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Comovements of budget deficits, exchange rates, and outputs of traded and non-traded goods.

I. INTRODUCTION

The total United States budget deficit was roughly zero at the beginning of 1981. After some ups and downs, the deficit reached $140 billion in early 1985 and remained high compared to deficit levels experienced in peacetime years prior to 1981. During the period 1981-1985, the U.S. dollar appreciated sharply relative to foreign currencies in both nominal and real terms. The current account of the U.S. balance of payments moved from a surplus of $6.0 billion in 1981 into a series of large, recurrent deficits reaching an annual rate of $120 billion by mid-1985.

The simultaneous occurrence of these events suggests that budget deficits cause a country's currency to appreciate which in turn reduces the country's "international competitiveness." Stories are reported in the popular financial press and conventional wisdom is used to link these events. Using the identities of national income accounts, it is shown that budget deficits must crowd out domestic spending by raising the domestic saving-investment gap. In addition, the deficits can be financed by the rest of the world through the generation of a deficit in the current account of the balance of payments. Typically it is argued that the rise in the rate of interest and real appreciation of the dollar are necessary in order to bring about the saving-investment gap and the current account deficit needed to finance the large U.S. budget deficits.

This paper attempts to provide an alternative structural explanation of these comovements in exchange rates and government budget deficits. My model expands on previous work to include fiscal policy considerations in a stochastic setup. It shows that within a simple two-country cash-in-advance constraint model it is possible to have a positive correlation between increases in the budget deficit and exchange rate appreciation. Additionally, it is possible to have a negative correlation between exchange rate appreciation and a reduction in domestic traded goods production. The implication, then, is that the usual "twin deficits" argument about the linkages between budget deficits, exchange rates and trade deficits is only one of a number of possible explanations of the correlations that appear in the data of the 1980s.

The model I have used in this paper is (as far as I know) the first international general-equilibrium-monetary asset-pricing model with endogenous budget deficits. Most of the explanations that relate exchange rates and the federal government's budget deficit or the trade deficit are based on a particular disequilibrium theory of exchange rates. The model of this paper, however, is based on an equilibrium model of exchange rates. It is based on simple economic principles. It uses the national accounts definition of the government's nominal budget deficit as an increase in the dollar value of the government's holdings of money and bonds. A change in the domestic productivity of traded goods and the money supply yields a change in both the nominal price of bonds and the government budget deficit. A change in the supply of domestically produced traded goods also yields changes in their relative price (the real exchange rate). Repeated disturbances to the supply of traded goods and the money supply create a correlation between budget deficits and real exchange rates.

Recently Branson and Love |1988~ and Ceglowski |1989~, among others, blame the real exchange rate as the primary cause of U.S. industries' weak performance in the 1980s. It is important to realize the real exchange rate itself is an endogenous variable. Its behavior, as I will show, is a result of underlying economic changes. Hence, it is incorrect to blame decreased U.S. competitiveness on the real exchange rate. Moreover, most popular models which presume a relationship between budget deficits and real exchange rates attribute no role to the monetary sector. This paper demonstrates the importance of bringing both monetary and real sectors into the model in order to analyze such relationships.

The rest of the paper is organized as follows. Section II presents some preliminary empirical results for the period 1974:I-1989:II. In particular, it reports correlation and regression results regarding budget deficits, the real exchange rate and the outputs of traded and non-traded goods. Section III reviews some of the conventional wisdom often cited in policy discussions and the popular press as explanations of reduced U.S. competitiveness in world markets. The analysis focuses on the federal budget deficit, which is viewed as the major driving force behind the appreciation of the U.S. dollar. This, in turn, is thought to be a cause of reduced U.S. competitiveness. In section IV, I discuss a dynamic economic model that could explain the correlation between dollar appreciation and increases in the U.S. budget deficit. The model is a version of the much-used Lucas |1982~ model for pricing international financial assets. Conclusions are discussed in section V.

II. SOME CORRELATION AND REGRESSION RESULTS

The central point of Feldstein's |1986~ article is to present empirical evidence in support of the view that budget deficits cause a currency to appreciate. He regresses the real exchange rate between the U.S. and Germany on a measure of the budget deficit in the United States and a set of other variables. For the period 1973 to 1984 (twelve annual observations), he finds that the estimated effects on the real exchange rate are strong and robust to the inclusion or exclusion of other variables. Branson and Love |1988~, on the other hand, outline a theory that assumes that the movements in the nominal exchange rate cause movements in the real exchange rate. These, in turn, cause movements in the supply of (tradable and non-tradable) output and employment and, hence, the trade balance. Their empirical results indicate that appreciation of dollar over the period 1970:I-1986:I caused a large unemployment loss in manufacturing. They do not find any significant employment loss in the U.S. non-traded goods sectors. This evidence is part of the basis for the story relating U.S. budget deficits and the appreciation of the dollar and the dollar's appreciation and U.S. competitiveness.

