An Accounting Framework and Some Issues for Modelling How Exchange Rates Respond to the News

International Finance Discussion Papers Number 200

January 1982

AN ACCOUNTING FRAMEWORK AND SOME ISSUES FOR MODELLING HOW EXCHANGE RATES RESPOND TO THE NEWS

by

Peter Isard

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

January 1982 Peter Isard*

An Accounting Framework and Some Issues for Modelling How Exchange Rates Respond to the News

I. introduction

This paper develops a framework of approximate accounting identities that is used to discuss the limitations of existing empirical models of exchange rate determination. The poor explanatory power of the empirical models of the Seventies has now been well documented by Meese and Rogoff (1981, 1983) and Backus (1981). In this paper the limitations are first addressed by using the accounting framework to demonstrate that some commonly-adopted behavioral assumptions cannot jointly explain a major portion of exchange rate movements. The middle sections of the paper address some issues in modelling how "news" leads to revisions in the expectational terms that enter the exchange-rate accounting framework. The final sections illustrate the issues by drawing inferences and conjectures about the types of news that contributed to the major swings in mark/dollar exchange rates (spot and forward) during 1980-81. The paper stops short of using the accounting framework as a building block for conducting regression tests of specific behavioral assumptions about the expectational terms.

Most empirical models of exchange rate determination seem deficient in anchoring the "level" of the expected path of the (real) exchange rate. The observed level of an exchange rate can be explained in terms of expectations about the’ level of the exchange rate that will prevail at any future date, but the exchange rate level expected at some future date must be anchored independently to explain the general level of the expected exchange rate path. This point is clear from interest-rate parity conditions under the assumption of risk neutrality, and the argument extends to finite-horizon portfolio-balance analysis under the assumption of risk aversion, as emphasized by Dooley and

Isard (1981a).* One feature of the accounting framework is to provide a building

~2-

block for using the notion of long-run goods-market or balance-of-payments equilibrium to construct a behavioral model that anchors expectations about the long-run real exchange rate.

The accounting framework also describes the general (non-behavioral) form of the "ropes" that link the observed spot and forward exchange rates to the anchored but unobservable level of the expected long run real exchange rate. Under risk neutrality, the long-term real interest differential is the link between the observed level of-the (price-adjusted) spot rate and the expected long run real spot rate. Equivalently, the expected long-term inflation differential is the link between the observed level of the (price-adjusted) long-term forward rate and the expected long-run real spot rate. For the risk-averse case a longterm exchange risk premium is added to the ropes. The general form of the accounting framework can accommodate survey data, macro-model forecasts, autoregressive forecasts or analytic structural models of inflation expectations. Similarly, it can accommodate either structural models or alternative representations of the risk premium. By characterizing the rope, moreover, the accounting framework suggest that quantitative discussions of exchange rate volatility can benefit from focussing on the length of the rope. In particular, if it is expected to take T years for the real exchange rate to converge to its long-run level, then the percentage change in the spot exchange rate that should be associated with a ceteris paribus shift in the term structure of nominal interest differentials (and hence real interest differentials) is the percentage point change in the compounded T-year interest differential, or roughly T times the change in the T-year interest differential as commonly measured in percentage

points per annum.

9

-3-

The accounting framework is developed in section II by manipulating the covered interest rate parity condition and some definitional identities. Attention is focussed on one resulting form of the exchange rate equation in which the observable long-term forward rate, deflated (or price-adjusted) by the observable ratio of current domestic and foreign price levels, is approximately identical (in logrithmic form) to the sum of three unobservable terms: the expected long-run real exchange rate, the expected long-term inflation differential and the expected long-term premium for bearing exchange risk. The framework emphasizes the different channels through which news can lead to changes in observed exchange rates (and/or interest rates and/or price levels) by generating revisions in the unobservable expectations terms.

Section III applies the accounting framework, using a time-series of OECD inflation expectations (forecasts) for 7 industrial countries, to construct measures of the extent to which observed changes in exchange rates (between 6 foreign currencies and the U.S. dollar) can be "explained" under the commonly-adopted assumptions of time-invariant expectations about the long-term real exchange rate (or purchasing power parity level, PPP) and the risk premium. Under these assumptions the substantial observed variability of spot exchange rates can only be explained by substantial variability in longterm real interest differentials. To the extent that real interest differentials are expected to vanish beyond the long run horizon, this in turn suggests that exchange rate variability has been associated with variability in the shape of the term structure of nominal interest differentials (relative to the shape of the term structure of expected inflation differentials), -and that the traditional use of short-term interest differentials in exchange rate equations may be a poor substitute for a focus on long-term interest

differentials.

ah.

Section IV provides some empirical evidence on the length of the horizon over which real interest differentials are expected to persist, which is assumed to be roughly the same as the length of time that is expected to elapse before the real exchange rate converges to its long run value. The evidence compares survey data on long-term inflation expectations, collected at several points in time between early October 1980 and early September 1981, with data on the 2-5 year and 5-10 year forward nominal interest rates that are implicit in the term structures of yields on dollar and mark-denominated Eurodeposits and Treasury issues. The evidence supports the assumption that it is expected to take longer than 2 years, but perhaps less than 5 years, for the real exchange rate to converge to its long run value.

Empirical work on exchange rate determination has made only limited

progress in modelling the news (see Dornbusch 1980a; Frenkel 1981; Isard 1980; Longworth 1980), despite the strong presumption that changes in exchange rates predominatly reflect revisions in expectations in response to the news (see Mussa 1979). Sections V-VII focus on some issues in modelling expectations of the long-run real exchange rate, the long-term inflation differential and the premium for bearing exchange risk. Sections VIII and IX illustrate the issues by focussing on the major swings in mark/dollar exchange rates (spot . and 5-year forward) during 1980-81 and by drawing inferences or conjectures about the extent to which the swings were "explained" by revisions in each of the three expectational terms. Section X summarizes the main points that emerge from sections V-IX.

An appendix discusses how the accounting framework can be used as

a basis for forecasting.

— 5=

II. An Accounting Framework

The framework developed in this section can be divided into two parts: an anchor and a rope. The anchor is a theory about the expected long-run real exchange rate based on notions of balance of payments equilibrium and consistent with the conditional expectation of long-run purchasing power parity. The rope that links observed exchange rates to the expected long-run real exchange rate is provided by the interest rate parity framework, as modified to allow for risk premiums. |

The rope can be characterized by combining the covered interest rate parity condition

(1) s=f+ R, - RB

with definitions of the risk premium (2) risk® =s° - £

and the real exchange rate

(3) sreal = s + Pp Py

where s,f,s denote the logarithms of the nominal values of the spot, forward and expected long-run spot rates, in units of currency

A per unit currency B

Ry oR denote nominal own rates of interest on assets denominated in currencies A and B, as compounded over horizons that extend until the long-run is reached Pa>Pp denote the logarithms of the price levels in countries A and B

and a superscript e labels the variable as an expectation. Together (1) -(3) imply

e e e . e (4) s = sreal + Pa 7 Pp - risk + R Ry

+6- It is convenient to express the expected future logarithmic price levels in

A terms of expected rates of inflation (, a) using the approximations

e_ “Ae (5) Pa = Py + Py e Ae (6) Ph = Pat P,

It is also convenient to introduce traditional definitions for real interest

rates e Ae (7) ry, = R, - Py Ae 8 es - (8) ra =R, - PE

Substitution then converts (4) into

_ _ ese ee aoe

(9) S = (Py Pp) + (rB r,) + sreal risk

Equivalently, when all observable variables are transposed to the left side (10) fadj = Pe - i + sreal~ - risk~

where the manipulation uses condition (1) and defines a price-adjusted forward rate

(11) | fadj = f+ Pp - Pa

Condition (11) is analagous to condition (3). It is important to emphasize that the nominal forward rate is adjusted by current price levels rather than forward price levels; in a risk neutral world it would not be an unbiased estimator of the expected future real exchange rate unless the future relative price level was expected to equal the current relative price level.

Much of the discussion below will focus on equation (9), but (10) is more attractive for applying the model empirically since it imposes prior coefficient values on observable price and nominal interest rate levels. Models in which interest rates or money supplies are treated as "causing" the exchange

rate, rather than as jointly endogenous variables, have been shown to involve

-7specification bias by Glaessner (1979). Caves and Feige (1980), and Meese and Rogoff (1981), among others.

