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Competitive depreciation and the role of distorting taxes in an interdependent economy
Journal of International Money and Finance 32 (2013) 462–477
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Journal of International Money and Finance journal homepage: www.elsevier.com/locate/jimf
Competitive depreciation and the role of distorting taxes in an interdependent economyq Satoko Takamatsu* School of Political Science and Economics, Waseda University, 1-6-1 Nishiwaseda, Shinjyuku-ku, Tokyo 169-8050, Japan
a b s t r a c t JEL classification: E52 E63 F42 Keywords: Competitive depreciation Inflation Welfare spillover Monetary policy International cooperation
This paper investigates the manners in which international cooperation in monetary policies affects the rate of inflation in a twocountry sticky-price model. Within reasonable parameter values, international monetary coordination increases the steady-state inflation for given tax policies. When the tax regime is endogenously chosen, however, self-oriented monetary policies can engage in competitive depreciation and induce a higher average inflation than the first best inflation rate. 2012 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, there have been calls for Japan and China to alter their exchange-rate policies. While Japan’s efforts to weaken the yen and China’s implicit peg to the U.S. dollar may be good for domestic employments in these economies, the policies can trigger competitive depreciations and systematic inflation. China has begun to pose concerns about inflation and is often thought to signal the upcoming revaluation. Are these policies good for Japan and China but bad for the rest of the world? Would Japan, China, and the rest of the world achieve a better management of inflation with increased international cooperation on exchange-rate policies?
q The author would like to thank R. Anton Braun, Shin-ichi Fukuda, Masahiro Kawai, Hiroshi Ohashi, Maskoto Saito, Yasuyuki Sawada, and a referee for their comments. In addition, the author also acknowledges the financial support from Grants-in-Aid for Scientific Research. * Tel.: þ81 3 3202 4240. 0261-5606/$ – see front matter 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jimonfin.2012.05.022
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Rogoff (1985) provides one answer to these questions. He argues that increased international monetary cooperation may raise the rate of inflation. Using a sophisticated modern framework, Obstfeld and Rogoff (1995) also show that the surprise monetary expansion has a positive welfare spillover. In light of these prominent papers, has the Mundell–Fleming–Dornbusch result of competitive devaluation become outdated? More recent literature suggests that this is not the case. Some studies (Betts and Devereux (2000) and Jensen (1997), among others) show that monetary expansion can produce a negative welfare spillover under enriched environments. In considering these pros and cons, the literature thus far assumes that no distorting taxes are present or that taxes merely play secondary roles in supporting the monetary policy. In reality, taxes distort decision making in the private sector, and it is interesting to discover what happens if we relax these assumptions. This paper addresses this question and finds that, in the absence of an endogenous choice of tax policies, international monetary cooperation raises the rate of inflation. On the other hand, if taxes are set in accordance with the monetary regime, competitive depreciation is possible. Our model considers a two-country economy similar to that of Obstfeld and Rogoff (1995, 2000), except for the presence of distorting taxes. Goods markets are under monopolistic competition and the prices in producers’ currencies are set before the technology shock occurs. Prices are inefficiently high due to monopoly markups and price setting under uncertainty, which potentially motivates governments to correct. Since the tax policy is chosen by collective opinions within a country, it has an implementation lag and cannot react to ex-post productivity shocks. The monetary policy, on the other hand, is implemented by a delegated decision-maker such as the central bank and can be determined under discretion. Prices are sticky and hence do not respond to policy shocks in the short run. Once prices are set and all shocks have been revealed, each monetary authority supplies money. We examine how the optimal rate of money growth changes with cooperation between monetary authorities. This paper assumes that governments monitor utility from consumption and the disutility of work effort. Owing to the law of one price and unit intratemporal elasticity,1 consumptions are equated and produce no conflict between nations. However, since there are no markets to trade the risks of country-specific fluctuations in production, labor is a source of conflict between the objectives of different countries. Each monetary authority has the incentive to use contractions to reduce work efforts in favor of their own country and expansions to increase consumption. By cooperating, countries endogenize the exchange rate externality that improves the purchasing power of foreign residents. Other things being equal, each central bank depends on the other to expand its money supply and to benefit overseas consumers, at the cost of reducing their own residents’ leisure. This positive welfare spillover can be overturned, however, when distorting taxes are endogenously determined. If a fiscal authority switches its objective in accordance with the international cooperation regime, the Pigouvian subsidy is optimal under cooperation and the coordinated monetary policy produces no inflation or deflation. On the other hand, under reasonable parameter values, the self-oriented tax policy can be less likely to boost the aggregate demand compared to the monetary policy, which gives the monetary policy an incentive to engage in competitive depreciation. One of the most notable results on the international welfare spillover of monetary policy is the “beggar-thy-neighbor” effect indicated by Mundell (1963, 1964), Flemming (1962), and Dornbusch (1976). In contrast to these works, Rogoff (1985) analyzes a reduced-form model and argues that inflation might be systematically higher under monetary cooperation than under monetary noncooperation. Obstfeld and Rogoff (1995) further develop a model using micro-foundation, which analyzes the short-run deviation from the steady state and demonstrates that monetary
1 In order to insulate the effect of monetary expansion on the current account when extending the analysis to a multiperiod setting, the intratemporal elasticity is set to unity so that the expenditure-switching effect and the change in the real price of products directly offset each other.
