貿易政策於不同匯率制度與價格僵固性下之福利分析

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貿易政策於不同匯率制度與價格僵固性下之福利分析

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中 華 民 國 97 年 10 月 31 日

Welfare Implications of Tariffs under Alternative Nominal Rigidities

Yu-Ning Hwang

1

Department of Economics

National Chengchi University

October 2008

ABSTRACT

Tariff is one of the major protection policies in international trade and has been a long-lasting issue in international economics. This paper uses a two-country dynamic general equilibrium model to examine the effects of the tariff on the world economy under alternative nominal rigidities: producer-currency pricing (PCP) and local-currency pricing (LCP) where the exchange rate pass-through and expenditure-switching effects are absent. This study finds that the effects of the tariff on the output and welfare do vary with the price setting strategies. A tariff is expansionary for the imposer’s economy under both PCP and LCP. The tariff’s impact on its trade partner is contractionary under LCP, but absent under PCP. The difference primarily comes from the exchange rate pass-through effect that differs under PCP and LCP. The alternative nominal rigidities also result in different effects on welfare. While a tariff improves the welfare of the domestic households under PCP, it worsens the welfare of the foreign country under LCP.

Keywords: Keyword：Tariff, Nominal Rigidity, Exchange Rate Pass-Through, Expenditure Switching Effect JEL Classifications: F13; F41; E42

1 *

Yu-Ning Hwang is an Assistant Professor in the Department of Economics at National Chengchi University, Taipei, 116 Taiwan. Comments are most welcome. Contact details: e-mail to [email protected]; Tel.: 886-2-29393091 ext. 51641.

1. Introduction

One of the primary protection policies is the imposition of tariffs. In recent years, many cases are

going on among major countries

2

. While this is a widely used policy tool, the welfare evaluation of the

trade policy is important to the authorities. This is a long-lasting issue in the literature, but whether the

tariff is beneficial to the country which levies the policy still remains controversial. Early studies reach

certain consensus though. (Mundell (1961), Boyer (1977), Chan (1978) and Eichengreen (1981)) As

surveyed by Krugman (1982), the tariff is contractionary under a flexible exchange rate regime, but

expansionary when the exchange rate is fixed. However, these studies are based on ad hoc assumptions

of behavior and the policy is examined in a small open economy. Not too many endeavors have been

devoted to evaluate this issue with intertemporal optimization in the past decades. The absence of

micro-foundations implies the failure of the welfare assessment of the protection. Sen and Turnovsky

(1989) are the first who use an intertemporal optimization framework to study the effects of

unanticipated permanent, anticipated temporary, and anticipated permanent tariffs on a small open

economy. They find that both output and employment are suppressed by the tariff in the short and long

run. The role of capital accumulation is emphasized, which is the main factor that drives current account

movements.

Nevertheless, a small open economy framework neglects the transmission mechanism of shocks

across countries. As for now, the only study using a two-country dynamic general equilibrium model to

study tariffs’ effects is Fender and Yip (2000). The two-country framework permits the evaluation of

tariff’s impacts on the foreign country. Their model consists of imperfect competition and nominal

rigidity. The role of monopolistic competitions which lead to inefficient outcomes is stressed. It shows

that the tariff decreases both output and employment. As in traditional models, the impacts of a

permanent tariff on welfare face tradeoffs, mainly from its impacts on output and consumption through

terms of trade movements. In a monopolistically competitive environment, however, the elasticity of

2

For example, in 2004, the European Union (EU) imposed a retaliate tariff on U.S. exports for the export tax subsidy applied by the U.S. government to U.S. producers. In 2006, the EU placed anti-dumping tariffs on goods exported from China. The producers of the EU seem to be the only winner, while retailers and consumer groups opposed to the move.

substitution among goods is crucial to the tariff’s net effect on the welfare.

Thus, the objective of this study is to examine the effects of tariffs on the global economy with a

two-country dynamic general equilibrium model with monopolistic competition and nominal rigidity.

Equipped with the micro-foundation, the model provides a great platform for welfare analyses of

policies. Different Fender and Yip (2000), this research centers on the tariff’s effect under alternative

nominal rigidities. In contrast to the producer-currency pricing (PCP) setting under Fender and Yip

(2000), as traditional models specify, this study emphasizes the exchange rate pass-through and

expenditure-switching effects that are absent under the alternative price stickiness, local-currency

pricing (LCP). The importance of the pricing strategies is

revealed

by Devereux and Engel (2003). They

show that the currency for the pricing setting has important implication for optimal exchange rate regime.

The optimal exchange rate regime under PCP is flexible, while a fixed exchange rate regime is optimal

under LCP.

3, 4

Following Devereux and Engel (2003), empirical findings also support LCP for firms that

actively conduct international trades.

In addition to its implication for exchange rate flexibilities, the degree of exchange rate pass-through,

which determines how much the tariff is passed upon the import prices, certainly has important

implications for the macroeconomic fundamentals and welfare. In particular, while the LCP behavior

prevails in the world, how tariffs may impact on the global economy is critical for policy makers.

To examine tariffs’ effects qualitatively for the policy analysis, we use the model in Obstfeld (2006)

where analytical solutions are available and introduce permanent tariffs for the imports in the home and

foreign countries respectively. In this model, nontradable goods are present and all the prices are

predetermined one period ahead. While relative tariff rates cause exchange rate movements, the absence

of exchange rate pass-through under LCP leads to different impacts on the home and foreign outputs and

3

Nevertheless, their result is challenged by Obstfeld (2006), who argues that the result in Devereux and Engel (2003) comes from the symmetric reactions of consumption to idiosyncratic shocks when nontradable goods are absent. In an economy with nontradable goods, the monetary authorities in these two countries set divergent interest rate rules and thus nominal exchange rate flexibilities are needed for the asset market to achieve the equilibrium where the uncovered interest parity holds.

4

Moreover, Devereux, Engle and Stoggard (2003) consider endogenous pricing strategies instead. They find that PCP is the optimal pricing strategy when exchange rate fluctuations are small while LCP is the optimal under greater exchange rate fluctuations.

welfare from the PCP case.