Equations (9) and (10) apply to any horizon for expectations. In this paper they are discussed in terms of a long-term horizon, based on the view that the most plausible behavioral hypotheses for anchoring an expected future exchange rate are hypotheses about the real exchange rate that is consistent with long-run goods-market or balance of payments equilibrium. In empirical analysis based on condition (10), fadj is represented by a priceadjusted 5-year forward rate after Section IV presents evidence suggesting that investors expect it to take longer than 2 years for the real exchange rate to converge to its long-run equilibrium value.

The right-side terms in condition (10) represent unobservable expectations. The spirit of condition (10) is that news about the factors on which expectations are based leads to unobservable revisions in expectations and observable changes in exchange rates (and/or interest rates and/or price levels). The usefulness of condition (10) is for testing behavior hypotheses about the expectational variables. Insofar as the expectational variables are unobservable, the behavioral tests must be implicit or indirect, and given that three expectational variables enter the exchange rate equations the tests are joint or simultaneous tests of three behavioral hypotheses. This paper is oriented toward addressing the inadequacies of commonly-adopted behavioral hypotheses and stops short of subjecting alternative hypotheses to regression tests.

III. The Inadequacy of Some Common Behavioral Assumptions In principle, all of the expectational terms on the right side of

condition (10) should be treated as variables. Sections V-VII will address

-§-

the issues of modelling the expectational terms. This section uses the accounting framework in conjunction with OECD inflation expectations (forecasts) to argue that under the common assumptions of time invariant expectations about

the long-run real exchange rate (PPP level) and the risk premium, only a minor portion of observed changes in exchange rates can be explained by focussing

on the relationship between exchange rates and short-term interest differentials -- as is commonly done -- without explicitly taking account of changes

in nominal interest differentials that can be earned on investments. beyond

a 12-month horizon.*

The empirical exercise is to construct a time series of "residual" changes in the spot exchange rate that cannot be "explained" by observed changes in price levels or 12-month nominal interest differentials, or by revisions in the 12-month OECD inflation forecasts. The construction is based on a formula derived by first differencing condition (9), assuming time~ invariant values of sreal© and risk®. Reflecting the limited horizon of the OECD inflation forecasts, the real interest differential is truncated beyond

the 12-month horizon. This leads to

(12) resid, = s, - S._) + (@y - Pay ~ gq ~ Ppery + Bg - Bye, tse nN aw e AN a~ e - By- Reig, car 7 Pa 7 Pee, tao * Pa ~Pwreia, tt

where t runs through semi-annual observations, corresponding to the semiannual dates of the OECD forecasts. Given the assumptions underlying the derivation of condition (12), the proper interpretation is that resid measures the sum of the changes in the expected long-run real exchange rate, the expect— ed return for bearing exchange risk, and the real interest differential beyond

a 12-month (i.e., 2 period) horizon. The OECD forecasts are published for

~9-

seven countries (Canada, France, Germany, Italy, Japan, the United Kingdom and the Urited States) and thus provide time series of "residual" changes in the exchange rates between the U.S. dollar and six other currencies.

Table 1 shows the observed, explained and residual changes in the logrithms of exchange rates, which correspond to percentage changes in the levels of exchange rates. (The explained changes are computed last as the differences between the observed and residual changes.) For 39 of the 48 entries the residual changes are larger than the explained changes. As noted above, the residual changes can be viewed as the error terms that arise from the joint assumptions that the expected long-run real exchange rate and exchange risk premium are time invariant, and that real interest differentials are not expected to persist for longer than 12 months. The residuals are generally too large to attribute to differences between OECD inflation forecasts and "true" measures of inflation expectations. Accordingly, the evidence suggests that at least one of the following propositions must be true. Either (1) expectations about the long-run real exchange rate (or PPP level) vary widely over time, or (2) the exchange risk premium is large and variable or (3) substantial real interest differentials are frequently expected to persist for longer than 12 months. Thus, to the extent that there is some long run hori-~ zon beyond which real interest differentials are expected to vanish, the assumptions of time invariant expectations of the long-run real exchange rate and the risk premium would suggest that exchange-rate variability has been associated with variability in the shape of the term structure of nominal interest differentials (relative to the term structure of expected inflation differentials), which in turn suggests that the traditional use of short-term interest differentials in exchange rate analysis may be a poor substitute for

a focus on long-term interest differentials.

-10-

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~12- IV. The Persistance of Real Interest Differentials: How Distant is the Long Run?

Condition (10) provides a useful analytic framework only to the extent that the right-side expectational terms can be modelled, and among these terms, the expected future real exchange rate cannot be easily modelled (or convincingly assumed to be constant) without appealing to the notion of a long-run steady state. For purposes of empirical analysis it is important to focus on forward exchange rate observations for a maturity that exceeds the expected length of the convergence interval over which the real exchange rate moves to its long-run steady-state value (following an isolated, ceteris paribus shock that disrupts an initial steady-state equilibrium).

For many currencies, adequate historical data on forward exchange rates against the U.S. dollar are not available for maturities longer than 1 year. For a few currencies, including the mark, 2-year and 5-year forward rates against the dollar are available (or can be constructed from Eurocurrency deposit rates) on a daily basis. This section argues for using the 5-year forward rate in condition (10), based on evidence suggesting that it is expected to take longer than 2 years, but perhaps less than 5 years, for the real exchange rate to converge to its long run level.

The evidence is presented in table 2. The first two rows of table. 2 present time series of Bache survey data on the average annual rates of U.S. inflation expected over the first and second halves of a 10-year horizon. The two series are assumed to provide upper and lower bounds on the U.S. inflation rates that were expected from the end of the second year through the end of the fifth year. The expected 2-5 year U.S. inflation rate declined from early October 1980 through early September 1981, and there is a strong

presumption that any revisions in expected long-term German inflation rates

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. : : ‘ . . ; a Table 2: Long-term inflation expectations and nominal interest rates

Early — Early Early Early Early October January .May ‘September November ‘1980... © (1981 1981 “4981 1981

Expected U.S. inflation?

0-5 years 9.4 8.9 8.4 7.8 7.9

5-10 years 8.3 7.8 7.3 7.4 7.5

2-5 years 8.3-9.4 7.8-8.9 7.3-8.4 » 7.4-7.8 7.5-7.9 Eurodollar rates”

2 years 12.5-13.1 14-14.5 16.4-16.8 17.5 14.6-14.8

5 years 12.5-13.0 13.9-14 15.9-16.5 16.8-17.0 14.9-15.3

2-5 years 12.5-13.0 13.5-13.9 15.5-16.3 16.3-16.7 15.0-15.6 Euromark rates

2 years 8.3-8.6 9-9.3 11.1-12 12.5 11

5 years 8.3-8.5 9-9 .3 10.4-11 11.9 10.6

2-5 years 8.3-8.5 9-9.3 9.9-10.3 11.5 10.4 Euro-differential

2-5 years 4.2-4.6 4,5-5.8 5.7-6.1 4.9-5.1 4.7-5.2 Treasury differential? Sept./Oct. Jan. Apr./May Aug. /Sept.

2--5 years 3.7/3.7 3.6 4.2/3.7 4.9/5.6

5-10 years 3.3/3.1 3.3 3.2/3.0 3.1/3.4 a. In percent per annum.

b. Based on survey data on 5 and 10-year U.S. inflation expectations collected

quarterly since mid-1980 by Richard B. Hoey, Vice President of Bache Halsey Stuart

Shields Incorported. Data represent simple averages of the expectations of about 350 institutional investment decision makers, as published in Bache Institutional Research Letters.

c. The 2 and 5-year interest rates represent yields (paid once a year) on fixed

term deposits, as collected daily by the Bank of America and made available through

Data Resources Inc. The 2-5 year rates represent implicit fixed-term yields computed in the traditional manner.

d. Based on averages within each month of market yields on U.S. and German Treasury debts, by horizon to naturity, as published in the Federal Reserve Bulletin and

the Monthly Report of the Bundesbank (Series 2, Table 8c).