This section presents some more empirical evidence on these correlations. The data run from 1974:I to 1989:II.(1) The upper portion of Table I reports correlations between the real exchange rate, |rho~ = E|P.sub.G~/|P.sub.US~ (where e is the nominal exchange rate, i.e., the dollar price of deutsche marks, |P.sub.G~ (|P.sub.US~) is the CPI for Germany (the U.S.)), and different measures of budget deficits, |D.sub.i~, and between the real exchange rate and outputs of traded (x) and non-traded (z) goods.(2) Four different measures of budget deficits are used. |D.sub.1~ is the opposite of the federal nominal deficit (GGFNET) series from the National Income and Product Accounts. The variable GGFNET is simply receipts minus outlays. Thus |D.sub.1~ = -GGFNET is the difference between federal outlays and receipts. The variable |D.sub.2~ is |D.sub.1~ divided by the GNP and |D.sub.3~ is |D.sub.1~ divided by GNP deflator. Finally, |D.sub.4~ = (MVF|D.sub.t~ / |GD.sub.t~ - MVF|D.sub.t - 1~ / |GD.sub.t - 1~), where MVFD is the nominal market value of gross federal debt (end of period) and GD is the GNP deflator.(3) Thus, |D.sub.4~ is a proper measure of a real deficit. Note that the way the real exchange rate is defined, an increase in |rho~ means a dollar depreciation and a decrease in |rho~ means a dollar appreciation. Therefore, if increases in the budget deficit and the appreciation of the dollar are positively correlated, we would expect, in the present context, a negative correlation between |rho~ and |D.sub.1~. Such a negative correlation is also expected between |rho~ and other measures of budget deficits, but |rho~ and |chi~ should be positively correlated. In other words, a reduction in domestic traded goods production and a real exchange rate appreciation are expected to be negatively correlated.

The results reported in row one at the top of Table I are correlations between the levels of variables. The correlation coefficient between |rho~, the real exchange rate, and |D.sub.i~, the budget deficit, has the expected negative sign, and all these correlations are highly statistically significant. The correlation between |rho~ and |chi~ (traded goods) has an incorrect sign and is statistically insignificant. However, I have serious doubts about the validity of the significance levels reported in row 1. After all, it is by now well known that there is TABULAR DATA OMITTED a presumption that economic variables are integrated of order one. If so, the marginal significance levels reported in row 1 are grossly inflated. Indeed, most of the variables reported in Table I are found to be non-stationary for the sample period.(4) In this case it is more appropriate to calculate and report the correlations between changes in the variables. The results reported in row 2 at the top of Table I are correlations between changes in the variables. It is seen that, except for |delta~|D.sub.4~, measures of changes in the deficit are significantly correlated with the changes in the real exchange rate.(5) However, one surprising aspect of the correlations between changes in the real exchange rate and the deficit is that they are all positive, contrary to expectation.

Table I also contains some regression results. Equation (i) of Table I presents the least-squares estimates of the real exchange rate equation. The only independent variable considered in the real exchange rate equation (i) is the |D.sub.2~ measure of the budget deficit--the deficit as a percentage of GNP. The change in the budget deficit variable (|delta~|D.sub.2~) includes the current plus two quarters of lags. Residual serial correlation is not a problem for the estimated equations (i)-(iii), as measured by the Durbin-Watson (D-W) statistics or by more appropriate direct estimation of an autoregressive process of the error term. Equation (i) indicates significant effects of current and two-quarter lagged budget deficits. Additional lagged terms, considered out as far as six quarters, were individually and jointly insignificant in the real exchange rate equation. The estimated coefficient on the |delta~|D.sub.2, t~ variable is positive. However, the estimated coefficients on the |delta~|D.sub.2, t - 1~ and |delta~|D.sub.2, t - 2~ variables have the expected negative signs. Note that the sum of current and all lagged coefficients is negative and the F-value for the joint hypothesis that all three |delta~|D.sub.2~ coefficients are zero is 4.30, which exceeds the 1 percent critical value of 4.16. The real exchange rate regression equations were also run three times, each time using a different measure of the budget deficits as the independent variable. Equations with |delta~|D.sub.1~ (the simple deficit) and |delta~|D.sub.3~ (the deficit divided by the GNP deflator) had similar results as presented in equation (i). For the equation with |delta~|D.sub.4~ (the change in the market value of federal debt) as the independent variable, the estimated coefficients on the |delta~|D.sub.4~ variable were neither individually nor jointly significant at the standard levels of significance.

Row 2 in the top portion of Table I also contains the results of the correlation between changes in the real exchange rate and changes in the outputs of tradables and non-tradables. It is seen that the changes in the output of tradables and non-tradables are not statistically significantly correlated with the changes in the real exchange rate. Moreover, it is seen that the correlation between changes in the real exchange rate and changes in traded goods is negative which contradicts the stylized fact mentioned above. The lower portion of Table I presents the regression estimates of the output equations of traded and non-traded goods. Equations (ii) and (iii) include a secular trend variable, t, the relative price of energy, E (a structural variable), the unemployment rate, U (a cyclical variable) and the real exchange rate.(6) These equations were also tried with additional lagged terms on |delta~E, |delta~U, and |delta~|rho~ not reported in Table I. These additional lagged terms were not only individually insignificant in the output equations but also worsened the fit of these equations as measured by adjusted |R.sup.2~. The estimated output equation (ii) for traded goods shows that the estimated coefficients on the |delta~|rho~ variables are (individually) statistically significant only at the 12 to 13 percent level. However, the F-statistic testing the null hypothesis that the current and lagged exchange rate variables do not affect the output of traded goods is 2.74, resulting in the rejection of the null hypothesis at about the 5 percent level. Moreover, the sum of the estimated coefficients on the three exchange rate variables is positive, as predicted by the theory.(7) Finally, the estimated output equation (iii) for non-tradables indicates that only the estimated coefficient on the |delta~||rho~.sub.t-5~ variable is statistically significant at the 3 percent level. The F-statistic testing the hypothesis that the six current and lagged exchange rate variables do not affect the output of non-tradables is 1.6, which can not be rejected even at the 15 percent level.(8)

