rate in the
short run, in the. very .long run the spot rate converges
to S*.11
Third, thecu111ulative intervention is larger when the
outcome ofintervel1tionis notqredible. Equation(13}is
now the starting poinf for· a .sequence of intervention
actions, . rather than representing • . the total .• intervention.
Cumulative intervention over Tperiods is now given by:
(18)
wlij;Cb =
T
T
snfa 1=1
Snja 1=1
-a~LLUI = -a~ L
{3l-1 (s
*
-sO>'
where the second equality follows because, from equations
(15) and (16), Ax, W- 1(s* - so), Over 'an infinite horizon, cumulative intervention is:
=
lim w~..
IiC = -asx(s • -so> T-+(XJ
.lirnl··~
. {31.i.·•.
LJ
L.J
b
T~(XJ
J.
1
1=1·
Snja
1=1
(18')
a(s • -sO>
(1 - a)srifa '
which exceeds intervention in equation (13) by
cumulative. intervention. As can be .seen in Chart 1, if the
rate of intervention is very large (a= .975),the first-period
change in the exchange rate will besmall,but subsequent
exchange rate changes will decline very gradually. If the
rate of intervention .is smaller (a=0.90) the first period
change .in •. the exchange rate will be· quite large, but
subsequent exchange rate changes will drop off more
steeply. The reader can verify that cumulativeintervention
in equation(18').increaseswith the. rate of intervention a.
Instability
The preceding analysis predicts a gradually declining
rate· of change in the exchange rate. At times, however,
changes in the exchange rate ac.celefate·· l"atheftharf die
down gr~d.ually. There is no easy way of modeling s~ch a
pt()cess. ()Ileway toproc.eed is to ~ssume that speculators
believe that the adjustment to the target exchange rate will
need.to be .larger the longer the. gap between tl:1e •spot and
the target exchange rate persists.
To motivate this last assumption, consider a country
whose large trade surpluses provoke threats of protectionist retaliation by its trading partners. Agentssetthetarget
exchange rate s,*, which now may vary from period to
period,at a level they think will reduce trade surpluses by
enough toavertretaliation. Theyrevisetheirestimate ofst *
upward if the news .this period indicates no reduction in the
trade surplus or complaints by trading partners. OtherWise,
the target s,* remains unchanged or is lowered. We can
think of a situation where intervention prevents equilibrium exchange rate adjustment, resulting in a sequence
of increasing trade surpluses. This in turn prompts a
sequence of upward revisions in st * that are associated with
~ccelerating. appreciation .• over .several •periods.. In •this
manner, theinteraction between intervention and expecta-
tions may·be destabilizing. 12
To illustrate this argument in. a simple way,. assUme that
the target or equilibrium exchange rate grows at the constantrate (1 + <1» when the exchange rate is below target,
where <1»0. Suppose also that in period lthere is a shock
that raises the target exchange rate by a factor (1- <1», so
that (S1* = (1 + <I»so*)' Then, so long as the positive gap
between the target and actual exchange rate remains, in
subsequent periods,
a{3(s • -sO>
(l-a)Snja
By suitably modifying equation (14), we havethefollowing
sequence of shocks to expectations:
Fourth, the rate ofintervention influences the pattern of
exchange rate adjustment over time, as well as the total
22
Economic Review / 1992, Number 1
Bymodifyirigequation (15), we·find that the change in the
c;:x6hilllge rate in each period is now governed by
Tlie solution to this difference .equation, derived in AppendixB, implies ,that:
(22).1s,=(1-0l)Sx(So· (1 +if»IZI-fjl-ISO )'
wher~Zt ,is· defined in AppendixB . .In equation (22), the
Rath()ftheexchange rate is unstable, and the rate, ofchange
in the exchange rate increases overtime. ThIs instability is
associated with the shocks to exchange rate expectations,
w6ic6areincreasil1g .in each period. Equating, t in
equations (21) (first equality) and (22), we can express the
shocks to e)(pectations interms of the starting values ()fthe
target and spot rates:
aS
Effects on Velocity and Asset Prices
In the unstable. case just described, the target r~te is
growing each period, producing increases in theexpeeted
rate of appreciation in'each period . According'to equations
(4) to (6), these period..to-period changes in exchange rate
expectations· will affect the price level and domestic interest rates as well as, the exchange rate. FUrthermore, the
government's intervention rule implies that these shocks to
expectationswillbeassociatedwith increases in the money
supply and matching increases ,.in the .. netforeign, asset
holdings ofthecentralballk. .To determine the combined
effects ofshocks to exchange rate. expectations anclmoney
creation on the cumulative change in thepricelevel,note
thatequatidn•• (5).impliesthat:
l'
.(26)
l'
l'
Lap, =PxLAx, +pn/awLAf,Cb,
1=1
1=1
1=1
wh.ere,fromequation (5), Px <0; Pnfa = Pm - Pf>O. Applying (23) and (25) to (26) we obtain:
Cumulative changes in the exchange rate and cumulative
intervention now, grow without bound and are respectively
described by: "
(26').
7'..
L.
,'=1
(24)
and
where we use equation (23) to obtain equations (24) and
(25).
In the precedingwe have. assumed that speculators ac~as
if<f> isfixed,so thats/ increasesJorever. This assumption
allows us to solve a difference equation. In reality,however, the value of<f> and the contillued accumulation of
positive changes to the exchange rate. in equation (24) will
depend on news about the external balance or the reactions
oftrading partners or other pertinent events. Once agents
receive the news that trade surpluses have fallen· Or that
trading partners are satisfied with the currentlevel ofthe
exchange rate, exchange rate appreciation will·cease,and
may even, sharply reverse.direetion if s* falls below St.
Federal· Reserve Bank of San Francisco
.L (so' (I +~)'Z,-P'-'s,,)~1J
.!.OlSP .]..
I#J, =p., - '
,
'"
sn/a
1'
1=1
Equation, (26) shows. that.the inflationary· effects of the
seguenceof increases in the money supply due to intervention(PnR}IlI~=laf/b>O) are, offset. by .the. deflationary
effectsofthesequence ofpositive shocks to exchange rate
expectations(pxI~= rAxt<O). Asa result,' less than pro..
p()rtional'· increas~s in· the price level· maybe. associated
with money growth. Given a constant leveFof real' GNP,
this may resultin persistent declines in velocitY (the ratio
of nominal GNPto money).
Equation (26') shows howthe path of t4e, price level
depends· on the underlying behavioral and intervention
parameters. Itis apparent from (26') that velocity may decline at an accelerating rate influenced by the magnitude of
<f>. Also, the deflationary effects of shocks to exchange rate
exp~tationswilltend to be larger,the larger isthe,impact
ofexpectationsontqeprice level (Px)' If these deflationary
effects .aresllfficiently large, the•money growth. resulting
from int~rventioncould • be associated with· a declining
rather,than increasing price level. Thus, an increase in the
money supply resulting from intervention will be associated .with·· a less ·than proportional increase in. inflation
(and possibly deflation) and with persistent and acceleratingdeclines in velocity.
23
To determine the impact of shocks to exchange rate
expectations and associated intervention on asset prices,
we use equations (6), (23), and (25) to obtain:
(27)
where, from equation (6), ix<O;.im<O;~<O, and we as"
sumethat itifa=im-it<O. Equation (27) saysthat both the
sequence .of .increases. in .• expected appreciation and the
expansion in. net foreign assets and. money will contribute
to persistent and accelerating declines in the domestic
interest rate, or, equivalently, to persistent and accelerating
increases in the domestic bond price. As noted in ·our
earlier discussion of the implications ofinstitution.al characteristics, the magnitude of the changes in the domestic
interest rate (or domestic asset price) will be larger if the
domestic bond is a poor substitute for Qomestic money or
the foreign asset (in such a case the results in Appendix A
imply that ix and itifa will tend to rise in absolute value).
To sum up, the preceding discussion illustrates how the
credibility of intervention policy may affect the pattern of
exchange rate adjustment. When the outcom~ of intervention is credible,.any degree of eJl.change rate stability can
be achieved at .the cost of a. sufficiently large, (lne-time
change in the money supply. When the •. outcome of interYyntion is not c:redible, however,. intervention can lead to
persistent and possibly accelerating changes in e~change
rates, the m(mey supply, velocity, and asset prices . .T1nder
certain conditions, .intervention may even amplify. the
cumulative change in the exchange rate ratherthan reduce
it. The increased exposure to external shocks thatmay be
associated with unsterilized intervention is typically of
great concern topolicymakers.
Reducing the Exposure to External Shocks
The government may attempt to reduce the eco~omy's
exposure to external shocks in three ways. First, the
monetary effects .of exchange. rate intervention .may be
offsetby adjusting domestic credit. Such a policy is kIl.own
as "sterilized intervention," and can be described by the
rule:
where "I is the degree of sterilization. The central bank
. balance sheet equation (7) then implies that the change in
24
the. money supply. associated with intervention is Ilm/=
(1-"1 )wllt;eb.. IUs apparent thatthechange in the money
supply associated with intervention falls as the rate of
sterili1;atioIl'yrises. Nevertheless, there is a limit to how
much. policymakers can sterilize. One difficulty· is that
sterilization may be incompatit>lewith the government's
exchange rate policy, as it reduces the impact of intervention on. the eJl.change rate. With sterilization, the change
in the exchange rate associated with government interven-.
tionis:
wher~ f~fa -;Snfa <Oandtl1e gap between the twoexpressiRnsi~creases'Yiththerate.ofsterilization "I. The effect of
sterilized intervention on the exchange rate falls as therate
of sterilization "I'rises. If sterilization is complete ("I = 1),
so that therds no change in the money supply, the impact of
intervention on the· exchange. rate is entirely the result
Rfthe exchange of foreig~fordomestic bonds, as reflected
inthe t~11Il- sj»lli/b. .secause. sfdeclines as, the degree of
substitutability increases, the impact of sterilized intervention also declines. Intuitively, sterilized intef\Tentionprovides the speculator with a domestic bond rather than with
har"n,...:.&::r. .fn..... ·f.ha.f..,......:o.;...,...." nC'lS"'~
moneyl11e~cJ.,,<,15'" ~\.u U.l"" J.V.l,",.l5Ha~ "'I..
0
"
",
'0
••••••
The ...,.._.. . . 0+.....,...
.111
............
e,l~al.~l lll~
sUbstitutability of the domestic bond for the foreign asset
relinquished by the speculator, the smaller the impact on
the exchange rate.
Aside •from being potentially less effective, sterilized
intervention may require the government to issue debt
instruments in order to bring about sufficiently large
adjustments in domestic credit, ifcentral bank holdings of
marketable securities are insufficient. In the absence of
changes in fiscalpolicy,theintertemporal government
budget constraint implies that government debt instruments issuedtoday mustbe redeemed by printing money at
sometime in the futlue. Thus sterilization may reduce the
changeinthemoney supplytoday at the cost of a larger
change in the money supply in the Juture.
Second,thegoyernment. can. impose capital· controls.
Suchcontrols tend tpinsulatetheeconomy from the impact
~f .·exchange rate expectations. by.• making. it difficult for
speculators to transact inforeign exchange markets .. Capital controls reducesx ' Px' i x in equations (24), (25), (26'),
and (27). Inspection ofthese equations shows thatover any
finite· horizon,cumulative • changes in the.exchange rate,
intervention, and any related disturbances to the domestic
price level and the domestic interest rate associated with a
shock to exchange rate expectations decline as these coeffi.... -~cients-decline;-Ifthecontrols-areso extensive that they are
Economic Review / 1992, Number 1
interpreted as a major regime shift, they may also drivethe
target exchange rates,* below the spot rate and cause a
reversal in the path of the exchange rate. While this
possibility is not explicitly modeled here, it was probably
important in Taiwan's. case.
Third;the.government can reduce. the rate ofinterven"
tion, thus allowing the exchange rate to float more freely in
eachperiod:.As suggested-by our discussion of Chartl,
reducing the tate ·.of intervention tends to reduce the
persistence ofchanges in the exchange rate attributable to a
one-time shocktoexchange rate expectations.
1l1.···TAIWAN's EXPERIENCE
To. analyze Taiwan's experienceinthe 1980s, we examine the path· of the exchange rate and some.of the factors
Chart.2
TahNal'l " ...'
currelltAccountandExchangeRates
BIllions US$
Index
140
6
5
,
130
Current Account
(left scale)
4
3
120
Real Trade-weighted
NTPollar (right scale)
110
~~.t>ti\.
2
1
100
\
90
-1
Nominal US$/NT$ E)(change Rate
(right scale)
+-----,,---.--r----r-:-..,.--~-----,""7""'......,..-----,-,.""7""'.,,-----+
80
1980 1981 19821983 1984 19l15 19861987 1988 1989
Chart 3
, Taiwan
Change~. i.n Reserves, $hort-ter l11
C~pital Flows, and the current Acc.ount
11
10
9
8
7
'C
o
i6,
c.
a=O.90
i5
~
4
3
2
~~.~ . ;,.~.~
1
.
o+m-""":'!r"'"'TTlJTT'r'!'IT!~;;;?ii'm'!!!"I'I'I'!l'!!!!l'TTl'Tl!!!1"'""TT1'!~~~
1
. 10
20
30
40
50
60
70
80
90
100
period
Federal Reserve Bank of San Francisco
25
that may have influenced exchange rate behavior. For this
purpose, Chart 2 shows the nominal US$/NT$ exchange
rate, the real trade-weighted' NT dollar, .and· the current
account in the 1980s. We also examine the pattern of
intervention of the central bank by reviewing changes in
foreign exchange reserves by the central bank, and its two
rnajordeterminants-short-term capital flows • and the
account, illl1stratedin. Chart 3. 13
InChart'3, changes in the foreign exchange reserves of
the central bank are a proxy for intervention. To ascertain
the suitability of this proxy, we needto do twothings. First,
we need to determine the extent to which changes in
reserves resultfrom shocks toexchangerateexpe~tations,
as only such changes can be said to correspond to interven.:.
tion in foreign exchange markets. To deal with thisques~
tion, we note that when there are positive shocks to
exchange rate expectations speculators attempt to acquire
domestic assets, and the central bank intervenes to dampen
the resulting upward pressure on the exchange rate. These
actions will simultaneously be reflected in the balance of
payfuents accounts as an increase in short-term capital
inflows and in the foreign exchange reserves held by the
central bank. The converse holds when there are negative
shocks to expectations. Thus, ahigh correlation between
short-term capital flows and changes in foreign exchange
reserves indicates whether such changes largely reflect
intervention.