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surprise has a positive welfare spillover. Such a property of monetary expansion, that is, the beggar-thy-self effect, corresponds to the case of exogenous tax determination in this paper.2 Under enriched environments, however, it became apparent that monetary cooperation can be welfare improving. Jensen (1997) qualifies Rogoff’s result (1985) by arguing that if wage-setters are non-atomistic and inflation averse, cooperation leads to higher employment and possibly lower inflation. Betts and Devereux (2000) consider the pricing-to-market model in which the relative risk aversion is limited to unity. They show that a monetary authority has an incentive to engage in competitive depreciation for a high degree of pricing-to-market. In addition, although the interest of their paper is not necessarily policy coordination, Corsetti et al. (2000) develop a center-periphery model and show that devaluation can be the optimal strategy for neighboring countries. Tille (2001) also demonstrates that positive monetary shocks have a beggar-thy-neighbor effect if home and foreign goods are close substitutes. This paper contributes to this body of literature by demonstrating the case in which monetary cooperation can produce a lower inflation with the generalized specification of tax schemes. Clarida et al. (2002) design the production subsidy such that the steady-state inflation is zero a priori and analyze how well the monetary policy can offset unanticipated disturbances. Benigno and Benigno (2003) show the importance of sales tax in controlling the inflationary bias of the monetary policy. They derive the condition in which price stability is efficient in a two-country model, but the behavior of a biased monetary policy is not fully articulated. It is important to note, however, that a more detailed policy implication can be obtained in an environment in which distorting taxes affect the private sector’s behaviors as in the real world. Braun (1994) argues that personal and corporate income tax rates have significant effects on postwar US business cycle fluctuations. Benigno and Woodford (2005) suggest that assuming an output subsidy that attains the zeroinflation steady state is not realistic, and propose to analyze the steady state in which output is inefficient owing to the distorting taxes on sales revenues or labor income, in addition to the monopoly markups. In light of these observations, our producer–consumer economy analyzes the systematic inflation/deflation, that is, how the monetary policy behaves in the distorted steady state, by considering two cases: one with constant sales taxes and the other with sales taxes synchronized with monetary regimes. Our framework that the monetary policy can have a negative welfare spillover is consistent with Svensson and Wijnbergen (1989). Using a multi-period model, they show that monetary spillover effects may be either positive or negative, depending upon whether the intertemporal elasticity of substitution exceeds the intratemporal elasticity of substitution. In their model, goods markets open before asset markets, and monetary policy affects the economy of tomorrow. In our model, since money transfer occurs before goods trading, the monetary policy works today. The inverse of the consumption elasticity of money demand in the present paper corresponds to their intertemporal elasticity. We clarify that, even without savings devices, monetary expansion can have either a positive or a negative international spillover. This paper is organized as follows. Section 2 outlines the analytical framework. In Section 3, we derive a closed-form solution for the private sector’s equilibrium. Section 4 discusses the monetary policy and provides the numerical implications. Section 5 discusses the effects of a tax policy. Section 6 concludes the paper.
2. Model We consider a two-period model and refer to these periods as time 0 and 1. There are two symmetrical countries, the home and foreign countries. All households are consumer–producers called yeomen. Each yeoman specializes in the production of a differentiated good using his or her own labor
2 It is known in the literature that new open economy macroeconomics (NOEM) models can produce implications that run contrary to the textbook results of the Mundell-Fleming model. For instance, Çenesiz and Pierdzioch (2009) incorporate efficiency wages into an NOEM model and find that financial market integration increases the fiscal multiplier. In addition, Darius (2010) suggests that a government expenditure shock depreciates the nominal exchange rate and generates real effects under the fixed rate system.
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and is the only producer of that good. Individuals are indexed by intervals such that h˛[0,n], and f˛(n,1]. Goods are produced under monopolistic competition, and their prices are inefficiently high. Expost prices can be further inefficient because yeomen are supposed to set their product prices one period in advance. Yeomen inelastically supply labor and therefore products. All goods are tradable. At time 0, fiscal authorities announce the time 1 tax rates, and yeomen pre-set product prices in the domestic market, Ph or Pf. At the beginning of time 1, productivities are revealed. At time 1, monetary authorities inject money, the exchange rate is determined, yeomen produce output and consume, and fiscal authorities levy sales and lump-sum taxes. 2.1. Household The preference for a home yeoman of type h is defined over consumption Ch, the real balance Mh/P, and the work effort from production Yh.
Uhh
Ch
1r
1r
þc
1ε M h =P 1ε
k
Yh
n ;
n
where r > 0, r s 1, c > 0, ε > 0, ε s 1, k > 0, and n > 1. M represents the money holdings at the beginning of time 1 and reduces transaction costs. The coefficient c is constant. A home economic agent of type h produces one unit of a single differentiated good h by using one unit of their own labor input, which yields the disutility from work effort. k is a country-specific productivity shock. A decline in k represents technological progress, which economizes on inputs. The consumption comprises two types of composites, CH and CF, each of which constitutes the differentiated brand of home Ch0 or foreign goods Cf, respectively.
Chh
CHh n
!n
CFh
!1n
1n
0 B1 ; CHh hB @ 1q n
Z
1
q q1
q 0 1q1 Z 1 q1 C 1 q q dh0 C ; C h h@ Cfh df A ; 1 F A ð1 nÞq n
n h q1 0
Ch0
where 0 < n < 1 and q > 1. Price indexes are defined as the minimal cost of purchasing one of the corresponding consumption composites.
