The macroeconomic dynamics of tariffs: a symmetric two-country analysis.

I. Introduction

This paper examines the macroeconomic dynamics of tariffs. The adverse microeconomic effects of tariffs have been exhaustively discussed in the international trade literature. However, there are still some debate and discussion on the effects of tariffs on the macroeconomy. In the mainstream open economy macroeconomics literature, it is argued that the impact of imposing a tariff is likely to be contractionary under flexible exchange rates.(1) This view, however, has been challenged first by the Cambridge Economic Policy Group (Cripps and Godley [3]) and more recently by Ford and Sen [7]. Given the fact that commercial policies have recently returned to playing a more central role in policy debates, this then leads to a revival of interest in the effects of tariffs on macroeconomic aggregates.

One important drawback of the analyses in the literature is that they all assume that the domestic economy faces a given world price of imports, i.e., they focus exclusively on small open economies, with virtually no attention being devoted to two-country models.(2) It is surely a question of relevance to examine the cross-country impact of protection. Although considerable effort has been devoted to examine the international transmission of fiscal and monetary policies recently (Corden and Turnovsky [2]; Svensson and van Wijnbergen [13]), little has been done on commercial policies in a two-country framework.(3) It is our intention, therefore, to relax the small-country assumption to study the transmission effect of tariffs.

In this paper, we discuss how likely a tariff will be beggar-thy-neighbor. Our main concern is the dynamic effects of a tariff on domestic and foreign aggregates. We pay special attention to the distinction between anticipated and unanticipated permanent tariff changes.(4) The case of a temporary tariff is also examined. The analysis is conducted in a modified two-country Mundell [11] - Fleming [6] - Dornbusch [4] model of two symmetric economies which originally used by Turnovsky [15] to study the international transmission of stabilization policies.(5,6) The choice of the assumption of symmetry is intentional because it allows us to apply the Aoki [1] averages-differences method to solve for the dynamics of the system. This method has the advantages of rendering the analysis tractable and providing insight into the solutions.(7) Moreover, as pointed out by Turnovsky [15, 139] ". . . symmetry is not unreasonable as a first approximation, since there is no a priori reason for, say, the United States and Europe to differ in terms of their aggregate behaviour in any systematic way."

The organization of the paper is as follows. In the next section, a detailed description of the analytical framework is provided and the Aoki decomposition procedure is applied to the model. Section III studies the steady-state equilibrium and the solutions to the dynamics. The macroeconomic effects of tariffs, both anticipated and unanticipated, are examined in section IV. Section V discusses the effects of a temporary tariff. Finally, there is a sixth, concluding section.

II. The Analytical Framework

The Basic Model

The framework adopted here is a dynamic two-country version of the Mundell-Fleming-Dornbusch model studied by Turnovsky [15]. The two countries involved are symmetric in structural parameters so that we can apply the Aoki [1] average-difference solution method to the dynamic system. There is complete specialization in production and a single common trading bond. Perfect-foresighted consumers in each country are assumed not to hold foreign currency.(8) The domestic economy is described as:

[Mathematical Expression Omitted]

M - [Pi] = [[Alpha].sub.1]Y - [[Alpha].sub.2]i (2)

[Pi] = [Delta]P + (1 - [Delta]) ([P.sup.*] + E + T) (3)

[Mathematical Expression Omitted]

where Y denotes the real output deviation about its natural rate level; P is the (logarithmic) price of output; [Pi] is the (logarithmic) consumer price index; E is the (logarithmic) nominal exchange rate, defined as the domestic currency price of foreign currency; T denotes the (logarithmic) tariff wedge; finally, i and M represent the nominal interest rate and the (logarithmic) nominal money stock, respectively. The restrictions on the structural parameters are as follows: 0 [less than] [[Beta].sub.1] [less than] 1, [[Beta].sub.2] [greater than] 0, [[Beta].sub.3] [greater than] 0, [[Alpha].sub.1] [greater than] 0, [[Alpha].sub.2] [greater than] 0, 1 [greater than] [Delta] [greater than] 1/2 and [Gamma] [greater than] 0. We denote foreign variables with an asterisk.