Second, we need to assess thelikelyeffects,of systema~
tic changes in foreign exchange reserve holdings that are
unrelated to intervention. In the case of Taiwan, the main
source of such systematic changes was the requirement, in
effect until July 1987, that exporters surrender their foreign
exchange earnings (see SectionI). The path of the current
account balance thus provides an indicator of the influence
of the trade sector on foreign exchange res,erves.
As illustrated in Chart 3, changes in reserves are highly
correlated with short-term capital flows, in spite of. a
widening gap between the level of changes in foreign
exchange reserves and short-term capital flows in the
course of the 1980s. This widening gap is attributable to
the rising current account surpluses that are also shown in
the chart. Thus, changes in foreign exchange reserves
appear to be a reasonably good proxy for intervention in
Taiwan in the 1980s.
current
Patterns in the Exchange Rate, Capital Flows,
and Intervention
Inspection of Charts 2 and 3 suggests that the1980s may
be divided into three periods. In the first period, 1980:1.:.
1985:3, there was a downward trend in the US$/Nr$
exchange rate up to 1982, followed by a period of stability.
,
26
Iri this period, the exchange rate against the US. dollar on
average depreciated ata. compound· annual rate, of just
under 2 percent, in spite of growing current account
sUrpluses. The real trade-weighted exchange rate also
exhi9ited ,a. slight· downward trend. Short-term . capital
flows and the associated intervention were relatively slllall
(capital outflowS averaged $128 million per quarter),and
showed no systematic trend. The relative tranquility in
foreign exchange ,markets. suggests. that speculators did
not doubt the government's ability to limit movements.in
theNTdollm;over this period. In terms of the model developed in Section II, it appears th~t adjustments in the
~x.cba.ng~rlitein response to shocks could be described by
equation (11).
Doubts aboutthegov~rnment'sability to preventthe NT
dollar from appreciatingagainstthe US. dollar appear to
have arisen in the mid-1980s. One reason is that the NT
dollar's relative stability against a falling US. dollar in
198? was •. associated with· a. shlifP real trade-weighted
depreciation that was incompatible with Taiwan's growing
extemalsurpluses (Ctiart 2). In this context, the statement
-by theG-5 industrial countries, following their SepteIDber
.1985Plaza,meeting, that the US. dollar should depreciate
further apparently created expectations that the Taiwan
governmentwouldhave to allow the NT dollar to appreciate against the U.S. dollar. This perception was reinforced
in;thecQurse of the', second 'half of the 1980s, ,as Taiwan's
trading partners , notably the US., openly expressed concernabol1tTaiwan's trade surplus and government exchange rate policy.
These developments provide the context for the behavior
of the exchange rate and short-term capital flows inthe second period, 1985:4to aboutl987:4. In this period,the rate
ofa~preciation in the NT dollar accelerated every quarter
fornearlytwoyears, from a compound annual rate of 2.2
percent in 1985:4 to apeak of nearly 31 percent in 1987:3.
Qn, average, the NT dollar appreciated against the US.
dollar at a compound annual rate of 14 percent in
1985:4-1987:4, comparedto an averagedepreciation of 1. 8
percent in the first period. There was a concomitant
increase in short-term capital inflows, which averaged
nearly U$$2.4 billiOIlper quarter, compared to average
outflows of US$128 million. in the first period. Largely as a
result of stepped-up intervention, the acclJmwation. of
foreign exchange reserves rose to. an average of U$$6.5
billion aquarter,from an average of under $1 billion in the
first period. By comparison to other economies, or to
'Taiwan's ownbist()rical experience, the amount of intervention was unprecedented. Taiwan's foreign exchange
res~rvesrose to a peak ofUS$77 billion in1987, third after
.Japan and, Germany in ·that year. (In domestic· currency
terms, foreign assets held by the CentralBarik ofChina
ECODomicReview / 1992, Number 1
(CBC) increased from NT$504billion in 1983, to a. peak of
Nf$2;26 trillion in 1987, about 30tiines its Ievelten years
earlier.)
The. discussion in Section II '.suggests that the. apparent
instability of the NT dollar and ofcapitalinflows over this
period may have been partlythe result pf government intervention in foreign •exchange markets,' in. a situation where
the exchange rate outcome of· such intervention. was not
crediblebecallseof rising current accountsur.plusesand
~xpressions of concern byTaiwan's majottradingpartners.
Inparticlllar, the behavior ,of thee"change rate oyer this
period appears .to be roughly consistentwith•the unstable
casedes(:ribed;,.byeqllation.(24),.while.·thesharp.• ac(:eleratipnillinterVentionappears to conformto equation(25). 14
The'. government sought 'to limit; 'the··jmpactofshocks
from the, external sectorin a number of ways (see discus,.
sioninSection I). First,!t s~ught to curb short-term capital
inflowsbyfreezing.the external liabilities of the banking
sectorat.the,end of May 1987 and then again in October
1987~Second, •it· attt::mpted to reduce the link between
ctirrentaccountsurpluses and changes inforeign exchange
reserves by lifting all restrictions on current account trans,.
actions irtJult 1987, including the requirement thatforeigl1
currency expOrt revenues be exchanged for domestic currency. Third~"it shifted to floating exchange rates in April
1989~
.
These policy measures were followed by maikedchanges
inthe. patt~TI1~of external distur~ances(llld their impact on
foreign exchange reserves, which characterized the third
period" 1988-1989. Restrictions, on, capital,·inflowS •prevented speculators ,from freely acquiring'Nf dollar assets,
contributing to a slowdow?.inthe rate of appreciation.'of
the. NT dollar to '8.3" percent, (the NT dollar actually fell
sharplY late inthe period, a declinethat continuedin1990).
Tbere was .also a reversal in short-term, capital inflows to'
averag~putflows of U$$1.2billion per q\larter,15 Thus, in
the later part of the 1980s, short-term capital flows had a
conthictionary irtflllenceon foreign exchange reserVes and
on the domestic monetary base.
The liberalization of current account transactions and
the shift to floating had strong effects oothe accumulation
offoreign exchange reserves of the central bank. As is
apparent. in Chart 3,/the gap between changes in foreign
exchange reserves and short-term capital flows 'was largely
eliminat~q.after 1987, when the requirementthatexporters
SUrrender theirforeign exchange reserves was suspended.
Changes in foreign' exchange' reserves diverged sharPly
from short-term capital flows after the shifttofloating in
the .second half of 1989, suggesting that the government
had stopped intervening.
.
Federal Reserve Bank of San Francisco
Effects onfheDomesticMoney Supply,
Velocity, and Asset Prices
The effects of intervention on the money supply were
influenced by the government's sterilization policy. To
describe this policy, we examine the patterns of changes in
net foreign assets and in domestic credit (the two components of the monetary base in equation (7)), reported in
Table 2. The table suggests that in the first two perioo;, net
( fpreign asset. expansion was associated with large reductions in domestic credit. The contraction in domestic credit
was largely accomplished through the issuance of interestbearing short-term central bank certificates of deposits and
savings bonds, as the supply of Treasury securities is
limited by Taiwan's conservative fiscal policy. Tabl~ 2,also
shows that domestic credit expanded very strongly in the'
third period. This appears to have been related to earlier
sterilization policy, as the Central Bank created money to
redeem its maturing short-termliabilities in that period)6
In spite of the high rate of sterilization, Table 3 shQ~s
that the rate of base money growth accelerated from an
average annual rate of 16 percent in the period 1980:11985:3 to 35 percent after 1988. The acceleration in money
Table 2
GroWthiin.• • coRlPonents
of monetary base
(billions ofNT dollars)'
80:2c85:3
85:4-87:4
88:1-89:4
Chllngein
foreign assets
Change in
domestic credit
1btal
. change
35
158
-24
-26
-128
79
11
30
55
Table 3
Growth in money and velocity
(compound annual rates in percent)
80:1c85:3
85:4-87:4
88:1-89:4
Money base
Ml
Mlvelocity
16.4
28.3
34.8
16.0
44.5
16.7
-2.6
-20.2
-2.5
27
growth initially reflected the direct expansionary effects of
intervention policy. However, base money gr()wthcontinuedto accelerate even after . the reversal of capital
inflows in 1988. One reasonisthat the government shifted
to floatipg exchange rates in April 1989, which limited the
contractionary influence of capital outflows on the monetarybase.
.
•Another . reason. for the. ·acceleration.iin . • base··Jl19Iley
gro\Vth in the. later partof the 1980sisthatthe rede~pti911
9fs~ort-termCBCpaper had astrongexpansio~ary imp~ct
ol!d?~estic credit. Thus, effo~ts to liIIlitmolletary growth
tlu'oughsterilization in the ll1id-1980scontributed to more
rapid~9Iley .growth later in the decade. 17
I'Ve growthofMlaccelerated fro~16 percentin the rrst
period toabout<44 percent inthe secondperi
even faster
t~anthe rate of growth ill the monetary base.In the third
pe~od,however, MlgroWth slowe?to abottt half the. rat~of
gr()'Xt~in tne monetary base. ()ne possibl~expla.nati?nis
thatthe efforts by speculators t() exchangetheirNTd()llar
deposits for foreign assets offset the expansionary impact
of the rapid growth in the monetary base.
The acceletati?nin money growth did. not result in
cO:r;respondingly large increases in inflation. In fact, inflationdeclined (from a compound annual rate of 6 percent in
the first period to 2.3 Percent in the second period) as
money growth accelerated, suggesting that increases in the
demand for Ml exceeded the growth in tt~e money supply.
Speculators were •apparently .llotint~~estedin. purchasing
g()ods with the .!'rT. dollars . thtY a.cquir~? in the foreigll
exchange. market, but held them on the expectation of
earning large gains ·frotn· currency appreciation. In line
with this, Ml velocit~declinedata20petCent annuiu rate
in thep~riodlQ8~:4-1Q87:4, c()lJlparedt02 percent in the
firstperiod; Inflation picked up and the decline in velocity
slowed sharply in the last two years of the 1980s,as the
curbs on capital inflows took effect and the speculative
demand for NT dollar assets ceased. Thesharpfiuctuations
in velocity are consistent with the predictions ofthe model
.
discussed earlier. 18
od,
tions. Asishown in Table 4, Taiwan's domestic money
market rate fellin comparison to foreign short-term rates
(the3-monthe odollar rate) as the. 1980s progressed,but
llf
the relative decline in domestic interest rates was· quite
limited. The reason is that Taiwan's domestic money
marketinteracted quite extensively with intemationalfinancial markets.
stafk<ionirast~ the prices of assets that were· not so
cl()sely linked by arbitrage to.extemalmarkets increased
sharply; L,andppcesrose as muchas250 percentbetween
I987and1989. Increasesin stockprices were even steeper.
AsshowninTable 5,the compound annual rate of growth
ofstdckprlcesitrTaiwan acceleratedfroIll 2 percent inthe
first halfofthe1980sto 70 to 80 percentin the second half.
'fable5also i shows.that<the.·increases··in ···Taiwan's···. stock
price.wereseveralorders of magnitude larger than stock
priceincreases inJapan and the U. S., .which also experiencedstockmarketbooms.inthe.second·halfofthe•• 1980s.
Taiwan'![sto:kpriceindex rose from 162 at the end of1986
to1557by the end of 1989, raising pricelearnings ratios of
listedcotnpanies to over 55 by the end of 1989 (compared
to 13in the U.S., and 62 in Japan).19
··.tn
Jable.4
Changesir'l interest rates
(annual rates in· percent)
l\t:oney market
interest rate \
80:1-85:3
85:4-87:4
88:1-89:4
28
-0.4
-0.05
0.05
-0.3
-0.2
-0.1
TableS
Effects on Asset Prices
While the expansion of liquidity did not result in an
increase in inflatioll in the short run, our earlier disqussion
suggests that it should have resulted in an increase in asset
prices or (equiyalently) declilles in interest rates..Furthermore, the effects on asset prices should have been smaller
in those domestic asset markets that are more tightly linked
by arbitrage to foreign asset markets, or· where. domestic
assets are closer substitutes for foreign assets . The results
of Tables 4 and 5 are toughly in line with these expecta-
3-month
Eurodollar rate
~h~ngesinstock
•prices
(compound annual rates in percent)
80:1~85:3
85:4-87:4
88:1-89:4
Thiwan
Japan
u.s.
2
81
72
15
29
16
10
7
14
Economic Review I 1992, Number 1
IV..
CONCLUSIONS
In this paper we have attempted to explain certain
puzzling features of the behaviorof exchange rates, money
velocity, and asset prices inTaiwan in the 1980s by suggesting a different way· of looking at the interaction. between
exchange market intervention and exchange rateexpectations .. Using a simple theoretical framework, we have
discussed how the credibility of intervention policy may
affect the. pattern of adjustment in the exchange rate,
velocity, and asset prices. When the outcome ofintervention is.·credible, .any•degree of exchange rate stability can
be achieved at the cost of.a suffici~ntly large, one~time
change in the money supply. When the outcome of interv~ntion is not credible,.however, .intervention can lead to
persistent, and possibly accelerating, changes in exchange
rates, the money supply, velocity, and asset prices. Under
certain conditions, inte~ention may even amplify the
cUffiulativechange inthe exchange raterather than reduce
it.A-Ii infotmal examination of the data suggests thatthe
model developed in the paper can be used as a framework
for explaining Taiwan's experience.
Two implications ·of Taiwan's experience are worth
highlighting. First,disturbances to foreign exchange and
domestic asset markets in a developing economy need not
arise from unsustainable fiscal and monetary policies and
macroeconomic instability. Foreign exchange rate intervention may be associated with large disturbances to asset
markets evenWin astable and 'well-managed economy.
Second, there is a little recognized potential tradeoff
between the.d~sire to protect tradable goods production by
limiting exchange rate movements and the desire to stabilize in foreign exchange and domestic asset markets. In
economies with a high degree of capitli mobility, and
where intervention policy is not credible, efforts to protect
the tradable goods sector through such intervention may
contribute to instability in asset markets. This effect may
be more pronounced when domestic and foreign assets are
not good substitutes.
ENDNOT-ES
1. The upward pressure on the NT dollar appears to have been related to
Taiwan's current account surpluses, which on an anriual basis averaged
close to 14 percent of GNP between 1983 and 1988, and reached a peak
(on an annual basis) of over 20 percent in 1986. These surpluses appear
to be the largest ever recorded in the world. By comparison, at their
respective peaks in the 1980s, current account surpluses reached 1.1 to
1.2 percent of GNP in Japan and Germany, and 7.7 percent in Korea.