0 P ¼ PHn PF1n ; PH
1 ¼ @ n
Z
111 q
n
0
q dh0 A ; P ¼ @ 1 Ph1 0 F 1n 0
Z
1 n
111 q Pf1q df A
P represents the consumer price index; PH, the price of home consumption composite; and PF, the price of foreign consumption composite. Ph0 represents the price of the home brand h0 in the home currency, and Pf, the price of the foreign brand f in the home currency. Given these assumptions, it is easy h or C h : to derive an individual h’s demand function for good h0 or f and the corresponding composites CH F
CHh ¼ nðPH =PÞ1 C h ; Chh0
CFh ¼ ð1 nÞðPF =PÞ1 C h ; q ¼ n1 ðPh0 =PH Þq CHh ; Cfh ¼ ð1 nÞ1 Pf =PF CFh :
The home yeoman’s budget constraint is given by
0 1 Z n Z 1 0 f M h þ PC h þ T ¼ M0h þ ð1 sÞ@ Ph Chh dh0 þ Ph Ch df A; 0
(1)
n
where T represents a nominal lump-sum tax per capita imposed by the domestic government, s < 1 is the tax rate on the nominal income derived from yeoman h’s production activity, and Ph is the price of the home brand h in a foreign currency.
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Foreign economic agents have identical preferences; however, the realization of the foreign shock, namely, k , might differ from k ex-post. The process fk; k g follows the Markov process and has a unique stationary distribution. Other parameters are the same in both countries. An “*” is used to represent foreign variables. All home yeomen are symmetric and have the same preferences and budget constraints. Consequently, we omit the superscript h. The same applies for foreign agents. 2.2. Fiscal and monetary authorities The fiscal authority in the home country levies an output tax on its residents at the rate of s, for eliminating factors that distort the level of output, including monopolistic distortions. It also collects lump-sum taxes T and receives transfer of the seigniorage from the central bank TM. The home government’s budget constraint is given by
0 1 Z n Z 1 h0 0 f @ s Ph Ch dh þ Ph Ch df A þ T þ T M ¼ 0: 0
(2)
n
The monetary authority earns seigniorage from the private sector and transfers it to the fiscal authority.
M ¼ M0 þ T M :
(3)
The foreign authorities have similar constraints. 3. Market equilibrium Since the goods markets are monopolistically competitive, each yeoman in the home country faces the aggregate demand curve ChW hnCh þ ð1 nÞCh . The goods market clears when Y ¼ ChW . The pricing rule Ph is determined in the currency of the producer at the end of time 0. The representative home agent chooses the pricing rule Ph by maximizing the expected utility E{U}, subject to the aggregate demand and the budget constraint (5). E{.} denotes the mathematical expectation conditional on the information available at time 0. An optimally chosen product price relates to the expected utility from consumption and the expected disutility from work effort:
EfkY n g ¼
1s n W o E C UC ;
Q
where
q Qh ; q1
C W hnC þ ð1 nÞC;
and UC ¼ C r :
(4)
Given the goods market clearing condition, the first-order necessary conditions are rearranged as follows in a symmetric equilibrium:
Ph ¼
n !1
n QE k PC W : W ð1 sÞE C UC
(5)
The markups Q are imposed owing to monopolistic distortion. We consider an environment in which the law of one price applies. Denote the exchange rate, that is, the home currency price of foreign currency, as S. Foreign currency prices Ph are set so that Ph ¼ Ph =S, once S is revealed at time 1. Though Ph cannot be changed at time 1, the exchange rate uncertainty makes Ph , and therefore P*, unknown a priori. Analogous expressions apply to foreign goods. When the foreign tax rate is s ,
0
n 11n
QE k P C W A ; Pf ¼ @ ð1 s ÞE C W UC Pf ¼ Pf S:
where
UC ¼ ðC Þr ; (6)
At time 1, individuals choose the consumption level C and nominal money balances M. A home agent maximizes the utility subject to the budget constraint (5) and the nonnegativity constraints C 0 and M 0. The first-order necessary condition for the money holdings is as follows:
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C r ¼ cðM=PÞε :
467
(7)
Eq. (7) is a money-demand function in which the consumption elasticity of money demand is r/ε. Given the productivities, government policies, and initial values, the market equilibrium is defined as a set of allocations and prices that satisfy the yeoman’s optimization problems; the cost minimization of purchasing goods; the budget constraints (1)–(3); and the goods market clearing conditions and their foreign counterparts. The unitary elasticity of substitution between home goods composite CH and foreign goods composite CF imply that PhY ¼ P(nC þ (1 n)C*). Combined with this relation and budget constraints (2) and (3), the private sector’s budget constraint is reduced to C ¼ C*. Since there is no home bias in the consumption of goods and because all goods are tradable, the law of one price implies that S ¼ P/P*. Thus, S ¼ M/M*. Given this exchange rate, the consumption per capita and individual work effort can be written as the function of exogenous and predetermined variables. The decomposition of utilities into two factors shows the policymakers’ objectives: average utility and short-run deviation. 3
ð1rÞ3
1r r M E C 1r C 1r C 9; 8 W ¼ ¼ 1r 1r 1r > > > > > > r ð1 Þ 3 = < r E MW > > > > > > ; : 0 3
k
1
1n
r A k@MMW
Yn
¼
n
1 s n 1r o 8 0 E C 1 n 9; nQ 3 < = 1 r E k@MMW A : ; 0 3
n
(9)
1n
r1 A
k @M MW 1 s n 1r o 8 0 k ¼ E C 1 n 9; n nQ 3 < = 1 r E k @M MW A : ; Y
(8)
(10)
1n 0 11n 1 1r 0 0 n1þr B C B C C B B C B C C B B C B C C B1B 1r 1s 1 s C C C B B 8 B where E C ¼ B B 0 1n 9C B 8 0 1n 9C C BQB < B < C 3 3 =C =C 1 1 C C C B B B @ @E k@MMr A A @E k @M Mr A A A W W : : ; ; 8 9 n > >n1þr > < ð1rÞ3 > = 1n r E MW ; MW hMn M : > > > > : ;
3 This money demand does not depend on the interest rate, simply because there is no next period. The multi-period extension of our model produces the money-demand function that depends positively on consumption and negatively on the interest rate.