-14-

we re upward? , thus implying an even greater decline in the expected inflation differential. By contrast, there were increases over the same period in the differentials between the implicit 2-5 year nominal yields on dollar and markdenominated assets, as shown for both Eurocurrency deposits and Treasury issues.

Such evidence indicates that real interest differentials beyond a 2-year horizon were not time invariant, which rejects the assumption that real interest differentials were expected to vanish within a 2-year horizon. Unless the substantial changes in 2-5 year real interest differentials were offset by equal and opposite changes in the implicit 2-5 year risk premium, the evidence also rejects the assumption that the real exchange rate was expected to converge to its long-run level within a 2-year horizon.

The bottom row of table 2 presents data on the differentials between the implicit 5-10 year nominal yields on U.S. and German Treasury issues; data are not available on Eurocurrency yields for maurities longer than 5 years. The data on Treasury differentials are constructed from term structures of the average yields within each month. Together, the data in the bottom row and the 2nd row from the top might be judged as a weak rejection of the hypothesis that real interest differentials beyond a 5-year horizon are time invariant; but the evidence does not suggest substantial variation in the 5-10 year real interest differential.

To summarize, the evidence in table 2 argues against the assumption that real interest differentials are expected to vanish within 2 years, and thus argues against using a 2-year (or shorter maturity) forward rate in applying the accounting framework. Furthermore, the evidence is not strongly critical of using a 5-year forward rate, which is the only alternative for

which adequate data are available.

-15- V. Some Difficulties in Modelling Inflation Expectations

With respect to modelling the expected inflation terms on the rightside of condition (10), the traditional use of long-term nominal interest rates as proxy variables for long-term inflation expectations is inadequate, since it implicitly denies any difference between the paths of nominal interest rates and expected inflation rates over the horizon that is required to reach the long run. This point is underscored in section IX below, where it is argued that the sharp appreciation of the dollar in the first half of 1981 was associated with a downward revision in U.S. long-term inflation expectations in response to fiscal policy news; yet long-term dollar interest rates rose in the periods following the arrival of the fiscal policy news.

The apparent responsiveness of inflation expectations to fiscal policy news during 1981 also poses the challenge of modelling inflation ex-' pectations in a rational forward-looking context that spells out the channels through which budget deficits are assumed to influence inflation, whether through the money-supply mechanism or the Phillips curve. As section IX will emphasize, the data on prices, monetary aggregates, activity indicators and current budget deficits did not jump contemporaneously with the fiscal policy news of 1981. Thus, to capture the revisions in inflation expectations (without relying on survey data) requires not only a forward-looking rational-expectations model but also measures of expected future values of "explanatory" variables (in the inflation equation) that are not merely generated from autoregressions.

VI. The Expected Long-run Purchasing-Power-Parity Level It seems unacceptable to model real exchange rates without relying

on some notion of goods-market or balance-of-payments equilibrium. Ina

-16-

world of two countries, each producing a different good, the domestic price levels can be related to nominal money supplies, but an additional balanceof-payments condition is required to explain the relative price level or real exchange rate. In a Hechsher-Ohlin-Samuelson world in which the two countries each produce the same two goods, the production possibilities frontiers and consumer indifference maps, which together determine the domestic relative price levels for each country under autarky, must be supplemented with a balance~-of-trade condition (or perhaps a more broadly defined balance of payments condition) to determine the common relative price level that emerges under international trade.

Many analytic models of exchange rate dynamics assume that the world economy is expected to converge to a steady state in which the real "exchange rate is consistent with long-run balance of payments equilibrium; examples include Kouri (1976), Dornbusch (1976) and Calvo and Rodriguez (1977). In principle, the existence of a long-run balance-of-payments constraint, regardless of its particular form, implies that the expected long-run value of the real exchange rate (if expectations are formed rationally) will vary over time in response to any shocks that generate revisions in expectations about the long-run values of other variables that influence the balance of payments. Thus the expected long-run PPP level should, in principle, be viewed as an endogenous variable.>

The empirical literature on exchange rate determination has taken only limited steps to endogenize the expected long-run real exchange rate, most notably those by Hooper and Morton (1982). The argument that the longrun PPP level is inprinciple a variable, of course, leaves open the question of whether it varies sufficiently to have a major influence on observed ex-

change rates.

-17-

The major shifts in the relative price of oil during the 1970s provides the strongest case for arguing that revisions in expectations about the long-run PPP level may have been empirically important over the past decade. The evidence seems clear (though not scientifically extracted with formal techniques) that news which leads to small changes in the outlook for the relative price of oil has a significant and predictable (ex post) impact -in the hours or days during which the news is digested -- on the exchange values of the currencies of countries that are relatively well-endowed or relatively poorely-endowed with energy resources. A major difficulty that arises, however, in trying to identify such changes in exchange rates with revisions in expectations about the long-run PPP level is that the economic stabilization policies pursued by different countries have responded differently to oil-price shocks. In terms of the accounting framework developed in section II, empirical evidence that month-to-month movements in exchange rates reflect significant responses to changes in the expected long-run PPP level must be extracted from a joint test of behavioral specifications for the expected long-run PPP level, the expected long-term inflation differential and the expected long-term return for bearing exchange risk. Identification is thus complicated by the fact that behavioral specifications for the latter two expectational facters cannot realistically abstract from the perceived or , expected responses of stabilization policies to the oil-price shocks. In particular, inflation expectations are sensitive to revisions in expectations about monetary growth paths, and the risk premium is sensitive to revisions in expectations about fiscal budget deficits.

The difficulties of modelling expectations and quantifying the news can hardly be avoided, however , in any serious attempt to resurrect faith in

structural exchange rate models. The starting point for modelling the expected

-18long run real exchange rate is to specify the long-run balance of payments constraint as a relationship between a constant steady-state level of the real exchange rate and a list of other variables. In general, the long-run values of these other variables are not knownwith certainty but, presumably, can be described in terms of subjective probability distributions. Consistently, the balance of payments constraint can be viewed to anchor the longrun real exchange rate in terms of a probability distribution that depends, under rationality assumptions, on the joint probability distribution of the other variables. For purposes of estimating an exchange rate model based on condition (10), the expected value of the long-run real exchange rate must be characterized to replace sreal~ with a testable behavioral hypothesis, and the variance of the long-run real exchange rate is an important component of the risk premium, as will be discussed in section VII.

Several contributions to the literature have addressed the notion that unexpected shifts in (variables that influence) the current account lead to revisions in expectations about the long-run real exchange rate; see Dooley and Isard (198la), Hooper and Morton (1982) and Mussa (1980). None of these contributions, however, has provided a satisfactory description of the balance of payments constraint. Dooley (1980) has emphasized that the balance of payments is a concept of net debt flows between geographical regions and no longer a good measure of net debt flows denominated in any particular currency unit .° This implies that any long-run constraint on the balance of payments owes its existence to the political risk of default rather than to exchange-rate risk. In a more recent paper, Dooley (1981) suggests that market mechanisms impose the long-run balance of payments con-

straint via increases in political risk premiums, and consequent exchange

-19-

rate adjustments, which serve to prevent cumulative current account deficits from ever reaching a level at which debt service costs make default optimal for the debtor country.

The general nature of such a bound on cumulative balance-of-payments flows does not impose a rigid constriant on the balance of payments during any particular year in the long-run unless an assumption is made that constrains all years to be similar once the long-run is reached. The latter assumption can be justified, however, not only on grounds of analytic convenience but also by the argument that long-run foresight is too imperfect to place any faith in predictions of how economic variables will fluctuate around their long-run trends. In sum, the assumption of a finite bound on cumulative balance of payments flows together with the steady-state assumption of smooth growth of economic activity after the long-run is reached imply an expected balance of payments-of zero over any finite interval of the infinite long-

run horizon.’

With this justification, it is instructive to provide a simple characterization of the steady state. In the 2 country context, real output can be imagined to grow at the same constant real rate of interest in each country, with balance of trade. If one of the two countries holds net claims on the other, the stock of these net claims also grows at the real interest rate and thereby amounts to a reinvestment of net interest income from abroad. Thus, net interest payments remain a constant proportion of the output of the debtor country, so the incentive to default never increases. Similarly, the wealth of the creditor country, as measured by portfolio size, increases over time in absolute size but remains stationary relative to income, and real transfers

never occur.