III. CONVENTIONAL WISDOM

In this section I briefly discuss some of the popular stories told to describe the events in the first half of the 1980s.(9) The most popular story is based on the national income identity.

The GNP identity that constraints flows in the economy is

GNP = C + I + G + NX = C + S + T

where C, I, G, NX, S, and T denote consumer expenditures, gross domestic investment, government purchases of goods and services, net exports of goods and services, gross private domestic saving, and tax revenue. All flows are in real terms. This can be rewritten as a version of the flow-of-funds identity:

(1) (G - T) = (S - I) - NX.

Equation (1) says that the total government deficit must equal the sum of the excess domestic private saving less net exports.

According to conventional macroeconomic theory, given income, net exports depend positively on the real exchange rate, eP*/P (where e is the nominal exchange rate, i.e., dollars per unit of foreign exchange, and P*(P) is the foreign (domestic) price level), and (S - I) depends positively on the real interest rate. The endogenous adjustments that would reduce net exports (NX) and increase net savings (S - I) are a decrease in the real exchange rate and an increase in the real interest rate. Some combination of these changes would restore balance in equation (1), given an exogenous increase in the government's budget deficit (G - T).(10) The national income view of the short-run adjustment mechanism can, of course, be related to the more popular story involving capital flows. Identity (1) can be written as

(2) G - T = (S- I) - NFI = (S - I) + NFB

where NFI and NFB (= -NFI) denote net foreign investment by the U.S. and net foreign borrowing, respectively. Equation (2) says that an increase in the deficit must be financed either by an increase in domestic savings or an increase in net foreign borrowing (decrease in net foreign investment). The shift in the deficit raises the U.S. interest rate, increasing S - I. The high interest rates attract foreign capital or lead to a reduction in U.S. lending abroad, appreciating the dollar. The process continues, with the interest rate increasing and the real exchange rate falling, until the increase in excess saving and the current account deficit add up to the originating shift in the deficit.

This brings us to early 1985. At the time Branson |1985~ wrote his article, the dollar had already started to decline. He argues that the decline of the dollar can be explained in terms of expectations. The continuous accumulation of debt in the future, he argues, would raise the current risk premia and would thereby have induced a dollar depreciation.

IV. AN ALTERNATIVE EXPLANATION

Now I turn to a theory which provides an alternative structural explanation of the correlations found in recent data. I demonstrate that the empirical results are consistent with the implications of this model. The model is based on earlier works by Stockman |1980~, Helpman |1981~, and Lucas |1982~. Non-traded goods are introduced into the framework by Stockman and Dellas |1989~. The Helpman model is deterministic, and he and Stockman and Dellas do not discuss the issues related to budget deficits.

The Model

There are two countries, home and foreign, each with an equal number of infinitely lived representative households. At the beginning of each period t households in the home country receive an endowment of |x.sub.t~ units of traded goods X, and |z.sub.t~ units of non-traded good Z, while households in the foreign country receive |y.sub.t~ units of traded good Y and |z.sub.t*~ unit of non-traded good Z*. All four goods are perishable.

Each country has its own money. Let home and foreign money supplies be denoted by |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ respectively. The rate of money growth will be denoted by

|Mathematical Expression Omitted~,

where ||omega~.sub.t~ and ||omega~.sub.t*~ are assumed to be independently and identically distributed. Money is introduced into the households' optimization problem through cash-in-advance constraints. In each period t, households trade moneys, assets, and goods in particular ways. The timing of the trades follows Lucas's |1982~ model. Each period consists of two subperiods of asset and product market trades. Asset market trade (where currencies and assets are traded) is followed by product market trade. The cash-in-advance constraints require that goods purchased in the period t product market be paid for with money that is carried into those markets from the period t asset market. Money may be acquired during the period t asset market or may be carried over from the previous period. Money acquired from selling goods during the period t product market is not collected until the end of the period and cannot be used for purchases until t + 1. I assume purchases of the home country's goods are paid for with the home country's money; purchases of the foreign country's goods are paid for with the foreign country's money. The assets are one-period state-contingent nominal claims and are available in all currencies. Taxes are paid to the government at the beginning of each period's asset market trade.

