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FEDERAL RESERVE BANK OF DALLAS September 1989 • • ConOInlC CVICW Demographics and the Trade Balance John K. Hill Recent Trade and Exchange Rate Movements: Possible Explanations Evan F. Koenig This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org) Economic Review Federal Reserve Bank of Dallas September 1989 President and chid ExeaitWe Offlcer Robert H. Boykin First Vice Presideot and Chief Operating OffIcer williarri H. Wallace Senior Vice President and Director of llesearch. Harvey, Rosenblum Vice President and AsIIodate DIrector of Reseaa'Ch Gerald P. O'Driscoll, Jr. Vice President andl!cOnomic AdvIsor W. Michaf.!l Cox Assistant Vice President and SeniOr Economise Stephen P. A. Brown Economists National and1nternattonal Jqhn K. Hill Robert; T. Clair Evan F. Koenig Kenneth M . Emery Joseph H . Haslag Linda C. Hunter Cara S. Lown Mark A. Wynne RegionaJ arid Energy William C. Gruben Mine K. Yiicel William T. LOng III Keith R. Phillips Lori 1. Taylor EcUtors Virginia M . Rogers Janis P. Simmons The Economic Review is published by the Federal Reserve Bank of Dallas. The views expressed are those of the authors and do not necessarily reflect the positions of the Federal Reserve Bank of Dallas or ." " the Federal R~rve System. Subscriptions are available free of charge. Please send requests for single-copy and multiple-copy subscriptions, back issues, and address changes to the Public Affairs Department, Feqeral Reserve Bank of . Dallas, Station K, Dallas, T.e xas 75222, (214)651-6289, Articles may be reprinted on the condition 'that the source is credited and the Re5eilfCh Department is provided with a copy of the publ,ication " containing the reprinted material, < l Contents Page 1 Can demographic changes account for the rapid growth of the u.s. trade deficit during the 1980s? Hill finds that recent and projected shifts in the age composition of the u.s. population are capable of producing large swings in the trade balance. He concludes that much of the current trade deficit reflects mutually beneficial international exchange. To that extent, the deficit should not be interpreted as a sign that u.s. living standards will decline. To analyze the relationship between demographics and the trade balance, Hill uses a simulation model that projects movements in the trade balance solely on the basis of changes in the age composition of the population. In his simulations, U.S. net exports move from a deficit of 2 percent of GNP in the early 1980s to a surplus of 4 percent of GNP by the early part of the next century. Surprisingly, the majority of the increase in net exports over this period is due to a decline in the rate of domestic investment, rather than a rise in the national savings rate. Demographics and the Trade Balance John K. Hill Page 13 What role do trade deficits play in the international economy? How do changes in productivity, investment, and government purchases affect trade patterns and exchange rates? What are the likely consequences of monetary shocks? Koenig explores these questions by using a simple set of diagrams. His analysis suggests that cyclical movements in output and investment are capable of explaining much of the recent variation in trade flows. Recent Trade and Exchange Rate Movements: Possible Explanations Evan F. Koenig John K. Hill Senior Economist and Policy Advisor Federal Reserve Bank of Dallas Demographics and the Trade Balance oes the u.s. trade deficit signal a future decline in living standards for citizens of the United States? The answer depends on what is causing the deficit. Trade deficits arise whenever national saving falls short of domestic investment. If the deficit is due to a consumption binge, then the deficit will indeed signal a fall in living standards , If, on the other hand, the deficit is investment driven, in the sense that foreign investors find the United States to be an attractive place to invest, then the deficit is a sign of a growing economy.1 The purpose of this article is to evaluate the role of demographics in the evolution of the U.S. trade balance. We seek to determine whether historical fluctuations in the size of U.S. birth cohorts can help to explain the trade deficits of the 1980s. To the extent they are a product of demographics, the deficits simply represent an exchange of goods across time between citizens of different ages in different nations of the world. As such, the deficits indicate nothing about the direction of change in U.S. living standards. We base our analysis of the relationship between demographics and the trade balance on simulations of wealth and capital accumulation in the United States during the period 1980- 2009. The simulations combine a standard theory of savings behavior with information on past and projected variations in the number and age distribution of U.S. households . Our purpose is not to accurately replicate or forecast the U.S. trade balance, but rather to gain a sense of magnitude of the effect demographic changes may have on the trade balance. We simply ask whether, on the basis of conventional analysis, we should expect D Economic Review - September 1989 demographic factors to playa significant role in the evolution of the U.S . trade balance. The results show that basic changes in U.S. demography are capable of producing large swings in the trade balance. In our simulations, U.S. net exports move from a deficit of 2 percent of the gross national product (GNP) in the early 1980s to a surplus of 4 percent of GNP by the year 2009. The bulk of the rise in net exports over this period is attributable to a decline in the rate of domestic investment. Only 20 percent of the change in net exports is due to an increase in the savings rate. The reasoning behind our results is simple. During the 1980s, the adult population of the United States was very young. Young workers require a large amount of capital but have accumulated only a small amount of wealth. A young age distribution, therefore, serves to produce an excess demand for capital. In a closed economy, this excess demand would prompt a substantial rise in interest rates . With an international capital market, however, the gap between required capital and accumulated wealth can be financed by an inflow of foreign capital. This is precisely what has happened. The U.S. trade deficit represents the flow of foreign capital needed to redress the imbalance between the domestic demand for and 1 Martin Feldstein and Robert Lawrence have been vehement in painting to the federal budget deficit as a primary cause of the decline in national savings and the attendant rise in the trade deficit Milton Friedman is prominent among those who regard the trade deficit as a reflection of a favorable us investment climate. 1 the national supply of capital. As the U.S. population ages, more and more individuals will reach a stage in their life cycle where accumulated wealth exceeds the capital required to support their labor supply. When this happens, the United States will turn from being a net borrower to a net lender in the world capital market The trade account will move from a position of deficit to a position of surplus. Chart 1 Life-Cycle Profile of Household Wealth Percent of earnings of entry·level male worker 2,500 The model The concept of the trade balance we focus on is net exports, as defined in national income and product accounting. Net exports measure the difference between national saving and domestic investment 2 A deficit in net exports represents the net inflow of foreign capital needed [0 finance any gap between aggregate saving and investment. Without international capital movements, a nation's trade account would be forced to balance. In a world with integrated capital markets, trade imbalances become the rule rather than the exception. We base our analysis of the relationship between demographics and net exports on simulations of u.s. wealth and capital accumulation. The simulation model provides for the basic channels through which demographic changes alter the trade balance. Otherwise the model is extremely simple. There is no government saving or investment. There is no technological change. We assume that foreign capital is available in unlimited quantities at an unchanged interest rate. We also assume that households are identical except for age . With these assumptions, simulated movements in the u.s. trade balance can only reflect 2 3 2 The excess of national saving over investment is more properly identified by the current account surplus. which differs from net exports in that it includes net international transfer receipts . For the United States. the two measures differ very little And in our simulations. the two measures are equivalent We chose to sacrifice some conceptual accuracy to be able to use a term that is more familiar to the general readership See Dornbusch (1980, 19-24) for a discussion of the relations between the various sectoral balances in national income accounting For an insightful and compact review of the empirical validity of the life-cycle model. see Baskin and Lau (1988) changes in U.S. demographics. Net exports are calculated as the difference between aggregate saving and investment We construct time paths for saving and investment by combining information on the number of U.S. households by age group with life-cycle profiles of wealth and labor supply for a representative household. Time path of national saving. Saving is defined as change in wealth. We compute aggregate wealth by multiplying the wealth of a representative household at a given age by the number of u.s. households of that age, and then summing over all ages. Chart 1 shows the individual age-wealth profile used in our calculations. We derived the profile from the life-cycle model of saving, as popularized by Franco Modigliani, Richard Brumberg, and Albert Ando (see Appendix A). In the model, households attempt to smooth consumption over time by saving when earnings are high relative to family needs and dissaving when earnings are relatively low. The optimal wealth profile is "hump-shaped," reflecting a pattern of accumulation during the preretirement years followed by a drawing down of wealth during retirement Empirical evidence is supportive of many of the basic tenets of the life-cycle model-specifically, the notion that households attempt to smooth consumption over time and that saving rates vary systematically with age.' The principal Federal Reserve Bank of Dallas adult age of 42. At that point, labor supply begins to decline-slowly at first , tracking the decline in worker productivity, and then more rapidly as labor-force participation falls off. Chart 2 Life-Cycle Profile of Effective Household Labor Supply Percent of labor supply of entry-level male worker 300 DemographUctrends 200 100 o 20 30 40 50 60 70 80 Age criticism of the model is that it overstates the rate at which households draw down their wealth late in life.' By overstating the rate of dissaving among the elderly, we risk distorting the path of net exports during periods of significant change in the share of the population aged 60 and over. Fortunately, there is little movement in this part of the age distribution over our period of analysis. Time path of domestic investment. Capital is assumed to be infinitely lived. Gross investment, therefore, is simply the change in capital. We compute the stock of U.S. domestic capital by multiplying the capital required to support household labor supply at a given age by the number of U.S. households of that age, and then summing over all ages. In our model of production, there is a constant ratio of capital to labor. 