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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 Opinions expressed in the Economic Review do not neces sarily reflect the views of the management of the Federal Reserve Bank of San Francisco, or of the Board of Governors of the Federal Reserve System. The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the Bank’s Research Department under the supervision of Jack H. Beebe, Senior Vice President and Director of Research. The publication is edited by Judith Goff. Design, production, and distribution are handled by the Public Information Department, with the assistance of Karen Flamme and William Rosenthal. For free copies of this and other Federal Reserve publicatons, write or phone the Public Information Department, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco, California 94120. Phone (415) 974-2163. Printed on recycled paper with soybean inks. 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: North Holland. Central Bank of China. Financial Statistics, Taiwan District, Republic of China various issues. 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). 34 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 REFERENCES Friedman, Milton. 1957. A Theory of the Consumption Function. Princeton: Princeton University Press. Adams, EG., and E.W. Green. 1965. "Explaining and Predicting Aggregate Consumer Attitudes." International Economic Review (September). Fuller, Wayne A. 1976. Introduction to Statistical Time Series. John Wiley & Sons. _ _ _ _ _ and L.R. Klein. 1972. "Anticipatory Variables in MacroEconometric Models." In Human Behavior in Economic Affairs: Essays in Honor of George Katona, eds. Strumpel, Morgan, and ZOOn. Amsterdam: Elsevier Scientific Publishing Co. Ando, Albert, and Franco Modigliani. 1963. "The Life-Cycle Hypothesis and Saving: Aggregate Implications and Tests." 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