Let |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ denote quantities of home and foreign money that the representative household in the home country carries into the period t product market. This money is carried over from period t - 1 and/or acquired from period t's asset market. The household purchases |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ units of two traded goods and |Mathematical Expression Omitted~ units of non-traded goods. Purchases of these goods at the period t product market are constrained by the cash-in-advance constraints (3) and (4).

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where |P.sub.xt~ and |P.sub.zt~ are the nominal prices of X and Z in terms of home money, M, and |P.sub.yt~ and |P.sub.z*t~ are the nominal prices of Y and Z* in terms of foreign money, N.

Let B(|s.sub.t + 1~) and B*(|s.sub.t + 1~ denote the amounts of home and foreign money (nominal bonds) that the home agent purchased at time t asset market for delivery at the time t + 1 asset market conditional on the state being |s.sub.t + 1~. The state vector will be specified shortly. Let |e.sub.t~ be the nominal exchange rate (the price of N in terms of M). Then the home agent's budget constraint as he enters the period t asset market is

|Mathematical Expression Omitted~

where |W.sub.t~ is total nominal wealth in period t. In (5), |P.sub.B~(|s.sub.t + 1~, |s.sub.t~ is the nominal pricing function associated with the home money. It provides the present values in terms of home money at time t in state |s.sub.t~ of promises to state contingent assets of home money at time t + 1 given that state |s.sub.t + 1~ occurs. |P.sub.B*~(|s.sub.t + 1~, |s.sub.t~) is similarly interpreted for foreign money. |W.sub.t~ is constructed as follows. The household enters the asset market with (|P.sub.xt - 1~|x.sub.t - 1~ + |P.sub.zt - 1~|z.sub.t - 1~ units of home currency collected from the sale of goods in the t - 1 goods market and |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ units of unspent cash. It then pays ||tau~.sub.t~ units of home money in taxes to the home government and collects B(|s.sub.t~) and B*(|s.sub.t~) units of home and foreign currencies. The household's total nominal wealth is then given by

|Mathematical Expression Omitted~

The government of each country buys some of that country's goods in the competitive market for each good. Let |g.sub.t~ be total real government expenditures and assume that spending on each good follows a stochastic process:

|Mathematical Expression Omitted~

and each ||theta~.sub.it~ is assumed to be independently and identically distributed with support between zero and one. Let |Mathematical Expression Omitted~ be the home government's home money holdings. The home government's goods market constraint is

|Mathematical Expression Omitted~

Let |Mathematical Expression Omitted~ be the amount of home currency that the home government promises in period t - 1 to pay at time t contingent on the state of the world being |s.sub.t~ = (|x.sub.t~, |y.sub.t~, |z.sub.t~, |z.sub.t*~, ||theta~.sub.xt~, ||theta~.sub.yt~, ||theta~.sub.zt~, ||theta~.sub.zt*~, ||omega~.sub.t~, ||omega~.sub.t*~. The state vector follows a stochastic process, the outcome of which is known at the beginning of the period. Taxes are paid to the government at the asset market each period in the currency issued by the government. The home government's flow budget constraint is therefore

|Mathematical Expression Omitted~

The sequence of flow budget constraint (7) fully characterizes the constraints on government behavior if the intertemporal budget constraint (8) is satisfied.

|Mathematical Expression Omitted~

In (8) the product operator is defined by

|Mathematical Expression Omitted~

and it is assumed to be one if i |is less than~ k. Since the nominal bond payments, |Mathematical Expression Omitted~, are predetermined in period t, and because the time series of government spending and money creation are assumed to be exogenous, the intertemporal government budget constraint restricts the path of debt and taxes.

The representative home household chooses consumption and end-of-period assets to maximize

|Mathematical Expression Omitted~

subject to (3), (4) and (5). Following Helpman |1981~ and Lucas |1982~, I concentrate on the equilibrium in which the one-period nominal interest rate in each currency is positive. In this case there is an interest cost to choosing |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ larger than |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~, while there is no corresponding benefit. Thus (3) and (4) will hold as an equality and will be substituted in (5), and this new constraint will be labeled as |Mathematical Expression Omitted~. The value function of the home household's problem is then

|Mathematical Expression Omitted~

where the maximization is over current choices of consumption of three goods and new holdings of assets (bonds) and is subject to |Mathematical Expression Omitted~. The first-order conditions for this maximization problem are

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where ||lambda~.sub.t~ is the multiplier on the period t budget constraint given by |Mathematical Expression Omitted~. In (10) and (11) the partial derivative of the period utility function with respect to its ith argument is denoted by |U.sub.i~, i = 1, 2. |V.sub.1~ denotes the derivative of the utility function V with respect to its only argument. There is an analogous optimization problem for the representative agent in the foreign country, which maximizes

|Mathematical Expression Omitted~

subject to the foreign analogs of (3) to (5). The discount rate is assumed to be equal across countries as is the function U. However, tastes for non-traded goods may differ across countries. The foreign government is also constrained by the foreign analog of (6) to (8).