5 Thus, the age-capital profile of an individual household is simply a multiple of the household 's labor-supply profile. Chart 2 shows the labor-supply profile used in our calculations. Our measure of labor supply accounts for age-related variations in both worker productivity and labor-force participation (see Appendix B). The shape of the profile during the first half of the life of the household reflects the effects of gains in the productivity of the male worker and changes in the rate of female laborforce participation during the child-rearing years. Effective household labor supply peaks at an Economic Review - September 1989 In addition to the wealth and labor supply profiles, our simulations require information on the number and age distribution of U.S. households. Our method of constructing these data is based on a simplified description of household formation . Households are formed by two individuals of age 21. The household lives for a period of 60 years, w hen the last adult member dies. To measure the number of households formed in any given year, we simply sum the number of men and women who were of age 21 in that year and then divide by two (see Appendix C). This procedure fails to account for the variety and complexity of household formation patterns. But it does allow us to faithfully recognize historical and projected variations in cohort size. Chart 3 show s our figures on annualized rates of growth in the total number of U.S. households. During the early 1980s, the number of households rises at an annual rate of 1.6 percent. The high rate of growth during this period reflects both a large number of household bitths (involving individuals born in the early 1960s) and a , A low rate of wealth decumulation can be explained either by longevity and medical risk in the face of imperfect annuity markets (Davies 1981) or by a shift in preferences lale in life with the household increasing its taste for bequests The evidence seems to favor the former explanation The motive to transfer wealth at death does not appear strong The rate of decumulation among the elderly is not significantly affected by the presence or number of children (Hurd 1987). and estate data show that bequeathed wealth is shared equally by children, which is inconsistent with some models of inlergenerational altruism. 5 The aggregate production function takes the Cobb-Douglas form The equilibrium ratio of capital to labor is KIL = (wlr) a (1 - a} -', where w is the wage rate, r is the real interest rate, and a is capital's distributive share In our reported simulations, the wage rate is normalized at unity, r = OS, and a = .20 Thus, the capital-labor ratio is 5 0 3 Chart 3 Chart 4 Growth in the Number of U.S. Households (Annualized rate) Age Distribution of U.S. Households Percent of Total Percent 100 3 80 60 2 40 20 1990 • o 1980 1990 2000 2010 NOTE: Data are based on a stylized representation of household formation and dissolution. See the section in the text on demographic trends_ small number of deaths (among individuals born at the turn of the century). Except for a small and brief upturn around 1990, the growth rate then falls through the middle part of the 1990s. By 1996 the rate is down to 0.5 percent, only onethird of its value in 1980. The growth rate does rise somewhat during the late 1990s and on into the early pa11 of the next century. But by 2009, the rate is still only one-half as large as it was in 1980. Chart 4 provides information on the distribution of households by 10-year age group. Movements in the age distribution reflect two significant episodes in U.S. demographic history: (1) a period of low numbers of births during the 1930s, as the economy struggled through the Great Depression, and (2) the post-World War II baby boom, w hich produced an unusually large number of births from the late 1940s through the first half of the 1960s. During the 19805, the most significant increases in population shares occur in the age groups 31--40 and 41-50. The rise in the share of the younger group marks the entry of the babyboom generation into this age bracket. The rise in the share of the older group reflects the aging of the baby-bust generation and its exit from the 21 -31 31-40 51-60 61-70 2000 • 41-50 . 2010 71-80 NOTE: Data are based on a stylized representation of household formation and dissolution . See the section in the text on demographic trends . group. Large declines in population shares occur in age groups 21-30 and 51-60. The decline in the share of the younger group is associated with the aging of the baby-boom generation. The decline in the share of the group aged 51-60 marks the entry of the baby-bust generation into this age group. The pattern of movements in population shares that appears during the 1980s is repeated during the 1990s and 2000s, except that the pattern manifests itself in groups that are 10 and 20 years older. During the 1990s, the population shares of groups 41-50 and 51-60 rise, while the shares of groups 31--40 and 61-70 fall. During the first decade of the next centUlY, population shares increase for age groups 51-60 and 61-70, and they decrease for groups 41-50 and 71-80. illustrative calculations We show in Table 1 a set of crude projections for aggregate saving, investment, and net exports. In contrast to our final projections, the ones in the table are by decade rather than individual year, and they are built up from data on households by 10-year age bracket rather than individual age Nevertheless, the simple ca1culaFederal Reserve Bank of Dallas Table 1 Saving, Investment, and Net Exports by Decade: Illustrative Calculations 1980-1989 S) (2.2) (6.6) (10.6) (16.9J (9.1) (6.9) ( 90.9) (I 11.8 .1 + 13.7 5.3+ 14.7 3.9+ 12.3 -.9 + 3.9 .9 + 0.0 1.8 123.6 :. NX 90.9 -123.6 -32.7. 1990-1999 S)= ( 2.2 _ (6.6J (10.6) ~6.9) (9.1)_ (6.9) _(05.4J (I 11.8J 2.9+ 13.7 .1+ 14.7 5.3+ 12.3 3.9+ 3.9 .9+ 0.0 .9- 89.5 :. NX 105.4 -89.5 15.9. 200()'=2009 = = = = = = 6.6 ) -2.9 +~0.6) 1+(16.9) 5.3 +(9.1) 3.9 +(6.9) -.9 (144.4) (S) (112.2.8) 2.1 ~13.7 14.7 12.3 3.9 0.0 66.9 = + = I : . NX = 144.4 -66.9 = 77.5. NOTE : Aggregate saving (5) is calculated as l: wt:.H, where w is the average wealth of a household in age bracket i and tlH, is the change in the' nur'nber of ho~seholds in age bracket i over the decade in question. Aggregate investment (I) is calculated as I k, tlH" where k, is the average capital required to support the labor supply of a household in age bracket i. Net exports (NX) are the difference between saving and investment The age brackets used in the calculations are 21 - 30, 31-40,41 - 50, 51 - 60 , 61 - 70, and 71-80. Household wealth and required capital are expressed as a multiple of the annual earnings of an entry-level male worker. Numbers of households are in millions. tions do serve to clarify the simulation modd and to provide insight into the nature of our findings . In the table, aggregate saving (S) is calculated hy multiplying the average wealth of a household in a given age bracket by the change in the number of households in that agc hrackct over the decade in qucstion, and thcn summing over all age brackets. Similarly, aggregate investment (J) is computed by multiplying the average cap ital required to support household labor supply in a given age bracket by the change in the number of households in that age bracket, and then summing over all age brackets. Net exports (NX) are the difference between aggregate saving and investment. Economic Review - September 1989 During the decade of the 1980s, national saving is insufficient to fund domestic investment. Roughly one-quarter of u.s. investment must be financed by inflows of foreign capital. The transfer of capital is accomplished by having the United States run a balance of trade deficit. The trade accou nt then moves (0 a position of surplus during tbe 1<)90s, as saving increases and investment declines . This trend continues into the early part of the next century. Over the period 2000- 2009, national saving is more than twice the size necessary to fund domestic investment. The United States begins to run a substantial trade surplus . The projected cycle in the U.S. trade balance can be explained by the aging of the baby-bust 5 Chart 5 Chart 6 Time Path of Net Exports/GNP Time Paths of Saving/GNP and Investment/GNP Percent Percent 5 8 4 National savIng/GNP 3 2 4 0 ., 2 Domestic investment/GNP -2 -3 1980 1990 2000 2010 and baby-boom generations. During the 1980s, the aging of these generations produces large increases in the number of households aged 31- 40 and 41- 50. Households in these age brackets are capital deficient, in the sense that their accumulated wealth is less than the capital needed to support their labor supplies. The result is a shortfall of aggregate saving relative to investment. As time passes, the demographic bulge moves into older age brackets . During the period 2000- 2009, large increases in population occur in the age groups 51- 60 and 61-70. For households in these age brackets, accumulated wealth exceeds required capital. As a