-20 Such a framework can be described formally in terms of a balance of

payments condition

(13) ANCE, = X, - SREAL,M, + Ty NCF an import demand function (14) log (M/Y) =a,7 at, 7 Z, ao k sreal, and an export function (or foreign import demand function) (15) log (V0) = by - bit, + So bok sreal, where M,X denote import and export volumes Y,Y" denote domestic and foreign incomes in real terms NCF denotes net domestic claims on foreigners in real terms r denotes the domestic and foreign real interest rates (which need

not be distinguished for purposes of describing the steady state) SREAL denotes the level (as distinct from the logarithm) of the real exchange rate The steady state is characterized by trade balance, by equal domestic and foreign real interest rates r, and by constant growth at rate r of domestic and foreign output, of net claims on foreigners, and hence of domestic and foreign incomes. Thus, conditions (13) - (15) can be solved for the steady-

state logarithmic level of the real exchange rate

(aj-b,) + (b,-a,)F + log (¥/Y")

ay + by - 1

(16) sreal =

. a e . where ay = Zag \° b, = by and Y/Y is the constant steady-state ratio of

domestic and foreign incomes,

-21-

Condition (16) translates directly into a rational model of the expected long-run real exchange rate that appears in the spot and forward rate equations (9) and (10)... The expected long-run real exchange rate depends, loosely speaking, on expectations of the long-run ratio of domestic to foreign activity levels, on perceived values of the exchange-rate elasticities of import and export volumes, and on expectations or perceptions

= . : e : . about r, a.» dD > ay and by: Revisions in sreal , accordingly, can arise from fe) fe) .

revisions in expectations about the long-run values of y/y* or r, or from revisions in perceptions about the values of the exchange-rate elasticities or the other parameters. It is worth repeating that while sreal’ is the mean of a subjective probability distribution, the range of the distribution may be wide and the variance high. The notion of long-run balance of payments equilbrium need not anchor the long-run real exchange rate at a point.

Condition (16) stops short of modelling how expectations about Y/Y* and r and perceptions about the parameter values are formed and/or revised. But together with the Marshall-Lerner condition (i.e., the assumption that its denominator is positive) it provides a place for a number of phenomena that are viewed to influence exchange rates. (1) An oil discovery in country A can be viewed -- within the simple structure of trade equations (14) and (15) -to raise the perceived long-run value of bo or lower the perceived value of ao? thereby appreciating currency A. (2) A rise in the relative price of oil can be viewed to raise by for oil exporting countries and to raise ay for oil importing countries, with well-recognized effects on exchange rates. (3) Larger-than-expected trade deficits (surpluses) in the short run that persist and do not merely reflect unexpected changes in the explanatory variables that enter trade equations can lead to revised perceptions of parameter

values, to associated revisions in expectations about the long-run real

-22exchange rate, and thereby to observed currency depreciation (appreciation). (4) Surprises about the extent to which a country's trade balance is improving (deteriorating) following currency depreciation (appreciation) may lead to upward revisions in perceptions of the elasticity parameters a

2 and b

27 to an associated revision in expectations about the long-run real value of the currency, and thereby to a change in observed exchange rates. (5) To the extent that a surprisingly sharp domestic recession (boom) is viewed to permanently lower (raise) the level of domestic output relative

to foreign output, the domestic currency should appreciate (depreciate); accordingly, activity shocks that are not expected to be completely offset can generate a positive correlation between shifts in the trade balance toward surplus (deficit) and currency appreciation (depreciation). (6) To the extent that policy actions (e.g., tax measures or other "supply-side" shocks) raise the domestic share of world markets at any given real exchange rate, the ay and by parameters will shift, with ayn bo declining and thereby generating an appreciation of the expected long-run real value of domestic

e currency (i.e., a decline in sreal ).

VII. The Expected Premium for Bearing Exchange Risk

By its definition in condition (2), the expected long term premium for bearing exchange risk is the difference between the expected long-run nominal spot rate and the observed long-term nominal forward rate. A nonzero risk premium owes its existence to three factors: (i) a non-zero probability, and hence some risk, that the future spot exchange rate may differ from its expected level, (ii) private investors' aversion to that risk, and (iii) a difference between the currency composition of public debts that are forced (at market-clearing prices) into the portfolios of private investors (as an aggregate) and the currency-composition of the aggregate portfolio that would minimize the risk assumed by private investors; (see Dornbusch

1980b). Without any one of these factors the risk premium would vanish.

-23-

Attempts to assess the empirical importance of the risk premium can be classified into three approaches. Dooley and Shafer (1976), Hansen and Hodrick (1980, 1983), Cumby and Obstfeld (1981) and Meese and Singleton (1982), among others, have employed a variety of methods to examine the time series properties of spot exchange rates and forward exchange rates (or interest differentials); such studies have generally concluded that the assumption of market efficiency implies that the risk premium is significantly greater than zero, although not necessarily very large. As a second approach, Dooley and Isard (198la)and Frankel (1981, 1982) have tested the significance of simple structural models of the ex ante risk premium in explaining the ex post change in the exchange rate (over and above the forward premium); these studies have found weak evidence of a small risk premium. As a third approach, Krugman (1981) has derived a structural form for the risk premium and inserted "reasonable" values of the structural parameters to calculate the extent to which the risk premium might be judged to change in association with given changes in asset stocks and wealth variables. Krugman also finds no reason to believe that the risk premium is large.

The Krugman-type exercise is repeated here with “more reasonable" parameter values. The purpose is to challenge Krugman's impression of the order of magnitude of the risk premium and to suggest in particular that changes in the risk premium may have accounted for a substantial portion of the swings in the mark/dollar rate during 1981, which strongly coincided (as documented in section IX below) with shifts in the outlook for U.S. budget deficits. Given the limited objective of being suggestive, the formulation of the risk premium has been simplified in two important ways: by ignoring

differencies in the portfolio preferences of U.S. and foreign residents (i.e.,

~24-— wealth effects), and by assuming that both U.S. and foreign residents optimize with respect to the dollar value of their terminal wealths. Under these simplifications the 5-year risk premium can be derived from a utility-maximizing framework as the product of the coefficient of risk aversion (u), the perceived variance (v) of the ratio of the 5-years-future spot rate. to the current 5-year forward rate, and the share (Q) of dollar-denominated public debt in global private holdings of dollar and market denominated public debts; see Dornbusch (19806), Isard (1980) or Krugman (1981). (17) risk® = uv -Q As the optimization problem is generally formulated, the asset-share variable is a current, beginning-of-period concept. A more realistic formulation for a rational expectations environment would provide an explicit role for expectations or subjective probability distributions about the future paths of asset stocks and wealth variables. In the absence of such a formulation, a third major simplification in what follows is to interpret Q, heroically, as an endof-period concept.

With. this basis and interpretation of condition (17), a Krugman-type calculation can be generated under the suggestions that u = 4, that yv = 1/4 and that Q changed by at least 2 percent during the early months of the Reagan Administration. These numbers suggest that changes in the risk premium "explained" at least a 2 percent appreciation of the dollar against the mark during the first half of 1981. The value u = 4 is taken from Grossman and Shiller (1981), who place it within the range of estimates that have been published in the literature, and who argue as well that a value of at least 4 is suggested by an empirical application of their model of stock-price variability. The value v = 1/4 reflects the assumption that the subjective probability distribution

-25-

of the 5-year future spot rate is normal, with a mean value of 2 marks per dollar (roughly equal to the 5-year forward rate), and with 67 percent of the probability attached to the range between 1 and 3 marks per dollar; hence the variance of the 5-year future spot rate is 1 and the variance of the ratio of the future spot rate to the forward rate is 1/4. Finally, the alleged change of at least 2 percent in Q is based on the perception that the fiscal policy proposals in the early months of the Reagan Administration, and their acceptance by a surprising margin-of-victory in a House of Representatives vote on May 7, reduced the cumulative outlook for U.S. budget deficits over a 5-year horizon by at least $100 billion. Given an initial value of Q=.8, based on the initial trillion dollar stock of U.S.-public debt and the 1/4 trillion dollar-equivalent stock of German public debt, a change of at least $100 billion, or 10 percent, in the expected stock of U.S. public debt suggests a change of at least 2 percent in the expected ratio of U.S. to U.S. plus German public debts.