Equation (1) is the goods market equilibrium condition for the domestic economy. Private demand for output depends negatively on the real rate of interest and positively on the relative price. It also depends positively, though less than proportionately, on output in the other country.(9) Equation (2) describes the money market equilibrium; real money demand is a positive function of real income and a negative function of the nominal interest rate. The consumer price index (CPI), given by equation (3), is a weighted average of the home good price and the foreign good price, with the weights being the expenditure shares on home ([Delta]) and foreign goods (1 - [Delta]). Following Turnovsky [15], we assume that residents in both countries have a preference for their respective home good and so [Delta] [greater than] 1/2. Finally, equation (4) gives the sluggish price adjustment of the domestic economy in terms of simple Phillips curve relationship.(10)

Similar relationships can be postulated for the foreign country:

[Mathematical Expression Omitted]

[M.sup.*] - [[Pi].sup.*] = [[Alpha].sub.1][Y.sup.*] - [[Alpha].sub.2][i.sup.*] (6)

[[Pi].sup.*] = [Delta][P.sup.*] + (1 - [Delta])(P - E + [T.sup.*]) (7)

[Mathematical Expression Omitted].

Equations (5)-(8) have analogous economic interpretation as equations (1)-(4). Finally, we close the model with the following interest parity condition implied by the perfect substitutability between domestic and foreign bonds:

[Mathematical Expression Omitted].

Equation (9) states that arbitrage by risk-neutral agents keeps the domestic interest rate equal to the foreign rate plus any expected capital gain that can be had by holding wealth in assets denominated in the foreign currency. Under perfect foresight, the anticipated capital gain is set equal to the actual appreciation of the foreign currency.

The Aoki Decomposition

Given the "sameness" assumption of the two countries, the dynamic analysis can be simplified by applying the decomposition method of Aoki [1]. The procedure involves the definition of the averages and differences for any variable X, namely,

[X.sup.a] [equivalent] (X + [X.sup.*])/2 (average),

[X.sup.d] [equivalent] X - [X.sup.*] (difference).

As is standard in the literature, we assume the adjustments of prices are sluggish, i.e., P and [P.sup.*] move continuously everywhere, while the nominal exchange rate, E, is free to jump in response to new information. Using (3) and (7) to eliminate the CPIs ([Pi] and [[Pi].sup.*]), we obtain the following decoupled system:

Averages:

(1 - [[Beta].sub.1] - [Gamma][[Beta].sub.2])[Y.sup.a] = -[[Beta].sub.2][i.sup.a] (10)

[M.sup.a] - [P.sup.a] = [[Alpha].sub.1][Y.sup.a] - [[Alpha].sub.2][i.sup.a] + (1 - [Delta])[T.sup.a] (11)

[Mathematical Expression Omitted].

Differences:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

With the assumption of symmetry, equations (10)-(12) describe the average world economy. Equations (10) and (11) are the corresponding IS and LM curves, respectively, and equation (12) is the Phillips curve that determine the adjustments of the average price level. To assure well-behaved stability properties, we assume the IS curve, (10), to be downward sloping in the [Y.sup.a] - [i.sup.a] space, which requires the following restriction on the parameters:

1 - [[Beta].sub.1] - [Gamma][[Beta].sub.2] [greater than] 0.

Similarly, equations (13)-(15) describe the differences in the two economies.

III. Equilibrium Analysis

Steady-State Solutions

In this subsection, we characterize the steady-state solutions for the endogenous variables which help to gauge our dynamic analysis in the subsection below. In the steady state, all the dynamics cease and so [Mathematical Expression Omitted]. This implies that [Mathematical Expression Omitted] and [Mathematical Expression Omitted], where the "overbar" notation denotes steady-state value of a variable. Thus the long run equilibrium relationships of the goods and money markets are:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Solving these equations then give us the steady-state solutions:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

There are interesting implications from the above steady-state solutions. First, equation (20) implies that the expenditure-switching tariffs have no effects on the interest rate in the long run. From (21), we can see that the domestic (foreign) tariff causes a one-to-one appreciation (depreciation) of the real exchange rate. Such an induced one-to-one movement of the real exchange rate will then insulate the domestic (foreign) price level from the effects of the domestic (foreign) tariff.(11) Thus, from equations (22) and (23), the imposition of a tariff by the home (foreign) country affects only the foreign (domestic) prices in the long run. According to equation (24), an increase in the domestic tariff rate raises the nominal exchange rate, E.