This paper is structured as follows. Section 2 outlines the specifications of the model. In Section 3, we

conduct the analysis of the tariff’s implications for a flexible-price economy. Section 4 then discusses

the different prices and consumptions under PCP and LCP. Section 5 and 6 analyze the impacts of a

tariff on the production and welfare. Finally, we present our conclusion in Section 7 and discuss areas for

future research.

2. The model

2.1

Production

There are two countries, home and foreign. Each country produces both tradable and nontradable goods.

H

Y and

denote traded and nontraded goods produced in the home country, while

and

denote traded and nontraded goods in the foreign country. For each type of goods, the good market

structure is monopolistic competition, with a lot of firms producing similar but slightly different goods

and competing with each other in the market. Labor is the only input in the production process.

Production functions follow the form:

N

Y

Y

_F * N Y , ,, H t t H t Y =AL Y_{N t,} =AL_{t N t,}

(1a)

where

A

_t

is an autocorrelated country-specific productivity shock.

H

and

indicate home tradable

and nontradable goods respectively. The foreign production functions follow the analogous form and are

indexed by asterisks.

N

* * * , ,

,

F t t F t

Y

=

A L

Y

_{N t}*_,

=

A L

_t* *_{N t,}

(1b)

The real shock in the economy is characterized by technological innovation. The logarithm of

productivity shocks, indicated by lower-case

a

_t

and

*

, evolve with the following AR(1) process:

t a

(

)

2 1 , ,

1

,

t a a t a t a t a

a

= −

ρ

a

+

ρ

a

₋

+

ε ε

∼

N(0,

σ

)

(2a)

(

)

* * * * * * * 1 , _, 1 , t a a t a t _{a t a} a a a N * 2 (0, )

ρ

ρ

₋

ε

ε

σ

= − + + ∼

(2b)

The productivity shock is the only exogenous shock in the economy. Because the productivity shock

follows a lognormal distribution, all the endogenous variables in the economy are lognormally

distributed as well.

2.2

Consumption

There is a continuum of varieties for each type of good. Home goods are indexed from

while

foreign goods are indexed from

. Consumers in each country consume a variety of goods,

composed of home and foreign tradable goods and domestic nontradable goods. For any individual in

the home country, the composite consumption index is in the Cobb-Douglas form:

(0,1) j∈ (1, 2) j∈ i

1 1

(1

)

T N

C C

C

γ γ γ γ

γ

γ

− −

=

−

(3)

T

C and

C

_N

are indices of traded and nontraded consumption and

γ is the share of spending on tradable

goods in total expenditure

. Tradable consumption is composed of equal share of home and foreign

tradable goods,

PC

H

C and

C

_F

:

1/2 1/2 2 T H C = C C_F

(4)

where

,

/( 1) 1 ( 1)/ 0

( )

d

H T

C

C j

j

θ θ θ θ − −

⎡

⎤

=⎢

⎥

⎣

∫

⎦

/( 1) 2 ( 1)/ 1

( )

d

F T

C

C j

j

θ θ θ θ − −

⎡

⎤

=⎢

⎥

⎣

∫

⎦

,

/( 1) 1 ( 1)/ 0

( )

d

N N

C

C j

j

θ θ θ θ − −

⎡

⎤

=⎢

⎣

∫

⎦

⎥

and

θ

is the price elasticity of substitution among goods and

θ

> . The home aggregate price index for

1

the composite consumption is

1

T N

where

( )

1 1 ₁ 1 0 H T i P P i di θ θ − − = ⎡ ⎤ =⎢ ⎥ ⎣

∫

⎦

,

( )

1 2 ₁ 1 1 F T i P P i di θ θ − − = ⎡ ⎤ = ⎢ ⎥ ⎣

∫

⎦

,

( )

1 1 ₁ 1 0 N N i P P i di θ θ − − = ⎡ ⎤ = ⎢ ⎥ ⎣

∫

⎦

and

τ

is the home tariff on the goods imported from abroad. Therefore, home demand for each

commodity can be derived as

( ) T( ) T H H P h C h C P θ − ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦

,

( ) ( ) T T F F P f C f C P θ − ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦

,

( ) ( ) N N N P h C h C P θ − ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ N

(6)

Home demand functions for home and foreign goods are

1 1 2 H H T T P C C P − ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦

,

( )

1

1

1

2

F F T

P

C

P

τ

−

⎡

+

⎤

= ⎢

⎥

⎣

⎦

C

T

and home demand functions for traded and nontraded goods are

1 T T P C C P

γ

⎡ ⎤− = ⎢ ⎥_{⎣ ⎦}

,

1 (1 ) N N P C P

γ

⎡ ⎤− = − ⎢ ⎥_{⎣ ⎦} C

The parameter

τ

is the constant tariff associated with the protectionism policy of the home government.

Variables in the foreign country are in analogous forms and indicated by asterisks.

2.3 The Utility Function

Consumers face the following intertemporal maximization problem as follows:

max

1 1 0 0 1 1 t t i t t s i t E C ρ

β

ρ

+ ∞ − = ⎛ − ⎜ − ⎝ ⎠

∑∑

κ

L ⎞_⎟

(7a)

s.t.

(

)

( )

1 * * 1 1 , , , , , , t i i i i i i i i i t t t t t t t t H t H t t H t H t N t N t t s

PC

B s

s D s

PWL D

P Y

ς

P Y

P Y

T

+ + + i

+

∑

≤

+ +

+

+

+

(7b)

The utility of individual depends on consumption of the composite good,

, and the disutility from

labor supply.

i C_ti

by the labor supplied. 1

ρ

is the elasticity of substitution and we assume

ρ

>15

. Real money holding

does not enter the utility function because we use the interest rate rule as the monetary policy, rather than

the control over the money supply in the economy.

ς

t

is the nominal exchange rate measured by the

home currency price of the foreign currency.

We assume that asset markets are complete. That is, there is a complete set of state-contingent

securities

D s

( )

_t

in the budget constraint.