result, aggregate saving exceeds investment. Simulation results The simulation model was used to generate values for U.S. net exports for each year beginning in 1980 and ending in 2009. Chart 5 shows the results , expressed as a percentage of GNP. Demographic factors are seen to have a clear and sizeable influence on the time path of net exports. During the early 1980s, net exports are in deficit by an amount equal to 2.2 percent of GNP. Then, with the exception of a brief decline from 1989 to 1991 , net exports rise steadily through the early part of the next century. By 1993, the trade ac- 0 1980 1990 2000 2010 count is balanced. By 2009, net exports are in surplus by an amount equal to 4.4 percent of GNP. Changes in aggregate saving and investment underly the movements in net exports. These changes are shown in Chart 6. The trade deficits of the 1980s are the produ ct of a high rate of domestic investment and, to a lesser extent, a low rate of natio nal saving. The closing of the deficit that takes place from 1980 through the early part of the 1990s is due entirely to a drop in the rate of investment. The savings rate actually falls slightly over this pe riod. The rise in net exports that occurs from the mid-1990s through the first decade of the next century. however, is the result of both an increase in the savings rate and a decline in the rate of investment. To evaluate the sensitivity of our findings , we recomputed the path of net exports using alternative values for the model's basic parameters . The values projected for net exports in any given year proved to be fai rly sensitive to alternative specifications of the model. The general shape of the time path of net exports was robust, however. All of our simulations showed the u.s. trade account to be in substantial deficit during the 1980s and to then move steadily toward a position of substantial surplus by the early pat1 of the next centllly. Federal Reserve Bank of Dallas Conclusions During a period of significant demographic change, the health of an economy should not be evaluated on the basis of simple historical comparisons of macroeconomic aggregates. In our simulations, basic changes in U.S . demography produce large changes in national saving, investment, and net exports. All of this takes place in a model in which individuals lead identical economic lives. Thus, the movements in the aggregates indicate nothing about variations in living standards. The movements simply reflect the effects of fluctuations in the size of successive birth cohorts. What caused the trade deficits of the 1980s? We cannot rule out the possibility that the deficits are partly a manifestation of poor national savings Economic Review - September 1989 performance. But our results dearly demonstrate that demographic factors played an important role. Given the age distribution of the population, for the United States to have had balanced trade during this decade was not optimal. Future living standards, therefore, have not been jeopardized as greatly as the raw statistics might indicate. It is also true, however, that future economic statistics may not be as favorable as they will appear. As the population ages, national saving and net exports are certain to rise. This will occur whether or not the federal budget deficit is eliminated or new poliCies are adopted to encourage private saving. If the United States truly does suffer a national savings problem, policymakers could be falsely reassured by trade surpluses that have more to do with aging than genuine savings reform. 7 Appendix A Construction of Life-Cycle Wealth Profile The household's wealth profile is derived from an optimization problem in which the household maximizes its life-cycle utility by choosing a time path of consumption that is financially feasible. The problem can be stated formally as max L (1 + O}l-W; (cJN;}-P subject to L (1 + r}l-i(y; - c) = 0, where ois the rate oftime preference, (1 + p}-l is the elasticity of intertemporal substitution, C is household consumption in period i, N i~ effective family size in period i, r is the inter~st rate, and y; is labor income in period i. The problem is solved by choosing the c;- Household wealth then is built up sequentially as where w; is wealth at the beginning of period i.lnitial and terminal wealth are assumed to be zero. The data and parameters required to solve the problem are determined as follows. Utility parameters. The rate of time preference, 0, is set equal to .015. In choosing a value for p, we follow Hall (1988) who argues that the elasticity of intertemporal substitution is substantially less than one and is probably near zero. We assume (1 + p}-l = .3. Interest rate. Households are able to borrow and lend freely at a single rate of interest. The interest rate is given in the world capital market and is unchanged throughout the period of analysis. In our reported simulations, r= .05. 8 Labor income. We compute household labor income as the market wage times the household's effective labor supply. Both the wage and the labor supply of the household are measured in units of the labor supply of an entry-level male worker. In view of our assumptions of a constant interest rate and a two-input technology with no technological change, the wage rate is constant over time and can be normalized at unity. The process of constructing the household's labor supply profile is described in Appendix B. Effective family size. We derive a time path of equivalent adults by combining a set of consumption weights for individuals of different ages with a time path of family size and age composition. The consumption weights, which are shown below, are consistent with the results of empirical studies of adult equivalence scales (see Deaton and Muellbauer 1980, 191-213). Age ~ Weight .25 .6:=15. .33 12::2.Q .50 2.1.::2.5. 1.0 &:aQ .75 We determined family size and age composition as follows. Households are formed by two adults of age 21. One of the adults lives through the age of 75 and the other through the age of 80. The fertility pattern of the household is representative of the patterns of women born in the 1940s and 1950s (Glick 1977). The household has two children. The first is born when adult members are 27, and the second is born 3 years later. The children remain in the home until they are 21. Federal Reserve Bank of Dallas Appendix B Construction of Life-Cycle Labor-Supply Profile The time path of household labor supply reflects both the labor-force participation rates of the male and female and age-related variations in worker productivity. Labor supply in period i is given by low. The pattern of male labor-force participation is consistent with cross-section data, which show a decline in participation for men beginning in their late 50s. Relative to the data, our numbers are a little high for men between the ages 56-65, but a little low for men older than 65. Our figures on female laborforce participation reflect two things: (1) a basic participation rate of 80 percent for women who are neither in their childbearing years nor nearing retirement [as projected by the Bureau of Labor Statistics (1984, 48-50) for women born in the late 1940s and early 1950s], and (2) the effect of young children on female labor-force participation [as estimated by Bowen and Finegan (1969), with an update and adjustment for more widespread use of day care]. where p 7 and p; are the labor-force participation rates of the male and female, and 9 T and are the ratios of male and female earnings to the earnings of an entry-level male worker. The 9 T are computed from an age-earnings equation estimated by Welch (1979, Table 6, p. S85) for white males with 1-3 years of college. The term is assumed to be independent of age and equal to 1.3. The assumed time paths of male and female labor-force participation are shown be- g; g: Age of Male Participation rate (Percent) 21=55. 100 5.2::2Q 61-65 85 70 ~ o Age of Female Participation rate (Percent) Economic Review - September 1989 ~ 27-34 ~ 40-55 .5.Q::2Q 61-65 80 60 70 80 65 50 ~ 0 9 Appendix C Demographic Data We base our analysis on a representative household composed of two adults who begin their economic life at age 21 and die at a given age. We calculate the number of households of vintage t by dividing by two the total number of individuals of age 21 in year t. A straightforward way of doing this would be to use the number of individuals of age 21 who were residing in the United States in year t. Because of immigration, however, this method will understate the economic contribution of the group (for example, the number of residents aged 30-34 in 1980 was 3.6 percent greater than the number aged 20-24 in 1970). To acknowledge the influence of immigration on wealth and labor supply in the United States, we represent the number of individuals of vintage t by the number of age (21 + a) who were living in the United States in year (t + a). The term a must be positive to make some adjustment for immigration, but it cannot be too large or we will overstate the lifetime contribution of immigrants to the economy and fail to recognize individuals who died early. Somewhat arbitrarily, we choose a = 16. When possible, we measure the number of individuals of vintage t by the 10 number who were of age 37 and residing in the United States in year (t + 16). Our calculations are based on the following data: (1) an historical series on the size of the U.S. population by 5-year age group for the years 1946-87, and (2) Census Bureau projections by 5-year age group for the years 1988-2000 and by individual age for every fifth year beginning in 2000 and ending in 2025 (see U.S. Bureau of the Census 1984). For the period 1946-2000, where data are available in successive years, we measured the number of residents aged 37 by taking one-fifth the total number in the age group 35-39. This provides a series on number of households for the vintage years 1930-84. Because of data limitations, we measured the size of vintages 1921-29 by using the number of residents in the age groups 40-44 and 45-49 during the years 1946-50. To obtain the number of households of vintages 1985-2010, we use the projections made by individual age for every fifth year of the next century. For example, the size of vintages 1987-91 is calculated from projections of the number of residents aged 35--39 in the year 2005. Federal