To lend futher support to the suggestion of substantial changes in the risk premium, section IX will present graphical evidence that movements in mark/dollar exchange rates during 1981 coincided strongly with fiscal policy news. As will also be detailed, survey data on long-term U.S. inflation expectations suggest that revisions in inflation expectations can only explain about half of the apparent responsiveness of the exchange rate to fiscal policy news. Such arithmetic raises the possibility that the 5-year risk premium changed by as much as 5 to 10 percentage points during the early part of 1981 -- even more than suggested by the calculations based on the over-

simplified condition (17) -- or by as much as 1 to 2 percentage points when

~26-

measured in per-annum units. On a priori grounds, it does not seem implausible that rational investors may have been so uncertain and risk averse to have required an additional expected long-term yield of 1 to 2 percent per annum on their mark-denominated portfolio holdings, given the rosy expectations created early in the Reagan Administration.® Unfortunately, there seems to be no basis for a refined judgement of whether the risk premium could have changed so much without the analytical equipment of a forward-looking formulation of the risk premium in terms of expected future asset stocks and wealth variables, along with a better empirical assessment of parameter values and the extent to which expectations of future asset stocks and wealth variables have shifted.” VIII. Explaining the Volatility of the Dollar During Spring 1980

This section and the next focus on the behavior of spot and forward mark/dollar exchange rates during 1980-81, using the accounting framework as a basis for drawing inferences and conjectures about hte response of these exchange rates to major elements of the news. In this section the focus is on the extent to whichthe rise and fall of the dollar during January-May 1980 can be "explained" by changes in the compounded long-term real interest differentail. The assessment involves a straight forward analysis of how much of the swing can be "explained" by changes in the compounded long-term nominal interest differential and an informal analysis of whether the magnitude and timing of changes in the residual can be plausibly attributed to revisions in expectations about the long-term inflation differential. The obverse’ of this question is whether it is plausible that the risk premium and the expected long-run value of the real exchange rate remained constant throughout the period.

Figure 1 shows the behavior of the mark value of the dollar from

October 1979 through early December 1981, both on a spot basis and for 3-month

—-27-

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~28-

and 5-year forward maturities. It is interesting to note that the correlation between the spot and 5-year forward rate is high, though not as near-perfect as the correlation between the spot and 3-month forward rates.

Given the empirical evidence presented in section IV and the fact that 5 years is the longest maturity for which adequate data are available on forward rates (or on differentials between interest rates on Eurodollar and Euromark deposits), the analysis for the most part adopts the assumption that the long-run is expected to be reached within 5 years. This essentially amounts to assuming that real interest differentials are expected to vanish in less than 5 years —- the equivalent (under risk neutrality) of the assumption that the real exchange rate is expected to converge to its long-run level in less than 5 years. Some consideration is also given to the assumptions that the long run is expected to be reached within 1 year or within 2 years -i.e., that real interest differentials are not expected to persist beyond 1 or 2 years. The data represent time series of Wednesday observations. An alternative focus on weekly-average observations conveys virtually the same impressions.

Figure 2 shows cumulative percentage changes since the beginning of

1980 in the spot rate and the 5-year price-adjusted forward rate 10

Based on condition (10), in the absence of revisions in expectations about the longrun real exchange rate or changes in the risk premium, movements in the 5-year price-adjusted forward rate could be interpreted entirely as revisions in expectations about the differential between German and U.S. inflation rates over a 5-year horizon.

To judge the maintained hypothesis that movements in the price-

adjusted forward rate can be interpreted as revisions in the expected 5-year

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-~30-

inflation differential (measured per annum on the left scale in Figure 2 and per 5 years on the right scale), the data period is divided into 5 subperiods. During January there was little movement in the two exchange rates. Subperiod II on the graph began right after the U.S. budget proposals and the Economic Report of the President were releasedon January 28th and 30th, respectively. The subsequent three weeks brought an upward revision in the expected pace of U.S. inflation: by February 6th it had been discovered that the U.S. Budget had substantially underestimated the costs of military outlays for fuel; by February 13th new data showed a strong acceleration in U.S. retail sales during January; by February 20th it had been revealed that U.S. wholesale prices had jumped 1.6 percent during January, a sharp acceleration for December; and on February 22nd it was reported that U.S. consumer prices had also accelerated sharply in January. Consistently, the dollar depreciated forward over this subperiod, while downward pressures on the spot value of the dollar were offset by a 1-1/2 percentage point increase in the Eurodollar rate relative to the Euromark rate (per annum).

The news of the January rise in U.S. consumer prices ushered in subperiod III on the graph as financial markets, according to Reuters, reacted "perversely". The consumer price data strengthened expectations of further anti-inflationary policy measures by the U.S. authorities -- expectations that were confirmed by the new budget proposals and monetary and credit actions of March 14th. Under the maintained hypothesis, the path of the forward rate would imply that the expected U.S. infaltion rate, looking out over a 5-year horizon, was revised downward over the course of a month by roughly 2-1/2 percentage points per annum relative to the expected German inflation rate.

The revision in inflation expectations was associated with an increase in real

=-31-

long-term dollar interest rates relative to real long-term mark interest rates and led to a strong appreciation of the spot dollar, even though nominal Euromark rates moved up somewhat faster than Eurodollar rates.

Subperiod IV on the graph began on March 27th with the decision, announced following the fortnightly meeting of the Bundesbank Central Council, that German credit policies would be left unchanged. The apparent upward revision in expectations about the pace of German inflation, relative to U.S. inflation, was supported on April 2nd by the report of a full half percentage point drop in the German unemployment rate during March. Additional support may have been provided by major new banking legislation, passed by the U.S. Congress on March 28th, which strengthened the Federal Reserve's control over money and credit growth. During the first four trading days of April, spanning the long Easter weekend, the spot and forward values of the dollar wavered around levels 4 percent higher than where they had closed on March 26th.

Then they dropped the full 4 percent on April 9th. Among the news that may

have led to the dollar's drop was the announcement late on April 8th that the German Government had arranged to borrow one billion marks from the U.S. Government, the release of data on April 9th indicating no change in German industrial production during February, and the prediction by a respected U.S. banker that dollar interest rates would soon begin to tumble. The first and second itemssuggested less pressure on the German money supply, given the authorities' reluctance to push interest rates higher, while the third item may have provided

a revised impression of how contractionary a stance the Federal Reserve had taken.

Subperiod V started on April 16th, the day that U.S. prime rates began the rapid descent from their peak. By the end of May the 5-year Euro~

dollar rate had fallen by more than 4 percentage points per annum, and by

~32roughly 2-1/2 percentage points relative to the 5-year Euromark rate. Meanwhile the expected pace of U.S. inflation was revised downward, particularly in response to the May 2nd announcement that U.S. unemployment had skyrocketed from 6.2 percent in March to 7.0 percent in April. Consistently, the 5-year forward dollar appreciated sharply in response to the May 2nd announcement.

The story provides reasonable explanations for the direction of swings in spot and forward rates under the maintained hypothesis. Are the magnitudes of the swings in the 5-year forward rate also plausible estimates of revisions in inflation expectations? Is it plausible that the inflation differential expected over a 5-year horizon could have first increased (during subperiod II) by about 1 percentage point per annum and then declined (through the end of May) to roughly 3 percentage points per annum less than what had been expected during January? Changes of such magnitude in the relative U.S. and German inflation outlooks were discussed by the financial press, although without explicitly looking much further into the future than the end of 1981. A convincing answer seems precluded by the absence of published inflation forecasts that extend as far as 5 years into the future and are revised frequently enough to provide an interesting time series. |!

A major empirical point about the Spring 1980 example is that changes in real interest differentials, when compounded or integrated over a long-term horizon, can potentially explain a substantial degree of exchange rate volatility. The above analysis has focused on the revisions in expected inflation differentials that are implied by the joint hypothesis that Spring 1980 was explained entirely by changes in real interest differentials and that real interest differentials were not expected to persist beyond a

5-year horizon. For comparison, and despite the evidence to the contrary

-33-

presented in section IV, it is interesting to consider what the joint hypothesis would imply if real interest differentials were only expected to persist for a year or two. Accordingly, in Table 3 the third and second columns from the right have been constructed to represent the revisions in expected inflation differentials that are implied when the joint hypothesis is modified by assuming that real interest differentials were not expected to persist beyond horizons, alternatively, of 1 year and 2 years. The joint hypothesis seems implausible under either of these cases.