6 B s

(

_t+1 s_t

)

is the home-currency price of the

state-contingent security toward each future state

s

_t+1

. The individual household receives wages from

labor and collects revenues from the sale of good produced. Because output in the commodity market is

determined by demand,

indicates the amount of the good sold and the market demand for the good.

The government transfers all the tariff revenue

to consumers.

Y

t

T

7

is the nominal wage for each

unit of labor supplied,

.

t

W

i

L

. i H t Y

,

Y

_{N t}i_,

and

* . i H t

Y

denote the demand functions of the goods produced by

home producer. Since all the consumers are assumed symmetric, we will drop the superscript

i

throughout the paper.

According to the maximization problem as specified above, the Euler equation is obtained as follows:

(

)

1 1

1

t t t t t

C

i E

P

P

ρ ρ

β

− − + +

⎛

⎞

=

+

_⎜

⎝

⎠

t

C

⎟ (8)

where the definition of the nominal interest rate

i

t

is defined as follows:

(

)

(

1 1

1/ 1

t t t s

i

B s

+ +

+

=

∑

s

t

)

. Note

that the nominal interest rate in this model is the policy determined by the government and thus is

exogenous to consumers’ optimization.

Because consumers in the home and foreign countries face the same asset prices, the risk-sharing

5

The range of the elasticity of intertemporal substitution varies in a wide range. Most of the empirical studies support that the elasticity is smaller than unity, which implies ρ> . While most of the papers assume 1 ρ >0 (for example, Obstfeld (2006), Devereux and Engel (2003)), the assumption of ρ> in this paper is primarily for analytical simplicity.1

6

Because all the exogenous shocks are lognormal, there will be a continuum of states. The specification of discrete states here can be extended to continuous states directly.

7

As explained in Obstfeld and Rogoff (1998), the Cobb-Douglas preference implies the current account balance is zero if the initial debt is zero. However, if the tariff is imposed, the current account is not necessarily balanced unless the tariff revenue is returned to consumers to subsidize higher consumption expenditure caused by the tariff.

condition in the complete asset markets holds for all states

8

:

* * t t t t

C

C

P

P

t ρ ρ

ς

− −

=

(9)

t

ς

is the nominal exchange rate, defined as the home-currency price of one foreign currency. Since the

purchasing power parity does not hold in our model due to the existence of nontradable goods and tariffs,

this condition implies that consumptions do not generally equal across countries.

. Following the monetary policies adopted in Obstfeld (2006), the interest rate rules in these two

countries are as follows:

9

(

)

ln 1

+

i

_t

= +

i

ω

p

_t

(10a)

(

*

)

ln 1+i_t = +i

ω

p_t*

(10b)

The monetary authority in each country adjusts the nominal interest rate in reaction to the domestic price

levels and shocks from both countries. The foreign monetary policy follows an analogous form.

10,

.

11

3. Flexible prices

To understand how sticky prices would affect the economy, we have to know how the economy works

under flexible nominal prices. Assume that the central bank does not respond to productivity shocks so

that the nominal interest rate rule is simplified as 1

+ = +

i

_t

i

ω

p

_t

in the flexible-price case.

The tradeoff between labor supply and consumption is:

8

The derivation of this equation is in the appendix.

9

Amato and Laubach (2004) find that a simple interest rate rule can nearly lead to the optimal allocation for any degree of habit formation. They adopt an inertial interest rate rule where the interest rate reacts to the past interest rate, the inflation rate and the output. The optimal monetary policy suggests a super-inertia interest rate rule that, in which the current interest rate reacts more than one hundred percent to its past value. The coefficient incorporating the nominal interest rate’s reaction to the inflation rate is 2.37 when there is no habit formation. Both of these two responses of the interest rate decrease with the degree of habit formation.

10

Following Obstfeld (2006), we assume there is no nominal shock to the interest rate rule. This case can be extended easily.

11

Kollmann (2002) calibrates a dynamic general equilibrium model with a small open economy framework to find the optimal monetary policy rule. His finding supports the inflation targeting policy rule and the response of the central bank to a one-percent of the price level increase is 3. Bergin, et al. (2007) finds the similar inflation targeting rule and the parameter in reaction to the inflation rate is 5.0.

* * * t t t t t t

W

W

C

C

P

P

ρ ρ

_κ

−

₌

−

_{= (11)}

Substituting this equation back into Eq. (9), we can see that

. In a monopolistic competition

market, firms will set the price as a fixed markup over the marginal cost for the home and foreign

countries; that is,

* t t W =

ξ

Wt , 1 t H t t W P A

θ

θ

= −

and

* , *

1

t F t t t

W

P

A

θ

_ξ

θ

=

−

respectively. Therefore, combined with the

relative wage, relative price is simply the relative productivity across countries:

* * , , * , , H t H t t F t F t t

P

P

A

P

=

P

=

A

The combination of Eq. (11) and the composite price index yields the consumptions in these two

countries respectively:

(

)

1 1 * 2 2 2

1

1

t t t

C

A

A

k

γ γ _{γ ρ}

θ

_τ

θ

− ₋

⎡

−

⎤

=

_⎢

+

_⎥

⎣

⎦

,

(

)

1 1 *

1

₂ * ₂ * ₂

1

t t t

C

A A

k

γ γ γ _ρ

θ

_τ

θ

− −

⎡

−

⎤

=

_⎢

+

_⎥

⎣

⎦

(12)

Eq. (12) shows that shocks are shared across countries. The home consumption increases with positive

home and foreign shocks because higher productivity lowers both the domestic and foreign prices. On

the contrary, higher tariff increases the domestic import price level and thus reduces the consumption.

However, the imposition of the tariff affects the consumption in the domestic economy only. The share

of the tradable goods in the overall consumption determines the magnitude of these effects.