Reserve Bank of Dallas References Boskin, Michael]., and Lawrence J. Lau (1988), "An Analysis of Postwar u.s. Consumption and Saving," Stanford University, mimeograph. Bowen, W., and T.A. Finegan (1969), The Economics of Labor Force Participation (Princeton: Princeton University Press). Davies, James B. (1981), "Uncertain Lifetime, Consumption, and Dissaving in Retirement," Journal of Political Economy 89 (June): 561-77. Deaton, A., and J. Muellbauer (1980), Economics and Consumer Behavior (Cambridge: Cambridge University Press). Dornbusch, Rudiger (1980), Open Economy Macroeconomics (New York: Basic Books). Glick, Paul C. (1977), "Updating the Life Cycle of the Family," Journal of Marriage and the Family (February): 5-13. Hurd, Michael D. (1987), "Savings of the Elderly and Desired Bequests," American Economic Review 77 (June): 298-312. U.S. Department of Commerce, Bureau of the Census (1984), Projections of the Population of the United States by Age, Sex, and Race: 1983 to 2080, Current Population Reports, Series P25, No. 952 (Washington, D.C.: Government Printing Office). U.S. Department of Labor, Bureau of Labor Statistics (1984), Employment Projections for 1995, Bulletin 2197 (Washington, D.C.: Government Printing Office). Weich, Finis (1979), "Effects of Cohort Size on Earnings: The Baby Boom Babies' Financial Bust," Journal of Political Economy 87 (October): S65-S97. Hall, Robert E. (1988), "Intertemporal Substitution in Consumption," Journal of Political Economy 96 (April): 339-57. Economic Review - September 1989 11 Evan F. Koenig Senior Economist Federal Reserve Bank of Dallas Recent Trade and Exchange Rate Movements: Possible Explanations T he rate at which we have been able to exchange our products for goods produced overseas has varied substantially over the past decade After several years of comparative stability, in 1980 this "real exchange rate " began a sustained rise (Chart 1). Increases continued until early 1985, at which point the real value of the dollar was fully 25 percent above its 1980 level. Subsequently, the real exchange rate has fallen sharply, and it now lies below its level of 10 years ago. The U.S. merchandise trade deficit has followed a pattern similar to that of the real exchange rate, but with somewhat different timing. The deficit rose from 1980 through 1985, falling, finally , in mid-1986. Are movements in the trade deficit and the real exchange rate systematically related? If so, can movements in one variable be said to "cause" movements in the other? This article uses a simple analytical apparatus to gain insight into these questions and to suggest some answers . Built into the apparatus is the notion that output and asset prices adjust qUickly to new information. Built into the apparatus too is the notion that the decisions of households are functions of their expectations, as well as the notion that expectations are formed rationally, in the sense that they are fully consistent with what the model predicts will actually transpire. In its assumption that expectations and output prices respond quickly and completely to new information, the present analysis is representative of the "equilibrium" approach to exchange rate determination. l The equilibrium approach contrasts with more traditional models, which often Economic Review - September 1989 assume that households are myopic, and that output prices adjust sluggishly in response to shocks. 2 The analysis developed here does not rule out sluggish wage adjustment (wage stickiness). Thus, while the market for output always clears, the assumptions underlying the model do not preclude involuntary unemployment, and monetalY policy may have real effects. Like Frenkel and Razin (1987), I assume that households are free to borrow and lend overseas. As world financial markets become more fully integrated, this assumption becomes increasingly realistic. :\ The analysis undertaken here suggests that swings in the trade deficit and exchange rate over This article has benefited from comments and advice provided by John K Hill, Stephen P A Brown, Linda C Hunter, Jo Anna Gray, Joseph H Haslag, and Cara S Lawn 1 For a useful introduction to equilibrium exchange rate modeling, see Stockman (1987) For other examples of the equilibrium approach, see Siockman (1980) and Stockman and Svensson (1987). 2 For traditional analyses of trade deficit movements over the past decade, see Helkie and Hooper ( 1987, 1989). Hooper (1989), Hooper and Mann (1987), Krugman and Baldwin (1987), and Sachs (1988) Dornbusch (1976) develops a model in which output prices are sticky but agents have rational expectations Dornbusch's analysis is limited to an economy that is small in international capital and output markets 3 For discussion of the degree of international financial integration, see Fieleke (1988), Kasman and Pigott (1988), and Radecki and Reinhart (1988) Chart 1 U.S. Trade Deficit and Real Exchange Rate Exchange rate (Index, 1980 = 100) Trade deficit Billions of 1982 dollars 130 200 120 150 11 0 100 100 50 Trade deficit 90 80 '75 '77 '79 '81 '83 o '85 '87 ·50 SOURCE OF PRIMARY DATA: Organ ization for Econom ic Cooperation and Developme nt the past decade were, to a substantial degree, the natural consequence of strong cyclical movements in output and investment in the United States relative to movements in these variables overseas. The high U.S. trade deficits during the middle 1980s, therefore, are probably at least partly the result of the tight monetary policy pursued early in the decade in a successful attempt to bring down the rate of inflation. The simplest models If the objective is to gain insight into trade flows, one needs a model with at least two countries and at least two goods. The two goods may be a Single commodity in each of two distinct time periods or two distinct commodities in a single time period. In either case, provided the total quantity of each of the two goods is taken as given , one can use a diagram called an Edgeworth box to depict the economy's equilihrium and analyze its response to shocks. Trade across time. Consider a world in r 14 - 4 Homotheticity means that, for given prices. the demand for aI/ goods rises proportionately as household wealth in· creases In the present context, I assume that a doubling of household wealth results in a doubling of the demand for both current and future output, given the real rate of interest which there are two countries, two periods, and only a single commodity. People within each country are identical and have homothetic preferences across current (period 0) and future (period 1) output. 4 The easiest approach is to think of the two countries as having equal populations. Each citizen of the home countIy-say, the United States-would, in the absence of trade , possess Yo and YI units of current output and future output, respectively, net of investment expenditures and government purchases (if any) . Similarly, each citize n of the foreign country-say, Japan-is endowed with y7 units of output in period i, after investment and government spending. Both U.S. and Japanese endowments are taken as given. If tastes, the time pattern of endowments, or both vary across countries, trade will he mutually advantageous . Citizens of both countries act as price takers. That is , each individual feels free to trade current output for future output at a market rate of exchange that is independent of his or her own actions. The rate of exchange-in this case, because trade is across time, unity plus the real rate of interest-adjusts instantaneously to equate the demand for loans to the supply Chart 2 depicts an Edgeworth box . The length of the box is Yo + y(~-the total amount of output available for current consumption in the two countries-and its height is YI + y;-the total amount of output available for future consumption . If current consumption and future consumption by U.S. citizens, Co and c I ' respectively, are measured from the lower left-hand corner of the box, and if current consumption and future consumption by the Japanese, c; and c~, are measured from the upper right-hand corner, then each point in the box represents a division of currentperiod and future-period output between citizens of the two countries . The (hypothetical) endowment , or no-trade , allocation is located at point E. Each household can , if it wishes, consume its endowment. It may , instead, want to trade away some of its current output for additional future consumption, lending output overseas in period O. (Because all citizens within a country are identical, in eqUilibrium no within-country lending will occur.) Alternatively, a household may want to borrow in period 0, sacrificing future output in order to obtain additional current consumption. The household 's borrowing-lending possibilities Federal Reserve Bank of Dallas Chart 2 Edgeworth Box, Showing Endowment and Equilibrium Points y; ~ ~ T C 0 Budgelline. slope ,. - (1 + ra ) Japanese indifference curves . .. .. Japan u c·1 Japanese Incomeexpansion Future output path U.S. 11 Indifference ourves r U.S. incomeexpansion path United 1......