Finally, an increase in the nominal money supply by a country increases its price level proportionately, as can be seen from equations (22) and (23). An increase in the domestic (foreign) money supply causes the domestic currency to depreciate (appreciate) proportionately. The world interest rate and the relative price, however, are not affected by changes in nominal stock of money.

Solutions to Dynamics

Given the decoupled system of averages and differences in section II, we obtain the solutions to the dynamic adjustment of the economy in two steps. We first solve for the averages and the differences and then transform the solutions to the original variables. We begin the analysis at time zero when the world economy is in steady state: [Mathematical Expression Omitted], [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. The tariff policy to be studied is one that is announced at time zero and is supposed to be effective at time [Tau], with [Tau] [greater than or equal to] 0. If [Tau] = 0, then we have the case of an unanticipated tariff; while [Tau] [greater than] 0 represents the case of an anticipated tariff. The new steady state corresponding to the disturbed system can be written as

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

We first study the dynamics of the averages. Manipulating equations (10)-(12) together with (22) and (23), we have

[Mathematical Expression Omitted]

where [Lambda] = -[Gamma][[Beta].sub.2]/[Gamma] [less than] 0 with [Gamma] = [[[Alpha].sub.2](1 - [[Beta].sub.1] - [[Beta].sub.2][Gamma]) + [[Alpha].sub.1][[Beta].sub.2]] [greater than] 0 and [Mathematical Expression Omitted] is the steady-state value of the average world price level. The solution of the first-order differential equation, (25), is:

For 0 [less than or equal to] t [less than] [Tau],

[Mathematical Expression Omitted]

[Y.sup.a] = 0 (27)

[i.sup.a] = 0 (28)

and for t [greater than or equal to] [Tau],

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

From (25), it is clear that the dynamics of the average world economy is governed by the average world price level. Since the dynamic adjustment of the average price is assumed to be sluggish, the solution variables do not respond in anticipation of the future tariff change, as is given by equations (26)-(28). At the moment the imposition of the tariff takes place (t = [Tau]), equations (29)-(31) imply that the world economy converges monotonically to its new steady state.

Next, we turn to the dynamic solutions of the differences. Similar manipulation of equations (13)-(15) reduces the system to the following matrix equation in terms of the price differentials and the nominal exchange rate:

[Mathematical Expression Omitted]

where

[a.sub.11] = 2[[[Alpha].sub.1][[Beta].sub.3] + (1 - [Delta])[Phi]]/[Delta] [greater than] 0

[a.sub.12] = -[2[[Alpha].sub.1][[Beta].sub.3] + (1 - 2[Delta])[Phi]]/[Delta]

[a.sub.21] = 2[Gamma][[[Alpha].sub.2][[Beta].sub.3] + [[Beta].sub.2] (1 - [Delta])(1 - 2[Delta])]/[Delta] [greater than] 0

[a.sub.22] = -[Gamma][2[[Alpha].sub.2][[Beta].sub.3] + [[Beta].sub.2][(1 - 2[Delta]).sup.2]]/[Delta] [less than] 0

[Phi] = 1 + [[Beta].sub.1] + [Gamma][[Beta].sub.2](1 - 2[Delta]) [greater than] 0

[Delta] = -[[Alpha].sub.1][[Beta].sub.2](1 - 2[Delta]) + [[Alpha].sub.2][Phi] [greater than] 0.

The determinant of the coefficient matrix, [a.sub.11][a.sub.22] - [a.sub.12][a.sub.21], can be shown to be equal to -2[Gamma][[Beta].sub.3]/[Delta] which is negative. We, therefore, have one positive and one negative characteristic roots which imply saddlepoint stability of the system.