Because all the variables follow lognormal distribution, take logarithms for the Euler equation Eq. (8)

under flexible prices. Substitute the interest rate rule, consumptions in Eq. (12) and solve the price level

recursively, then we can write the price level in terms of expected future consumption growth and

variances of endogenous variables, which are assumed constant over time:

2 * 2 1 1 1 1 log 1 2 2 2 2 a t t t c a p

ρ

γ

a

γ

a

β

i

ρ

σ

σ

ρ

ω ρ

ω

⎛ ⎞ − ⎡⎛ ⎞ ⎤ = _⎢⎜ − _⎟ + _⎥+ _⎜ + + + + _⎟ + − ⎣⎝ ⎠ ⎦ ⎝ ⎠ 2 p

σ

cp

(13)

All lower cases denote the logarithm of the variables. Because both the exchange rate and prices can

adjust freely, none of the tariff influences the home aggregate price level. However, relative tariff drives

exchange rate movements. The combination of consumption and price level, Eq. (12), (13) and the

risk-sharing condition, Eq. (9) yields the nominal exchange rate:

(

)

₍

*

₎

,

1

1

FP t t t a

a

a

_ξt

ω

γ

ξ

ω ρ

−

=

−

+ Γ

+ −

(14)

where

(

)

* ,

2

FP t ξ

γ τ τ

−

Γ = −

Here we make use of the fact that

log 1

(

+  when τ

τ

)

τ

is small. This equation holds under the

assumption that

. It is shown that higher home productivity reduces home prices

relative to foreign and thus the nominal exchange rate depreciates in reaction to the relative productivity

movement. On the other hand, greater home tariff leads to the nominal exchange rate depreciation to

diminish the magnitude of the domestic demand shift from import to the home goods due to the tariff.

* 1 , 1 ,

FP FP

t c t t c t

E

₋

Λ =

E

₋

Λ

Following past studies, we are interested in whether the tariff policy is contractionary or expansionary.

In the monopolistic competition market, because the productions of each country consist of the goods

sold to the domestic and foreign markets, the home production can be obtained from the world demand

for home goods, Eq. (6), combined with relative prices:

* , ,

t H t N t H,

Y Y

=

+

Y

+

Y

_t

(15)

Substituting prices from Eq. (11), the home tradable prices and consumptions in Eq. (12) with Eq. (15)

yields:

(

)

(

)

(

)

(

)

(

)(

)

(

)

1 * 1 * *

2

1

1

1

1

1

exp

2

2

2

2

2

1

2

1

1

2

1

exp

2

2

2

2

t t t t t

Y

a

a

a

a

ρ ρ

γ

ρ

γ

ρ

γ ρ

γ

θ

_τ

κθ

ρ

ρ

ρ

ρ γ ρ

γ

ρ

γ ρ

ρ

γ θ

_τ

κθ

ρ

ρ

ρ

⎧

⎛

−

−

⎞

−

−

⎫

−

⎪

⎪

⎛

⎞⎛

⎞

= −

_⎜

_⎟⎜

_⎟

_⎨⎜

_⎟

+

+

_⎬

⎝

⎠⎝

⎠

⎪

⎩

⎝

⎠

⎪

⎭

⎧

⎛

−

−

⎞

−

−

⎛

− −

⎞

⎫

−

⎪

⎪

⎛

⎞

+

_⎜

_⎟

_⎨⎜

_⎟

+

+

_⎜

_{⎟ ⎬}

⎝

⎠

⎪

⎩

⎝

⎠

⎝

⎠

⎪

⎭

(16)

where

(

)

, 1 0 2 FP FP t H t Y Y

γ ρ

τ

ρ

⎛ − ⎞ ∂ _{= >} ⎜ ⎟ ∂ _{⎝ ⎠}

,

(

)

, * 1 2 0 2 FP FP t F t Y Y γ ρ ρ τ ρ ⎛ − − ⎞ ∂ _{= <} ⎜ ⎟ ∂ _{⎝ ⎠}

.

The home tariff is expansionary for its domestic output when

ρ

>1

, but the foreign tariff is

contractionary for the home production.

While the current home tariff has a direct negative effect on the

aggregate consumption by raising up the aggregate price level, it also causes the home demand to shift

toward the home produced goods due to the deterioration of the home terms of trade. The substitution

effect in the latter dominates and thus the overall home production benefits from the protection policy.

On the other hand, the foreign tariff reduces the foreign aggregate consumption as well as the import

from home firms to the foreign market, and thus leads to lower home export. Note that, the future tariff

plan does not influence the production.

The welfare under flexible prices can be evaluated by the expected utility:

1 0

1

1

i t

E

C

ρ

κ

ρ

−

⎛

−

⎜ −

⎝

⎠

i t

L

⎞

_⎟

t

Where

Lt =Yt /A

.

4. Optimal Pricings and Equilibriums under Alternative Nominal Rigidities

The optimal pricings under PCP and LCP are listed in Table 1. The results are essentially same as

those in Devereux and Engel (2003), except that the aggregate price level in the equation contains the

tariff. Prices are predetermined one period ahead before the profit is realized. Producers choose optimal

prices by maximizing expected profits. The first-order derivation of a home firm with respect to the

price of the goods sold in the domestic economy is as follows:

, , , 1 , , ,

0

i i i H t H t H t t t t i i i t H t H t H t

P Y

Y

C

L

E

P

P

Y

P

ρ

κ

− −

⎧

⎡

∂

⎤

∂

∂

⎫

⎪

₋

⎪

₌

⎢

⎥

⎨

_∂

_∂

_∂

⎬

⎢

⎥

⎪

⎣

⎦

⎪

⎩

⎭

Other firms follow the same pricing process. However, the price setting for export firms varies with PCP

and LCP. Under PCP, producers choose optimal prices in their own currency to maximize expected

profits as the traditional pricing adopted by Fender and Yip (2000). Prices for goods sold in the foreign

country are converted into the foreign-currency prices by using exchange rates, thus the law of one price

holds for tradable goods. Under LCP, producers preset prices in consumers’ currency so there is no

exchange rate pass-through onto export prices. Therefore, the law of one price may not hold.