- - - - States Yo ~------ oo ------'~ Current output are captured by a budget line that passes through the endowment point and has slope -0 + ro)' where r;) is the real rate of interest. Equilibrium is at point A, where citizens of both countries are on the highest indifference curves they can attain, given the budget line, and the total quantities of current and future output demanded by u.s. and Japanese citizens match the quantities available . In Chart 2, U.S. and Japanese households have deliberately been given equal endowments of both current output and future output. (Point E lies in the center of the Edgeworth box.) The only motivation for trade is then a difference in tastes . The chart depicts the case in which the United States has a greater rate of time preference than does Japan- that is, U.S. citizens place relatively greater emphasis than the Japanese on current, as opposed to future, consumption. (The indifference curves of U.S . citizens are relatively steep.) Accordingly, in equilibrium, U.S. citizens exchange some of their endowment of future output for additional current consumption, in the form of Japanese imports. (Point A is below and to the right of point E.) The United States, in other Economic Review - September 1989 words, runs a trade deficit in the current period, financed by a sale of bonds to the Japanese. The bonds are paid off, with interest, in period 1, when the United States has a trade surplus. The real rate of interest is higher than it would have been had U.S. citizens had the same low rate of time preference as the Japanese. In the real world, where a nation's citizens are not identical, a country will appear to have a high rate of time preference if family ties in the country are weak (so that those currently alive care little about the welfare of future generations) or if a relatively high proportion of the population is either very young or very old (for the young and the elderly tend to have low savings rates).5 A generous income tax deduction for interest payments or unfavorable tax treatment for interest 5 Empirical results obtained by Slemrod (1988) suggest that the proportion of the population that is elderly has a greater influence on the savings rate than does the proportion that is young Hill (1989) contends. elsewhere in this issue. that demographics are an important determinant of long-term trends in the trade deficit 15 income and capital gains might also cause people to favor current over future consumption 6 ,7 Insofar as the United States is characterized by relatively weak family ties, a younger-than-average population, and tax laws that discourage savings, Chart 2 suggests that this countlY can expect to experience trade deficits. The Reagan-era defense buildup may also have contributed to the deterioration in the nation's trade picture during the 1980s. Chart 3 demonstrates the effects of a temporary increase in US. government purchases. H In the diagram, I assume that tastes are the same across countries. Consequently, in the absence of any difference in endowments, there would be no trade. The Edgeworth box corresponding to this hypothetical, notrade situation is drawn in solid lines, with equilibrium and endowment points cOinciding at point E. The equilibrium real rate of exchange (unity plus the real interest rate) is measured by the magnitude of the slope of the solid budget line passing through E. The effect of a temporalY increase in US. government purchases is to reduce both the period-O endowment of the representative US. citizen and the horizontal dimension of the Edgeworth box by an amount equal to the change in US. government purchases. In Chart 3, the endowment point remains at E, but E is no longer an equilibrium. To see that the equilibrium must change, consider what would happen to US, and Japanese demand for current and future consumption in the absence of interest rate adjustment- • See, for example, Feldstein (1988) 7 16 Strictly speaking, relatively high U 5 tax rates on unearned income would drive a wedge between the U 5 and Japanese budget lines-making the U 5, line relatively fiatrather than alter the slope of U S. indifference curves The effects of a flattened budget line, however, are much the same as those of a steepened set of indifference curves 8 For an alternative interpretation of the role of the defense budget in the international economy, see Ayanian (1988) 9 Chart 3 will accurately depict the response of the world economy to a US monetary shock only if the Japanese monetary authority chooses to insulate Japan's price level from changes in the US money supply Chart 3 A Temporary Decline in Available U,S. Output ~~~~ _______________________ , Ja~ Future output ... .•... .' ,i'" " : .. ' o· : Unit States .,' .. ' .. ' .,' " " " ,. Current output that is , in the absence of any rotation of the budget line, With unchanged endowments and an unchanged interest rate, the Japanese would face exactly the same maximization problem as before and, so, would continue to desire consumption at point E. US. citizens, however, would feel poorer. With homothetic preferences, their desired levels of current and future consumption would fall proportionately. In the chart, US. citizens would wish to consume at point B. With the Japanese trying to consume at E and US. households trying to consume at B, there would be an excess demand for current output and an excess supply of future output. The relative price of current output-unity plus the real rate of interest-would therefore rise, steepening the budget line. Equilibrium is attained at a point somewhere within the shaded triangle, where the United States runs a current-period trade deficit, financed with borrowing from Japan. Any shock that tends to reduce the availability of U S, output over the short term will have effects like those depicted in Chart 3, triggering increases in the real interest rate, the US. trade deficit, and US. foreign indebtedness. Insofar as money wages in the United States respond sluggishly to unexpected changes in policy, Chart 3 will, in particular, depict the response of the world economy to a surprise slowing of the rate of growth of the US. money supply.9 This conclusion follows from the fact that an unanticipated slowing of money growth retards domestic inflaFederal Reserve Bank of Dallas Chart 4 An Increase in U.S. Investment Slope =-(1 t 1'0) Future output ............. ...... United States .. ..... ' .... : ,,' ........ ", L,:::: ................................... .................. .. . tion, which, given sticky money wages, drives up the real cost of labor to u.s. firms and thereby makes production in the United States less attractive . During the early 1980s, of course, this country experienced its worst recession since World War II-a recession that many economists attribute, at least partially, to restrictive monetary policy. 10 Milton Friedman, among others, has pointed out that a country in which the investment climate is relatively favorable is likely to run a trade deficit. I I Chart 4 illustrates how this deficit might arise. The initial equilibrium is located (by assumption) at point E, which is also the endow ment point. As in the previous diagrams , the slope of the budget line through E is equal , in absolute value, to unity plus the real rate of interest. An expansion of U.S capital investment reduces the amount of current output available for consumption by U.S. citizens in the absence of trade-that is , it reduces yo-while increasing U.S. citizens' endowment of output in the future (increasing Yj) . 12 In Chart 4, the effect is to reduce the width of the Edgeworth box while increasing its height. The endowments of Japanese citizens do not change. If the real interest rate failed to adjust, U.S. citizens would want to consume at point B, while the Japanese would wish to continue to consume at E. The resultant excess demand for current output can be eliminated only if the interest rate rises, steepening the budget line. The new equilibrium allocation will be somewhere in the Economic Review - September 1989 shaded triangle below and to the right of point E, implying that the United States will run a trade deficit in the current period and a surplus later, in period 1 Note that the results obtained in Chart 4 would be little altered, qualitatively, if there were no decline in Yo but, instead, simply an increase in Yj ' The point is that, in general, people become more anxious to borrow the worse off they are now, relative to how well off they expect to be in the future. In Chart 3, U.S. households want to borrow because the amount of output available to them in the current period has declined. They would be equally anxious to borrow if they anticipated a future increase in the amount of available output-an increase due, perhaps, to an expected future decline in government purchases or a future improvement in productivity. In Chart 4, greater investment spending has an especially strong impact on the real interest rate and trade deficit because it not only reduces the amount of output available to U.S . households in the current period but also increases the amount of output available to them in the future. Similarly, any decline in the current endowment of Japanese households, or improvement in their future prospects, will create an incentive for Japanese borrowing and tend to give rise to a Japanese trade deficit. If the current endowments of both U.S. and Japanese households decline, relative to their future endowments, whichever set of households has suffered the larger decline will r o An alternative view is that the recession was a delayed response to the sharp increases in oil prices in 1979- 80. The United States, as a net importer of oil, is hurt when the pnce of oil rises Japan and most European countriesmore dependent on foreign oil than the United States isought to have been hit especially hard, however, and therefore ought to have experienced larger increases in their trade deficits than did the United States. That they did not suggests that oil shocks alone do not go very far in explaining trade flows during this decade " See Friedman (1988), Obstfeld (1985), Tatom (1988), and US President (1985, 1986) 12 This analysis treats investment as exogenous In a more complete model, the rise in investment m(ght be triggered by an anticipated increase in the future productivity of capital 17 be borrowers in the new equilibrium. 13 Trade across commodities. Consider a world in which there are two countries, two distinct commodities- one produced exclusively in the home country (in the United States) and one produced exclusively overseas (in Japan)-and a single time period. Citizens within each country have identical, homothetic preferences for U.S. and Japanese products. (The tastes of U.S. citizens are not necessarily the same as those of Japanese citizens, however.) Because there is only one time period, no opportunity to borrow or lend exists. Trade must therefore be balanced; that is, for each countlY the total value of imports must equal the total value of exports. The value of U.S. output in terms of Japanese output--called the "terms of trade" or "real exchange rate"- and the pattern of imports and exports will vary in response to changes in the relative availability of the two commodities. Suppose, for example, that the total quantity of u.s. output available to u.s . and Japanese households declines. This decline might occur as a result of increased u.s. government purchases of U.S. output or as a result of a fall in U.S. production due, as discussed earlier, to unexpectedly restrictive monetary policy. Chart 5 depicts the impact on the real exchange rate and the volume of imports and exports. The preshock equilibrium of the world economy is captured in the Edgeworth box drawn with solid lines. The horizontal and vertical dimensions of the box represent, respectively, the total quantities of u.s. products and Japanese products available for consumption. The quantities of u.s. and Japanese products consumed by U.S. households are measured from the lower lefthand corner of the box, while the quantities of U.S. and Japanese products consumed by Japanese households are measured from the upper right-hand corner. In the absence of trade, only u.s. output would be available to U.S. citizens, and only Japanese output would be available to the Japanese. The endowment point for the econ- >3 18 Exceptions can arise if households in one country are more willing than households in the other country to adjust the timing of their consumption in response to a change in the interest rate Chart 5 A Decline in Available U.S. Output Slope = -€ j . ..... ~ ~;:~ .i··· ~ .