The interpretation of equations (10) to (12) is straightforward. Equations (13) and (14) involve the purchase of state-contingent government bonds or purchase and delivery of state-contingent monies in the next asset market. Consider equation (13). If a unit of home money to be delivered in a particular state |s.sub.t + 1~ is purchased today, the nominal price is |P.sub.B~(|s.sub.t + 1~, |s.sub.t~), and the price expressed in terms of home money times the marginal value of nominal wealth is the marginal utility cost to the asset holder. The value received in return is the marginal value of the unit of home money conditional on the realization of the particular state times the marginal utility of wealth in that state times the probability of that state being realized. Equation (14) has an analogous interpretation. These equations must hold for all possible future states.

Equilibrium requires that world demand and world supply be equated for the traded goods X and Y and for all assets, and that demands and supplies within each country for non-traded goods Z and Z* be equated. The assumption of positive nominal interest rates yields a fixed transactions velocity of money:(11)

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

Lucas considers an equilibrium without non-traded goods where consumption of traded goods is equal across countries. Here, following Stockman and Dellas |1989~, domestic private consumption is assumed to be |Mathematical Expression Omitted~ and foreign private consumption is assumed to be |Mathematical Expression Omitted~, where |Mathematical Expression Omitted~, and h |is an element of~ (0, 1) and the utility function is homothetic. Nominal prices of goods are

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~, i = 1, 2, and |Mathematical Expression Omitted~ are evaluated at equilibrium domestic consumption, and |Mathematical Expression Omitted~, i = 1, 2, and |Mathematical Expression Omitted~ are evaluated at equilibrium foreign consumption. The nominal exchange rate is given by

|Mathematical Expression Omitted~

The second expression in (19) makes it clear that the relative prices of non-traded goods in each country in terms of that country's export good, |Mathematical Expression Omitted~ and |V.sub.1~/|U.sub.1~ (= |P.sub.z~/|P.sub.x~) and the terms of trade, |U.sub.2~/|U.sub.1~ (= e|P.sub.y~/|P.sub.x~), will affect the exchange rate.

Definitions and Comparative Statics

From (7) the government's nominal budget deficit, |D.sub.t~, can be defined as

|Mathematical Expression Omitted~

which is simply a deviation of government expenditures from taxes. Now using (10), (13), and (15), we can rewrite (20) as

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

From now on I will assume |x.sub.t~, |Y.sub.t~, |z.sub.t~, and |z.sub.t*~ are i.i.d. random variables. That is, |s.sub.t~ is assumed to follow an i.i.d. stochastic process. In that case A in (22) is constant and since |Mathematical Expression Omitted~ is predetermined, the partial derivatives of |D.sub.t~ with respect to ||omega~.sub.t~ and |x.sub.t~ can be written as

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where |GDP.sub.t~ is gross domestic product, |x.sub.t~ + |z.sub.t~|P.sub.zt~/|P.sub.xt~, and |r.sub.x~ is the elasticity of the marginal utility of x evaluated at equilibrium domestic consumption, |Mathematical Expression Omitted~, i.e.,

|Mathematical Expression Omitted~

Expression (23) shows that an increase in home monetary growth, ||omega~.sub.t~, unambiguously raises the budget deficit. From the definition of the nominal deficit, we can think of the government as an issuer of money and bonds--rather than a holder of these assets. Therefore, an increase in money and bonds means the government is dissaving. Hence, the term budget deficit simply refers to this dissaving. Equation (23) shows that an increase in home money directly increases the home government's dissaving. It clearly indicates the movements in the U.S. deficit of the 1980s could, in part, be attributed to the actual fluctuations in the money stock.(12) Note, there is another component in (23) that also contributes to a higher deficit. The nominal price (present values) of bonds is negatively related to the marginal utility of nominal wealth which is reduced from an increase in ||omega~.sub.t~. Thus, an increase in ||omega~.sub.t~ raises the price of nominal bonds and with it creates a higher deficit.

Expression (24) shows that an increase in current home traded goods has an ambiguous effect on the budget deficit. |D.sub.t~ is the nominal deficit, and since |Mathematical Expression Omitted~ is predetermined there is no revaluation effect. A change in |x.sub.t~ changes the marginal utility of nominal wealth, and hence changes the nominal prices of bonds. The exact effect depends on the elasticity of the marginal utility of home traded goods, |r.sub.x~.

I define the real deficit, |d.sub.t~, in terms of home traded goods as

|d.sub.t~ |is equivalent to~ |D.sub.t~/|P.sub.xt~.

The derivative of |d.sub.t~, with respect to |x.sub.t~ is then

|Mathematical Expression Omitted~

which is more complicated than expression (24). This complication arises through the revaluation of the existing debt in terms of home traded goods. Here |s.sub.x~ is the share of production of the traded good X in the home country's gross domestic product, |x.sub.t~/|GDP.sub.t~.

The real exchange rate (to be consistent with empirical measure), defined as the relative price of foreign goods in terms of the home goods, is

|Mathematical Expression Omitted~

The derivatives of ||rho~.sub.t~ with respect to |x.sub.t~ and ||omega~.sub.t~ are

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

Equation (27) indicates that an increase in the supply of domestic traded goods raises (lowers) the relative price of foreign (domestic) goods and thereby, as observed in equation (19), also depreciates the domestic currency (raises e). An increase (decrease) in |rho~ means depreciation (appreciation) of the real exchange rate. Thus, an increase in home traded goods depreciates the real exchange rate.