Table 1: Optimal Pricings under PCP and LCP

PCP LCP

(

)

( )

1 , , 1 1 / 1 t t t t PCP PCP H t N t t t E PC A P P E C ρ κθ θ − − − ⎛ ⎞ = _{= ⎜ ⎟} − ⎝ ⎠ , , LCP LCP PCP , H t N t H t P =P =P * , , PCP PCP H t H t P =P ς_t

(

)

(

)

* * 1 * , *1 1 / 1 t t t t LCP H t t t E P C A P E C ρ κθ θ − − − ⎛ ⎞ = ⎜_{⎝ −} ⎟_⎠ * , , PCP PCP F t t F t P =

ς

P

(

_{( )}

)

* 1 , 1 1 / 1 t t t t LCP F t t t E P C A P E C ρ κθ θ − − − ⎛ ⎞ = ⎜_{⎝ −} ⎟_⎠

(

)

(

)

* * * 1 * * , , *1 1 1 t t t t PCP PCP F t N t t t E P C A k P P E C ρ θ θ − − − ⎛ ⎞ = _{= ⎜ ⎟} − ⎝ ⎠ * * * , , , LCP LCP PCP F t N t F t P =P =P

In monopolistic competition markets, the production is determined by consumption demands. To

examine the effects of the tariff on the output in the equilibrium, we need to know the price and

consumption first. The explicit solutions of prices and consumption can be obtained by taking similar

steps in the flexible-price case. Because all variables are lognormally distributed, we can easily derive

1

t t

E C₋

and

* 1

t t

E C₋

from prices in Table 1 by using the price indices in Eq. (5).

Under LCP, the logarithm of the combination of

P

_{H t}LCP_,

and

P

_{F t}LCP_,

yields

E c_{t−1 t}LCP

in terms of

exogenous productivity shocks:

(

)

(

)

(

*

)

* 1 1

1

2

log

log 1

1

2

2

2

LCP t t t t ca t t _ca Ec

E c

θκ

γ

τ

γ

E a

σ

γ

E a

₁

σ

ρ

θ

ρ

ρ

ρ

− −

−

−

=

−

+ +

+

+

+

−

−

+ Λ (17)

where

includes all the moments associated with the expectation under the lognormal distribution.

Negative productivity shocks and higher tariff raise the aggregate price level and thus lead to lower

consumption level. The share of tradable goods,

Ec

Λ

γ , dictates these impacts. Use the fact that

E P_{t t+1}=P_t+1

,

then the log-linearized Euler equation for home households, Eq. (8), can be written as:

(

) (

)

2 2 1 1

1

log

log 1

2

t t t t t t c

c

E c

β

i

p

p

ρ

σ

ρ

+ +

⎡

⎤

=

−

_⎢

+

+

−

−

+

_⎥

⎣

⎦

(18)

By taking the expectation one period ahead and substituting

E c_{t t+1}

from Eq. (17), we can derive the

explicit solution of

p which essentially contains the information available at the period

_t

t

− . Eq. (8)

1

with the substitution of

p and

_t

p

_t+1

generates

c_t

.

Under PCP, however, the exchange rate pass-through complicates the computation. The exchange rate

can be driven by the tariff as well as macroeconomic discrepancies and thus affects the terms of trade

and the international demands for tradable goods. The price and consumption in these two countries can

not be solved separately, but we need to find the global equilibrium. Define

x_tT = +x_t x_t*

and

*

D

t t t

x = −x x

represent the sum and difference of the variable

x and

_t x_t*

. We can obtain

E c_{t−1 t}T

from

the logarithm of the combination of

PCP_,

and

:

H t P * , PCP F t P

(

)

1 1 1 ln 1 ln 2 1 T T T t t t t t E c E a

γ

τ

2

κθ

ρ

ρ

ρ

θ

− = − − + − ⎛⎜ ₋ ⎞⎟ ⎝ ⎠

(19)

Let

(

)

(

)

* , 1 2 2 PCP PCP PCP t H t

p = −

γ

p +

γ

p_{F t,}

so that the home aggregate price level

p can be written as

_t

(

γ

2

)

ξ

_t

+

p

_t

+

(

γ

2 log

) (

1

+τ

)

. By doing so, we can separate the predetermined part in the aggregate

price level from the nominal exchange rate which fluctuates with innovations. Substitute the aggregate

price level into the Euler equation, then we can obtain the dynamics of the aggregate price index similar

to Eq. (18):

( )

(

)

(

)

2 2 1 1

1

2 log

log 1

2

T T T T T t t t t t t c

c

E c

β

i

p

p

ρ

σ

ρ

+ +

⎡

⎤

=

−

_⎢

+

+

−

−

+

_⎥

⎣

⎦

T

Following the similar steps in the LCP case, we can solve

T

and

.

t p ctT D t p

and

D t c

can be derived

by substituting the nominal exchange rate from the risk-sharing condition into

and

. The

impacts of the tariff on the price and consumption are listed below where

, PCP H t P P_{F t}*_,PCP , xτ

on the variable

x

and

Γ_x,τ

represents the impacts from

τ*

.

Table 2: Macroeconomic impacts of tariffs in the home country

Prices

, , 0 PCP LCP pτ pτ Γ = Γ =

,

_,* _,* 0 PCP LCP pτ pτ Γ = Γ =

Consumptions

, , 2 PCP LCP cτ cτ γ τ_ρ − Γ = Γ =

,

* * , , 0 PCP LCP cτ cτ Γ = Γ =

Nominal exchange rate

, ,

2 PCP LCP ξ τ ξ τ γ τ Γ = Γ = −

,

* * * , , ₂ PCP LCP ξ τ ξ τ γ τ Γ = Γ =

Interestingly, the impacts of tariff are identical under LCP and PCP, however, the adjustment mechanism

behind differs. Since prices are predetermined, the permanent tariffs reduce expected consumptions as

well as the prices. Under PCP, the exchange rate movements caused by the tariff discrepancy offsets the

ex ante terms of trade and thus the law of one price holds ex post. While the exchange rate pass-through

is absent under LCP, the expected consumption drops directly with the permanent tariff and thus LCP

firms’ ex ante pricing react more to the tariff than PCP firms.