~. .' ..' .... .... ·'·-··-·~-. S-=-.--p-ro-d.,..u-Ced-O-u-tp-u-t- - - - " E L:.. ••_•• _..._ - - -:: omy is thus located at the lower right-hand corner of the box. The real exchange rate, £ , which determines the slope of the budget line through the endowment point, adjusts until the world output market clears-say, at point A. In equilibrium, U.S. and Japanese households are on the highest indifference curves they can attain, given the budget line, and the total quantities of u.s. and Japanese products demanded match the amounts available. When the amount of available u.s. output falls , the width of the EdgewOlth box shrinks. In the absence of any price adjustment, U.S. citizens would feel poorer and wish to cut back proportionately on their consumption of U.S. and Japanese products. In the diagram, u.s. citizens would want to consume at point B. Japanese citizens, on the other hand, would face an unchanged budget line and, accordingly, would want to continue to consume at point A. With U.S. citizens trying to consume at B and the Japanese trying to consume at A, there would be excess demand for U.S. output and excess supply of Japanese output. The relative price of U.s. output would therefore rise, rotating the budget line clockwise about E. The new equilibrium will lie somewhere within the shaded region. The higher price of U.S . output has two partly conflicting effects on Japanese consumers. First, it induces them to substitute away from U.S. output and toward Japanese output. Second, it makes them feel poorer, inducing cutbacks in Federal Reserve Bank of Dallas their demand for the products of both nations. The net result is a decline in Japanese imports from the United States and an ambiguous change in Japanese consumption of Japanese output. (Because total Japanese output is not affected, the change in US. imports from Japan must then also be ambiguous.) If the rise in the relative price of us. output is sufficiently large, US. households may actually be better off than they were in the original equilibrium. 14 Indeed, US. wealth may rise to such an extent that US. consumption of both US. and Japanese products increases. In summary, any shock that reduces the amount of US . output available for consumption will tend to drive up the real exchange rate and lower Japanese consumption of US. output. The impact on Japanese consumption of Japanese output, and on US. consumption of both US. and Japanese output, is ambiguous: it depends on the ease with which Japanese output can be substituted for u.s. output. Analyzing exchange rate and trade deficit movements simultaneously To explain movements in the real exchange rate and the trade deficit simultaneously, one needs a model with two countries (the United States and Japan) and four goods: two commodities (US.-produced output and Japanese-produced output) in each of two periods. Fortunately, results are essentially the same as those obtained from the simple models discussed above-provided U.S. and Japanese products are good substitutes and provided u.s. and Japanese households have identical, homothetic preferences. 15 Within-period determination of the exchange rate. With identical, homothetic preferences, Japanese citizens will, for any given exchange rate, e, want to consume US. and Japanese products in the same proportions as do US. citizens, regardless of the absolute or relative levels of wealth of the two countries. The ·exchange rate clearing the output market, then , must be that which equates the common consumption ratio to the ratio of us. output to Japanese output: in an Edgeworth box like that of Chart 5, the equilibrium allocation must be on the diagonal connecting the lower left-hand and upper right-hand corners of the box. Exactly where along the diagonal Economic Review - September 1989 eqUilibrium occurs is unimportant. What is important is that the equilibrium exchange rate must increase as the diagonal becomes steeper, in order to induce households to consume a higher ratio of Japanese products to u.s. products. Formally, del e = (dy*l y* - dyl y)l a, (1) where a is the elasticity of substitution between US. output and Japanese output. Thus, a decline in the amount of US. output available to consumers-the result, perhaps, of an increase in US. government purchases of US. output or, if the money wage adjusts sluggishly, of restrictive US. monetary policy-will put upward pressure on e, just as in the one-period, two-commodity model discussed earlier. Trade between periOds. What factors influence international borrowing and lending in a two-country, two-commodity, two-period model? As noted above, people try to borrow when they expect their economic situation to improve and try to lend when they expect their economic situation to deteriorate. In the two-period, one-commodity model, where US.-produced goods and Japanese-produced goods were perfect substitutes, a reduction in the availability of currentperiod US. output necessarily made US. citizens worse off. A temporary increase in US. defense expenditures, accordingly, resulted in overseas borrowing by US. citizens. In the one-period, two-commodity model, however, where US.produced goods and Japanese-produced goods were not perfect substitutes, the possibility arose that with a sufficiently inelastic demand for US.produced goods, an increase in US. defense expenditures might actually make US. citizens better off. This finding suggests that, in a model combining within-period and between-period trade, whether a temporary decline in US. output stimulates borrowing or, instead, lending by U S. citizens depends on the elasticity of substitution between US. products and Japanese products. 14 '5 See Bhagwati (1958). For a more complete. more formal analysis, see Frenkel and Razin (1987) . 19 Such is indeed the case. If (J is greater than unity, a decline in U.S. output makes U.S. households worse off, relative to Japanese households. If (J is less than unity, on the other hand, a decline in U.S. output makes U.S. households better off, relative to the Japanese. 16 In the former case, the results obtained in our analysis of the twoperiod, one-commodity model carry through without any important modification. The latter case requires a substantial rethinking of our earlier analysis. As a practical matter, we can measure the "economic situation" of u.s. households by looking at how much aggregate output they would be able to consume in the absence of international borrowing and lending. Call this output the "aggregate endowment" of U.S. households. We can then determine whether (J is greater or less than 1 '6 17 For a more careful derivation of these results, see the Appendix The endowment of the United States (for example) is measured by aggregate us consumption p lus merchandise exports less merchandise imports The "foreign country" is all the countries of the Organization for Economic Cooperation and Development (GECD) except the United States (Besides the United States, the members of the OECD are Canada, Japan. Australia, New Zealand, and most of the countries of northern, western, and southern Europe.) The real exchange rate is measured as the average value of US manufactured exports divided by the average va lue of foreign manufactured exports, as computed by the OECD " A regreSSion of the level of the exchange rate on the level of the endowment ratio yields the following results In(£) = 3.359 - 1 924In(E/E'), (249) (430) R' = 28, after correction for first-order serial correlation of the residuals Here E and E' denote, respectively, US and foreign aggregate endowments, and the figures in parentheses are standard errors (The reported R2 is for the structural portion of the equation alone The total R 2 is 0.90) Because of the difficulty, statistically, in rejecting nonstationarityof the eXChange rate and endowment ratio in such a short sample period, I also ran a regression in first differences The estimated coefficient of the change in the endowment ratio was negative- which is consistent with CJ> I- but not significantly so (The estimated coefficient was - 0476, with standard error 0,321 ) Movements in exchange rates are notoriously difficult to explain See Meese and Rogoff (1983, 1985), 20 Chart 6 Real Exchange Rate and Endowment Ratio Endowment ratio (In EJE') Inverse exchange rate (-In E) -44 -.53 -4.5 -.55 -4.6 -.57 -4.7 -,59 Endowment -4.8 -49 - 61 ra\o '75 '77 '79 '81 '83 '85 '87 -.63 NOTE: The endowment ratio, E/E', measures the amount of aggregate output that would be available to U.S consumers in the absence of international borrowing and lending , relative to the amount of aggregate output that would be available to foreign consumers SOURCE OF PRIMARY DATA: Organization for Economic Cooperation and Development by examining the relationship between changes in the exchange rate and changes in the ratio of the u.s. aggregate endowment to the foreign aggregate endowment. According to the above discussion, the endowment ratio is an increasing function of the ratio of available U.S.