2. A similar pattern of rapid money growth, low inflation and declining
velocity, and asset price inflation was obserVed in Japan iri the~second
half of the 1980s.
3. For more details on the institutional characteristics of Taiwan's
financial sector see Cheng (1986), Kuo (1989), Liang (1988), Shea
(1990), Yang (1990), and Wang and Kim (1990).
4. In particular, the interest-setting arrangements prevailing in Taiwan
in the 1980s·apparently introduced a certain amount'of rigidity· in .
deposit rates. Yang (1990) notes that the variation in bank rates in
Taiwan tends to be smaller than the variation in market rates. She also
refers to a study she has carried out using vector ARIMA techniques
which finds that the bank rate in the 1980s adjusted about a month after
the freely-determined money-market rate. (The latter rate is the rate set
in the short-terni bills exchange market established in 1976.) Some
interest rate policies were also designed 'to subsidize credit to certain
priority sectors, specifically the export sector up to the 1980s, and later
the high-tech sector.
5; Strictly speaking, equation (3) also applies ex post to the national
income accounting identity in levels rather than in logs. The present
approach can be seen as an approximation that simplifies the exposition
without changing the qualitative results.
6. For a full description of this type of model, see Branson and
Henderson (1985).
7: One way to thirik about this is to argue that lack of domestic financial
market development raises the transacti~ns cost associated with investing\ in domestic marketable securities. Under these conditions, the
influence of the external sector in affecting domestic interest rate
deterniination is reduced. For a demonstration of these effects, see
Niehans (1991)~ A similar argument appears to underlie the specification adopted by Edwards and Khan (1985).
8. The assumption that the weight w is constant is an approximation that
has no effeCt on the qualitative results of the model. Such an approximation would not be needed if the variables were expressed in levels rather
than in logs. For a similar1log-linear approximation of the central bank
balance sheet, see Flood and Hodrick (1985).
9. To derive (12), note that the effect of unsterilized intervention on the
exchange rate is given by sml1mt - sfl1J] = (sm - sf)l1m~ = I1sf, where
we use Il1m]1 = Il1ftl. Applying equation (10), we have I1sf= -al1x],
which yields equation (12).
10. The agents in the model use information about the target exchange
rate in forming their expectations. This is part ofthe information set we
would expect rational agents to use. A fully developed rational expectations model would require us to assume that (i) exchange rate
expectations depend on the rate of intervention and on the structure of
the economy and (ii) the government takes into account how intervention affects expectations when formulating exchange rate policy. The
equilibrium under these conditions is more difficult to derive and is a
topic for future research.
Federal Reserve Bank of San Francisco
29
1L The long"run ineffectiveness of intervention can also be seen in the
moregenetal case of equation (17). Note that
lim';"
lim T _
as,=(l-a)$q-+oo
P' I(S * -sO> =(s· -so>
,-I
.
..... ,-I
where. we use. lim
p'_I =__1_ = 1__..
T.... oo D
T-+oo
f
1=1
E
I
-p s.(1-a)
12. An .altemative way of modeling instability in the path of the
exchange rate is to use a monetary<approach to the exchange rate with
rational expectations and pick the unstable solution of the difference
equation for the ex~hange rate. The disadvantage of this approach is that
no intuition is offered for the underlying process that generates the
explosion. Certain arguments have also been offered to rule out such
explosive processes. Still another approach isto analyze what happens
when an expected change in monetary policy is not realized over the
SamPle period (the "peso problem"). Obstfeld (1989) shows that such a
situation can lead to an exchange rate process that is indistinguishable
from an explosive speculative bubble. In Obstfeld's framework, persistent appreciation may arise if speculators expect that the government
will have to reverse its monetary policy (or its unsterilized intervention
in exchange markets, in the case consideredin the text) at some time in
the Juture. In the· text we suggest the· alternative possibility that
intervention itself may contribute to the apparent instability.
13. Theun,derlying data used in Charts 2 and 3 and the Tables in this
section were obtained from various issues ofthe Central Bank ofChina's
, Financial Statistics, Taiwan District or the International Monetary
Fund's International Financial Statistics. The real trlide-weighted NT
dollar illustrated in Chart 2 was constructed by taking the geometric
weighted llverageof the exchange value of the NT dollar withrespect to
the currencies of eight of its tiading partners, including the U. S. dollar,
the yen, and the deutschemark. The weights were based on Taiwan's
total bilateral trade with these trading partners in 1980..
16. Sterilization policies produced sharp fluctuations in the amount of
interest-bearing liabilities of the CBC. The outstanding value of these
liabilities increased from NT$14 billion in 1983 to a peak ofnearly NT$
1.2 trillion in 1987. They subsequently fell to NT$ 415 billion at the end
of 1989, as the CBC retired short-term liabilities as they came due.
17. This point is made in Yin (1990). The episode can be thought ofas an
illustration of Sargent and Wallace's unpleasant monetarist arithmetic,
where-absent changes in fiscal policy-the issuance of government
bonds to reduce money growth today leads to more rapid money growth
in the future; For a discussion of unpleasant monetari~t arithmetic see
Sargent (l987b).
18. In contrast to the sharp fluctuations in narrow money aggregates,
there was no acceleration in M2 growth between the first and second
periods. It appears that speculators acquiring NT dollar assets preferred
to hold readily convertible or liquid assets, like Ml, rather than the less
liquid components of M2. This appears to have offset significantly any
tendency fot the deiriand foiM2 to rise as a res\dt ofthe overallincrease
in the demand for NT dollar assets. In line with this view, there was a
smaller (rather than larger) rate of decline in M2 velocity as the decade
progressed.
19. Other. factors .also appear to have contributed to the very steep
increases, in Taiwan's stock prices. FIrst, stock prices may have been
undervalued, as the rate'of increase in stock prices in Taiwan up to 1985'
was low given Taiwan's exceptional economic performance. Second, the
expansion in liquidity in the mid-1980s appears to have triggered a
speculative bubble in Taiwan's stock markets that lasted until the end of
the ,decade (the existence of a bubble is suggested by the fact that
Taiwan's stock market subsequently lost as much as 80 percent of its
value in 1990).
14. An alternative explanation is that a sequence of shocks to exchange
rate expectations in 1985-1987 (absent in 1980-85) that resulted in
persistent and accelerating appreciation. ijowever, it is not obvious what
these shocks could be. As we shall see,onthe domestic side, money
growth accelerated in the second period, so that the persistent. and
accelerating appreciation in the NT dollllFcannot be explained by
progressively tighter monetary policy. There w~re no dramatic changes
in Taiwan's fiscal policy that could explain real appreciation either. On
the external side, current account surpluses had been increasing since
the early 1980s, so in this respect the period 1985-87 was not very
different from 1980-85. The main shocks that may have affected
exchange rate expectations differently in 1985-87 were the real tradeweighted depreciation of the NT dollar in 1985, which predates the
persistent appreciation of the NT$ against the U. S. dollar, and the onetime decline in oil prices late in 1986. As these were one-time shocks,
something else must explain why the appreciation persisted and accelerated in 1985-87. We suggest that the effects of intervention on expectations played an important role.
15. The effects of the freeze in external liabilities were already apparent
in 1987. As can be seen in Chart 3, short"term capital flows drop from a
peak of around $ 3.7 billion to nearly zero between the first and third
quarters ofl987, with a concomitant dip in the accumulation of foreign
exchange reserves by the central bank. There was an even larger drop
between the fourth quarter ofl987and the first quarter of 1988.
30
Economic Review /199kNumber 1
ApPENDIX A
RESPONSES TO SHOCKS INA STATIC, SMALL OPEN
ECONOMY MODEL
Differencing the system (1) to (3) yields:
Al
"[' -1
-1
The sign of equation A4 is actually ambiguous, because the
decline in the demand for the foreign asset tends to lower
the domestic inter~st rate, whiletht~concortlitant increase
in the demand for money tends to raise the domestic interest I"ate. The intuitively plausible ca~e i~ <0 is selected
here.
.
Money supply
-1-:
Ji j
-.m
. ".
{a+oJ o
-1···· ..· .tii
0.'. ].•• .• [.• L• •. •1
.\•p•.•. 1..] .
-bR
L\s,
A6
AT
L\i
b +(a+b )
---!..=i - r
w <0
L\m,
m
DET
A8
where the structural coefficients are discussed in the text.
The iilverseof the matrlx.on the left~hand side'is:'
Foreign assets
A2
Jibr
-m,b r
mj ]
_1_ -b -(a+b )
b
-1
DET
r
w
r
[
Ji(a+b w )
-m;(a+b) Ji-mj
,
where DE.T= -'-'b+nt.[b
+a +b w'. ] < 0·,.
Jirl
r
ids assumed that aw + bw +br>O. From the preceding, we
can derive the reduced form responses of the exchange rate,
the domestic interest rate and the price level toa variety of
shocks.
Exchange rate expectations:
A9
AlO
All
SUmming equations A5, A8, and All yields equation (4) in
the text. Summing A3, A6, anq A9 yields equation (5),
while summing A4, A7, and AlO yields equation (6).
A3
A4
L\i
1
+(a+b»m
+bf'I<O
Ax =ix =--[-(b
DET
r .'
w.
x
rJx
_I
1
A5
Federal Reserve Bank ofSan Francisco
31
ApPENDIXB
Special cases
THE P4TH OFTlfE SpOTEXCHANGERATE UNDER
ALTERNATIVE EXPECTATIONS ASSUMPTIONS
Case 1: s/=s*
To illustrate how the solutions to difference equations·iri
the text are derived, consider the most general case:
When the target exchange rate is the same in every period,
B2 implies
I-I
B4
sl=~lso+(l~O!)s..s·L~i.
i=O
The. firstequality in equatiOnBLsays.that the change in
the exchange rate in this. period depends. on the rate. of
intervention a, the reduced forrnresp?nse. of the exchange
rate to a •shock toexchangeTat~.expectationssx(from
equatipn(4) in the text), and the magnitude oftheshOC1cto
exchange rate expectations this. period .:Ut . The second
equality shows that the shock toexchangerat~ expectations
depends on the gap between the target exchange rate this
period s/and last period's exchange rate S,-I.
RewritingBl yields
In the very longTun, we have
B5
where •the •. second equality follows·. because (1-- ~) =
(L-a)sx. The rate of change in the exchange rate each
period is now governed by:
1-1
B6
1-2]
As, =Cl "a)s,,' .~/l'"~
$' •-;(1 "$)W-' s,·
[
W-~(l __ O!)sx(s •
Recursive substitution into B1' yields the following solution (alternatively, see Sargent (1987a.) Chapter9):
I-I
B2
-so>.
It follo\vs from equation,B6 that ,as
t~oo, ,,~t - lan.d~st
asymptotically approach zero. Equation (B6)corresppnds
to equation (16) in the text.
sl=~lso+(l-a)sxL(hl : i ,
i=O
where So isth~initial value of th~ spotexchange rate. The
changeinthe spot rate in each period is given by:
Case 2:
Sl·
=s··; ·s,,=l
From the definition of ~ given earlier; this case implies that
~ = a. Equation B6 thenbecotnes
B3
This is the. case plotted. ill Chart 1.
where in the second equality we use
32
(1-~) =
sx(l-a).
EconomiccReview I 1992,. NUlDber 1
Given an initial target exchange rate
change rate in eachperi()dis givellhy:
so* ,the target ex-
Substituting into equation B2, the spot rate is now given
by:
1-1
B9
sl=.Wso+(l-a)s)'o·b{Ji(l+</>y-i.
i=O
.
It is apparent from equation'B8 that St now grows without
bound. Intervention cannot prevent this. It can also be
shown that the rate of change in the exchange rate will
accelerate indefinitely. To see this, note that the change in
the spot exchange rate is now:
BIO
As=
I
To simplify notation, define
t= 2,3, ... ,
lim
t~oo
Z
-~
I
1~2[
Zt= 1- (l-{J)E '
(1 +</»
i=O
~
(1 +</»
]'. ;
i
where Zt= 1 when t= 1 and
</>
-
(l-a)sx +</>
Rewriting BIO,
Equation BIO', which is equation (22) in the text, shows
that the appreciation in the exchange rate now accelerates.
FederalReserve Bank of San Francisco
33
REFERENCES
Branson, William H. , and DaleW. Henderson. 1985. "Specification and
Influence of Asset Markets." In Handbook of InternationalEconomics Volume II, ed. R.W. Jones and P.B. Kenen. Amsterdam:
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Central Bank of China. Financial Statistics, Taiwan District, Republic
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Central Bank of China, Economic Research Department. 1989. Flow
ofFunds in Taiwan. District, Republic of China, 1965-1988
(December).
Cheng,Hang~Sheng
in
..1986."Financial Policy and Reform Taiwan,
China." In Financial Policy and Reform in PacijicBasin Countries,.ed. H.Chellg. Lexington, Mass.: Lexington.Books.
Edwards, Sebastian, and Nt0hsin S. Khan. 1985. "InterestRate Determination in Developing Countries: A ConcePtual Framework."
IMFStajJPapers 32 (September).
Hood, Robert P., and Robert J.Hodrick. 1985.• "Central Bank Intervention in a Rational Open Economy: A Model with Asymmetric
Information." In ExchangeRate M(lnagementUnder Uncertainty,
eLJ:S. Bhandari. Cambridge, Mass.: MIT Press,
Knigman,Paui. 1979. "A Model of Balance of Payments Crises."
Journal of Monry Credit and Banking 11 (August) pp. 311-325.
Kuo. Shirley. 1989. "Liberalization of the Financial Market in Taiwan
in the 1980s." The International Commercial Bank of China
Eco/U)mic Review (July-August).
Lessard, D.R., and J: Williamson, eds. 1987. Capital Flight and Third
World Debt. Washington, D.C.: Institute for International Economics.
Liang, Kuo-shu. 1988. "Financial. Reform., Trade and Foreign"
Exchange Liberalization in the Republic of China." The International Commercial Bank. of China Economic Review (MarchApril).
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Niehans, Jurg. 1991. "Capital Mobility. with Transaction Costs:· (A
Concept and Applications." Working. Paper PB91-03 (April).
Genter for Pacific Basin Molletary and Ec()nomic Studies, Federal
Reserve Bank of Sall Francisco.
Obstfeld,Maurice. 1989. "Peso Problems, Bubbles and Risk in the
Empirical Assessment of Exchange-Rate Behavior." In Financial
Risk: Theory, Evidence and Implications ,ed.Courtenay C. Stone.