5. Welfare Implication of the Tariff under PCP

Because the law of one price holds under PCP and the government refunds the tariff revenue to

consumers, the current account balance remains zero under the assumption of Cobb-Douglas preferences

and zero initial debt.

12

The balanced current account states that the condition

holds for all periods. Therefore, the home output under PCP can be written as:

H H N N H

PC

=

P Y

+

P Y

=

P Y

12

The refund of tariff revenues assures the purchasing power of domestic households, even with the presence of tariff, and thus the zero current account balance which holds in Obstfeld and Rogoff also holds here.

(

)

( )

(

)

_{( )}

(

)

(_{( )})

(

)

( )

(

)

(

)

(

)

(

(

)

)

2 2 1 * 2 1 _{2 1 4 1} 4 1 2

1

1

2

exp

1

2 1

2 1

4 1

4 1

PCP PCP PCP t t t t t

Y

C

C

c

c

ργ ργ γ γ γ γ _γ

_τ

_γ

_τ

γ

γ

γ

ργ

ργ

γ

_τ

_τ

γ

γ

γ

− + _∗ − − − − ∗ ∗

=

+

+

γ

⎧

⎛

⎞

⎛

⎞

⎛

⎞

⎛

−

⎞

⎫

⎪

⎪

=

⎨

_⎜

⎜

₋

+

⎟

_⎟

−

_⎜

⎜

₋

⎟

_⎟

−

⎜

_⎜

₋

⎟

_⎟

+

⎜

_⎜

₋

_⎟

⎟

⎬

⎪

⎝

⎠

⎝

⎠

⎝

⎠

⎝

⎪

⎩

⎠

⎭

(20)

Here we let

log 1

(

+

τ

)

≈ . Thus, the impact of tariffs on the home output is:

τ

(

1

)

0

2

PCP PCP t t

Y

Y

γ ρ

τ

ρ

−

⎛

⎞

∂

=

_⎜

_⎟

>

∂

_⎝

_⎠

,

_*

0

PCP t

Y

τ

∂

=

∂

The sign of

∂Y_tPCP ∂

τ

is positive as

ρ

>1

, while the output is independent of the foreign tariff. The

home production benefits from the deterioration of the terms of trade caused by the home tariff.

Apparently, the effect of the foreign tariff on the home export is diminished by the exchange rate

adjustment.

Proposition 1:

Under PCP, the home tariff is expansionary for the home country while the foreign tariff

stays independent of the home production.

The expected utility can be obtained from the consumption and the expected labor supply which is

essentially determined by the production level for monopoly firms. Substituting the optimal pricing into

the expected labor supply, the expected utility under PCP is mainly a function of home consumption:

(

)

(

)

(

)

1 1 1 2 2 1

1

1

1

1

1

1

exp

1

1

2

PCP PCP PCP PCP t t t t t PCP t t c

W

E U

E

C

E c

ρ

θ

ρ

θ

ρ

θ

_ρ

_σ

ρ

θ

− − − −

⎡

−

⎤

=

=

_⎢

−

_⎥

−

⎣

⎦

⎧

₋

⎫

⎡

−

⎤

⎪

⎪

=

_⎢

−

_⎥

_⎨

−

+

_⎬

−

⎣

⎦

⎪

_⎩

⎪

_⎭

(21)

(

1

)

0

2

PCP PCP t t

W

W

γ ρ

τ

ρ

−

⎛

⎞

∂

=

_⎜

_⎟

<

∂

_⎝

_⎠

13

,

*

0

PCP t

W

τ

∂

=

∂

Different from its effect on the output, the home tariff places a negative impact on the home welfare.

There is a tradeoff between consumption and labor supply in the utility evaluation. While higher

consumption raises the utility level, greater labor supply which generates higher income reduces the

utility level. Because the home tariff increases the home production, the negative effect of higher labor

supply on the utility dominates the welfare gain from higher consumption. The foreign tariff does not

influence the home welfare as it does to the home production and consumption for the same reason.

Proposition 2:

the home tariff lowers the home welfare, while the home welfare is independent of the

foreign tariff’s impact.

6. Welfare Implication of the Tariff under LCP

Under nominal rigidity, the production is determined by demand. Therefore, the home output under

LCP can be written as follows with the substitution the LCP optimal pricing into the output in Eq. (16):

(

)

₍

₎

1 2 * 2 2 _{, , *} * * , , 1 2 1 2 1 H t F t LCP t t t F t t H t P P Y C P P γ γ γ

γ

γ

τ

τ

− − _{⎛ ⎞} ⎛ ⎞ ⎛ ⎞ _{⎜ ⎟} = −⎜_{⎝ ⎟ ⎜}⎜ ₊ ⎟_⎟ + _{⎜ + ⎟} ⎠ ⎝ ⎠ _{⎝ ⎠} Ct

Substituting the optimal pricing into the output, then the home production can be written as:

{

}

{

}

1 1 * * * * 1 1 1 1 exp 2 1 exp 2 LCP LCP LCP LCP t t t t t LCP LCP LCP t t t t t t YF Y c E c E c E c E a

γ

θ

_ρ

κθ

γ θ

_τ

_ρ

κθ

− − − − − ⎛ ⎞⎛ ⎞ _{⎡ ⎤} = −_{⎜ ⎟⎜ ⎟ ⎣} − _⎦+ + Λ ⎝ ⎠⎝ ⎠ − ⎛ ⎞ _{⎡ ⎤} + _{⎜ ⎟} − +_⎣ − _⎦+ + ⎝ ⎠ t YH a Λ

where

Λ

_YH

and

Λ

_YF

represent the related moments. The impacts of tariffs on the home production are

13

Here, we let Γ_U,τ = −(1 ρ)Γ_c,τ instead of (1−ρ)Γ_c,τ because the impacts of the tariff on the welfare is not solely

(

)

,

1

0

2

LCP LCP t HT t

Y

Y

γ ρ

τ

ρ

⎛

−

⎞

∂

=

_⎜

_⎟

>

∂

_⎝

_⎠

, (22)

*

(

)

, 1 1 0 2 LCP LCP t F t Y Y

γ ρ

τ

ρ

⎡⎛ − ⎞⎤ ∂ _{= − <} ⎢⎜ ⎟⎥ ∂ _{⎢⎣⎝ ⎠⎥⎦}

where

Y

_{HT t}LCP_,

denotes the home goods sold in the domestic economy,

Y

_{H t}LCP_,

+

Y

_HLCP_*,t

. The home tariff

raises the production in the home country. Instead of being a portion of the total home output, the home

tariff affects the home production through the domestic consumption of the home goods, while the

foreign tariff ‘s impact is solely from the foreign consumption. Since the exchange rate movements do

not affect tradable prices, the ex ante terms of trade movement due to the imposition of the tariff remains

ex post. The foreign tariff improves the home terms of trade, reduces the demand for the home export

and finally results in lower home production.