-produced output to available foreign-produced output if, and only if, (J is greater than unity. Movements in the real exchange rate, on the other hand, are always negatively related to movements in the output ratio (equation 1). Therefore, exchange rate movements will be negatively related to changes in the endowment ratio precisely when (J is greater than unity. Chart 6 contains plots of the (logarithms of the) endowment ratio and the inverse of the real exchange rate. 17 The relationship between these series is clearly positive: the real value of the dollar falls when the aggregate endowment of the United States rises relative to the foreign endowment. IH Therefore, (J must be greater than unity. Again, (J greater than unity means that decreases in the availability of U.S. products make U.S . households worse off relative to Japanese Federal Reserve Bank of Dallas Chart 7 U.S. and Foreign Consumption Growth Rates Percent per quarter 3 2 o -1 Evaluating the model -2 Do the models developed in this article yield predictions that are broadly consistent with movements in trade flows and consumption observed over the past decade? If so, which of the policy or other shocks that the analysis suggests might be important have been the chief contributors to these movements? Comparing the model's predictions with the data. The most clear-cut prediction of the model developed in this article is that movements in aggregate consumptio n will be correlated across countries and will be positively related to changes in both domestic and foreign aggregate endowments. That changes in consumption arc correlated across countries is a conseque nce of tw o facts: (1) in a model in which international borrowing and lending are unrestricted, everyone faces the same real interest rate , and (2) the real interest rate measures the cost of consumption today relative to consumption tomo rrow. That changes in consumption are positively related to changes in endowments then follows from the requirement that the sum of domestic and foreign consumption equal the sum of the domestic and foreign e ndowments. Chart 7 plots the growth rates of u.s. and foreign consumption. The positive correlation between the series, p articularly since 1980, is evi- -3 75 77 79 '81 '83 '85 '87 SOURCE OF PRIMARY DATA: Organization for Economic Cooperation and Development househo lds , while decreases in the availability of japanese products, similarly, primarily hurt the Japanese. Thus , as in the two-period, one-commodity model, a temporary drought-induced or policy-induced decline in U.S. output levels, relative to those in japan, will tend to result in a U.S , trade deficit. A temporalY increase in the ratio of u.s. to j apanese government purchases, or in the ratio of u.s. to japanese investme nt spending, will have a similar effect. Indeed, a change in the investment ratio is likely to have a particularly strong impact, as higher investme nt spending tends not only to decrease the amount of output available for consumption today but to increase the amount of output available for consumption in the future. In summary, movements in the real exchange rate are entirely driven by contemporaneous changes in the relative ava ilability of home-produced and foreign-produced output. Movements in the real interest rate, on the other hand, are driven by changes in the availability of current output relative to that of future output. Thus, a temporary decline in the availability of u.s. products results in increases in both the real value of the dollar and the real interest rate. The mode l makes this prediction regardless of whether the output decline is due to increased government Economic Review - I purchases, to a supply-side shock, or to restrictive monetary policy. The effect of the output decline on the trade balances of the United States and the rest of the world depends velY much on the elasticity of substitution between u.s. products and foreign products. The more readily foreigners can find substitutes for u.s. products, the greater is the portion of the burden of lowe r U.S. output that is borne by u.s. citizens and , furthermore , the greater is the likelihood that the US. merchandise trade account will go into deficit I ') September 1989 '9 This reasoning applies to intertemporal substitution opportunities as well: the more readily foreigners can substitute future consumption for current consumption, relative to th e ease with which we can do the same, the greater is the likelihood thai we will respond to a temporary fall in U S output by increasing borrowing from abroad See footnote 13 21 dent. 20 That consumption growth is indeed positively related to growth in domestic and foreign endowments is confinned by the following regression results: I1ln( C) = .0030 + .528111In(E) C.OO] 3) (.0867) Chart 8 U.S . Trade Surplus and Endowment Ratio Endowment ratio (In EJE') U.S_trade surplus (In ElC) 0 -,53 - 02 -. 55 -.04 -. 57 -.06 -.59 -.08 -, 61 + .186311In(E* ), (. 1150) and I1ln(C*) = .0029 + .4413111n(E*) (.0010) (.0902) + .118511In(E) , (.0681) Here C and C* denote, respectively, U.S . and foreign rates of aggregate consumption, and E and E* denote U.S. and foreign aggregate endowments. (The figures in parentheses are standard errors .) The analysis in [he preceding section suggests that temporary increases in the u.s. endowment of aggregate output, relative to the foreign endowment of aggregate output, tend to be associated with U.S trade surpluses and foreign trade deficits . Charts 8 and 9 contain plots of the (logarithm of the) endowment ratio, along with measures of the U.S. trade surplus and foreign deficitY Apparently, a strong positive rela tionship exists between the endowment ratio and the foreign trade deficit. The re lationship b e tween the endowment ratio and the U ,S, trade surplus is less straightfolward. Part of the problem may b e that borrowing and lending decisions are forward- - 10 The correlation coefficient over the entire sample period is The correlation coefficient over the period since 1980 is 0470 (with marginal significance level 0004) As restrictions on international capital flows ease, this correlation will probably increase further. o 294 (with marginal significance level 0 031) 21 22 '77 '79 '81 '83 '85 '87 - 63 SOURCE OF PRIMARY DATA : Organization for Economic Cooperation and Development. Chart 9 Foreign Trade Deficit and Endowment Ratio Foreign trade deficit (In C'/E') Endowment ratio (In ElE') -.53 .04 Endowment ratio .02 -. 55 a -.57 -. 02 -.59 -.04 -. 61 -.06 20 '75 '75 '77 '79 '81 '83 '85 '87 -.63 SOURCE OF PRIMARY DATA: Organization for Economic Cooperation and Development. The US tra de surplus is measured by In(ElC), which closely approximates th e US merchandise trade surplus expressed as a fraction of U 5 consumption The foreign trade deficit, similarly, is measured by In(G-/E') Federal Reserve Bank of Dallas I Chart 10 Output and Endowment Ratios Output ratio (In YIV') Endowment ratio (In ElE') -.58 - 53 -.60 - 55 -.62 -.57 -.64 - 59 - 66 -.68 Endowment ratio '75 '77 '79 '81 '83 '85 '87 -.61 - 63 SOURCE OF PRIMARY DATA : Organization for Economic Cooperation and Development. looking: they depend on expected future endowment ratios, not just the current ratio. Thus , as pointed out in the analysis above, changes in investment spending are likely to have a larger impact on the trade deficit than one would predict from their effect on the current endowment ratio alone. This larger impact results precisely because higher investment spending today implies that more output will be available for consumption in the future. That increases in the rate of investment spending in the United States, relative to investment spending abroad, have an especially strong negative effect on the U.S. trade surplus is confirmed by regression analysis.22 Interpreting recent experience. We have seen that, as predicted, fluctuations in the aggregate endowment ratio have been an important determinant of movements in trade flows and exchange rates during the past decade. What has driven changes in the endowment ratio over this period? Have they been the result of changes in the amount of aggregate output available in the United States relative to the amount of aggregate output available abroad? Or have they been due to changes in the relative shares of output consumed by government or devoted to investment:> Charts 10 and 11 shed light on this issue. Economic Review - September 1989 Chart 10 plots the endowment ratio and the ratio of U.S . to foreign gross domestic product. While the two series have important similaritiesboth decline steeply in 1981, for example, and trend upward from 1984 on-they also have some noteworthy differences. Thus , while aggregate U.S. output generally increased relative to aggregate foreign output from 1975 through 1977, the endowment ratio declined. From 1978 through 1980, while the output ratio trended downward, the endowment ratio was constant or tre nding upward . In 1983, aggregate U.S. output rose sharply relative to aggregate foreign output; yet the endowment ratio was stagnant. Finally, since 1986 the endowme nt ratio has been increasing much more rapidly than the U.S.-foreign aggregate output ratio. The divergent movements in the endowment and output ratios must be due to swings in the fraction of aggregate output devoted to investment and government purchases in the United States, relative to the fraction of aggregate output devoted to investment and government purchases 22 Even though there are good reasons for believing that, over the long term, the consumption-endowment, endowment, and investment ratios are stationary, it is difficult to rule out the existence of unit roots over the short sample period for which data are available Wh ether regressions in the levels of the series or in their first differences are more appropriate is, th erefore, unclear Fortunately, results are not particularly sensitive to the specification adopted. When changes in the us trade surplus are regressed on changes in the endowment and investment ratios, one obtains I'>ln(E/C) ~ - 0007 + 33461'>In(E/E') (,0007) (0665) - 5392I'>(I/Y-I'/Y'), R' ~ 42 . ( 1843) where I and Yare aggregate U S_investment and output. respectively, and I' and Y' are their foreign counterparts The corresponding results for the foreign trade deficit are I'>ln( C' /E') ~ - 00005 + 25901'>In(E/E') (00065) (0594) - 34021'>(I/Y - I"/Y') , FI' ~ 32 . (.1644) The figures in parentheses are standard errors. 