Proceedings of the Eleventh Annual Economic Policy Conference
of the Federal Reserve Bank of St. Louis. Boston: Kluwer.'
Sargent, Thomas J. 1987 aMaeroeconomicTheory. Orlando: Academic
Press.
Sargent, Thomas J.1987b. Dyna,micMacroeconomic Theory. Cambridge, Mass., Harvard University Press.
Shea, Jia-Dong. 1990. "Financial Development inTaiwan:AMacro
A11alysis." Presented atC()nference on Financial Development in
. Japan, Korea and Taiwan sponsored by the Institute of Economics,
Academia Sinica,ROC and The Pacific Basin Studies Program,
Columbia University. Taipei, TaiWan, August 27-28.
Wartg,Yen-Kyun,and· Wan-Soon. Kim.• 1990.·."AReformollthe
Forward Foreign Exchange. Market alld Foreign Exchange Rate
Determination. Policy in Korea,· with F<>reign pxchallge .Policy
Experiences of Taiwan." In Economic Development in EasfAsia
and Southeast Asia: Essays in Honor of Professor Shinichi Ichi"
mura, ed. Seiji Naya and, Akira Takayama.
Yang, Ya-Hwei. 1990. "AM~cro Analysis ofFinancial Development in
Taiwan." Presented at Conference on Fin.an9ial Developmentin
Japan, Korea and Taiwan sponsored by the Institute ofEconomics,
Academia Sinica, ROCand The Pacific Basin Studies Program,
Columbia University, August 27-28 Taipei, Taiwan.
Yin, Norman. 1990. "The Progression and Development of Money
Games." (InChinese.) Presented at Confere~c~on ~ocial ~on
struction: Money Games and Their Eeffects on Society, sponsored
by the China Time Foundation. Augustl6-:18 Taipei, Taiwan.
Economic Review ./ 1992, Number 1
Consumer Sentiment: Its Causes and Effects
Adrian W. Throop
Research Officer, Federal Reserve Bank of San Francisco.,
The autllor acknowledges helpful comments from the editorial committee, consisting ofRonald Schmidt and Bharat
Trehan, and able research assistance from Andrew Biehl
and Sean Kelly.
Thispaperfinds that consumer attitudes, as reflected in
surveys of consumer sentiment, have a significant influence on householdpurchases ofdurable goods. Normally,
consumer sentiment moves with current economic conditions and bears a stable relationship to a few economic
variables. At times ofa major economic or political event
like the Gulf War, however, consumer sentiment can move
independently from current economic conditions. At such
times it provides useful information aboutfuture consumer
expenditures that is not otherwise available.
Federal Reserve Bank of San Francisco
The 1990-91 recession has been widely attributed to a
collapse of consumer confidence following Iraq's invasion
of Kuwait and the military response of the United States
and its allies. Similarly, military victory for the allies was
generally believed to have dispelled the gloom about
prospects for jobs and business, thus helping to lead the
economy out of the recession. Consistent with this hypothesis, the Index of Consumer Sentiment constructed by the
Survey Research Center at the University of Michigan
dropped by a record, amount beginning in August 1990,
at the time Kuwait was invaded. With the successful completion of the war, the index then surged back to its
pre-recession level in March 1991. In April, however,
it dropped again and made no significant improvement
through the summer, as the economic recovery turned
sluggish. It therefore appeared to respond to both political
and economic events.
This is not the only episode in which swings in consumer
sentiment have been tied to the business cycle. The Michigan index generally has led other business cycles, and
three of its components are specifically included in the
Commerce Department's Index of Leading Economic Indicators. Therefore, changes in consumer sentiment could
have been instrumental in triggering earlier recessions as
well. Alternatively, however, sentiment ordinarily may be
just a reflection of economic cOhditions that generally
precede or coincide with a recession, without necessarily
being an independent cause of downturns.
This paper analyzes the causes and effects of consumer
sentiment as measured by the University of Michigan
survey index. 1 It addresses the following interrelated set of
questions. To what degree does consumer sentiment affect
consumption .spending? To the extent that it does, is
consumer sentiment generally an independent factor in
creating fluctuations in consumption spending, and, therefore, business as a whole, or does it usually simply respond
to economic adversity, thereby reinforcing but not initiating business cycles? When swings in consumer sentiment
occur, what specific economic variables are they related to
and are such relationships stable? Finally, can the influences on spending that are captured by sentiment be
predicted from readily available economic variables, or is
35
actual survey data on consumer sentiment necessary for
making the most accurate forecast of consumer spending?
In Section I of the paper, earlier work on the role of
consumer sentiment in consumer spending is· reviewed.
The role of sentiment in affecting consumer spending on
durables, as well as nondurables and services, is then
examined empirically in Section II. The relative significance of the individual components that go into the overall
index is analyzed here as well. Section III then examines
the extent to which consumer sentiment can be explained
by current economic variables. Section IV compares the
ability of the index of sentiment and the current economic
variables that are related to it to improve the accuracy of
forecasts of expenditures on consumer durables. The recent Persian Gulf War is a prime example of a situation
in which consumer sentiment may have been driven by
something other than current economic conditions-for
example, by expected repercussions on future economic
conditions or perhaps just by mass psychology.. Therefore,
this episode is examined separately. Finally, Section V
provides a summary and some conclusions.
It is found that changes in consumer sentiment normally
are caused by purely economic factors and that consumer
sentiment usually bears a stable relationship to just a few
economic variables. As a result, consumer sentiment usually is just a reflection of economic adversity or prosperity,
reinforcing rather than initiating business cycles. At times
of an unusual event like the Gulf War, however, consumer
sentiment can move independently from current economic
conditions. Therefore, the additional information that it
provides is of some usefulness in forecasting expenditures
on consumer durables. Finally, the relative importance of
the index's different questions in measuring overall con..
sumer attitudes, and hence their effect on durables purchases, differs during times of a major shock like the Gulf
War from normal times.
I.
BACKGROUND
The use of surveys to measure consumer sentiment was
pioneered by George Katona and his associates at the University of Michigan in the 1950s. The rationale for such
surveys is provided by the discipline of psychological economics. According to psychological economics, a household's response to a change in income or wealth depends
upon its attitudes at the time. Thus, consumer expenditures
depend not only on an ability to buy but also a willingness
to buy. 2
In contrast, in standard economic theory households are
assumed to react uniformly to changes in income or wealth
at different points in time. Although changes in attitudes
36
may matter for individual households, these individual
differences are assumed to cancel out for the economy as a
whole. But the law of large numbers applies to economic
situations only if random factors prevail. If the same factor
influences very many people in the same direction at the
same time, deviations add up instead of canceling out. An
obvious systematic factor that could produce relatively
uniform reactions is the acquisition of new information
through the mass media.
Katona argued that the attitudes that enter into consumer
sentiment are more than simply a reflection of the current
state of the economy. Therefore, they are not necessarily
related to current economic variables in any stable way.
Attitudes may be influenced by political and economic
events that are nonquantifiable. Also, similar economic or
financial developments may be perceived differently under
different circumstances. Katona's point is that, while a
purely mechanistic view of consumer behavior sometimes
may be correct, it is not necessarily and not always correct.
Particularly at turning points, consumer willingness to buy
may be an important and unpredictable independent factor
determining spending. If so, survey measures of consumer
sentiment could contribute importantly to both forecasts of
consumer spending and an understanding of consumer
behavior.
As part of this study, we examine the importance of
some of the individual questions in the index of sentiment
for explaining consumer spending. Since 1955 the Michigan Index of Consumer Sentiment (ICS) has contained five
questions, with equal weight. They are: 3
1. "We are interested in how people are getting along
financially these days. Would you say that you (and your
family living there) are better or worse off financially
than a year ago?"
2. "Now looking ahead-do you think a year from now
you (and your family living there) will be better off
financially, or worse off, or just about the same as
now?"
3. "Now turning to business conditions in the country as a
whole~do you think that the next 12 months will have
good times financially, or bad times or what?"
4. "Looking ahead, which would you say is more likely,that the country as a whole will have continuous good
times during the next 5 years or so, or that we will have
periods of widespread unemployment or depression, or
what?"
5. "About the big things people buy for their homessuch as furniture, a refrigerator, stove, television, and
things like that. Generally speaking, do you think now
is a good or a bad time for people to buy major
household items?"
Economic Review I 1992, Number 1
tends to lead both downturns and upturns; the Current
Conditions Index (CIND) based on questions I and 5 leads
downturns and some, but not all, upturns (Chart 2). The
correlation matrix in Table 1 shows that there is a high
intercorrelation among the responses to these five questions, with the exception of question 5. This question asks
As shown in Chart 1, the ICS tends to follow a cyclical
pattern, with a strong tendency to lead economic downturns and a lesser tendency to lead upturns. An Index of
Consumer Expectations (which is one ofthe 12 series in the
Commerce Department's Index of Leading Economic Indicators), based on forward looking questions 2,3, and 4,
Chart 1
Chart 2
Index of Consumer Sentiment (ICS)
Index
Index
Current and Expected Indices
120
110
Peak:
Peak:
100
100
90
80
80
70
60
60
40
50
L..L.-L..L.-L.L..L-IIIII~..l..
63
63
67
71
75
79
87
83
91
67
71
75
79
83
87
91
Shaded areas indicate periods of economic recession.
The dotted line denotes the peak of the 1990 recession.
Shaded areas indicate periods of economic recession.
The dotted line denotes the peak of the 1990 recession.
Table 1
Correlations Among Components of Index of Consumer Sentiment
Personal Finances
Current
Expected
Business Conditions
12 Mo.
Buying
Conditions
5 Yrs.
Current
1.0
Expected
.823
1.0
12 Months
.790
.874
1.0
5 Years
.753
.851
.958
1.0
.758
.547
.578
.523
Personal
Finances
Business
Conditions
Buying
Conditions
Federal Reserve Bank of San Francisco
1.0
37
directly about household attitudes with respect to the
purchase of major household items. The correlations between question 5 and all others are between .5 and .75,
while the intercorrelations among the others range from
.75 to .95.
Three main views on consumer sentiment have emerged
in the literature. 4 The first is the original one of Katona. In
this view, sentiment is an important predictor, along with
income, of spending on discretionary items like consumer
durables. However, in this view consumer sentiment is not
believed to be well represented by responses to any single
question or to bear any stable relation to aggregate economic variables. As a result, a survey of a set of questions
is deemed necessary in order to make accurate forecasts
of consumer spending on durable goods, particularly at
turning points. A second view is that sentiment mainly
measures optimism or pessimism about future economic
conditions. 5 Contemporary theories of overall consumption and saving strongly emphasize economic agents' perceptions of the current environment and expectations of its
future. Thus, in "life-cycle" or "permanent income"
theories of consumption, current spending on nondurables
and services, as well as on durables, depends importantly
on expected future income. The index of sentiment may
provide a better measure of this than conventional modeling based on past observations of incomes.
Yet a third view is that the most useful aspect of the
index of sentiment is a measurement of the uncertainty or
risk, associated with the likelihood of job loss and/or
severe income loss and attendant financial distress. 6 Although this probability is likely to be correlated to some
extent with current or expected economic conditions, it
affects consumer spending through different channels. A
higher probability of financial distress would lead an
individual household to save more in liquid form and less
in illiquid form, so that liquid assets are available to cover a
possible future short fall in future income. The most
effective way to do this would be to postpone expenditures
on consumer durables rather than on nondurables and
services. In this view, the most important dimension of the
index of sentiment is its measurement of confidence or
mistrust, rather than optimism or pessimism. It is possible,
however, that household perceptions of uncertainty or risk
can be measured equally well, or better, by economic
variables.
The rest of the paper attempts to discriminate among
these three views. We first focus on whether the index of
sentiment, or its components, provides useful information
for predicting consumer spending on either durables or
nondurables and services that is not contained in the usual
empirical models of consumer behavior. We next examine
whether measures of sentiment can be easily modeled with
38
readily available economic data. Finally, we ask whether
sentiment or its components, contain information for forecasting consumer spending that is not contained in other
economic data.
I/.
EFFECTS OF CONSUMER SENTIMENT
In modem consumption theory, households are viewed
as making a conscious attempt at achieving a preferred
distribution of consumption over their lifetime, subject
to the size of the economic resources expected to accrue to
them. Friedman's (1957) permanent income hypothesis
views consumption as a function of an anticipated longterm measure of income, equal to the expected yield on
human and nonhuman wealth. The life .cycle theory ·of
Modigliani and his colleagues takes this idea one step
further, allowing for the consumption of nonhuman wealth
towards the end of a household's lifetime. 7 In both theories
consumption refers not to current expenditures on consumer goods, but rather to the current flow of utility from
consumer goods, including the existing stock of consumer
durables. For simplicity, Friedman's permanent income
approach is adopted here.
In the permanent income framework, consumer expenditures on nondurables and services are simply a function
of permanent income. However, expenditures on consumer durables usually are viewed as following a stockadjustment process. The desired stock of consumer durables depends upon permanent income and interest rates,
and possibly also on attitudes measured by the in.dex of
consumer sentiment. Expenditures ondurables in any
period then become soine fraction of the difference between, desired and actual stocks.
Earlier .studies have found that consumer sentiment
significantly affects expenditures on consumer durables. 8
Using the permanent income framework, estimates of a
model of expenditures on durables that uses polynomial
distributed lags (a PDL model) for the period 1963.Ql
through 1990.Q4 are:
3
4
LGCD= -6.71 + 1.49 LYDP+La_)CP_i+L b_;ICS_i
(-12.5) (9.75)
i-I
j-O
+
.104 LKCD_ I
(1.12)
+ ,146e_ 1
(l.40)
4
L b_ =.OO311
j
j-O
R2= .996
(9.43)
S.E. = .0235
D.W.=2.02
and
Economic R.ev!ew / 1992, Number 1
3
4
LGCD= -6.75 + 1.55 LYDP+L a_)CP_i+L b_iCIND_i
(-15.3) (12.3)
i-I
i=Q
+ .0168LKCD_ 1
(.220)
simultaneity bias still may exist. Also, previously estimated models of consumer sentiment generally do have
highly serially correlated errors.
A Vector Error Correction Model
3
L
i-I
4
a_i = -.00808
(-6.13)
R2=.997
L
i-O
b_ i =·00418
(12.3)
S.E. = .0215
D.W.=1.99
where
LGCO = log of expenditures on consumer durables
LYDP = log of permanent income9
ICP = six-month commercial paper rate
ICS = index of consumer sentiment
CINO = current conditions component of ICS
LKCO = log of stock of consumer durables.