The issue of the horizon length over which real interest differentials are expected to persist is an important question for assessing the extent to-which exchange rate volatility can be associated with changes in real interest differentials. Section IV has begun to address the question empirically, but more extensive evidence and better tests are desirable, in particular to explore the question of whether real interest differentials beyond a 5-year horizon are substantial. Economists who have been inclined to think that real interest differentials are generally expected to vanish within a year or two must confront the reality of 5 to 10 year real dollar interest rates, as traditionally defined, rising well above 7 percent per annum in the first eight months of 1981 when measured with survey data on long-term inflation expectations. In the absence of a satisfactory explanation of the high level of long-term real interest rates it is difficult to conceive of the mechanism that might have been expected to eliminate real interest differentials within a 1 or 2 year horizon.

IX. The Mark/Dollar Rate from June 1980 through December 1981 This section uses the accounting framework to discuss plausible

explanations for the major swings in the mark/dollar rate between June 1980

-34-

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-36and early December 1981. Figure 3 illustrates that the swings in the 5-year forward rate were concentrated during 6 intervals: (i) mid-June to early September 1980; (ii) early September to early November 1980; (iii) late January to mid-February 1981; (iv) late April to early June 1981; (wv) mid- August through September 1981; and (vi) the first half of November 1981. Percentage changes in the 5-year forward rate during those intervals -roughly corresponding by construction to percentage changes in the spot rate after adjustment for associated changes in the 5-year nominal interest differential -- can be associated either with revisions in expectations about the ratio of German and U.S. 5-year inflation factors, or with revisions in expectations (explicit or implicit) about the long-run real exchange rate, or with changes in the risk premium. ->

With respect to the 10 percent depreciation of the forward dollar from mid-June through early September 1980, it seems clear in retrospect that the major economic surprises during that period led to upward revisions in expectations about U.S. inflation. Economists may never agree on how to specify a structural model of inflation, but few structural models would fail to find a role for either the unexpectedly-sudden bottoming out of the recession, the rapid rate of monetary growth or the dismantling of credit controls. Whether U.S. 5-year inflation expectations increased by 2 percentage points per annum, thereby "explaining" the entire depreciation, is subject to dispute. It does seem clear, however, that expectations about the duration of the recession began to be revised no sooner than early June but certainly by early July, consistent with the timing of the downturn in the forward rate. More specifically, the announcements on May 30 of a 4.8 percent April decline in the leading indi-

cators, and on June 6 of a jump in May unemployment from 7.0 to 7.8 pexcent,

-37-

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-38-

suggested a continuing sharp downtrend in activity; while the announcements on July 3 of a 7.7 percent June unemployment rate and on July 10 of a 1.4 percent rise in June retail sales were reported (e.g., by Business Week) to have taken almost all economic forecasters by surprise. A final point that seems clear about this period is that

news about the strength of economic activity was not transmitted through only one variable.

This last point may have useful implications for econometric modelling. Information about both the timing and magnitude of activity surprises can be increased by pooling a number of activity indicators rather than relying on a single indicator that is only sampled once a month. This is largely because every indicator of activity contains noise that market participants must sift out by focussing on a crosssection or sequence of indicators, and partly because focussing on a cross-section of indicators increases the frequency with which new information can be received. The same argument for pooling applies to econometric attempts to measure unexpected shifts in price variables, etc.

The second major swing in the 5-year forward rate -- the 19 percent appreciation between early September and early November 1980 -cannot be clearly attributed to major surprises about the states of the U.S. or German economies. The U.S. economy showed mixed signs of strength and weakness in early September and continued to show mixed signs in early November. The key events during the period were the national elections in both countries, of which the re-election of German

Chancellor Schmidt on October 5 was widely expected all along. The

-~39appealing hypothesis, then, is that the rise of the forward dollar during these 2 months mainly reflected shifts in the perceived probability of a Reagan victory. Reagan was perceived as good for the doilar in the senses of being more firmly committed than Carter both to reducing inflation (through fiscal policy and support for tight monetary policy) and to stimulating U.S. competitiveness (through tax incentives, removal of regulations, etc.). In addition, the perception that Reagan was more committed to reducing U.S. budget deficits may have had implications for the risk premium. At the beginning of September, Reagan and Carter were fairly even in the polls. As time passed, and particularly after the polls began to focus on electoral votes, the probability that Carter could defeat Reagan appeared to shrink fairly progressively .*

It is an exaggeration to say that the 5-year forward rate looks like a step function during 1981, but it is striking that the major shifts in the forward rate occurred during four brief intervals, suggesting that there were 4 major doses of news that were transmitted and digested fairly quickly. The first three major doses of news during 1981 concerned the outlook for U.S. budget deficits. The news was conveyed, in particular, by Reagan's January 29 press conference and February 5 television address; by his April 28 speech to Congress and the surprising margin-of-victory with which the budget proposals sailed through the House of Representatives on May 7; and by large upward revisions in estimated budget deficits that were officially announced in mid-August, followed by mounting political opposition to further large budget cuts. The second swing, from late April through early June, may also have reflected spillover effects of the French elections on German economic prospects as well as upward revisions in expect—

ations about the size of future German budget deficits. The beginning of

~AQ—

the fourth swing, in eariy November, coincided with announcements indicating a strong-than-expected recession in U.S. activity: in particular, with the announcements on October 29 of a 2.7 percent September decline in the Leading indicators and on November 6 of a jump in unemployment to an 8.0 parcent rate in October following a 7.5 percent rate in September. +>

Why should the dollar strengthen in response to a downward snaift in the expected path of U.S. budget deficits? One view is that a lower deficit reduces the likelihood that the Federal Reserve will monetize debt in excess of ies money growth targets (or in excess of some prespecified notion of an appropriate long-run money-growth path); accordingly the prospect of reduced deficits may lower inflation expectations. A second view is that lower U.S. budget deficits are likely to imply a slower growth of the supply of dollar-denominated public debt relative to the supply of public debt denominated in other currencies. Accordingly, the risk pramium on the dollar should decline. as was discussed in section VII. Given both the expected long-run level of the exchange rate and the interest differential, a lower risk premium on the dollar implies that markets clear at a lower expected rate of appreciation of the dollar, and hence implies higher spot and forward values of the dollar.

The 5-year forward dollar appreciated by nearly 25 percent against the mark between mid-January and mid-June of 1981, and by another 5 percent through mid-August. Under the assumptions that the real exchange rate was expected to converge to its equilibrium level within 5-years and that expectations were rational, how much of the appreciation can plausibly be associated with revisions in each of the three expectational terms in the

accounting framework?

-41-

It seems difficult to argue that the expected long run real exchange rate was revised substantially in a direction that strengthened the dollar during this period. The monthly and quarterly data on U.S. and German trade and current account flows fluctuated erratically but did not appear to reveal any persistant surprises. Perhaps the Reagan program was perceived to have supply-side effects that would allow U.S. businesses to compete more successfully in world markets at any given level of the real exchange rate, tut it is difficult to associate more than a 5 percent appreciation of the dollar with such explanations.

A much larger part of the dollar's appreciation can be associated with revisions in expectations about the long-term inflation differentials. As was shown in Table 2, the Bache survey suggests that the expected 5-year U.S. inflation rate per annum declined by 1.6 percentage points between early October 1980 and early September 1981; the Michigan Survey of Consumer Attitudes suggests a 1.5 percentage point decline between August 1980 and August 1981. Such revisions can "explain" an appreciation of 7-1/2 to 8 percent in the 5-year forward rate. Forecasts of German inflation over al or 2 year horizon were revised upward over the same period by 1 or 2 percentage points per annum, although the increase in German inflation seems generally to have been viewed as transitory. Thus, revisions in long-term German inflation expectetions may also have "explained" as much as a 7-1/2 percentage appreciation of the 5-year forward dollar, but not much more.