Uncertainly and Covariances

Now I will discuss the stochastic behavior of the budget deficit, the exchange rate and terms of trade in this model. Consider a world in which the sources of uncertainty are in home output of traded goods, |x.sub.t~ and home monetary growth, ||omega~.sub.t~. Then the approximate covariance between the real exchange rate, ||rho~.sub.t~, and nominal budget deficit is(13)

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~ is the variance of |chi~ and ||sigma~.sub.|chi~|omega~~ is the covariance between |chi~ and |omega~. Note from (29) the term |Mathematical Expression Omitted~ drops out, because ||rho~.sub.|omega~~ = 0. Now using (23), (24), and (27), one may write (29) as

|Mathematical Expression Omitted~

Equation (30) shows the sign of the cov(|rho~, D) is ambiguous. To get a feel for it, suppose the shock is only in |x.sub.t~. Then the second term in the bracket drops out and the cov(|rho~, D) is negative if |r.sub.x~ |is less than~ 1. This means real exchange rates are negatively correlated with budget deficits. An increase in home traded output reduces its relative price in terms of foreign goods (i.e., the real exchange rate (|rho~) as defined here increases) at the same time it reduces its nominal price if |r.sub.x~ |is less than~ 1. It also reduces the marginal utility, |U.sub.1~. However, the reduction in marginal utility is less than the reduction in |P.sub.xt~; as a result the marginal utility of nominal wealth, ||lambda~.sub.t~, increases when |r.sub.x~ |is less than~ 1.(14) This means the price of bonds decreases and the budget deficit decreases. Therefore, the budget deficit is negatively correlated with the real exchange rate. Note, the way the real exchange is defined, this implies increases in the budget deficit are positively correlated with exchange rate appreciation.

Now suppose the economy experiences shocks in both output of traded goods and the money supply. Assume the cov(|omega~, |chi~) is negative. We again have a negative covariance between nominal budget deficits and the real exchange rate if |r.sub.x~ |is less than~ 1, since the second term in the bracket is unambiguously positive. The implications of this result are more interesting in terms of recent events. First of all, one of the most popular stories, as advanced by Branson |1985~, about the events of the 1980s is based on "a simplified real model in which the monetary sector is not even invited to make a guest appearance."(15) Equation (30) shows the monetary and real sectors together might have contributed to the correlation between the appreciation of the dollar and increases in the budget deficit. Intuitively, a positive monetary and a reduced productivity shock in the traded goods sector in the 1980s might have caused the dollar to appreciate. Monetary shocks also directly contributed to the higher deficit. These shocks reduced the marginal utility of nominal wealth, and as a result bond prices increased. Thus, part of the higher deficit was also channeled through the bond markets. Hence variances in the output of traded goods and the money supply created a correlation between dollar appreciation and a higher nominal budget deficit. By following the same path of reasoning, we can also generate observed covariances between real budget deficits and real exchange rates.

One of the stylized facts of the flexible exchange rate period is that nominal exchange rates are highly correlated with real exchange rates.(16) In the appendix I show how the sign of the covariance between changes in the log nominal exchange rate and the nominal budget deficit could be anything depending on the value of |r.sub.x~.

The approximate covariance between the real exchange rate and the supply of home traded goods can be written as

|Mathematical Expression Omitted~

Equation (31) says that the real exchange rate and output of traded goods are positively correlated. This means a decrease in the supply of domestic goods lowers the relative price of foreign goods (|rho~)(i.e., the real exchange rate appreciates). It also appreciates the nominal exchange rate (see appendix).

As we have seen in section II, the relationship between these two variables in recent times is at best tenuous. However, at times if we observe a negative correlation between real exchange rate appreciation and a reduction in the output of traded goods, it would be incorrect to blame, as Branson and Love |1988~ and Ceglowski |1989~ among others do, the real exchange rate as the cause. Stockman |1987, 16~ writes:

An observer, seeing that dollar depreciation is associated with a fall in the relative price of exports and increase in the volume of exports, might conclude that the domestic country had become "more competitive" as a result of the depreciation of the dollar. But this interpretation is confused. The change in the exchange rate does not cause changes in relative prices or the quantity of exports. The change in the exchange rate is itself a result of an underlying economic change which also affects other prices and quantities.

The approximate covariance between the real exchange rate and output of nontraded goods is given by

|Mathematical Expression Omitted~

Even though equation (32) is consistent with the results reported in Table I, one should be very careful in interpreting this result. In this model, the real exchange rate is unaffected by changes in the supply of non-traded goods in either country. This strong result is a consequence of the separable utility function in traded and non-traded goods and does not extend to more general structures.

V. CONCLUSION

During the first half of the 1980s the U.S. experienced a huge budget deficit and a large appreciation of dollar. Conventional textbook stories link these events. Authors then set out models to show that the real appreciation of dollar reduced U.S. competitiveness in the world market.