The t-statistics (in parentheses) indicate a high degree
of statistical significance of the consumer sentiment index (ICS). In addition, the current conditions component
(CINO) of the index actually has somewhat more explanatory power than the overall index. (Each of the questions in
CINO contributes about equally to its explanatory power.)
A one-point change in CIND is estimated to move expenditures on consumer durables by 0.4 percent in the same
direction over a period of four quarters. About half of this
effect occurs in the contemporaneous quarter. Since CINO
can swing as much as 30 points between the peak and
trough of the business cycle, sentiment thus appears to be
able to move spending on durables as much as 12 percent
over a relatively short period.
Earlier studies of the causes and· effects of consumer
sentiment have been subject to two potentially serious
econometric problems, however. These are the interpretation of contemporaneous correlations and the possibility of
"spurious" relationships between time dependent variables. A common solution to the first problem of "simultaneity" is to specify some variables as exogenous that
affect other variables but are not affected by them. These
exogenous variables can then be used either as instruments
to proxy endogenous independent variables or as independent variables in reduced form equations. A difficulty with
this procedure, however, is that it is not always clear what
variables are truly exogenous in a macroeconomic system.
The second problem of "spurious" regressions arises
from the fact that variables that have random time trends
may appear to be correlated in finite samples, even though
there is no true relationship between them. 10 Although the
. low estimated serial correlation in the errors of the above
POL model of consumer durables suggests that likelihood
of spurious correlation due to random time trends is low,
Federal Reserve Bank of San Francisco
This study uses a "vector error correction" model to
avoid these problems. In such a model, all variables are
treated as potentially endogenous. Moreover, tests are
made to ensure stationarity in the variables in order to
avoid "spurious" regressions. 11 In addition, because the
change in any variable is assumed to be a function of its
own past changes as well as past changes in other variables,
a vector error correction system is a natural vehicle for
generating ex ante forecasts that use only.information
available prior to the forecast period. The variables we
initially consider in this framework are the log of expenditureson consumer durables (LGCO), the log of spending
on nondurables and services (LCNS), the log of personal
disposable income (LGYD), interest rates as represented
by the six-month commercial paper rate (lCP), and a
measure of consumer sentiment either (ICS or CIND).
The change in any variable is assumed to be a function of
its own past changes as well as past changes in the other
variables, with lags of one to four quarters being chosen.
The change in any variable also is assumed to respondto an
"error correction" term equal to the lagged difference
between the variable and its estimated equilibrium value.
A nominal interest rate, rather than a real one, is used
because of the importance of liquidity constraints for
households. 12 Theoretically, the lagged stock of durables
might also be included, but as in the PDL regression.s it
turned out to be statistically insignificant. The reason is
that, although a larger stock of durables reduces· the
difference between desired and actual stocks, it also generates more replacement investment, and the two effects on
investment spending tend to cancel each other out.
The stationarity tests that were performed are described
in Appendix A, as is the construction of the error
correction term. A "general-to-simple" modeling strategy was employed in which insignificant variables were
dropped from the model. The final equations of the estimated vector error correction system are shown in Table 2.
In the equation for consumer durables, the error correction
term is highly significant, whether the overall index of
sentiment (ICS) or just the current conditions component
(CIND) is used to measure sentiment, as shown in equations 1a and lb. Since the error correction term is stationary, the usual distribution for the t-statistic applies, easily
indicating significance at the 1 percent level or better.
Moreover, sentiment contributes significantly to the importance of the error correction term. 13
39
Similar to the results with the PDL model, the use of
CIND produces a lower standard error for thedurables
equation and a larger estimated response ofdurables expenditures to sentiment. Also, there are significant effects
of lagged changes in. both interest rates and sentiment
on changes in expenditures on consumer durables using
CIND, but not ICS. Recall that CIND contains the responses to one question that asks directly about household
attitudes with respect to the purchase of major household items,as well as responses to another question that is
highly correlated with those for the remaining questions in
the overall index of sentiment. As a result, CIND appears to
contain all the useful information in ICS for explaining
expenditures on durables.
Interestingly, short-run changes in spending on durables
(DLGCD) are more closely related to changes in spending
on nondurables and services (DLCNS) than to changes in
disposable income (DLGYD), as the latter is insignificant
in both equations la and Ib in Table 2. This is consistent
with the permanent income hypothesis, in which spending
on nondurables and services is proportional to permanent
income. If the desired stock of durables depends upon
Table 2
Estimated Vector Error Correction System
Sums of Coefficients on Lagged Changes in Independent Variables and Coefficient
on Error Correction Term (E.C.)
(1963.01-1990.04)
Independent Variables
Dependent
Variable Constant aLGCD
I
aLCNS
aLGYD
aICP
la.
LlLGCD
-.00758
( -1.22)
2.380
lb.
aLGCD
-.00578
(- .906)
2.296
(3.37)b
- .0011
(- 3.39)b
Ie.
aLGCD
-.00150
(- .186)
2.92
(2.IO)d
-.0232
(4.46)a
Id.
aLGCD
-.00395
(- .594)
2.194
(2.72)c
-.0242
(5.54)a
2.
aLCNS
.003307
(- 2.97)a
0.552
(4.71)"
-.0015
(3.18)b
3.
aLGYD
.00066b
(- .306)
1.075
(4.07)"
4.
aICPQ
.04299
(- .375)
.0437
(4.39)a
5a.
alcs
-.132
(- .294)
-3.07
(7.12)"
5b.
aCIND
.695
(- .452)
-3.616
(7.29)a
-.584
(2.50)C
aICS
aCIND
-.003
(4.41)a
-.00318
(2.91)b
E.C.
R2
S.E.
- .601
(- 8.44)a
.42
.0267
-.796
( -7.28)a
.48
.0254
-.0374 - .315
(2;32)d (- 3.22)a
.36
.0278
-.671
(-6.3W
.42
.0266
.17
.00476
.13
.00916
.13
1.173
.20
4.726
-.25
4.682
aU
0.0846
(2.291)C
- .150
(6.23)a
Levels of Significance (F-Statistic for lagged changes and t-statistic for constant and error correction term (E.C.»
aSignificant at 1%
bSignificant at 2..5%
CSignificant at 5%
dSignificant at 10%
40
Economic Review / 1992, Number 1
permanent income, then purchases of durables should be
more closely related to the current consumption of nondurables and services than to current income in the short run.
In the longer run, however, income should become a better
measure of permanent income, which is consistent with the
greater significance of disposable income than spending on
nondurables and services in the error correction term.
The error correction term does not playa significant role
in explaining changes in any of the variables besides
expenditures on durables. This is consistent with the
strong response of durables expenditures to sentiment,
leaving no significant adjustment to be done elsewhere.
The change in spending on nondurables and services (eq.
2) is found to depend only on past changes in the consumption of nondurables and services and past changes in
interest rates; and it is not influenced by consumer sentiment in any way. This result is not consistent with a rational
expectations version of the permanent income hypothesis
in which consumption responds only to new information
about permanent income, and hence is a random walk
unrelated to past values of any variables.I 4 But it is
consistent with a modified version of the rational expectations version permanent income hypothesis, in which
adjustment costs prevent an instantaneous response to
permanent income.
The finding that consumer sentiment significantly influences expenditures on consumer durables, but not spending on nondurables and services, suggests that consumer
sentiment is something other than just a better measure of
perceptions ofpermanent income. The important thing that
it seems to measure is the perception of uncertainty, or risk,
and· the corresponding probability of financial distress . If
the probability of financial distress is high, at the margin
households should prefer to hold liquid assets and consume
the income from them on nondurables and services, rather
than holding illiquid consumer durables. They would therefore allocate their consumption away from the satisfaction
provided by illiquid consumer durables and towards nondurables and services. However, greater uncertainty and
risk also should lead to precautionary increases in the
overall saving rate, causing a decline in total consumption. The effects on expenditures on nondurables and services appears to be approximately offsetting, leaving them
roughly unchanged. IS
Current changes in disposable income (eq. 3) are found
to be significantly related only to past changes in the
consumption of nondurables and services. This too is
consistent with a modified rational expectations version of
the permanent income hypothesis. If expectations are
forward-looking, then future changes in income should be
related to past changes in spending on nondurables and
services. I6 Current changes in the commercial paper rate
Federal Reserve Bank of San Francisco
(eq. 4) are found to be significantly related only to past
changes in itself. Changes in either of the sentiment
indexes (eqs. 5a and 5b) are related only to own past
changes and past changes in the commercial paper rate.
Thus, changes in sentiment cause changes in spending on
durables, in a statistical sense, and are not caused by them.
Response of Durables Purchases to Sentiment
and Other Factors
Next we examine how spending on consumer durables
responds to shocks to sentiment, as well to the other
variables. These shocks are set equal to the standard
deviation of the disturbances to each variable over the
sample periodP A disturbance to the system of first
difference equations is temporary. But its effect on the level
of spending on durables generally is permanent. Chart 3
shows that the effect on the level of durables expenditures
of an "average" shock to the current component of consumer sentiment (CIND) is about as large as the effect of a
shock from the commercial paper rate or from spending on
nondurables and services. Thus, consumer sentiment is
truly an important determinant of spending on durables, on
a par with other factors that usually are thought to be
important. The effect of a shock to disposable income on
purchases ofdurables is somewhat smaller. Finally, the
response of consumer durables to a shock to durables
themselves affects durables purchases only temporarily.
This occurs because a disturbance to durables is gradually .
eliminated through the response of durables expenditures
to the error correction term. I8
Chart 3
Dynamic Response of Consumer
Durables to an Increase in:
Percent
5.0
Consumer
Sentiment (CIND)
Consumer
Durables
2.5
JJ
,
_ _-
".."",,,,..,,,,
__
=~TmTM.....,."M'fT
11"lIlltlIIlIIUIIII~"'1I1 111111
~Dlsposable
Income
0.0.f-~,.......;..::..s..a...~----------
-2.5
Commercial Paper Rate
o
1
2
3
4
5
6
7
8
9
10 11 12
Quarters
41
We have thus established that consumer sentiment is a
statistically significant variable for explaining purchases of
consumer durables. Also, disturbances to consumer sentiment are important relative to other variables in explaining
the overall variation in expenditures on consumer durables. The next question is the usefulness of sentiment in
making actual ex ante forecasts of durables purchases. For
a preliminary answer, this vector error correction. system
(either eq. 1a or 1b and eqs. 2-5, Table 2) was estimated
over an initial sample period, here chosen to be 1963.Q11975.Q4. Next the estimated system was used to make a
forecast of spending on durables one, two, four, and eight
quarters ahead. Then the system was reestimated using
data from the initial sample plus the quarters just forecast.
The "new" system was used to generate a new set of
forecasts. Forecasting errors over the period 1976.Q1 to
1989.Q4for systems using either no measure of sentiment
(dropping eq. 5 and sentiment from eq. 1), or the ICS
(using eqs. 1a and 5a) or CIND (with eqs. 1b and 5b)
measures of sentiment, were then compared with those of a
naive model that forecasts future expenditures simply on
the basis of its trend rate of growth. These comparisons are
shown in Table 3.
Even without including a sentiment variable, the estimated vector error correction system forecasts expenditures on consumer durables more accurately than a naive
model does. The root-mean-squared forecasting error is
reduced by 25 to 40 percent, depending on the forecast
horizon (line 2 versus line 1, Table 3). Including the simple
model of ICS (eqs. 1a and 5a, Table 2) in the system
changes these forecast errors by relatively small amounts.
It raises the two-quarter-ahead root mean squared error
slightly, lowers the four-quarter-ahead error slightly, and
Table 3
Out of Sample Root Mean Squared
Errors in Forecasting InGCD
1976.Ql-1989.Q4
Quarters Ahead
1
2
4
8
1. Naive
.035
Vector Error Correction System
2. Without Sentiment
.034
.046
.070
.127
.042
.052
.077
3.
Basic Model with ICS
.034
.045
.048
.061
4.
Basic Model with CIND
.031
.037
.043
.050
42
reduces the eight-quarter-ahead error by 20 percent (line 3
versus line 2, Table 3). But substituting the simple model
ofthe CIND (eqs. 1b and 5b, Table2) measure of consumer sentiment in the system lowers the root mean squared
error by 12 to 35 percent, depending on the forecast horizon
(line 4 versus line 2, Table 3). Thus, for this period the
inclusion of consumer sentiment improves the accuracy of
ex ante forecasts of durable purchases markedly, but primarily only if the current conditions component of sentiment (CIND) is used.
III.
CAUSES OF CONSUMER SENTIMENT
This section addresses the issue of the underlying explanation of consumer sentiment and its important current
conditions component. Is sentiment mainly a psychologicalor anticipatory variable that is not easily explained by
current economic variables? Or is the sentiment index
basically just filtering current economic data? In the previous section, it was found that changes in consumer
sentiment, or in the current conditions cOlnponent of it,
could be forecast fairly well by past changes in interest
rates and past changes in sentiment itself. But if a better
economic explanation of consumer sentiment could be
found, better forecasts of durables spending might be
obtainable. Alternatively, if the sentiment index filters the
relevant economic variables poorly and also does not
contain any important purely psychological component,
better forecasts might be obtained by using those variables
directly. We examine these issues next.
The Traditional Approach
There is little consensus in previous studies on the set of
economic variables that might best explain consumer sentiment. However, one of the most coherent earlier ap~
proaches is Mishkin's "liquidity hypothesis" (1976, 1977,
1978). This hypothesis focuses on the illiquidity of consumer durables, which creates a loss for consumers if they
try to sell durables (or borrow against them) in an emergency. As a result, consumers who expect not to be able to
pay their bills readily would prefer holding liquid assets
rather than illiquid consumer durables. In effect, the
opportunity cost of holding consumer durables increases
substantially when consumers get into financial trouble.
Thus, as the probability of financial distress increases,
consumers lower their demand for durables. As discussed
earlier, the evidence of a positive response of spending on
durables to movements in consumer sentiment, in contrast
to the lack of response of nondurables and services, is
consistent with this view. It suggests the important thing
that consumer sentiment measures is perceptions of the
Economic Review / 1992, Number 1
probability of financial distress, rather than perceptions of
permanent income.