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Observe that a positive productivity shock in the home country merely reduces labor disutility in the home country. No other allocation is affected in the absence of active policy intervention. Then, consider the effects of monetary expansion. In response to the monetary shock, the exchange rate depreciates and consumer price index (CPI) increases by the share of foreign goods, whereas the producer-currency prices are predetermined. Accordingly, the real balance increases only by the fraction of n. Given the consumption elasticity of money demand r/ε (Eq. (7)), domestic consumption increases by nε/r. We refer to this effect as the expenditure-changing effect. In a foreign country, the depreciation increases the real value of foreign currency, thereby also increasing foreign consumption with the elasticity of nε/r. Regarding labor disutility, home residents only engage in the production of home goods, whose demand (Ph/P)1(nC þ (1 n)C*) is determined by the relative price and the aggregate demand. Monetary expansion has two effects on this. First, the depreciation of the home currency reduces the relative price of the home goods. Given the unitary intratemporal elasticity of substitution, the world expenditure shifts to home goods with the elasticity of 1 n, which is known as the expenditureswitching effect. Second, the expenditure-changing effect increases the world consumption with the elasticity of nε/r. Overall, the world’s demands for home goods increase with the elasticity of nε/r þ 1 n. There is a spillover effect on the overseas production, too. First, the depreciation of home currency weakens the price competitiveness of foreign goods by the fraction of n. On the other hand, the expenditure-changing effects that are already described boost consumption by nε/r in both countries. On balance, the demand for foreign goods increases by nε/r n. When r/ε > 1, the expenditureswitching effect dominates the expenditure-changing effect, and thus, monetary policy has a negative spillover on production. If r/ε < 1, that is, if the consumption elasticity of money demand is less than the intratemporal elasticity, the expenditure-changing effect dominates. 4. Monetary policy This section describes the monetary authority’s problems and optimal policies. The monetary authority chooses the rate of money growth mhM=M0 . We consider the situation in which no technology dictates that monetary authorities maintain their previously announced policies for some future period. 4.1. Policymakers’ objectives Policymakers care about the utilities of residents. Following the convention, we assume that the authority determines its policy by taking account of household utility relating to consumption and leisure. Real balances are neglected in the social welfare function because the coefficient c is quantitatively small. In this model, the cost of the sort-run nominal instability is already reflected in the household utility as a gap between the average utility and the short-run deviation in Eqs. (8)–(10). Without a further nominal anchor, the rational expectation equilibrium is available only when there is no inflationary bias. In order to have a finite inflation in equilibrium, we assume that the authority faces some cost U(m) in changing money supply. This cost can be interpreted as the administrative (non-budgetary) cost of adjusting money in circulation, or alternatively, the steady-state inflation/deflation averse.4 The cost function satisfies U(1) ¼ 0, U0 ð1Þ ¼ 0, U00 > 0, limm/0 U0 ¼ N, limm/N U0 ¼ N, and U0 þ mU00 > 0. The last three
4 The existing studies also consider the policy objectives different from those of the residents. Canzoneri and Gray (1985) incorporate the money growth into the policy maker’s utility by assuming that the government takes care of the cost of the steady-state inflation. In NOEM frameworks, Obstfeld and Rogoff (1996, p. 714) and Betts and Devereux (2000) introduce the inflation cost into welfare. Their specification, however, is not applicable to the nominal indeterminacy problem in our twoperiod model, because their cost function is minimized at zero CPI, not zero inflation. Moreover, introducing the inflation into the policy objective itself produces additional strategic interactions to manipulate the other country’s inflation cost. To avoid unnecessary complication, we modify their specification by simply assuming the cost of changing money.
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restrictions are regulatory conditions for the interior solution. It is assumed that each monetary authority maximizes the private agent’s welfare net of such a cost of changing money. We refer to the situation as “noncooperation,” when each authority cares only about the welfare of its own residents:
C 1r Yn Vh k UðmÞ; n 1r
1r
n
C Y V h k Uðm Þ: n 1r
Another situation that we consider is “cooperation” in which all the authorities jointly maximize the objective function, wV þ (1 w)V*.