Let [[Mu].sub.1] [less than] 0 and [[Mu].sub.2] [greater than] 0 be the characteristic roots of the above dynamic system of the price differentials and the exchange rate. Then the solutions to equation (32) are:

For 0 [less than or equal to] t [less than] [Tau],

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

and for t [greater than or equal to] [Tau],

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where the arbitrary constants, [K.sub.i] (i = 1, 2 and 3), are determined by:

[K.sub.1] + [K.sub.2] = 0 (37)

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Equation (37) is the initial condition of the price differentials, which is obtained by evaluating (33) at t = 0. Equations (38) and (39) follow from the assumption of continuous adjustment of the price differentials and the exchange rate at time [Tau]; specifically, we evaluate equations (33)-(36) at t = [Tau] and subtract (35) from (33) and (36) from (34) respectively.

According to equation (34), the nominal exchange rate undergoes an initial jump when the imposition of a future tariff is announced at time 0. As a matter of fact, such a jump in the exchange rate actually assure the stability of the system. After imposing the tariff at time [Tau], [P.sup.d] and E converge monotonically to their new steady-state values at rate [[Mu].sub.1], as indicated by equation (35) and (36). Moreover, from the solution time path of the exchange rate, whether it overshoots or undershoots depends upon the sign of the coefficient [a.sub.12], which is ambiguous a priori. However, since the classic paper of Dornbusch [4], it is known that overshooting in the exchange rate can easily occur in this type of models in which the exchange rate adjusts faster than goods prices. Thus, in order to be specific, we will concentrate on the more likely case that [a.sub.12] [greater than] 0.

We are ready to solve for the dynamic solutions in terms of the original variables. Combining equations (26)-(31) and (33)-(36), together with the facts that X = [X.sup.a] + [X.sup.d]/2 and [X.sup.*] = [X.sup.a] - [X.sup.d]/2, we have:

For 0 [less than or equal to] t [less than] [Tau],

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

Y = ([[Mu].sub.1][K.sub.1][e.sup.[[Mu].sub.1]t] + [[Mu].sub.2][K.sub.2][e.sup.[[Mu].sub.2]t])/(2[Gamma]) (40d)

[Y.sup.*] = -([[Mu].sub.1][K.sub.1][e.sup.[[Mu].sub.1]t] + [[Mu].sub.2][K.sub.2][e.sup.[[Mu].sub.2]t])/(2[Gamma]) (40e)

i = (1/2){[[a.sub.12]/([[Mu].sub.1] - [a.sub.11])][[Mu].sub.1][K.sub.1][e.sup.[[Mu].sub.1]t] + [[a.sub.12]/([[Mu].sub.2] - [a.sub.11])] [[Mu].sub.2][K.sub.2][e.sup.[[Mu].sub.2]t]} (40f)

[i.sup.*] = -(1/2){[[a.sub.12]/([[Mu].sub.1] - [a.sub.11])] [[Mu].sub.1][K.sub.1][e.sup.[[Mu].sub.1]t] + [[a.sub.12]/([[Mu].sub.2] - [a.sub.11])] [[Mu].sub.2][K.sub.2][e.sup.[[Mu].sub.2]t]}, (40g)

and for t [greater than or equal to] [Tau],

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where the constants, [K.sub.i](i = 1, 2and3), are given by equations (37)-(39).

IV. The Macroeconomic Effects of Permanent Tariffs

In this section, we investigate the international transmission of a unit increase in the domestic tariff, with the foreign tariff held constant, i.e., dT = 1 and [dT.sup.*] = 0. Moreover, for simplicity, the money supplies in both countries are held constant, i.e., dM = [dM.sup.*] = 0. At time 0, the tariff increase is announced to take effect at time [Tau]. From the steady-state solutions (22)-(24), we get:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Two types of permanent tariff policies can be studied: an unanticipated tariff ([Tau] = 0) and an anticipated tariff ([Tau] [greater than] 0). We analyze each of these policies in the following two subsections.