The accounting arithmetic associates the remaining 10 percent appreciation of the dollar with revisions in the expected 5 -year premium for bearing exchange risk. Is this plausible? To the extent that investors

are not: rational optimizers, a 10 percentage point change in the risk premium

-~42-

would have no meaning beyond that of a residual in the accounting framework, and the question of plausibility would not be meaningful. To the extent that investors do optimize, section VII has argued that a 2 percentage point change in the risk premium is plausible, based on an oversimplified representation of the portfolio optimization problem. It is an open question whether a better analytic framework and a reassessment of parameter values could establish the plausibility of a 10 percentage point change in tne risk premium.

The point that seems most clear about the behavior of the mark/ dollar rate during 1981, as has been illustrated in Figure 3, is that shifts in the fiscal policy out look were a major component of the news.1° This has important implications for how the news of 1981 must be quantified if regression analysis is to be useful for telling the story and helping to separate the effects that were channeled through inflation expectations from the effects channeled through the risk premium. Some commonlyemployed methods for capturing revisions in expectations are inadequate for the 1981 experience. In particular, long-term inflation expectations cannot be adequately represented by long-term nominal interest rates; longterm dollar interest rates rose by one percentage point from late January to mid-February and by another percentage point from late April to mid-May, while the fiscal policy news presumably led to donward revisions in U.S. long-term inflation expectations. Moreover, the fiscal policy news was not accompanied by contemporaneous jumps in price levels, activity variables, monetary aggregates or budget deficits, so that structural or autoregressive models of expectaticns based on current and historically observed

data are inadequate. Thus, to adequately capture the revisions in long-

-43-

term inflation expectations would seem to require either a time series of direct survey evidence on inflation expectations or at least a crude time series of future budget expectations or projections. And a crude time

series on the budget outlook also seems to be required if regression analysis is to have any hope. of adequately capturing revisions in the risk premium.

X. Summary

The evidence is clear that empirical exchange-rate models of the Seventies provide poor explanations of exchange rate behavior out of sample; see Meese and Rogoff (1981, 1983). Such evidence is not surprising in view of the limited attempts that have been made to model the news, given the strong presumption that exchange rate movements are predominantly unexpected, or equivalently, are predominantly a reflection of revisions in expectations in response to news; see Mussa (1979).

The first part of this paper has developed a framework of approximate accounting identities that describe observable spot and forward exchange rates in terms of three expectational terms: . an expected long-run real exchange rate, an expected long-term inflation differential and an expected premium for bearing exchange risk. Under the commonly-adopted assumptions of time invariant expectations of the long run real exchange rate (PPP level) and the risk premium, it is evident from the accounting framework that the substaitial historical short-run variability of observed spot exchange rates can only be explained by the hypothesis that expectations about long-term inflation differentials have varied substantially relative to observed long-term nominal interest differentials. This point raises the quest ion of how long real interest differentials are expected to persist, and some limit-

ed evidence has been presented suggesting that the answer is longer than 2

-44years but perhaps no longer than 5 years. An implication is that during periods in which the term structure of nominal interest differentials changes shape, exchange rate movements may be highly correlated with changes in long-term interest differentials but not as highly correlated with changes in short-term interest differentials, other things equal, which challenges the tradition of modelling exchange rates in terms of short-term interest differentials.

In principle, all three of the expectational terms in the accounting framework should be treated as variables -- or transmission channels for the news -- and the second part of the paper has discussed some issues in modelling expectations of the long-run real exchange rate, the long-term inflation differential and the long-term risk premium. The third part of the paper has discussed the major observed swings in mark/dollar exchange. rates (spot and 5-year forward) during 1980-81, using the accounting framework to draw inferences and conjectures on the extent to which revisions in each of the three expectational terms "explained" the exchange-rate movements. The following summary points have been argued.

It is difficult to model the long-run real exchange rate without some notion of a constraint on the long-run balance of payments; but given an hypothesis about the specific nature of the long run balance-of -payments constraint, it is straightforward conceptually to model how expectations of the long-run real exchange rate (or PPP level) are revised rationally in response to news that revises expectations about whatever variables or parameter values enter the long-run balance of payments constraint.

Quantitative discussions of exchange rate volatility can benefit from focussing on the length of the horizon over which real interest differen-

tails are expected to persist, or on the related question of how long it is

-45-

expected to take the real exchange rate to converge to its long run level.

If it is expected to take T years for the real exchange rate to converge to its long-run level, then the percentage change in the spot exchange rate that should be associated with a shift in the term structure of nominal interest different:iials, other things equal, is roughly T times the percentage-point per annum change in the T-year interest differential.

During 1981, major swings in the exchange value of the dollar coincided strikingly with major shifts in the outlook for U.S. budget deficits. The fiscal policy news may have been transmitted to the long-term forward rate through both revisions in long-term U.S. inflation expectations and changes in the expected premium for bearing exchange risk. Long-term nominal dollar interest rates did not move in the same direction as long-term U.S. inflation expectations in response to the fiscal policy news, nor was the fiscal policy news accompanied by contemporaneous jumps in prices, activity levels, money supplies or budget deficits. Accordingly, the influence of fiscal policy news on inflation expectations cannot be captured adequately without either survey measures of long-term inflation expectations or nodels linking inflation expectations to measures of expected future budget deficits (and/or money supplies) that are not generated from autoregressions.

Available survey data on long-term U.S. inflation expectations suggest that a major part of the fiscal policy news during 1981 was transmitted to the exchange rate through revisions in expected long-term inflation differentials. There is also a reasonable presumption, however, that the 5year risk premium "explained" changes of at least 2 percent in mark/dollar

exchange rates in response to swings of at least $100 billion in the

~46expected cumulative flow of U.S. budget deficits over a 5-year horizon. The sequence of budget news that arrived during 1981 May provide enough shortrun variability in asset-stock variables to capture the risk premium with a structural model, but existing structural models must first be refast.ioned into a rational-expectations framework that looks forward at expectec. future asset stocks. Moreover, autoregressive models are inadequate for capturing revision in expectations about future asset stocks in.response to the fiscal policy news that arrived during 1981.

A final point is that news about prices, activity, the balance of payments, the stance of monetary policy and most other classes of variables that enter exchange rate models is transmitted through multiple indicators drawn from each class of variable. Extracting news from pools of indicators enables market participants to filter out noise and to obtain more frequent observations, and econometric techniques that did likewise might prove more

efficient.

-47- Appendix: The Accounting Framework as a Basis for Forecasting

There is an analogy between explaining the observed behavior of exchange trates ex post and forecasting exchange rates ex ante in a context in which changes in exchange rates are associated with revisions in expectations in response to "news". The ex post problem is to test a structural equation ising either direct or proxy measures of expectations or behavioral models of how expectations respond to the news. The ex ante problem requires predictions of how much expectations will be revised in response to the news.

A forecasting methodology can be illustrated using the accounting framework and focussing on the risk neutral case for simplification. It is necessary to distinguish between “average market expectations" held at time t,E., and the forecaster's expectations or predictions at time t,E. It is also useful to define

(18) EAE. 417 EEL “7 BEL

where the forecaster may or may not be able to observe E. at time t. Condition (9) of the accounting framework, under the maintained assumption of risk neutrality, implies

B A

A B = - _ + ECG P rarey + (r -r) srea] ]

(19) E ttl, t+T t+T

s t ttl A similar condition can be written with E. replacing EY: Combining both of

these conditions with definition (18) and the risk-neutrality assumption

EeSiy = eee? and also using BE Sed = B Sta it can be shown that A B BA (20) EStay 7 fe egy = EAB yg @ Peay + Oa tap + Steal yy]

where T exceeds the length of time that it is expected to take for the real

exchange rate to converge to its long-run equilibrium level. Condition (20)

~48-

states that the time-t fore:ast of the spot rate at horizon t+l, if constrained to be consistent with the accounting framework, will equal the 1period market forward rate at time t adjusted for time-t forecasts of the extent to which "average market expectations" about "explanatory variables" will be revised between times t and t+l. The relevant explanatory veriables are the relative price level at t+l, the (T-1) period real interest differential at t+l and the long-run real exchange rate.