4.2. Monetary authority’s optimization problem Monetary authorities choose optimal policies at time 1, using information available after the shocks have been observed. In each case, the monetary authority solves the maximization problem, taking tax policies as given. When there is no cooperation between the authorities, each monetary authority separately maximizes V subject to (8) and (9) or V* subject to (8) and (10), taking tax policies as given. The firstorder condition to the problem of monetary authority in the home country is given by the following equation:
0
ð1rÞε
nε
mW r
8
r > <
9
ð1rÞε > =
r E mW > :
> ;
1n ε r1 A
k@mmW mU0 1n 1s 8 0 9 ¼ 0: where mW hmn m : þ1n 1 n > E C 1r r Q > ε < = r1 E k@mmW A > > : ;
nε
(11) The first term captures the consideration on the effects on consumption, the second term, the effects on production, and the third term, the effects on the cost of changing money. In principle, the monetary policy has two roles: stabilization and stimulation. First, it stabilizes the domestic labor disutility so that the pre-set prices are ex-post efficient. ð1rÞε=r ð1rÞε=r ε=r1 ε=r1 =EfmW Accordingly, mW g and kðmmW Þn =EfkðmmW Þn g fluctuate around one depending on the realization of productivities, in which the reaction function of each monetary authority has interdependence. Aside from these stabilization motives, there are four factors that induce the systematic inflation/deflation biasdn, r, Q, and s. The n captures the home bias in consumption.5 Since the monetary policy can control the entire domestic production but only the fraction n of consumption, policymakers are less motivated to implement the expansionary policy as compared to in a closed economy. According to the consumption elasticity of money demand r/ε, the effect on consumption is mitigated as nε/r. In the second term, the labor disutility is controlled by the elasticity of nε/r þ 1 n through the demand for home goods (See Section 3). Further, monetary policy offsets the markup and fiscal taxes, which distort the efficient price-setting that balances the expected utility from consumption and work effort. Since both the markup Q arising from monopolistic competition and distorting sales taxes lowers production, they are corrected by the monetary expansion. Considering all of these factors, monetary authority balances the benefit of changing money to the marginal cost of adjusting money, which is reflected in the third term. In the case of cooperation, monetary authorities maximize wV þ (1 w)V* subject to (8)–(10), taking the tax policies as given. The solution to the optimization problem of the monetary authority in the home country is described as follows:
5 Corsetti and Pesenti (2005) analyze the model that allows the equilibrium of non-rational expectation and find that the same type of bias might arise in the case of noncooperation.
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0
1n ε1 r k@m mA
ð1rÞε
W nε 1s 9w 8 8 0 þ1n 1n 9 r > r Q > > > > > = < ð1rÞε > < B ε1 C > = r r B C E mW E k@mW mA > > > > > > > > ; : : ; 0 1n
mW r
nε
ε
(12)
1 k @mr m A
W mU0 nε 1 s 8 0 9w ¼ 0: ð1 wÞ n 1 n r Q > E C 1r > > > ε 1 < = B r C E k @mW m A > > > > : ;
The first term captures the effects on consumption; the second and third terms, the effects on production; and the fourth term, the effects on the cost of change in money. Unlike under noncooperation, the additional term, w, appears in Eq. (12) under cooperation. The term w indicates the home country’s weight for labor disutility in the global objective of the policymakers. This explains the expansionary incentive. In addition, the optimality condition includes foreign productivity. For the foreign country’s policies, the mechanism through which the monetary policy affects the real economy is similar to that through which the home country’s policies operate. By cooperating, each monetary authority conducts a monetary expansion. The unilateral monetary expansion in the home country increases the aggregate demand and depreciates the exchange rate. When r/ε > 1, since the expenditure-switching effect exceeds the increase in the aggregate demand, the production disutility increases in the home country and decreases in the foreign country. Therefore, the benefit of monetary expansion is partially transferred to foreign residents at the cost of home labor disutility. In the case of mutual monetary expansion, on the other hand, the appreciation is ameliorated and the production of foreign goods also increases. Thus, when there is cooperation, each country can further benefit from mutually altruistic expansion. The comparison of these two regimes provides a proposition about the inflation; for reasonable parameter values (ex., 1 s < Q), cooperation yields a higher growth rate of money on average. To see this, take the expectation of Eqs. (11) and (12), respectively:
nε
r
ε
r
0 E mU 1s þ1n ¼ 1r ; r Q E C
nε
E mU0 1s ð1 nÞε 1 s : þ1n ð1 nÞ ¼ Q r r Q E C 1r
nε
(13)
(14)
The second equation uses the assumption w ¼ n. Let us define the right-hand side of each equation as LhEfmU0 g=EfC 1r g. Lemma 1.
L is greater under cooperation than under noncooperation when ð1 r=εÞð1 s Þ=Q < 1.