Mishkin argues that, besides depending upon the expected level and variance of income, the· probability of
financial distress should vary positively with the consumer's debt and negatively with his holdings of financial
assets. When indebtedness is high, the consumer has large
contractual payments for debt service that increase the
likelihood of financial distress, thus decreasing the demand for consumer durables. In contrast, larger holdings
of financial assets increase the consumer's buffer against
bad times, and so increase the demand for· consumer
durables. Thus, consumer sentiment (ICS) should be positively correlated with real financial assets of households
(FIN) and negatively correlated. with their indebtedness
(DEBT) at the beginning of the quarter. It should also be
positively correlated with transitory income (YDT), which
acts as a proxy for upside or downside risk.l 9 Also,
inflation in consumer prices (DLCPI) tends to affect consumer sentiment adversely because it is usually associated
with greater uncertainty.20 An updated estimate (sample
period 1963.Ql-1990.Q4) of Mishkin's model of les is:
ICS = 78.6 +.746 FIN - 1.94 DEBT + .169 YDT
(9.21) (2.61)
. (-2.17)
(4.41)
and its change, and interest rates. All of these variables can
be interpreted as measures of general economic uncertainty and risk, but without special emphasis on household
balance sheet positions.
When these explanatory variables are added to Mishkin's model of ICS, lagged ICS becomes significant, and
the significance of FIN, DEBT, and YDT evaporates. Of
the remaining variables, the rate of inflation (DLCPI),the
percent change in the S&P index of stock prices (DLSP),
and the change in the unemployment rate (DU) are statistically significant in explaining ICS, with a significaIlt
degree of lagged adjustment. The current conditions component of sentiment (CIND) turns out to be well explained
by this same set of variables as well as by the percent
change in the real price of oil (DLPOIL), also with a
significant degree of lagged adjustment. Thus, the preferred equations following the traditional approach for
selecting the set of explanatory variables are: 22
ICS = 28.2 + 2.97 DLCPI + 2.00 DLSP
(7.14) (4.99)
(3.51)
- 5.40 DU + .710 ICS_ 1 - .320 e_ 1
(-5.22)
(17.1)
(3.13)
R2= .967
S.E. =3.63
- 3.33 DLCPI + .708 e_ 1
(-6.01)
(9.99)
S.E. =4.15
D.W. =2.24
All of the variables have theoretically correct signs and
significant t-statistics. Note also that the decomposition of
the household balance sheet into its debt and financial
assets components in the liquidity hypothesis is supported,
since the absolute value ofthe estimated coefficient on debt
is more· than twice as large as on financial assets. The
independent variables in this model could potentially affect ICS with a lag for two reasons. First, the impact of
adverse conditions on consumer sentiment is likely to be
stronger the longer these conditions have persisted. Second, the effect of economic conditions on sentiment may
be "contagious," as consumers find out about the feelings
of others. These effects, if they exist, could be captured by
the inclusion of lagged ICS. But like Mishkin, we find that
the lagged IeS· is not significantly positive, suggesting an
absence of lagged adjustment.
While Mishkin's model seems to work reasonably well
as an explanation of consumer sentiment, other investigators have used a larger set of economic variables to explain
sentiment.21 These have included changes in stock prices,
the unemployment rate and its change, the real price of oil
Federal Reserve Bank of San Francisco
Significance level
ofLM test = .36
CIND= 20.1 - 1.10 DLCPI+ .193 DLSP- 9.60 DLPOIL
(6.15) (-2.38)
(3.55)
(-2.20)
- 5.74 DU + .798 CIND_ 1 - .418 e_2
(-5.82)
(23.6)
(4.22)
S.E. =3.83
Significance level
ofLM test = .70
An Expanded Error Correction
Model Approach
The equations for the levels of sentiment estimated by
the traditional approach are potentially "spurious," however, due to possible correlations caused by random time
trends. An indication that this is a possibility is that, in the
absence of correction for serial correlation or the use of
lagged dependent variables, the R2 is almost as high as the
Durbin-Watson statistic. 23 This suggests that some of the
independent variables are nonstationary and therefore possibly accidently correlated with consumer sentiment, the
level of which is also nonstationary.
Even if some of these variables are nonstationary, however, so long as they are cointegrated with sentiment they
can be used in level form in an error correction model.
43
Table 4
Expanded Error Correction Models of Consumer Sentiment
Summed Coefficients on Lagged changes in Independent Variables and Coefficients on
Error Correction Term (E.C.) and Dummy Variables
1963.01-1991.04
Independent
Variables
Dependent Variable
IlICS
IlCIND
Constant
-.119
(- .281)
.246
(.685)
IlICS
.481
(3.08)b
.229
(3.49)b
IlCIND
IlICP
-1.93
(2.80)b
-2.33
(2.07)c
IlU
-.262
( -3.41)a
E.C.
D72.1
Nixon wage and
price controls
D72.4
074.1-3
Oil embargo
075.2-3
D80.2
Carter
credit controls
D80.3
D87.4
Stock market crash
D87.1
D90.3-4
.235
(.620)
.356
( -4.59)a
-.0424
(4.53)a
-3.40
(6.l7)a
-3.19
(5.24)a
-6.36
(4.03)a
-7.21
(4. 16)a
-.229
(- 3.41)a
-.178
(- 2.83)a
5.8SC
(1.52)
3.27
(.801)
-11.2
( -2.98)a
-4.58
( -1.17)
-9.95
(-2.4W
-2.98
( -1.27)c
10.0
(2.50)a
9.34
(2.83)a
3.81
(- .99)
-8.29
( -1.97)b
11.0
(2.72)a
10.5
(2.35)a
-5.48
( -1.49)C
-5.61
( -1.43)c
5.05
(1.37)c
5.64
(1.43Y
-9.87
(- 3.45)a
-14.4
(- 5.41)a
Gulf War
D91.1
D91.4
-.204
( -3.15)a
.0905
(.218)
6.70
(1.66)b
-13.2
(3.37)a
Post-Gulf War
-10.2
( -2.52)a
jjz
.27
.55
.35
.51
S.E.
4.50
3.61
4.35
3.80
Levels of Significance (F-statistics for lagged changes and t-statistics for constant, E.C. term, and dummies)
aSignificant at 1%
bSignificant at 5%
cSignificant at 10%
Economic Review / 1992, Number 1
Therefore, we next examine the stationarity of the previous
menu of independent variables and their degree of cointegration with consumer sentiment. This allows us to
construct an error correction model that is free of spurious
correlation.
The stationarity tests that were performed are described
in Appendix B, as is the construction of the error correction term for models of sentiment. The only variables that
are both nonstationary in levels and cointegrated with
the two measures of consumer sentiment are the rate of
inflation in consumer prices (DLCPI) and the civilian
unemployment rate (D). Therefore, these variables are
used to construct error correction terms for both ICS and
CIND. However, other variables may contribute to shortrun changes in sentiment. In conformity with a "general-tosimple" modeling strategy, error correction models (with
4 lags) using inflation and unemployment were first estimated, and insignificant lagged changes were dropped.
The statistical significance of lagged changes in other
variables then was tested. The final error correction equations for explaining both measures of consumer sentiment
are shown in Table 4.
These expanded error correction models of sentiment
confirm the importance of changes in interest rates, and
changes in unemployment in the case of CIND, in conditioning short-run changes in sentiment. Changes in other
variables, except lagged changes in sentiment itself, are
insignificant. Also, a somewhat tighter fit is obtained for
CIND than for ICS. This is not surprising. The current
conditions component of sentiment should be more closely
related to current economic variables than the expected
conditions component. These expanded error correction
models of sentiment are quite different from those obtained
from the previous regressions in the levels of the variables.
Stock prices and oil prices are not included as independent
variables, but interest rates are, and the dynamics of the
effects of inflation and unemployment on sentiment are
more complex.
IV.
RELATIVE FORECASTING POWER OF
SENTIMENT INDICATORS
The expanded error correction models of consumer
sentiment improve the in-sample explanation of the change
in sentiment significantly, raising the coefficient of determination by 35 to 40 percent compared with simpler earlier
error correction models (Table 4 versus Table 2). But this
improved modeling of sentiment does not carry over into
any greater accuracy in forecasting spending on durables.
As shown in Table 5, the accuracy in forecasting durables
is worsened somewhat at all horizons with the expanded
models of ICS and CIND, even though actual rather than
Federal Reserve Bank of San Francisco
Table 5
Out of Sample Root Mean Squared
Errors in Forecasting InGCD
1976.Ql-1989.Q4
Quarters Ahead
Vector Error Correction System
With ICS
1
2
4
8
1. Basic Model
.034
.045
.048
.061
2. Expanded Model of
Sentiment
.034
.047
.054
.085
3. Actual Value of Sentiment
.034
.047
.059
.110
4. Basic Model
.031
.037
.043
.050
5. Expanded Model of
Sentiment
.031
.038
.049
.069
6. Actual Value of Sentiment
.031
.038
.043
.079
7. Actual Unemployment
and Inflation, instead of
Sentiment, in Durables
Equation
.032
.038
.045
.059
8. Actual Unemployment
and Actual CIND, instead
of Sentiment in Durables
Equation
.029
.035
.044
.081
With CIND
With Economic
Variables for Sentiment
forecasted values of inflation and unemployment are used
(lines 2 and 5).24 Furthermore, substituting actual survey
values of ICS or CIND for predicted values in the durables
equation does not improve the forecast of expenditures on
durables either, but on the whole tends to worsen it (lines 3
and 6).
Thus, this evidence suggests that in the 1976 to 1989
period consumer sentiment generally did not have an
important component that both helped to predict consumer
spending on durables and was not stably related to current
economic variables. Rather the opposite is suggested,
namely, that as good or better forecasts of expenditures on
durables might be obtained simply by using the economic
variables that are related to sentiment directly in a forecasting equation for durables, rather than using survey values
of sentiment. This possibility is examined by substituting
the unemployment rate and the inflation rate for sentiment
in the cointegrating equation for consumer durables (Table .
45
A2). The corresponding error correction model of expenditures on durables (Table 2, eq. lc) has a somewhat higher
standard error and somewhat lower coefficient of determination than before. But the resulting forecasts of durabIes expenditures, using actual values of unemployment
and inflation, are significantly more accurate than if the
actual survey value of ICS is used (Table 5, line 7 versus
line 3). Also, forecasting accuracy is about on a par with
that using the actual survey value of the more powerful
CIND measure of sentiment, being better at some horizons
and worse at others (Table 5, line 7 versus line 6). This
system also forecasts durables expenditures about as well
as the system containing either the simple (line 4) or
expanded (line 5) error correction models of CIND.
Finally,a . combination of indicators measuring sentiment was. tried. Both the unemployment rate and CIND
were included in the cointegrating equation for consumer
durables (inflation being omitted because it takes on the
"wrong" sign), shown in Table A2. Forecasts using the
resulting error correction model of expenditures on consumer durables (Table 2, eq. Id), and actual values of
unemployment and CIND, were not significantly more
accurate than ones using either unemployment and inflation or CIND alone. As shown in Table 5, at less than a
4-quarter horizon, the forecast error using both economic
variables and. sentiment (line 8) is slightly smaller than
when either is used alone, but at an 8-quarterhorizon it is
much larger.
Thus, over the 1976 to 1989 period,neither the overall
index of consumer sentiment (ICS), nor the more powerful
current conditions component (CIND), generally appears
to contain any information not already contained· in economic variables that is useful for forecasting expenditures
Consumer Sentiment (ICS)
Current Conditions Component of
Consumer Sentiment (CIND)
Predicted
....
90
.. ....
..
..
..
..
.. ..
..... .... ..........
......
........
...
110
100
80
'--_...L.-_--'--_---L..._---'-_----I_ _. L . - - - - J
90Q1 90Q2 90Q3 90Q4 91Q1
46
120
........ ...... . ...........•....
...........•...............
90
70
60
From August through October of 1990, the Michigan
index of consumer sentiment recorded the biggest decline
in any three-month period in its 44-year history; and over
the next year it failed to recover fully. This decline was
triggered by Iraq's invasion of Kuwait and the subsequent
military response of the United States and its allies.
As a result, consumer sentiment temporarily deviated
from its normal relationship with economic variables. 25
As shown in Charts 4A and 4B, the expanded errorcorrection models of consumer sentiment (estimated through
1990.Q2) fail to predict both the sharp declines in the ICS
and CIND measures of consumer sentiment from 1990.Q2
to 1990.Q4 and the subsequent increases from 1990.Q4 to
1991.Q3, even though the actual values of the explanatory
economic variables are used. While higher unemployment
tended to depress the predicted value of sentiment in this
period, falling interest rates and declining inflation worked
in the other direction. The net effect is a premctedinQrease
in the ICS measure of sentiment and only a small prediCted
decrease in the CIND measure. This is thus a clear case of
sentiment moving independently from current economic
Chart 48
Actual
80
The Gulf War and Consumer Spending
Chart 4A
110
100
on consumer durables. In particular, the substitution of unemployment and inflation for sentiment produces forecast
errors that are at least as small as those using sentiment
alone; and an even simpler model of sentiment based just
on interest rates also produces forecast errors at least as
small. Moreover, measuring consumer attitudes with a
combination of a sentiment index and economic variables
does not reduce forecast errors below those obtained by
using economic variables alone.
91Q2 91Q3
70
Actual
•••••• Predicted
I...-_..L..-_...L-._--L..._-I-_--'-_---'-_--I
90Q1 90Q2. 90Q3 90Q4 91Q1
91Q2 91Q3
Economic Review ! 1992, Number ].
conditions as the result of a major political event, and an
exception to the overall results for the 1976 to 1989 period.
Whether the effect of consumer attitudes on expenditures is better measured by the indexes of sentiment or
economic variables in this period is examined in Table 6.
This shows the root-mean-squared errors in forecasting
consumer expenditures on durables in the 1990.Q3 to
1991.Q3 period for models estimated through 1990.Q2.
The evidence here very strongly suggests that when sentiment and economic variables diverge, consumer spending
on. durables tends to follow the path of sentiment.
In the first place, forecasts of durables purchases from
the vector error correction system in this period have lower
errors if sentiment is omitted entirely than if the economic
variables usually explaining sentiment are employed. The
errors with either the basic (lines 2 and 5) or expanded
(lines 3 and 6) models of sentiment are both larger than
without sentiment (line 1), as are the errors from using
economic variables directly in the durables equation (lines
8 and 9). Thus, the economic variables that usually explain
sentiment do not contribute at all to the accuracy of
forecasts of durables purchases in this period.
Table 6
Out of Sample Root Mean Squared
Errors in Forecasting InGCD
Vector Error Correction System
1.