An Unanticipated Tariff

In this section, we consider a tariff policy that is announced and implemented instantaneously at time 0 (i.e., [Tau] = 0). We summarize the solution time paths in Figure 1.(12)

From equation (43), we know that the steady-state nominal exchange falls in response to the domestic tariff. In the short run, the imposition of the tariff raises the price of imports to domestic consumers. With the prices of home and foreign goods fixed instantaneously, this requires an appreciation of the domestic currency to clear the goods market. Given the assumption of [a.sub.12] [greater than] 0, the nominal exchange rate overshoots on impact its long-run response. Thereafter, it continues to rise towards its new steady-state level.(13)

The effect of the tariff on domestic output depends on the magnitude of the parameters [Lambda] and [[Mu].sub.1]. The imposition of the tariff decreases the average world output ([Y.sup.a]), but increases the difference ([Y.sup.d]). While this obviously implies a decline in the foreign level of output, domestic output will drop if and only if the decrease in average output exceeds the rise in the difference (i.e., [Lambda] is larger than [[Mu].sub.1] in absolute magnitude). Given that output and inflation are directly linked by the Phillips curve, the price level can rise or fall on impact domestically while it decreases abroad.

The ambiguous effects of the tariff on domestic output and inflation can be explained more intuitively. The direct expenditure-switching effect of tariff results in an increase in the relative price of foreign goods, leading to a rise in domestic demand, and hence in output and inflation. However, the fact that the nominal exchange rate immediately begins to rise following the imposition of the tariff, reduces the domestic rate of inflation, thereby raises the real rate of interest. This creates a contractionary effect on demand and output domestically. Moreover, the beggar-thy-neighbor effect of the tariff reduces the demand for domestic product abroad. The net effect on domestic output and inflation then depends upon which of these effects dominates. Notice that even if the tariff increases domestic output initially, such an expansionary effect will diminish immediately and will become contractionary eventually.(14) This is because the initial increase of domestic output is accompanied by a rise in the domestic inflation rate. Thus the domestic price level goes up and the real money stock decreases, thereby inducing a contraction in domestic output. Indeed, as long as domestic output is above its long-run equilibrium level, the Phillips curve relation implies that the price level will continue to rise and hence the contractionary force on output will continue. This "overshooting" phenomenon of domestic output, therefore, offers an interesting compromise between the conventional contractionary effect (e.g., Mundell [10]) and the expansionary effect (e.g., Eichengreen [5]) in the literature of the macroeconomics of protection. The tariff is both contractionary and expansionary in transition.

Finally, the initial appreciation of the domestic currency reduces the real money supply abroad. This leads to a rise in the foreign interest rate on impact. The subsequent decrease in the foreign price level together with the beggar-thy-neighbor effect of the tariff imply that there is an excess supply of money. Thus the foreign nominal interest rate declines over time. The effects on the domestic interest rate is in general ambiguous. However, from the interest parity condition, it follows that the rise in the foreign interest rate exceeds that of the domestic rate, which in fact may rise or fall. On the one hand, the initial appreciation of the domestic currency causes the domestic real money supply to rise, leading to a decline in the domestic interest rate. On the other hand, the rise or fall in domestic demand may generate an increase or decrease in the real money demand. Thus the overall effects on the interest rate is indeterminate. We illustrate both alternative time paths for Y, P and i in Figure 1.

An Anticipated Tariff

The tariff policy involved here is one that is announced at time 0 and to be implemented at a later date, says, at time [Tau]([Tau] [greater than] 0). The illustration of the time paths of the relevant variables are given in Figure 2.

Under perfect foresight, the long run appreciation of the domestic currency, anticipated from the imposition of the future tariff, causes the domestic currency to partially appreciate instantly. Since output prices are fixed instantaneously, this leads to an immediate increase in the relative price of the home good which then reduces domestic real output. The contraction of domestic real output further leads to a decline in the inflation rate and real money demand at home. Moreover, given the domestic nominal stock of money, the appreciation of the domestic currency results in an increase of the domestic real money supply. This requires the domestic nominal interest rate to fall to clear the money market.

After the announcement and before the implementation of the tariff, the domestic currency continues to appreciate which further reduces real output and the rate of inflation at home. The combination of the falling prices and output, together with the appreciating domestic currency, produces further downward pressure on the domestic nominal interest rate.