Lemma 2. L is increasing in the value of E{lnm}. The proofs of Lemmas 1 and 2 are given in the Appendix. These lemmas enable us to state the following proposition: Preposition 1. When the sales tax is invariant across the monetary regime, cooperation increases the average rate of inflation in the logarithm for reasonable parameter values ðð1 r=εÞð1 s Þ=Q < 1Þ. This condition is supported, for instance, when the foreign tax rate is positive or at least the subsidy does not exceed the markup ð1 s < QÞ, or if the money demand is sufficiently elastic (r/ε > 1) and
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1 s* > 0. Intuitively, policy cooperation reduces overseas labor disutility. When r/ε > 1, the expenditure-switching effect dominantly works, and the cooperative monetary expansion reduces foreign work effort and increases consumption. On the other hand, when r/ε < 1, an expansive monetary policy leads to higher work effort in the foreign country because the increase in the aggregate demand dominates. In this case, cooperation works to limit the monetary expansion. Unless the foreign tax is strongly negative, the benefit of cooperative monetary expansion on foreign consumption nε/r exceeds the foreign work effort ðnε=r nÞð1 s Þ=Q. 4.3. Calibration This section illustrates the numerical example of the optimal monetary policy under each regime. The parameter values in the baseline case are chosen as follows. Since the import share in consumption are about 10% in industrialized countries, we set n ¼ 0.9. Following Díaz et al. (2003), the coefficient of the relative risk aversion is set as r ¼ 2. Later in this section, we examine the sensitivity of the result to this parameter. As per the US micro data study by Heathcote et al. (2010), the household elasticity of labor disutility is assumed to be about 0.7 and n ¼ 2.4. These values for r and n are also consistent with the recent Bayesian estimations of the utility separable between consumption and leisure. Smets and Wouters (2003) introduce habit persistence in consumption and report slightly smaller estimations of risk aversion and elasticity of labor supply in the euro area. However, Smets and Wouters (2007) estimate values similar to ours for US data in the case of low habit persistence. In terms of the scale elasticity of money demand, the typical estimates are about unity, as indicated by Lucas (1988), among others. Therefore, the baseline case assumes r/ε to be unity, and we set ε ¼ 2. We focus on the steady state in which the productivity k is 20.25, so that individuals work for 1/3rd of the time endowment. The elasticity of substitution between goods is q ¼ 6 to produce the 20% monopoly markup. This markup is slightly smaller than that in Smets and Wouters (2003, 2007), but well within the ranges suggested by Rotemberg and Woodford (1995) for US data and by Adolfson et al. (2007) in their Bayesian estimation for the euro area. The rate of sales tax ranges from 5% to 20% among G7 countries. In the baseline case, the sales tax is set s ¼ s* ¼ 0.1. The adjustment cost function is specified as U(m) ¼ k[(m1 r 1)/(1 r) (m1 s 1)/(1 s)]. For any set of k > 0, r < 0, and s > 1 (and s / 1), this specification of U(m) satisfies the restrictions imposed in Section 4.1. To obtain the closed-form solution, we set r ¼ 1 and s/1. k ¼ 11 is chosen to produce the average annual money growth rate of about 2% under noncooperation. For these parameters, cooperation produces the 3.353% money growth, and noncooperation yields 2.025% money growth in the steady state, which verifies Proposition 1. Next, we examine the sensitivity. Fig. 1A)–1C) show how the optimized money growth in the home country changes with r. The tax rates are 20% in Fig. 1A), 10% (baseline) in Fig. 1B), and 20% in Fig. 1C). The dashed line represents the cooperative policy and the solid line represents the noncooperative policy. These figures demonstrate Proposition 1 that, for any value of r, cooperation yields a higher inflation. To understand the mechanism underling these figures, it is useful to rewrite the optimal policies. When s ¼ s ¼ s, the cooperative policy in Eq. (14) is reduced to
ε
r
1
1s
Q
E mU0 ¼ 1r : E C
(15)
The first term captures the expenditure-changing effect on consumption and the second term that on production. Because the work efforts in both countries are considered, consumption and work effort are equally weighted. As r increases, the marginal utility from consumption Cr increases, because consumption is less than one, and stimulates the monetary policy. At the same time, the increase in r weakens the expenditure-changing effects and makes the large monetary change unnecessary. The graphs show the balance of these conflicting motives. Fig. 1A) and 1B) demonstrate that the optimal money growth is positive as long as ð1 sÞ=Q > 1. If the tax completely offsets the markup, as in Fig. 1C), the money growth is zero. Note that, in this cooperative policy, expenditure-switching effects
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A
C
B
D
Fig. 1. Growth rate of money. The graphs in Fig. 1 compare the steady-state money growth mhM=M0 under noncooperation and cooperation. The vertical axis indicates the money growth. The horizontal axis represents the coefficient of the relative risk aversion r. The solid line represents the noncooperative policy in Eq. (13): ðnε=rÞð1 ð1 sÞ=QÞ ð1 nÞð1 sÞ=Q ¼ EfmU0 g=EfC 1r g; and the dashed line represents the cooperative policy in Eq. (14): ðε=rÞð1 nð1 sÞ=Q ð1 nÞð1 s Þ=QÞ ð1 nÞ 0 0 ðð1 sÞ=Q ð1 s Þ=QÞ ¼ EfmU g=EfC 1r g; where U(m) ¼ k[(m2 1)/2 lnm]. In this case, EfmU g ¼ kðEfm2 g 1Þ. As Eq. (8) implies, E{C1r} is calculated by ½ðð1 sÞ=kÞn ðð1 s Þ=k Þ1n =Q1=ðn=ð1rÞ1Þ . The tax rates in both countries are 20% in A), 10% (baseline) in B), and 20% in C). In D), noncooperative taxes are given by sN and s*N in Eq. (18), and cooperative taxes are given by sC and s*C in Eq. (19). Other parameters are n ¼ 0.9, ε ¼ 2, Q ¼ 1:2, n ¼ 2.4, and k ¼ 11. The productivity parameters k and k are set so that individuals work the 1/3rd of the time endowment in the steady state in the baseline case ðs ¼ s ¼ s ¼ 0:1; r ¼ r ¼ 2Þ : k ¼ k ¼ ð1 sÞ=Q=ð1=3Þv1þr ¼ 20:25:
are mutually canceled out. Since the depreciation of one currency implies the appreciation of the other, the expenditure switching produces a zero-sum benefit from the global perspective. When s ¼ s*, the consideration of the expenditure-switching effects on home production and foreign production completely cancel out each other. The noncooperative policy in Eq. (13) can be rewritten as follows.