Proposition 3:

The home tariff is expansionary for the home production while the foreign tariff has a

negative effect on the home output.

Following the same steps, the welfare under LCP is:

(

)

(

)

(

)

(

)

* 1 2 2 1 2 * * 2 1 1 1 1 1 exp 1 1 2 2 1 1 exp 1 2 2 LCP LCP LCP LCP t t t LCP t t c LCP t t _c W E U E c E c

ρ

γ

θ

_ρ

ρ

θ

ρ

γ θ

_τ

_ρ

_σ

θ

− − − =

σ

⎧ ₋ ⎫ ⎡ ⎛ ⎞⎛ − ⎞⎤ ⎪ ⎪ =_⎢ − −_{⎜ ⎟⎜ ⎟⎥ ⎨} − + _⎬ − ⎝ ⎠⎝ ⎠ ⎣ ⎦ ⎪_⎩ ⎪_⎭ ⎧ ₋ ⎫ − ⎪ ⎪ ⎛ ⎞ − _{⎜ ⎟ ⎨}− + − + _⎬ ⎝ ⎠ _{⎪⎩ ⎪⎭}

(23)

The tariffs impacts on the welfare can be stated as follows:

(

)

,

1

0

2

LCP LCP t H t

W

W

γ ρ

τ

ρ

−

∂

=

<

∂

,

_*

(

1

)

1

_,

2

LCP LCP t F t

W

W

γ ρ

τ

ρ

−

⎛

⎞

∂

0

= −

_⎜

+

_⎟

∂

_⎝

_⎠

>

to the PCP case, the positive effect of the home tariff on the labor supply places a negative effect on the

home welfare which dominates the positive effect of higher consumption on the utility. As we can see,

the home tariff’s impact on the home production is relatively limited under LCP than PCP as it

influences only part of the consumption and labor supply. Moreover, the foreign tariff now acts to

improve the home welfare by reducing the home export and labor supply.

Proposition 4:

The home tariff diminishes the home welfare, while the foreign tariff is beneficial. The

effect of the home tariff is small under LCP than PCP.

7. Conclusion

The objective of this paper is to investigate the effects of tariffs on an economy under alternative pricing

behaviors, PCP and LCP, which incur different exchange rate pass-through and expenditure-switching

effects. While most of past studies use static models to examine the tariff’s effect, this study conducts

the issue of the trade protection policy in a two-country dynamic general equilibrium model.

The analytical solutions shed light on the importance of the exchange rate pass-through in the

macroeconomic and welfare implications of the tariff. While the tariff has identical effects on prices and

consumption under PCP and LCP, different mechanisms arise. Under PCP, the exchange rate adjustment

offsets the ex ante price discrepancy and thus the law of one price holds. As a consequence, the home

tariff decreases the home production while the foreign tariff does not and its effects are removed by the

exchange rate movements. The lower labor supply associated with the lower production improves the

home welfare. The effects of the foreign tariff on the home output and welfare are absent. On the other

hand, the exchange rate fluctuations do not affect the ex post terms of trade under LCP. Therefore, firms

decrease the prices directly with the imposition of the home tariff which results in lower consumption

demand. It thus causes the home production contraction and welfare improvement.

Many interesting issues can be analyzed under this framework. As discussed in Mundell (1961), the

exchange rate regimes, flexible or fixed, may lead to different effects of the tariff on the economy. This

result may differ under the dynamic general equilibrium setting. Lastly, while the analytical solution in

the model can elucidate the effects of protection policy on the economy, this model is subject to certain

assumptions and thus fails to capture some important aspects of this issue. For example, we may

calibrate a more general specification of the model to observe the dynamic adjustment that

macroeconomic variables respond to a temporary protection.