At time [Tau], the anticipated tariff becomes effective which then raises the relative price of imports. The economic situation begins to reverse. The expenditure-switching effect of the tariff raises domestic demand and output, which in turn causes the price of home goods to increase.(15) The rising output prices and the constant nominal money stock together generate a decline in the domestic real money supply. Moreover, the increasing output raises the domestic real money demand which in turn causes the nominal interest rate to rise. As a matter of fact, the domestic interest rate first undergoes a discrete jump at time [Tau], after which it continues to rise towards its new equilibrium level. The rise of the interest rate together with the continuing appreciation of the domestic currency, however, creates an offsetting contractionary effect on real output, which then gradually falls to its long run equilibrium level. As this occurs, the rate of inflation is moderated and the home good price gradually approaches its steady-state level.

From time 0 to time [Tau], equations (26)-(28) imply that the average world economy remains stationary. As a consequence of the symmetry assumption and the fact that the appreciation of the domestic currency is a depreciation of the foreign currency, the foreign economy behaves as an exact mirror image of the home economy. Thus, for the period between the announcement and the implementation of the tariff, the domestic decline in real output, the price level and the nominal interest rate is fully matched by an increase in these variables abroad.

At the time the tariff is imposed, the relative price effect causes an immediate fall of foreign output which in turn leads to a decline in the foreign price level. However, the increase in domestic output generates some spillover effects on to demand and output in the foreign economy. These together with the continuing appreciation of the domestic currency lead to a modest increase in foreign real output after time [Tau]. Given fixed nominal money stock, the falling foreign price level requires a decrease in the foreign nominal interest rate to restore money market equilibrium. Notice that with a continuously falling exchange rate, the interest parity condition imply the nominal interest rate abroad always remains above the domestic one. Finally, all these variables converge monotonically to their new steady-state levels, as illustrated in Figure 2.

V. A Temporary Tariff

This section provides an analysis on the effects of a temporary tariff that is imposed for [Tau] periods and is eliminated afterwards. In general, the short-run effects on domestic aggregates are very complicated and usually ambiguous and are difficult to characterize. Fortunately, we can still obtain the dynamics of the nominal exchange rate, the foreign output and the foreign price level. Their time paths are illustrated in Figure 3.

The unanticipated temporary tariff appreciates the domestic currency for its whole duration. From time [Tau] on, the reverse happens and the nominal exchange rate adjusts back to the initial level. The time path for the foreign price level is qualitatively similar to that of the exchange rate. The temporary tariff is "beggar-thy-neighbor" as in the permanent tariff case. In particular, it has a greater initial beggar-thy-neighbor effect on foreign output than the permanent tariff. This is attributable to the fact that there is less instantaneous appreciation in the domestic currency in the current case. Another interesting aspect of this case is that the behavior of the world economy is qualitatively affected by the duration of the increase in domestic tariffs. For instance, the domestic currency will depreciate subsequent to the increase in tariffs if the shock is of brief duration, while it will appreciate if the rise in tariffs is prolonged. Such differential behavior in the nominal exchange rate will imply differential behavior in the domestic and foreign economies.

Finally, we like to point out that the relationship between the domestic and foreign interest rates is highly complicated. Unlike the permanent and anticipated cases, in which the foreign rate is always greater than the domestic, it is possible in the temporary case for the rates to switch positions during the transition.(16) Specifically, for a prolonged increase in tariffs, the foreign rate is initially greater than the domestic, but then falls below the domestic rate prior to the time domestic tariffs return to their original level.

VI. Concluding Remarks

This paper has conducted a dynamic analysis on the macroeconomic effects of tariffs in a symmetric two-country model. It is shown that the expenditure-switching tariff can be both expansionary and contractionary in transition. An unanticipated tariff has uncertain effects on domestic macroeconomic aggregates. An anticipated tariff is usually contractionary for the period between the announcement and the implementation due to the induced appreciation of the domestic currency under perfect foresight. Once the tariff is implemented, its expansionary expenditure-switching effect starts to work against and eventually dominates the contractionary effect from the exchange rate appreciation. For the international transmission of tariffs, it is shown that both an unanticipated and anticipated tariff (once implemented) suppress output and inflation abroad and lead to an appreciation of the domestic currency. Thus our finding is in accord with the conventional wisdom that a tariff is likely to be beggar-thy-neighbor. In particular, we find that the initial beggar-thy-neighbor effect is greater for a temporary tariff than a permanent one.