nε
r
1
1s
Q
ð1 nÞ
1s
Q
0 E mU ¼ 1r : E C
(16)
The first term captures the expenditure-changing effects on consumption and work effort, and the second term represents the expenditure-switching effect that increases the home production for overseas sales. For larger tax rates (Fig. 1A), any effects on work effort are less considered and the expenditure-changing effect on consumption is relatively important. When the tax rate is intermediate as in Fig. 1B), the expenditure-switching effect on work effort is stronger, and the authority is more motivated to deflate compared to Fig. 1A). In both cases, the deflation is more likely for a sufficiently large r, which works to reduce the weight given to consumption. If the tax rate completely offsets the markup, the expenditure-changing effects on consumption and work effort cancel out each other. In this case, the left-hand side of the noncooperative policy function (13) is independent of r. Fig. 1C) shows this case. The curvature of optimized m only reflects the expenditure-switching effect. 5. Endogenous tax policies and implications for inflation So far, this paper has assumed tax policies that are invariant across monetary regimes. They are determined independently of monetary authorities cooperating or not. In the course of the ongoing
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globalization, however, it is also possible that international monetary cooperation occurs as a part of a policy coordination package that includes tax policies.6 To gauge the impact of such a possibility, this section examines one plausible case in which both fiscal and monetary authorities in the same country share the same objective function and where tax rates are optimally chosen under each regime. We assume full commitment to the tax policy. This is justified if, for instance, there is a one-period lag in the implementation of the fiscal policy. Tax rates are usually legislated for, which is a time consuming process. Fiscal policymakers choose tax rates using the information available at time 0. The fiscal authorities act as Stackelberg leaders of the private sector, taking the monetary base as given. Under noncooperation, each fiscal authority determines its tax rule independently to maximize the expected welfare of its own country, E{V} or E{V*}, given the private sector’s allocation and pricing rules. In this case, sN and s*N satisfy the following:
2
3
3
2
n n 7 1 6 7 1 6 þ 1 n5 ¼ 0; 4 4 5 1 r n 1 sN 1r nQ 1 1 n n 3 3 2 2
(17)
1n 7 1 6 1n 7 1 6 þ n5 ¼ 0: 5 4 4 1 r n 1 sN 1r nQ 1 1
n
n
In each equation, the first term captures the effects on consumption, and the second term, the effects on production. In the first equation, the fiscal authority considers two effects of the tax cut in the home country: increasing consumption by n/[1 (1 r)/n] and deteriorating terms of trade Ph/Pf(¼[(1 s*)/(1 s)]1/n) by 1/n. As a result, production in the home country increases by [n/[1 (1 r)/n] þ (1 n)]/n. Thus, the change in the tax rate has a smaller impact on consumption than in the case of an autarky. Therefore, each government desires to retain the monopoly power in both markets, so that its residents produce less than that in an autarky, in order to avoid indulging in excessive work efforts. This is the reason why the fiscal authority limit decreases in the tax rate. Note also that producers require higher prices for their production as r increases, which decreases the expected value of income E{CWUC}, or as n increases, which increases work effort. Since the change in terms of trade is independent of these parameters, the impact of tax reduction on work effort is larger than that on consumption under a large r or n. This motivates the fiscal authority to discourage production by raising sales taxes. As seen in the second term, governments also offset the markup Q, and this term plays the role of decreasing the tax rate. Rearranging these conditions, we obtain the following optimal tax rates:
1 sN ¼
Q
; 1r 1n 1 þ1 n n
1 sN ¼
Q
1
1r
n
n þ1 1n
:
(18)
Note that when r/1, the producers’ pricing becomes independent of the expected value of income before tax E{CWUC}, which is evaluated using marginal utility from consumption. In this case, the fiscal authority’s incentive to limit the tax cut is ameliorated as compared to the case where r > 1. When fiscal authorities cooperate, they jointly maximize the expected world welfare E {wV þ (1 w)V*}, subject to (8)–(10). In this case, each government sets the tax rate under cooperation, sC or s*C, so that
6 The analysis in this section can also be considered as the cooperative framework toward regional integration or, alternatively, the first-best policies by a central planner in the integrated global system.