Coming up with numbers to plug into condition (20) as estimates

E (rP_x4y

A B of ECP -P Dia? Fy ttl, t+T

and Esreal |. may require some crude

T sampling and extrapolationof private inflation forecasts. Time-t fore-

casts for nominal interest differentials at ttl are implicit in the observable market yield curves and, together with forecasts of the relative price level and long-term inflation differential, can be used to infer E sreal ip

from condition (19) and the observed 1-period forward rate, f. AL’ The ’

predictions of what market participants will expect next period, the Eee terms, involve more extensive ad hoc assumptions. When the forecaster

is provided with a macroeconomic model, an arbitrary but appealing set of predictions is that market participants as of time t+l will have come to expect the outlook for inflation rates, interest rates and the long-run real exchange rate that the model is predicting at time t.

The latter assumption is particularly appealing in a context in which the model forecaster has more advanced information than other market participants about prospective data releases or policy announcements, but it loses appeal to the extent that it may be unrealistic to assume that mar-

ket participants base their expectations on the same model (or that rarket

participants will come to believe in the forecasting model before the date to

-49which the forecast applies). The forecasting exercise gets. much more complicated once the possibility of two different models is admitted, and. questions then arise about how rapidly the models should be assumed to adjust toward each other (or some true model) in response to forecast errors. Such considerations make clear that it is difficult to avoid some strong ad hoc assumptions in any exchange rate forecasting exercise. Nevertheless, a belief that the structure of an exchange rate equation is correct and that market expectations of variables that "explain" exchange rates are predictably wrong -- or likely to change in a predictable direction -- provides some hope that exchange rate forecasts can be more accurate predictions

than forward rates.

-50-

Footnotes

* I am especially indebted to Michael P. Dooley and Ralph W. Smith for many helpful discussions of issues addressed in this paper. I am also very grateful for constructive criticism received from William A. Allen, Bruce Brittain, Peter B. Clark, Sebastian Edwards, Robert P. Flood, Jeffrey A. Frankel, Dale W. Henderson, Peter Hooper, Kengo Inoue, Alexandre Lamfalussy, Jeffrey Marquardt, Warren D. McClam, Richard A. Meese, John Morton, Kenneth S. Rogoff, Jeffrey R. Shafer, Edwin M. Truman and John R. Wilson. The analysis and opinions of the paper do not necessarily represent the views

of the Federal Reserve Board or the individuals acknowledged above.

1. By constrast, Rodriguez (1980) develops a reduced-form exchange-rate equation for a rational-expectations portfolio-balance framework in which the coefficient on the exchange rate currently expected to prevail at horizon T converges to zero as T approaches infinity. The speed of convergence can be interpreted to depend inversely on the degree of substitutability between assets denominated in domestic and foreign currencies, and the assumption of imperfect substitutability or risk aversion is a necessary condition for the rational expectations assumption to "eliminate" the expected future exchange rate from the model by pushing the future to infinity; see Dooley and Isard (1981b).

2. The tradition of focussing on the relationship between exchange rates and short-term interest differentials partly reflects (and has contributed to) the fact that data on short-term interest rates that are comparable across currencies are more readily available than data on comparable long-term interest rates. The tradition also reflects an infatuation, prior to the development of Eurocurrency markets, with examining the relative behavior of spot and short-term forward exchange rates without providing a theory of the

absolute level of either.

~51- 3. Forecasts of German inflation, typically extending out over 1 to 2 year horizons, were generally revised upward as the mark depreciated against the dollar from October 1980 through mid August 1981.

4, The trends in the 2-5 year nominal interest differentials, computed for the samples of daily Eurocurrency observations and the 12 observations of Treasury differentials, pass the test of being significantly greater than zero with a high degree of confidence.

5. It is important to distinguish between conditional and time-invariant expectations of purchasing power parity -- i.e., between the relatively weak assumption that the expected PPP level can be shocked by new information, and the stronger assumption that the expected level of the long-run real exchange rate is exogenously given.

6. Many models of exchange rate dynamics assume that current account imbalances are "financed" entirely by assets denominated in one particular currency, which essentially amounts to assuming that residents of one of the two countries only hold assets denominated in their home-currency unit; an exception is Henderson and Rogoff (1981). The unrealistic nature of the assumption is not problematic for models such as Mussa (1980) or Dornbusch and Fischer (1980), in which risk neutrality is assumed and the role of wealth is directed through its influence on the excess demand for goods.

The assumption does raise problems, however, for interpreting the class of empirical portfolio balance models represented by Branson, Halttunen and Masson (1977, 1979), Porter (1979) and Martin and Masson (1979) , in wnich measures of portfolio stock variables have been constructed by equating net holdings of foreign-currency denominated assets to cumulative current account

imbalances (in some cases adjusted for direct investment flows).

-52-

7. %It is not being assumed that balance of payments fluctuations are expected to never occur, but rather that the ex ante subjectivé probability distribution of the balance of payments (over any interval after the long run is reached) has a zero mean.

8. Dooley and Shafer (1976) have computed average profit rates, over and above opportunity cost and transactions charges, that investors could have earned during recent years by using filter rules to operate speculative positions in the foreign exchange markets. These ex post measures lend support to the notion of risk premiums on the order of several percentage points per annum.

9. Dooley and Isard (1982) have estimated a rational expectations portfolio-balance model of the exchange rate which explicitly incorporates

the influence of the expected future paths of asset stocks and wealth variables on the risk premium, but which uses autoregressive representations of the expected future stocks of assets and wealths.

10. The 5-year forward rate is constructed from interest rates on fixedterm 5 year Eurodollar and Euromark deposits, as collected by the Bank of America and made available through Data Resources Inc. Similar interest rate data are available for 5-year Eurodeposits in Dutch guiders, Swiss francs and French francs. The data have two notable limitations. Markets are thin and on some days deposits are not transacted in each currency.

In addition, to the extent that the term structures of dollar and mark interest rates are not flat, the data allow only on approximate const::uction of 5-year forward rates, since interest on the 5-year deposits is paid at the end of each year. The price adjustment is achieved by assuming that the change in relative price levels over the 5-month period occurred at a con-

stant rate; i.e., the price adjusted forward rate is the forward rate adjusted

-53for the trend in relative price levels, which was taken to. be 7-1/2 percent at an armual rate during the first half of 1980. 11. Two sets of survey data are available on long-term U.S. inflation expectaticns. During each February beginning in 1975 the Michigan Survey of Consumer Attitudes has sampled answers to the question: "About what per~ cent per year to do you think prices will be (up/down) on the average during the next 5 to 10 years?" Beginnning in 1980 the question has also been asked during August. A second set of data has been collected quarterly by Bache beginning in mid-1980; see Table 2, note b. 12. With the exception of Fellner (1979), few models of exchange rate determination have focussed explicitly on the arithmetic of compounding interest rates and expected inflation rates over a long-term horizon. 13. This statement ignores covariance in implicitly viewing the nominal forward rate as the product of the expected ratio of price levels (or inflation factors), the expected real value of the future spot rate, and a risk factor. The 5-year forward rate is not adjusted for relative price trend, which was quantitatively minor during the period. 14. Even though Carter's predicted shares of the national and electoral votes edged up between early October and the Carter-Reagan debate on October 28, the fact that time was running out appears to have progressively reduced the perceived probability of a Carter victory. 15. The activity surprise may have generated a downward revision in longterm U.S. inflation expectations. (This hypothesis would be consistent with the Bache data in Table 2 if U.S. inflation expectations had been revised upward during September.) In addition, expectations of the long-run real

value of the dollar might conceivably have been revised upward during November

-54in response to the activity announcements, consistent with the behavioral model suggested by condition (16).

16. When the unexpected components of week-to-week changes in monetary aggregates are integrated over 1981, it is not clear that the net changes provided any significant news. Alternatively stated, the below target growth of adjusted M1~B and the above target growth of M2 can be viewed to suggest that monetary policy, on balance, was neither easier nor tighter than expected over the period as a whole. This is not to suggest that monetary policy had no influence on exchange rates. The dollar would have been weaker had the Federal Reserve pursued higher monetary growth targets; and dollar exchange rates did in fact fluctuate week-to-week in response to surprises about the weekly money supply numbers. The suggestion that on balance there was no surprise about U.S. monetary growth, moreover, does not imply that there was

no surprise about the path of dollar interest rates.

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