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計畫成果自評

1. 研究內容與原計畫相符程度：

本研究內容與原計畫主題相符，唯使用之研究方式不同。原計畫預計採用校

對模擬方式 (calibration) 針對關稅問題進行動態分析，而本研究內容則以一

理論模型之分析解來作關稅政策之評估。採用後者的主因是，分析解更便於

提供政策制定者評估相關變數變動時對於政策效果之影響

2. 達成預期目標情況：

本研究約達成原計畫預計目標之 95%

3. 研究成果之學術或應用價值：

本研究是以一兩國模型架構，於不同的名目僵固性 (producer-currency pricing

(PCP) 與 local-currency pricing (LCP)) 之下探討關稅政策對於總體經濟與福

利的影響分別為何。過往研究普遍僅採取其中一種名目僵固性 (PCP) 來進行

貿易政策之分析；然而近年來，實證研究發現，LCP 的現象遠較 PCP 普遍；

相關理論研究亦證實，不同的名目僵固性對於最適貨幣政策與匯率制度具有

重要的影響。因此本研究於學術上具有顯著貢獻。除此之外，本研究成果可

作為政府單位制定貿易政策之參考。

4. 是否適合在學術期刊發表或申請專利：

本研究預計於國際期刊上發表 1-2 篇文章。

5. 主要發現或其他有關價值等：

本研究主要是在探討匯率轉嫁 (exchange rate pass-through) 的程度對於貿易

政策之影響。在 PCP 之下，關稅可完全轉嫁至貿易財價格，使得匯率的變

動得以減緩關稅對於價格與消費的影響。另一方面，LCP 下，匯率無法轉嫁。

本研究發現，不論是在 LCP 或是 PCP 之下，本國關稅對於本國的產出皆具

有正面效果，並對福利造成負向的影響；但在 LCP 下，本國關稅對於本國

經濟的影響較小。另一方面，外國關稅在 PCP 的環境裡不會影響本國產出

與福利，外國關稅在 LCP 下卻會使得造成本國產出的下降以及福利的提昇

(因為勞動供給減少)。此研究結果與過往僅在 PCP 的設定下進行的關稅政策

評估所得之結果有所不同，並可提供貿易政策之政策制定者重要的訊息： 在

一普遍採取 LCP 的經濟體中，關稅政策的施行對於本國經濟所造成的影響

較小。

Macroeconomic Implications of the Trade Protection Policy

under Local-Currency Pricing

Yu-Ning Hwang

1

Department of Economics

National Chengchi University

June 2008

The 83rd Annual Conference, Western Economic Association International

報 告 論 文

June 30 2008

Abstract

The imposition of a tariff is the most widely used protection policy in international trades and has been a long-lasting issue in international economics. This paper uses a two-country dynamic general equilibrium model to examine the effects of the tariff on the world economy under local-currency pricing (LCP). Because prices are predetermined ahead of the time the consumption takes place, we emphasize the importance of the timing of the policy announcement and the information set for the expectation. The analytical solutions available in this model show that the information discrepancy between the producer and consumer is critical to the tariff’s impact on the aggregate consumption and production. Three alternative policy plans are considered. While the anticipated home policy shock causes contractionary impacts of the trade policy on the domestic output, whether the unanticipated permanent and temporary policy shocks are expansionary or contractionary depends upon how risk averse the agents in the economy are. In all cases, the foreign tariff reduces the home productions.

Keywords: Keyword：Tariff, Nominal rigidity, Local-currency pricing JEL Classifications: F13; F41; E42

1*

Yu-Ning Hwang is an Assistant Professor in the Department of Economics at National Chengchi University, Taipei, 116 Taiwan. Comments are most welcome. Contact details: e-mail to [email protected]; Tel.: 886-2-29393091 ext. 51641.

1. Introduction

One of the primary tools of trade protection policies is the imposition of import tariffs. In recent years, many cases are going on among the major countries. For example, in 2004, the European Union (EU) imposed a retaliate tariff on U.S. exports for the export tax subsidy applied by the U.S. government to U.S. producers. In 2006, the EU placed anti-dumping tariffs on goods exported from China. The producers of the EU seem to be the only winner, while retailers and consumer groups opposed to the move. Early trade literature shows that tariffs are contractionary (Krugman (1982)), such that prices go up and lower quantities are caused. The imposition of tariffs thus may turn to hurt domestic consumers’ welfare. Evaluating the influences of the trade policy on the economy, in particular, on the welfare, is an important job for the authorities.

This has long been an important issue in international macroeconomics, though not too many endeavors devoted to it with intertemporal optimization. There are consensus in the early studies, as surveyed by Krugman (1982), that monetary polices are contractionary in an economy with a flexible exchange rate regime while expansionary under a fixed exchange rate regime. However, these studies are based on ad hoc assumptions of behavior and a small open economy. The absence of micro-foundations implies the failure of welfare assessments of policies. The small open economy model also neglects the transmission mechanism of shocks across countries. Rare studies in the past two decades discuss the macroeconomic effects of tariffs based on intertemporal utility optimization and a two-country framework (Sen and Turnovsky (1989), Fender and Yip (2000)).

The effects of a tariff under alternative exchange rate regimes have long been discussed in literature. This issue was initiated by Mundell (1961). He uses a static model with nominal rigidity and argues that the output declines with the imposition of the tariff under flexible exchange rates, while increases under fixed exchange rates. The depressing effect under flexible exchange rates comes from the Laursen-Metzler effect, which suggests that the tariff induces higher saving while suppressing consumption. Because predetermined consumer prices were kept constant under fixed exchange rate, the tariff increases the import prices, improves the home terms of trade, and thus increases the world demand for home tradable goods as well as the domestic nominal

income.

After the collapse of the Bretton Woods System, researchers have paid much attention to trade policies under flexible exchange rates and more endeavors were devoted to this issue, such as Boyer (1977), Chan (1978) and Eichengreen (1981) among others. While Mundell uses a static model, Eichengreen (1981) uses a dynamic model to analyze the short-run and long-run effects of a tariff under flexible exchange rates. He finds that a tariff can be expansionary in the short run, contrary to Mundell’s argument, but contractionary in the long run. In general, the imposition of a tariff faces trade-offs: the direct effect on the welfare from the improvement of the terms of trade, which induce greater world demand for home goods, and the indirect effect from the appreciation of home currency. The studies based on Mundell’s framework were surveyed by Krugman (1982) who concludes the consensus that mostly coincide with the combination of Eichengreen and Mundell’s propositions.

However, these studies lack micro-foundations and thus fail to measure social welfare appropriately. Sen and Turnovsky (1989) use an intertemporal optimization framework to study the effects of unanticipated permanent, anticipated temporary, and anticipated permanent tariffs on the economy and, in particular, on the current account balances. They find that a tariff is contractionary both in the short run and long run. Both output and employments are suppressed. Their study emphasizes the role of capital accumulation, the main factor that drives the current account movements. While their study is based on a small open economy, the shock transmission mechanism is neglected.

Thus, the objective of this study is to examine the effects of the tariff on the economy in a two-country dynamic general equilibrium model with monopolistic competition and nominal rigidity. The monopoly power embodied in each monopoly firm justifies its ability to keep the prices unchanged for some periods in face of shocks. Equipped with micro-foundations, this class of model has been used for many international macroeconomic issues and policy evaluations in the past decade, after it was initiated by Obstfeld and Rogoff (1995). While most of the studies based on the model examine exchange rate regimes and international business cycles, relatively scarce studies focus on trade related issues. Bacchetta and Wincoop (2000) examine the relationship between exchange rate flexibility and trade, and find that exchange rate fluctuations do not affect