The analysis so far only considers an unilateral imposition of a tariff by the domestic country. It is straightforward, however, to establish that if both governments impose a tariff on each other (i.e., dT = [dT.sup.*]), then the nominal exchange rate remains unchanged. As a consequence, the effects of anticipated and unanticipated tariffs are identical since neither economy responds to the announcement of the future tariff. In this case, the adjustment takes place only when the tariff is actually imposed.

As a concluding remark, we would like to point out some promising extensions in this area. First, without an explicit specification of the import demand function, we are unable to apply the current analysis to examine the macroeconomic effects of tariffs under alternative disposition of the tariff revenue. As emphasized by Tower [14] almost two decades ago, how the tariff revenue is used is crucial as far as the effects of protection is concerned. Another interesting extension of the current model is to introduce wage behaviors explicitly so that we can compare the macroeconomic effects of tariffs under different types of wage rigidity (both real and nominal). Finally, as pointed out by Turnovsky [15], the symmetric two-country framework is well suited to considering strategic behavior by governments with respect to commercial policy and retaliation. We plan to pursue these iswues in subsequent work.

1. The original contribution is that of Mundell [10]; see Krugman [9] for a summary.

2. Ironically, in pure trade theory, the main focus of the analysis of tariffs is on the retaliatory interactions between countries.

3. The only exception that I am aware is Gardner and Kimbrough [8]. However, their main interest is in the trade account balances of the countries and they do not discuss the protection effects on output and inflation.

4. Anticipated and unanticipated policy changes usually generate very different effects on the macroeconomy; for example, see Persson and Svensson [12] for an analysis on the terms of trade changes.

5. Although it is well known that the Mundell-Fleming model is ad hoc, the study of macroeconomic dynamics in a two-country optimizing model with money is not tractable.

6. Our analysis can be viewed as an extension of Turnovsky [15] since he only focuses on the effects of permanent, but not temporary, policy changes.

7. Specifically, it enables us to decompose the original third-order dynamic system in the two output prices and the exchange rate into averages and differences of the relevant variables, which are of first-order and second-order respectively. This simplifies the solutions to the dynamics significantly.

8. For an analysis of tariffs with currency substitution in a small open economy under flexible exchange rates, see Eichengreen [5].

9. Since our concentration is on the macroeconomic effects of tariffs, we abstract government spending from the IS curve.

10. Notice that (4) incorporates the classical belief that output is given at the natural rate in the long run. We believe that this is a reasonable benchmark for studying any policy changes. In the long run, price (rather than output) changes should be the dominant adjustment mechanism in the economy. If money supply is growing at a constant rate over time, then (4) needs to be modified according to the famous Friedman-Phelps expectations augmented Phillips curve. Under perfect foresight, the expected inflation rate equals to the actual inflation rate which is just the nominal money growth rate in the steady state. Thus, output is again given at the natural rate level in the long run.

11. This can be derived from equation (21) wherein [Mathematical Expression Omitted].

12. The analytical solutions can be obtained from (41) using (42) and (43). The detailed derivation for this case as well as for cases in the following sections is given in a technical appendix which is available upon request.

13. If [a.sub.12] [less than] 0, then the nominal exchange rate does not overshoot. The domestic currency continues to appreciate towards its new long-run level.

14. If domestic output falls initially, then the effects are reversed (see Figure 1).

15. During the subsequent transition, output continues to rise above its steady-state level. This occurs at the point where the price level begins to rise.

16. Notice that once the tariff is eliminated (t [greater than or equal to] [Tau]), the foreign interest rate is always greater than the domestic.

References

1. Aoki, Masanao. Dynamic Analysis of Open Economies. New York: Academic Press, 1981.

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