Without Sentiment
1990.Q3-1991.Q3
.072
With ICS
2.
Basic Model
.095
3.
Expanded Model of Sentiment
.100
4.
Actual Value of Sentiment
.044
With CIND
5.
Basic Model
.119
6.
Expanded Model of Sentiment
.129
7.
Actual Value of Sentiment
.057
With Economic Variables for
Sentiment
8.
Actual Unemployment and Inflation,
instead of Sentiment, in Durables
Equation
.084
9.
Actual Unemployment and Actual
CIND, instead of Sentiment in
Durables Equation
.075
Federal Reserve Bank of San Francisco
Second, forecast errors are reduced by 20 to 40 percent
if the actual value of a sentiment index is used in the model,
compared with using no measure of sentiment atal!.
Interestingly, also in this period the broad ICS index of
sentiment gives lower forecast errors than the narrower
CIND index covering only current conditions, which is the
opposite of the results in the earlier 1976.Ql to 1989.Q4
period. The likely reason is that a major economic or
political event, such as the Gulf War, significantly alters
expectations of economic conditions relative to perceptions of current economic conditions, whereas normally
expected conditions tend to befairly highly correlated with
current conditions and do not add any significant information. This is indeed seen in Chart 2, where in 1990 the
index of expected conditions drops significantly more than
the index of current conditions.
The relative size and patterns of these forecasting errors
for the 1990.Q3 to 1991.Q3 period are shown graphically
in Chart 5A. The forecast of durables purchases from the
vector error correction system that is based on the. actual
value of the overall ICS index turns down immediately, due
to the sharp drop in expected conditions, and isToughly in
Ijne with the actual drop in purchases ofconsumer durables
in the latter half of 1990. The forecast based on the actual
value of the current conditions index (CIND) drops much
more gradually; and the forecast based on actual unemployment and inflation shows a sustained increase in
spending.
The accuracy of these forecasts depends in part on the
ability of the vector error correction system to capture an
unexpected decline in income, as well as on the effect of
consumer attitudes on spending. So a more precise reading
of the best measurement of consumer attitudes can be had
by looking at the predictive accuracy of the durables
equation alone, using··actual values of all the independent
variables. As shown in Chart 5B, this strongly confirms the
accuracy of the overall ICS index of consumer sentiment in
measuring consumer attitudes during the Gulf War. The
forecast of durables purchases using the ICS index follows
the actual pattern of spending quite closely. The forecast
using the CIND current conditions component shows a
small increase in spending, with the effects of declining
interest rates tending to offset the effects of the relatively
small decline in CIND. Finally, the durables equation that
substitutes unemployment and inflation for a measure of
sentiment forecasts even larger increases in spending because of large interest rate effects relative to the depressing
effect of higher unemployment.
The 1990-1991 period was an exceptional one, in which
consumer sentiment lost its anchor to current economic
conditions. However, sentiment remains cointegrated with
inflation and unemployment even if observations from this
47
period are included. This suggests that sentiment returned
to its long-run relationship with these variables once the
special circumstances associated with the Gulf War had
dissipated. This, in fact, appears to have occurred by the
second and third quarters of 1991, following the allied
victory in March 1991, as evidenced in Charts 4a and 4b.
When the expanded error correction model of sentiment
is estimated through 1990.Q3, instead of through 1990.Q2,
it still overpredicts changes in ICS and CIND in future
periods,suggesting that significant "unexplained" effects
on sentiment still were present. Then, if the end point of
estimation is moved up to 1991.Ql, the model significantly
underpredicts the change in sentiment as euphoria associated with the military victory in March drove it up. By the
second and third quarters of 1991, however, the special
influence associated with the Gulf War appears to have
gone. This is indicated by the fact that the economic model
of sentiment forecasts changes in either ICS or CIND
between the second to third quarter of 1991 with little error.
There actually have been several other periods when
consumer sentiment similarly became temporarily detached from current economic conditions. Dummy variables were introduced into the expanded error correction
models of both ICS and CIND to test for these influences.
As shown in Table 4, the statistical significance of these
dummy variables indicates that there were unusual effects
on consumer sentiment during the Nixon wage and price
controls, the 1973-74 oil embargo, the 1987 stock market
crash, and the Carter credit controls, in addition to the
450
440
period of GulfWar. The Nixon wage and price controls had
a positive effect on sentiment, while all of the other events
depressed sentiment.
V
SUMMARY AND CONCLUSIONS
This paper has used error correction models to examine
the causes and effects· of consumer sentiment. It finds
that movements in consumer sentiment cause changes in
spending on consumer durables in a statistical sense at all
times, but that expenditures on durables do not cause
sentiment. Furthermore, expenditures on nondurables and
services are not causally related to sentiment at any time,
consistent with the hypotheses that sentiment measures the
degree of uncertainty held by households, rather than just
optimism or pessimism about the future.
In normal times, the important thing that consumer
sentiment measures for forecasting durables expenditures
is household perceptions of the current state of economy,
including whether or not it is a good time to buy· major
household items. Ordinarily their perception of future
economic conditions does not move very differently from
their perceptions of current conditions, and so does not
have any· important additional. effect on durables pur~
chases. In fact, forecast errors normally are lower if only
the current conditions component of the sentiment index is
used, rather than the overall index. In addition, if economic variables such as the unemployment rate and inflation are substituted for the value of sentiment in a model
Chart 5A
Chart 5B
Actual and Predicted Expenditures
on Consumer Durables
Actual and Predicted Expenditures
on Consumer Durables
Billions of 1982 Dollars
Billions of 1982 Dollars
,
500
Economic Model
of Sentiment
480
430
460
Economic Model
of Sentiment
~
420
440
410
420
400
390
L.....-----JL.....-----JL.....-----JI------JI------J_----J_---'
90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3
Predictions using vector error correction system,
except for actual values of sentiment, unemployment
and inflation.
48
400
L----I'-------l_---L_---L.--=::=:I::~:......r....._......1
90Q1 90Q2 90Q3 90Q4 91Q1 91Q2 91Q3
Predictions using actual values of all independent
variables in the consumer durables equation from .
the vector error correction system.
Economic Review / 1992, Number 1
of durables expenditures, forecasts are usually at least as
accurate as when only the current conditions component of
the sentiment index is used.
This normal pattern tends to be reversed at times of an
unusual economic or political event like the Persian Gulf
War, however. Such an event can move expected economic
conditions independently from current conditions, and the
resulting change in consumer attitudes can significantly
influence expenditures on durables. 26 As a result, forecasting errors using the overall index of sentiment are lower
in such a period than if just the current conditions index
of sentiment is used. Furthermore, because sentiment
is affected by unusual factors in such a period, it becomes detached from current economic variables. As a
result, economic models of sentiment break: down, and
the substitution of economic variables for sentiment in
models of durables expenditures no longer produces superior forecasts. 27
The practical ability to use the sentiment index for true
ex ante forecasts of durables expenditures at the time of a
major shock is limited, however, by the fact that the lag
between the values of sentiment that are actually known
and future expenditures is relatively short. A majority of
the response is completed within two quarters and the full
response takes about four quarters. In contrast, in normal
times reasonably good ex ante forecasts of durables expenditures, using only information available prior to the
forecast period, can be made over spans as long as eight
quarters by modeling consumer sentiment with economic
variables in a vector error correction system.
ENDNOTES
1. The Michigan index is available for a longer period than the alternative measure compiled by the Conference Board. In addition, preliminary tests showed it to be a better predictor of expenditures on consumer
durables. See Throop (1991a).
2. A useful treatise on psychological economics is Katona (1975).
3. In compiling the ICS, for each question a "balance score" is
calculated equal to the proportion of households giving favorable replies
minus the proportion giving unfavorable replies, plus 100 (to avoid
negative numbers). The balance scores to the.individual questions are
summed, and then divided by the base year figure (1966).
4. Strumpel, Morgan, and Zahn (1972) contains representative studies
by leading economists and references to the rather large amount of
literature on this subject.
5. This point of view is well represented by Tobin in Strumpel, Morgan,
and Zahn (1972).
6. Juster and Wachtel (1972a, 1972b) have been consistent proponents
of this view. Although Mishkin (1976, 1977, 1978) also argues that
uncertainty is an important factor in consumer expenditures on durables, his work suggests that it is better captured by direct balance sheet
measures than by consumer sentiment.
7. See Modigliani and Bromberg (1954), Ando and Modigliani (1963),
Modigliani (1971), and Steindel (1981).
8. See, for example, Adams and Klein (1972) Juster and Wachtel (1972a
and b), Dunkelberg (1972) and Shapiro (1972), as well as the consumption sector of the DRI model ofthe U.S. economy described in Eckstein
(1983).
9. See endnote 19.
10. For further discussion of spurious correlations, see Hendry (1980)
Granger and Newbold (1974), and Campbell and Perron (1991).
11. Overviews of vector error correction methodology are provided in
Hendry (1986), Granger (1986), Hall (1986), Jenkinson (1986) and
Engle and Granger (1987). See also the appendixes to this study.
12. See, for example, Wilcox (1989).
13. When the equations are estimated in unrestricted form, as in Table
A3, the coefficients implied for the cointegrating vector are very close to
the originals, providing a check on the original estimates. Also,
t-statistics on the levels of ICS and CIND are 4 or more. Since the levels
of ICS and CIND are nonstationary, although coefficient estimates are
consistent the usual distribution for the t-statistic does not apply. A
larger than normal t value, somewhere on the order of the Dickey-Fuller
tests, is required for any level of significance. (On these points see
Banerjee, et al. (1986) and Stock and Watson (1988). The t-statistics
appear to be high enough to meet this test. Moreover, the indicated
significance of ICS or CIND is roughly as high as that of interest rates,
which clearly belong in the cointegrating vector.
14. Recent studies have found that consumption exhibits a lagged
response to income in some degree, contrary to the rational expectations
version of the permanent income hypothesis. As a result, changes in
consumption would be related to past changes in consumption. See Hall
(1978), Flavin (1981) and Nelson (1987).
15. The literature on the precautionary motive for saving includes
Leland (1968), Sandmo (1970), Dreze and Modigliani (1972), Zeldes
(1989), and Blanchard and Fischer (1989).
16. Campbell (1987), Cochrane (1990) and Trehan (1991) reach a
similar conclusion.
Federal Reserve Bank of San Francisco
49
17. Because errors in the different equations may be contemporaneously
correlated, an assumption needs to be made about their causality. The
common procedure is to order the variables so that errors in the
equations that are ordered first affect the errors in the other equations,
but are not affected by them. The "general-to-simple" modeling strategy that we employed Provides a useful guide for such ordering. For
example, interest rates and consumer sentiment affect spending on
durables, but are not affected by that spending. Therefore, it seems
reasonable to order interest rates and sentiment before durables purchases, so that disturbances to them affect durables but not vice versa. In
accordance with this approach, the complete ordering that was used is
ICP, CIND, LCNS, LGYD, LGCD.
18. These conclusions are relatively insensitive to the ordering of the
variables. Two alternative orderings were tried. In the first, the initial
ordering was reversed to give LGCD, LGYD, LCNS, CIND, ICP. In
the second, CIND and ICP were interchanged in this reordering. In both
alternatives, the response of durables purchases to shocks to sentiment
was reduced compared with the response to interest rates, but still was at
least half that of interest rates. The responses of durables to shocks to
nondurables and services, income, and durables were affected to lesser
degrees.
27. Gamer (1991) examines some of these same issues. He finds, as we
do, that sentiment ordinarily has little complementary value in forecasting consumer expenditures on durables when used with other macroeconomic variables. Although, he relates changes in durables
purchases to the level of consumer sentiment in an ordinary regression,
that finding is confirmed here by a richer error correction model.
Gamer also considers the ability of a Bayesian vector autoregression
(BVAR) model to forecast consumer purchases of durables in an
exceptional circumstance like the war in the Persian Gulf, with and
without using consumer sentiment. The BVAR model with sentiment
slightly outperforms the version without sentiment in this period, but
neither one comes close to predicting the sharp decline of durables
purchases in late 1990. Garner concludes that consumer sentiment helps
only slightly in forecasting durables purchases during the Gulf War. As
emphasized in this study, however, the reason why the BVAR model
with sentiment misses the sharp decline in spending on durables in this
period is not that sentiment did not help to explain consumer purchases,
but rather that in such circumstances the usual relationship between
sentiment and macroeconomic variables broke down. As a result, the
BVAR could not forecast the actual decline in sentiment that occurred,
thus missing the decline in durables purchases as well.
19. Transitory income (YDT) is defined as the difference between
current income and permanent income (YPD), where YDP is calculated
as ifil ~ a)ai(l + l)iYD _ i*' The parameter, a, was chosen to mini·
mize the error in predicting spending on nondurables and services. It
equals about 0.5.
20. Fisher (1981) and Taylor (1981) find a positive correlation between
the level and variance of inflation over time in both the U. S. and GEeD
countries. A more recent paper with similar findings is Ball and
Cecchetti (1990).
21. These studies include Adams and Green (1965), Hymans (1970),
Lovell (1975), and Eckstein (1983, ch. 5).
22. Variables in change form are all one-quarter changes. The unemployment rate is adjusted for estimated changes in the full employment
rate of unemployment over time due to demographic shifts.
Mishkin used a four-quarter change in consumer prices, as did we in
updating his model of sentiment. However, these equations switch to a
one-quarter change in consumer prices for DLCPI in order to be
comparable with the results of the subsequent error correction model of
sentiment. The insignificance of FIN, DEBT, and YDT and the significance of lagged ICS when other variables are added is not sensitive to
whether DLCPI is measured as a one-quarter or four-quarter change.
23. A high R2 relative to the D.W. statistic is generally regarded as a
possible indication of a spurious regression due to random time trends.
See Campbell and Perron (1991). The R2 and D. W. statistics are .73 and
1.12, respectively, for ICS and .50 and .70 for CIND, in the absence
of correction for serial correlation or the use of lagged dependent
variables.
24. The vector error correction system actually forecasts better using
predicted values of variables other than consumer sentiment rather than
actual values. This appears to be attributable to the difficulty of
measuring permanent income. Substituting actual for the predicted
values of ICP improves the forecast of LGCD a little, while substituting
actual for predicted values of LCNS and LGYn worsens it quite a lot.
25. Even including the period of the Gulf War, however, the measures of
sentiment remain cointegrated with unemployment and inflation.