In this paper I critically evaluate these models and examine whether these views are supported by data. For the period 1974:I to 1989:II, it appears the U.S. budget deficits and real exchange rates are correlated. There is also some sign of a weak association between reductions in the output of traded goods and exchange rate appreciation. I then develop an equilibrium model primarily to demonstrate how the observed correlation between budget deficits and real exchange rates and between the real exchange rate and outputs of traded goods are the implications of this optimizing model. The comovements of the variables, namely, budget deficits, interest rates, and relative prices, are shown to arise from underlying economic shocks such as monetary and/or output shocks.

A formal empirical test of this alternative model remains an open area of research. One possible way to test my model would be to calculate Solow residuals--the percentage changes in output less the percentage changes in inputs, where different inputs are weighted by their factor shares. The hypothesis to be tested is to see whether fluctuations in Solow residuals can explain fluctuations in the real exchange rate, as well as output of traded and non-traded goods.

APPENDIX

This appendix shows how nominal exchange rates and budget deficits are related. Since money growth rates, ||omega~.sub.t~ and ||omega~.sub.t*~ are stationary i.i.d. random variables with same conditional mean, the exchange rate is nonstationary. But changes in its log are stationary:

|Mathematical Expression Omitted~

The derivatives of (ln|e.sub.t~ - ln|e.sub.t - 1~) with respect to ||chi~.sub.t~ and ||omega~.sub.t~ are

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

where to simplify matters further, I have assumed that |U.sub.12~ |is equivalent to~ 0. The approximate covariance between the government's nominal deficit and the change in the log (nominal) exchange rate is

|Mathematical Expression Omitted~

Using (23), (24), (A2) and (A3), it is seen that the sign of the covariance between changes in the log nominal exchange rate and nominal budget deficit could be anything depending on the value of |r.sub.x~. Suppose the economy experiences an isolated shock to ||chi~.sub.t~ then (A4) reduces to

|Mathematical Expression Omitted~

which is unambiguously positive.

DATA APPENDIX

Following quarterly observations from 1974:I to 1989:II are obtained from Citibank tape: GGFNET, federal government surplus or deficit (-); GD, GNP deflator (1982 = 100); GNP, gross national product; CPI (all items); CPI for energy; GYAFF, agriculture, forestry, and fisheries; GYWM, mining; GYMD, durable manufacturing goods; GYMN, nondurable manufacturing goods; GYWC, construction; GYT, transportation; GYC, communication; GYUT, electric, gas, and sanitary services; GYNRW, wholesale trade; GYRR, retail trade; GYFIR, finance, insurance, and real estate; and GYS, services. The unemployment rate is taken from Business Conditions Digest. The nominal exchange rate (U.S. cents per Deutsche mark, AG.134) is taken from the International Financial Statistics tape. The German CPI is taken from (OECD) Main Economic Indicators.

Traded goods were deflated by the GNP deflator. Non-traded goods were deflated by the price of services.

1. The purpose of this section is to establish the stylized facts discussed above about the correlations between the budget deficit and real exchange rate and between the real exchange rate and outputs of traded and non-traded goods. To this end I experimented with different sample periods such as 1970:I to 1989:II, 1980:I to 1989:II, and some other periods. The results presented in Table I seem to be sensitive to different sample periods. For example, for the period 1970:I-1989:II, the marginal significance levels of the correlations are somewhat smaller than those reported in Table I.

2. The traded and non-traded goods indices are constructed using four traded goods--agriculture, forestry, and fisheries, mining, durable and non-durable manufacturing--and eight non-traded goods sectors including finance, insurance, and real estate, transportation, public utilities, wholesale and retail trade, etc. (see the data appendix for details). The overall quantity index for the non-traded goods sector (|z.sub.t~) is obtained as follows:

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~ is the output level of the non-traded goods sector i, |Mathematical Expression Omitted~ is the share in non-traded goods of sector i, and |Mathematical Expression Omitted~ is the share of non-traded goods in total output. The quantity index for the traded goods sector is constructed in a similar fashion.

3. The data on MVFD are kindly provided by Franklin Berger in the office of Michael Cox at the Dallas Fed.

4. I used augmented Dickey-Fuller unit root tests. Test were performed on the following variables: logarithms of the real exchange rate, tradable output, non-tradable output, GNP, |D.sub.4~, and the relative price of energy; three other measures of budget deficits; and the log of the unemployment rate. I could not reject the hypothesis of non-stationarity for any of these variables. The results are not reported here but are available to interested readers upon request.

5. One more measure of the real deficit was used: |D.sub.5~ |is equivalent to~ (MVF|D.sub.t~ + |M.sub.t~)/G|D.sub.t~ - (MVF|D.sub.t - 1~ + |M.sub.t - 1~) / G|D.sub.t - 1~, where M is the M1 definition of money stock. Similar results were obtained as with the |D.sub.4~ measure of the real deficit.

6. The specification of equations (ii) and (iii) is based on the model of Branson and Love |1988~. They derive output (or employment) equations for tradables, non-tradables and import-competing goods. They show that output (or employment) of any of these sectors will depend on the real exchange rate and the real income of home and foreign countries. In estimating the model they ignore the foreign variable, and the domestic income variable is broken into trend and cyclical components.