23 - 05 o - 06 - 01 - 07 -.02 - 08 - 03 ment-output ratio overseas. The resurgence of investment spending in the United States between 1982 and 1984 held down the endowment ratioand , therefore , put upward pressure on the real exchange rate and the U.S. trade deficit-long after U.S. production had begun to recover. Swings in government purchases, in contrast, have apparently played only a minor role in determining the hehavior of the endowment ratio and, hence, in influencing the U.S. trade deficit and the exchange rate. -.09 - 04 Concluding remarks - 10 - 05 - 11 - 06 With flexible output prices, the ahility to borrow and lend overseas guarantees that every country faces the same real interest rate at all times . Unless tastes shift toward current consumption and away from future consumption, any increase in this interest rate must be due to a decrease in the amount of aggregate output available, worldwide, to consumers today, relative to the amount they believe will be available in the future . Such changes in the intertemporal availability of output may he a consequence of temporary increases in investment expenditures or government purchases, of exogenous, temporary declines in the productivity of labor and capital, or-given nominal wage stickiness-of restrictive monetary policy. The United States will run a trade deficit when the contrast between present conditions and future prospects is stronger for u.s. households than for foreign households. Thus, a recession that is perceived to be temporalY, and that affects this country more severely than other countries, will tend to be associated with a trade deficit in the United States and trade surpluses overseas. An investment boom in the United States will reduce the amount of output available to U.S. consumers today and simultaneously increase the amount of output available to U.S. consumers in the future. If not accompanied by a similar boom overseas, it will, therefore, have a particularly strong impact on the trade balance. In contrast to the trade deficit, which depends partly on people's expectations about the amount of output available to them in the future, the real exchange rate is a function only of the current ratio of available U.S. output to available Chart 11 Relative Fraction of Output Devoted to Investment and Government and to Investment Alone Investment I/Y - I"/Y' - 12 Investment and government (I + G)/Y - (I + Gr/Y* '75 '77 '79 '81 '83 '85 '87 - 07 SOURCE OF PRIMARY DATA: Organization for Economic Cooperation and Development. overseas. 2} Chart 11 plots the difference between these fractions , along with the difference between the investment-output ratio here and the same ratio overseas. Note how closely the curves parallel one another. Evidently, most of the movements in the endowment ratio that are not accounted for by changes in relative output levels are due to changes in the u.s. investment-output ratio relative to the foreign investment-output ratio. From 1975 through 1977, for example, the U.S. endowment of aggregate output tended to decline relative to the foreign endowment precisely because u.s. investment spending was increasing relative to foreign investment. Between 1979 and 1980, during 1982, and between 1985 and 1988, the endowment ratio was stronger than it would otherwise have been because of declines in the investment-output ratio here relative to the invest- 23 If Y denotes the total amount of aggregate output available to US citizens in the absence of international borrowing and lending. G is the amount of aggregate output purchased by the U.S government. and I is the amount of aggregate output devoted to investment. then E = Y[l - (G + I)IY]. Similarly. E' = Y'[l - (G + I)*IY'j It follows that In(Ef E') In(YIY') - [(G + I)fY - (G + I)*IY"] = 24 Federal Reserve Bank of Dallas foreign output. Government budget deficits, as such, play no role in the determination of the exchange rate, the real interest rate, or the trade deficit in the model developed here. The assumption is that people form their expectations intelligently and, in particular, realize that any current budget deficit means higher t.axes later, while any current budget swplus means lower taxes later. 24 If the government chooses to finance temporary increases in its purchases by issuing debt, budget deficits may certainly be associated with currency appreciation, high real interest rates, and trade deficits. But association is not causation, and here the true causal impetus comes from the changed time pattern of government purchases. Similarly, restrictive monetary policy may-by triggering a recession-produce currency appreciation, high real interest rates, and a trade deficit and, at the same time, result in a decline in income tax revenues, producing a budget deficit. Recent movements in the real exchange rate between US. products and foreign products, and in the US. trade deficit, have apparently been dominated by the business cycle. When the US. economy enters a recession, the availability of US. products declines relative to the availability of foreign products. This decline puts upward pressure on the real exchange rate. Because US. products and foreign products are good substitutes, the rise in the exchange rate is insufficient to offset the recession-induced fall in the volume of US. exports. Thus, the decline in US. output makes US. consumers worse off, relative to foreign consumers. Because they believe that the effects of the recession will be temporary, US. households attempt to smooth their consumption paths by borrowing from overseas. In other words, the US. trade deficit widens. Changes in investment spending over the business cycle tend to smooth deficit and exchange rate movements. In the early stages of a recession, investment and output both decline, but investment declines faster. Consequently, the amount of output available to US. consumers does not fall as much as it otherwise would, and the exchange rate and trade deficit fail to rise as much as they otherwise would. On the other hand, once the economy turns around and production begins to increase, much of the increEconomic Review - September 1989 mental output is initially channeled into investment. As a result, the amount of output available to US. consumers may rise very little (may even decline) relative to the amounts available to consumers overseas. Indeed, historically the endowment ratio-and, hence, the u .S. trade picturedoes not reach its nadir until roughly two years after a recession ends. In the real world, as opposed to the abstract world analyzed in this article, international capital markets are not perfectly integrated, and output prices are not perfectly flexible. Extensions of the present analysis to allow for such imperfections would be highly desirable. Extensions to allow for endogenous investment, for uncertainty, and for trade in intermediate products would also be interesting. Nevertheless, preliminary empirical tests suggest that the analytical apparatus outlined here is a useful starting point for studying the evolution of the trade deficit and exchange rates during the 1980s. 24 This view of the rale of government budget deficits originated with David Ricardo and was resurrected by Barra (1974) Empirical supportfor the Ricardian view has come from a series of articles by Evans (1985. 1986. 1987) See also Ayanian (1988) 25 Appendix The Output Ratio and the Aggregate Endowment Ratio By assumption , in each period the utility function ofthe representative U .S. citizen can be written in the form u(c,im) = U[C(c,im)], where aggregate consumption, C(- ,-), is increasing and linearly homogeneous in U.S. consumption of U.S. products, C, and U.S. imports of Japanese products, im. Similarly, the utility function of the representative Japanese citizen is assumed to take the form u*(im*,c*) = U*[ C(im*,c*)), where im* and c* denote Japanese consumption of U.S. products and Japanese products , respectively , and where the subutility function, C(-,-), is identical to that of U.S. citizens. Intuitively, U.S. and Japanese households "produce" aggregate consumption from U.S. and Japanese commodities , using identical constantreturns-to-scale technologies. Households will allocate their spending across U.S. products and Japanese products so as to equate the marginal rate of substitution between the two types of output to their relative price, E. Using this optimality condition and Euler's Law, one obtains (A.1) dCIC = f)dclc + fJ*diml im, where f) and fJ* denote the fractions of U.S. and Japanese spending devoted to U.S. products and Japanese products, respectively, so that f)+ fJ* = 1. An analogous equation applies to dC*IC* . The aggregate endowment of U.S. households, E, measures how much aggregate consumption they would be able to enjoy in the absence of international borrowing and lending. Without international borrowing and lending, the budget constraint for U.S. households would take the form y= ce + im/ E, where ce and ime denote the amounts of U.S. and Japanese products that U.S. households would choose to consume under the balanced-trade restriction and where (as in 26 the main text) y denotes the amount of output produced in the United States and not absorbed by investment or government purchases. This budget constraint can be differentiated to obtain if one assumes that the initial equilibrium and the endowment points coincide. Combining (A.1) and (A.2), one obtains a formula for the percentage change in the aggregate endowment of U.S. households : dElE = dyl y + f)*dElE. (A.3) Intuitively, insofar as they purchase Japanese goods, U.S. households benefit from an increase in the real exchange rate . Together, equations 1 and A.3 imply (A.4) dElE = dyl y + (fJ* /cr) (dy* /y* - dyly) . Similarly, (A.4*) dE*I E* = dy*l y* + (f)/cr) (dyly- dy*Iy*). According to (A.4), U.S. households are better off as a result of an increase in U.S . output if, and only if, f)* is less than cr. But what of the change in the position of U.S. households relative to that of the Japanese? Subtract (A.4 *) from (A.4) to obtain (A.5) dElE - dE* I E* = (1 - 1/cr) (dyl y- dy*Iy*). Thus, an increase in the availability of U.S . products, relative to Japanese products, will raise the U.S . endowment relative to the Japanese endowment if, and only if, cr is greater than unity. Federal Reserve Bank of Dallas I .1 J References Ayanian, Robert (988), "Political Risk, National Defense and the Dollar, " Economic Inquiry 26 (April): 345-5I. Barro, Robert J. 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