26. In fact, the decline in consumer and business confidence at the time
of the Gulf War appears to have been the dominant impulse precipitating
the recession that began in the summer of 1990. See Throop (1991b).
50
Economic Revi.ew / 1992, Number 1
ApPENDIX A
In constructing a vector error correction system, one
first determines whether levels or first differences of the
variables are stationary (or trend-stationary as the case may
be) by using the Dickey-Fuller test, as described in Fuller
(1976). This test consists of regressing the first difference
of the variable in question on its own lagged level plus a
constant, a time trend, and lagged first differences as appropriate. I The null hypothesis that random disturbances
permanently affect the level of the series-making it
nonstationary-implies that the coefficient on the lagged
level should be greater than or equal to zero. 2 The teststatistic is just the ratio of the estimate of the coefficient to
its standard error, except that under the null hypothesis this
statistic does not have the usual t distribution. 3
Table Al presents the results of this test for the levels and
first differences of the logs of real spending on consumer
durables (LGCD), real spending on nondurables and services (LCNS), and real disposable income (LGYD), as well
as the levels and first differences of the six-month commercial paper rate (ICP), the index of consumer sentiment
(ICS) and the current conditions component (CIND) of
that index. In each case, three lags of the dependent
variable are.included to capture short-run dynamics.
Table Al shows that in levels form the t-statistic (shown
in parentheses) on the coefficient on the lagged level of the
dependent variable does not exceed the critical value for
any of the variables at even the 10 percent level of significance. So we cannot reject the hypothesis of nonstationarity for the level of the variable in all cases. By
contrast, we can reject the hypothesis of nonstationarity for
first differences at a 5 percent level of significance or less in
all cases.
These results indicate that standard statistical tests of
significance may be applied to regressions on these variables in first difference form because the first differences
are stationary. Therefore, a natural representation is a
vector autoregression in the first differences. However, this
form throws away information about longer-run relationships between the levels of the variables that may in fact
exist. Even though the levels of the variables are nonstationary, disturbances to them may be related, so they do not
tend to drift apart in the long run. In this case they are said
to be cointegrated.
We can test for the existence of such a long-run relationship by estimating an ordinary least squares regression and
examining the residuals from this regression for stationarity. A finding that th~ residuals are stationary means that
even though the variables in the regression are nonstationary, a linear combination of the variables is stationary.
Moreover, if the residuals from this regression are added to
Federal Reserve Bank of San Francisco
the vector autoregression in the first differences as an
"error correction" term, the residuals in those equations
will continue to be stationary, and the usual statistical tests
will continue to apply.
Table A2 shows the· cointegrating vectors that are obtained by regressing LGCD on LCNS, LGYD, ICP, and a
measure of consumer sentiment (either ICS or CIND).
Using either measure of sentiment, both LCNS and LGYD
have positive coefficients, the coefficient on ICP has. the
expected negative sign, and the coefficient on sentiment
has the expected positive sign. The Dickey-Fuller test
indicates stationarity in the residuals of the cointegrating
vectors at a 5 percent level or better. 4 . Therefore, the
estimated error (actual less predicted) from the cointegrating regression can be included as an error correction term.
When entered into the vector autoregressions, its estimated
coefficients will indicate the extent to which LGCD,
compared with other variables, responds to deviations
from the estimated long-run relationship.
A vector error correction system tends to be overparameterized since all lags on all variables are included.
Therefore, a "general-to-simple" modeling strategy was
employed in which insignificant variables were dropped.
On the basis of F tests, lagged changes in LGYD, ICP, and
ICS are dropped when ICS is employed as the measure of
consumer sentiment, while only lagged changes in LGYD
are dropped when CIND is the measure used. Also, LCNS
clearly is not a significant factor in the error correction
term, since dropping it from the cointegrating vector has no
effect on the standard error of the estimated equation for
consumer durables; and the cointegrating vector that omits
LCNS continues to pass the test for stationarity, as shown
in Table A2. The resulting vector error correction system
for explaining spending on consumer durables is shown in
Table 2 in the text.
IIf lagged first differences are included; this is called the augmented
Dickey-Fuller test.
2For example, in the simplest of time series processes, X=PX'~I +e,
where e is a random error. If p<l, then a random disturbance will not
pennanently affect the level, so that X will be stationary. But ifp;;'1 the
level of x will be pennanently affected, and therefore x will be
nonstationary.
Subtracting X,_I from both sides, At,= -(l-p)x'_I+e. Thus, if
p<l, then when At)s regressed onx,~ I' the coefficient on x,_lwill be
negative, indicating a stationary process. On the other hand, if p = I(a
unit root), the coefficient on X,_I will be zero, and the process will be
nonstationary. Similarly, if p> 1 and 1- p>O, the process also is
nonstationary.
3Critical values of this statistic are tabulated in Fuller (1976).
4Significance levels for Dickey-Fuller test on cointegrating equations
are tabulated in Engle and Yoo (1987).
51
Table A1
Augmented Dickey-Fuller Tests for Stationarity
(1963.01-1990.04)
A. Tests on Levels of Variables
LGCD
LeNS
LGYD
ICP
ICS
CIND
Constant
.549
(2.94)
.293
(2.43)
.462
(2.57)
.741
(2.41)
9.07
(2.44)
11.1
(2.40)
Trend
.00151
(2.65)
.000293
(2.14)
.000454
(2.17)
-.133
( -2.82)
-.0441
(-2.37)
-.0672
(-2.50)
-.0866
( -2.44)
-.109
( -2.53)
-.120
(- 2.43)
Coefficient on lagged level of dependent variable
B. Tests on Differences of Variables
Constant
Coefficient on lagged level of dependent variable
.0111
(2.63)
.00594
(3.39)
.00335
(2.98)
-.0430
(.374)
-.262
(- .530)
- .111
(.224)
-.918
( -4.60)a
-.755
( -4.l7)a
- .458
(- 3.41)b
-.957
( -5.24)a
-.743
( -3.62)b
-.910
( -4.07)a
Notes:
Each regression contains three lags of the dependent variable.
Levels of Significance:
aSignificant at 1%
bSignificant at 5%
52
Economic Review / 1992, Number 1
TableA2
Dickey-Fuller Tests for Cointegration
(1963.01-1990.04)
,--_Th_e_D_i_Ck_ey_-p_U_Il_er_t_es_ts_d_id_ll_o_t_ill_Co_rp_o_ra_t_e_an_Y_Ia_g_ge_d_d_if_fe_fe_ll_ce_s_of_t_he_f_es_id_u_aI_b_ec_a_u_se_th_e_y_w_er_e_n_ot_fo_U_ll_d_tO_b_e_S_ig_lli_fi_can_t.
Federal Reserve Bank of San Francisco
J
53
TableA3
Unrestricted Estimation of Durables Equation
(1963.1-990.4)
LlLGCD =
-4.29 + .0396 LlLCNS_ 1 + .0370 LlLCNS_ 2
(- 8.53) (.0669)
(.0656)
+
.791 LlLCNS_ 3 + .458 LlLCNS_ 4 - .591 LGCD
(1.36)
(.0797)
(- 8.47)
+
.989 LGYD
(8.59)
- .00716 lCP + .00153 ICS
(-5.92)
(4.14)
R2
= .444
D.W. = 2.48
S.E. = .0260
LlLGCD = -5.95 + .0338 LlLCNS_ 1 - .202 LlLCNS_ 2 + 1.04 LlLCNS_ 3 - .0671 LlLCNS_ 4
(-7.92) (.578)
(- .354)
(1.78)
(- .113)
.0000993LlICP -3
(.0409)
-
.0039 MCP -4
(-1.67)
-
.00232 LlCIND_ 1
(- 3.61)
-
.000729 LlCIND_ 2
(-1.16)
-
-
.00427 LlICP -I - .00446 LlICP_ 2
(1.61)
(-1.76)
.000467 LlCIND_ 3 + .000572 LlCIND_ 4
(- .794)
(1.07)
- .867 LGCD + 1.37 LGYD - .00744 ICP + .00317 CIND
(-8.00)
(8.00)
(-4.36)
(5.32)
R2
= .502
S.E. = .0246
D.W. = 2.12
I
Implicit Cointegrating Vectors Normalized on LGCD
....
l_LG_C_D_=_c_on_st_an_t_+_1._58_L_G_Y_D_-_.0_0_85_8_1C_P_+_.0_0_36_5_C_IN_D
54
J
!
LGCD = constant + 1.67 LGYD - .0121 ICP + .00259ICS
.
Economic Review / 1992, Number 1
ApPENDIX B
In constructing an expanded error correction model of
consumer sentiment, the stationarity of the menu of possible independent variables is examined first. Table BI
presents the results of such tests on the levels and first
differences of the variables discussed in the text.
The first difference of DEBT is not stationary. Therefore,
it cannot be cointegrated with consumer sentiment, which
is stationary in first differences. Nor can short-run changes
in sentiment truly be explained by changes in DEBT
because the former is stationary and the latter is not. Since
it does not make any sense to use FIN without DEBT, both
FIN and DEBT are therefore dropped. In contrast, YDT,
DLSP, DLPOIL, and DU are stationary in levels and so
cannot be cointegrated with consumer sentiment either.
However, since the first differences in these variables are
stationary, they may be related to first differences in
sentiment in the short run. This leaves inflation (DLCPI),
I
oil prices (LPOIL), unemployment (U), and interest rates
(ICP from results in Table AI) as possible candidates for
cointegration with consumer sentiment.
Turning to Tables B2 and B3, all four variables appear to
be significantly cointegrated with either measure of sentiment, although the inflation rate is the most closely related
(eqs. I to 4). Next, in combining each of the other variables
with inflation, unemployment improves the fit of the
cointegration relationship the most (eqs. 5 to 7). The
further addition of the price of oil to the relationship does
not materially improve the fit and generates a "wrong"
sign for the coefficient on oil prices (eq. 8). Alternatively,
adding the interest rate to the relationship worsens the fit
somewhat (eq. 9). This leaves inflation and the unemployment rate as the only variables that are cointegrated with
the measures of consumer sentiment. Therefore, the errors
from equation 6 are used to form the error correction terms
in the expanded error correction models of consumer
sentiment, shown in Table 4 in the text.
Table 81
Augmented Dickey-Fuller Tests for Stationarity
(1963.01-1990.04)
A. Thsts on Levels of Variables
Constant
FIN
DEBT
YDT
DLCPI
DLSP
LPOIL
DLPOL
U
DU
284.38
(0.56)
-74.1
(1.63)
0.792
(0.74)
0.002
(2.25)
0.0107
(1.70)
0.0155
(0.92)
0.0057
(0.72)
0.0153
(0.56)
0.0013
(0.05)
-0.463
(3.88)a
-0.139
(2.42)
-0.805
(4.87)a
-0.0328
(1.40)
-0.962
(5.68)a
-0.0412
(2.30)
-0.501
(4. 94)a
2.483
(2.39)
Trend
Coefficient on
lagged level
0.003
(1.36)
-0.0137
(2.06)
B. Thsts on Differences of Variables
FIN
DEBT
YDT
DLCPI
DLSP
LPOIL
DLPOL
U
DU
Constant
472.6
(2.44)
27.3
(1.92)
-0.509
(0.46)
0.00015
(0.35)
-0.0017
(0.26)
0.0057
(0.71)
0.0034
(0.40)
0.0833
(0.12)
0.0052
(0.18)
Coefficient on
lagged level
-0.945
(4.47)a
-0.148
(2.52)
-1.56
(5.72)a
-1.36
(5.32)a
-2.31
(7.84)a
-0.962
(5.66)a
-2.37
(8.50)a
-0.498
(4.90)a
-1.55
(6.8l)a
Notes:
Each regression contains three lags of the dependent variable.
Significance Levels:
aSignificant at the I % level
Federal Reserve Bank of San Francisco
55
Table 82
Dickey-Fuller Cointegration Tests on ICS
(1963.01-1990.04)
Constant
DLCPI
1.
99.7
(67.6)
-11.0
(-11.7)
2.
75.6
(35.3)
3.
85.8
(77.0)
4.
102.9
(40.9)
5.
94.2
(39.6)
-10.0
( -10.2)
6.
100.2
(75.1)
-10.9
( -12.8)
7.
103.6
(51.1)
-9.1
( -7.78)
8.
106.2
(31.1)
( -12.0)
101.4
(52.1)
-10.3
( -9.20)
9.
LPOIL
U
ICP
-14.8
( ~5.00)
-2.43
(3.47)
-2.18
( -7.67)
~11.9
-6.48
( -2.85)
-2.27
( -5.11)
-.790
( -2.71)
6.72
(l.88)
-3.41
( -4.56)
-2.10
( -4.27)
-.246
(- .825)
S.E.
R2
Dickey-Fuller
lest
8.07
.551
-4.91 a
10.91
.179
-2.33
11.48
.091
-2.14
9.76
.344
-3.13 b
7.81
.578
-4.90a
7.27
.635
-5.33 a
7.84
.576
-4.87a
7.19
.643
-S.64a
7.28
.635
-5.26a
Levels of Significance
aSignificant at 1%
bSignificant at 5%
56
Economic Review / 1992, Number 1
Table 83
Dickey-Fuller Cointegration Tests on CIND
(1963.01-1990.04)
Constant
DLCPI
1.
102.8
(61.1)
-7.15
( -6.64)
2.
87.2
(42.9)
3.
93.7
(91.5)
4.
105.2
(41.6)
5.
99.2
(35.6)
-6.50
(-5.67)
6.
103.2
(63.3)
-7.06
( -6.79)
7.
105.7
(44.9)
-5.71
( -4.21)
8.
108.3
(25.7)
-7.91
( -6.48)
9.
104.2
(43.7)
-6.57
( ~4.79)
LPOIL
U
ICP
-9.60
(- 3.42)
-1.70
( -2.64)
-1.46
( -5.10)
-4.21
( -1.59)
-1.60
( -2.95)
- .582
( -1.72)
5.76
(1.30)
-2.58
( -2.79)
-1.45
(- 2.43)
-.205
(- .561)
S.E.
R2
Dickey-Fuller
Thst
9.19
.281
-3.80a
10.35
.089
-2.67c
10.56
.051
-2.58c
9.79
.186
-3.15 b
9.13
.291
--'3.74b
8.88
.329
-3.80b
9.11
.294
-3.76b
8.85
.333
-3.92b
8.91
.325
-3.78 b
Levels of Significance
aSignificant at 1%
bSignificant at 5%
cSignificant at 10%
Federal Reserve Bank of San Francisco
57
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