7. From regression (ii) I have also calculated the partial correlation between changes in the output of traded goods and the real exchange rate. The following partial correlations (with P-values in parentheses) are obtained:

corr (|delta~||chi~.sub.t~, |delta~||rho~.sub.t~) = -.21(.11),

corr (|delta~||chi~.sub.t~, |delta~||rho~.sub.t - 1~) = .21(.10),

corr (|delta~||chi~.sub.t~, |delta~||rho~.sub.t - 2~) - .22(.10).

8. Equations (ii) and (iii) were also tried with the log first-differenced form of the variables concerned. P-values reported in Table I for these two equations remain almost unchanged with log transformation of these variables.

9. Ayanian |1968~ provides another possible explanation. He finds that U.S. defense expenditure and the real exchange rate are positively correlated. He attributes this correlation to the "safe haven" argument. He argues that an increase in U.S. defense expenditures encourages foreign investors to believe their assets will be safer in the United States than elsewhere. Thus, an increase in military expenditures in the U.S. should increase the foreign demand for dollar-denominated assets and, hence, the appreciation of dollar.

10. Branson |1985~ provides a precise description of the rise in the real interest rate and the appreciation of the dollar that achieves short-run equilibrium.

11. Svensson |1985a; 1985b~ relaxes this assumption and obtains an endogenous variable velocity of money. I abstract from the variable velocity for simplicity.

12. It may be useful to note that during the 1980s the U.S. nominal deficit grew about 3.6 percent per quarter, whereas the money supply grew about 2.0 percent per quarter. This calculation is based on the measure of the U.S. budget deficit (|D.sub.1~) I used in section II. The growth rate of money is the growth rate of M1 from the Federal Reserve Bulletin.

13. A complicated general formula to calculate the covariance of endogenous variables is provided by Svensson |1985b~ in footnote 24. The approximation I employ is discussed in Appendix A.6 of Stockman and Svensson |1987~. They also discuss the advantages of this method over comparative-statics exercises.

14. one can easily verify this. For example, the derivative of

|Mathematical Expression Omitted~

is positive if |r.sub.x~ |is less than~ 1.

15. This is quoted from Frenkel |1985, 4~.

16. See Mussa |1986~.

REFERENCES

Ayanian, Robert. "Political Risk, National Defense and the Dollar." Economic Inquiry, April 1988, 345-51.

Branson, William H. "Causes of Appreciation and Volatility of the Dollar," in The U.S. Dollar: Recent Developments, Outlook, and Policy Options, edited by the Federal Reserve Bank of Kansas City. Kansas City, 1985, 33-54.

Branson, William H., and James P. Love. "U.S. Manufacturing and the Real Exchange Rate," in Misalignment of Exchange Rates: Effects on Trade and Industry, edited by Richard C. Marston. Chicago: The University of Chicago Press, 1988, 241-75.

Ceglowski, Janet. "Dollar Depreciation and US Industry Performance." Journal of International Money and Finance 8, 1989, 233-51.

Feldstein, Martin. "The Budget Deficit and the Dollar," in NBER Macroeconomics Annual, edited by Stanley Fischer. Cambridge, MA: MIT Press, 1986, 355-92.

Frenkel, Jacob. "Comment on Causes of Appreciation and Volatility of the Dollar." National Bureau of Economic Research Working Paper No. 1777, 1985.

Helpman, Elhanen. "An Exploration in the Theory of Exchange Rate Regimes." Journal of Political Economy, October 1981, 865-90.

Lucas, Robert E., Jr. "Interest Rates and Currency Prices in a Two-Country World." Journal of Monetary Economics, November 1982, 335-60.

Mussa, Michael. "Nominal Exchange Rate Regimes and the Behavior of Real Exchange Rates: Evidence and Implications," in Real Business Cycles, Real Exchange Rates and Actual Policies, edited by Karl Brunner and Allan H. Meltzer. Carnegie-Rochester Conference Series on Public Policy, vol. 25. Amsterdam: North-Holland, 1986, 117-214.

Nakibullah, Ashraf. "The Cyclical Effects of Monetary and Fiscal Policies on Non-Traded Goods." Ph.D. dissertation, University of Rochester, 1990.

Stockman, Alan C. "A Theory of Exchange Rate Determination." Journal of Political Economy, August 1980, 693-98.

-----. "The Equilibrium Approach to Exchange Rates." Economic Review, Federal Reserve Bank of Richmond, March/April 1987, 12-30.

Stockman, Alan C., and Lars E. O. Svensson. "Capital Flows, Investment, and Exchange Rates." Journal of Monetary Economics, March 1987, 171-202.

Stockman, Alan C., and Harris Dellas. "International Portfolio Nondiversification and Exchange Rate Variability." Journal of International Economics, May 1989, 271-89.

Svensson, Lars E. O. "Currency Prices, Terms of Trade, and Interest Rates: A General Equilibrium Asset-Pricing Cash-in-Advance Approach." Journal of International Economics, February 1985a, 17-41.

-----. "Money and Asset Prices in a Cash-in-Advance Economy." Journal of Political Economy, October 1985b, 919-44.
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