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2
2 0
3
1
0
1
3
C n n n 6 B C B C 1s 7 1 6 7 1 4w@ þ 1 nA þ ð1 wÞ@ nA ¼ 0; 4 5 5 1 r 1 sC 1r 1r 1 sC Q 1 1 1 n n n 2 0 1 0 13 3 2 C 6 B 1n C 1s B 1n C7 1 6 1n 7 1 4w@ ð1 nÞA þ ð1 wÞ@ þ nA5 ¼ 0: 5 4 C C 1r 1s 1r 1r Q 1s 1 1 1
n
n
n
Unlike fiscal noncooperation, an additional term w appears in the second term, and the domestic policy becomes dependent on the foreign policy. This additional term w reflects the fiscal authority’s reduced care about the disutility from production in its own country, and it has a greater incentive to stimulate production. When the weight of social welfare is equal to country sizes, that is, w ¼ n, these optimal policies are reduced in equilibrium as follows:
1 sC ¼ Q;
1 sC ¼ Q:
(19)
In this case, the central planner chooses the efficient allocation by fully eliminating the monopoly distortion. 5.1. Implications for the inflation and exchange rates Suppose that each fiscal authority knows the monetary regime and maximizes the same objective that the monetary authority in the same country engages in. Under such an assumption, the left-hand side of the noncooperative policy (13) with s ¼ sN becomes
0 B nε þ1n B @ r
1 C 1 1 C: 1 nr 1n 1r A 1þ 1 1þ n ε n n
This is positive when r/ε < 1 (1 r)/n. Lemma 2 in Section 4 implies that, the noncooperative monetary policy has an incentive to inflate on average. Intuitively, either policy equally weights the deterioration of terms of trade with 1 n (See Eqs. (13) and (17)). On the other hand, consumption responds to monetary shock by nε/r, but to tax policy by n/[1 (1 r)/n]. When r/ε < 1 (1 r)/n, a monetary policy maker evaluates the benefit on consumption (net of the cost of increased labor disutility) higher than a tax policy maker does. In other words, the monetary policy not only offsets the increased tax but also creates inflation in equilibrium. When r/ε > 1 (1 r)/n, the opposite is true. The exceptional case with no inflationary/deflationary incentive (the left-hand side of Eq. (13) is zero) is obtained only when r/ε ¼ 1 (1 r)/n. On the other hand, s ¼ sC and s* ¼ s*C under cooperation brings the equilibrium monetary policy to a neutral stance regardless of the value of r. To summarize, we offer the following proposition: Preposition 2. When the sales tax is set to maximize for the same monetary objective in each regime, cooperation increases the rate of inflation on average when r/ε > 1 (1 r)/n and decreases it when r/ε < 1 (1 r)/n. Cooperation does not alter the rate of inflation when r/ ε ¼ 1 (1 r)/n. This phenomenon is depicted in Fig. 1D). Except for taxes, the parameter values are the same as those explained in Section 4.3. The difference between the roles of monetary and tax policies is based on the mechanism through which they control the consumer prices. Origin-based tax controls the prices Ph and Pf in the producer’s currency, while monetary surprise affects overseas consumer prices Ph ð ¼ Ph =SÞ and Pf ð ¼ Pf SÞ through the exchange rate. Under a noncooperative regime, in estimating the policy impact on consumption, both policies consider the marginal utility from consumption, but the tax policy also considers the feedback from labor disutility, which increases Ph and decreases consumption. Thus, the value of r has less importance in the tax policy than in the monetary policy, and
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the monetary policy is less (more) motivated to contract the economy than the tax policy when r/ε<(>) 1 (1 r)/n. Under cooperation, both policies offset any disproportionate effects on consumption and labor disutility, thus yielding no inflation bias regardless of the value of r. Therefore, the noncooperative regime results in competitive depreciation when r/ε < 1 (1 r)/n. Under our parameterization, the neighborhood around r ¼ 2, which yields the unitary consumption elasticity of money demand, supports the competitive depreciation story. Admittedly, the tax policies examined in this section should be subject to cautious examination. First, the fiscal authority may have other objectives, such as the provision of public goods and revenue requirements. In addition, if fiscal instruments are available only for the domestic objectives, tax policies should be interpreted independent of monetary regime, and the results in Section 4 are retained. However, independent countries can also coordinate the policy mix. For instance, regional integration can begin with the establishment of a comprehensive cooperative framework among participating countries. When we examine the potential costs and benefits of economic integration, the joint analysis of monetary and fiscal cooperation in this section applies.
6. Concluding remarks This paper has analyzed how the international cooperation of monetary policies alters the inflation rate in a simple sticky-price model. We have examined whether the traditional analysis of the beggar-thy-neighbor incentive of monetary policy, and thereby, competitive depreciation, exists or not. For the given tax rates, international monetary policy cooperation increases the average inflation rate. This result arises irrespective of whether or not the fiscal tax eliminates the monopoly distortions. When tax rates are set optimally to maximize the welfare in each regime, monetary cooperation can eliminate the inflation bias under noncooperation if the expenditure-changing effect of monetary policy is sufficiently strong, restoring the competitive depreciation story. Under the small expenditurechanging effect, on the other hand, cooperation prevents the deflation that would emerge under a noncooperative regime. One caveat is that the examined alternative setup assumes that the fiscal and monetary authorities share the same functional form of the objective. It is also interesting to examine the cases in which the fiscal and monetary authorities have separate policy objectives. For instance, we can consider the provision of public goods in the fiscal objective. For future research, we plan to relax the assumption of the law of one price and introduce local currency pricing into the environment of endogenous tax. Since the existing literature indicates that pricing-to-market itself can produce competitive depreciation, it is meaningful to see whether the combination of these two elements overturns the traditional beggar-thy-neighbor property again. Another possible extension is a multi-period model. While we focused on the two-period setting for the purpose of insulating intratemporal issues from intertemporal ones, the introduction of asset trading would provide an additional element with which policymakers evaluate welfare effects. When we consider repeated games, the time-consistency features may also arise. Further, it is worth examining the equivalence of a sales tax and other types of distorting taxes, such as a consumption tax. Although this is beyond the scope of this paper, considering government expenditure in addition to distorting taxes would also provide insightful results. Government spending increases the supplier’s income and hours worked and can further alter the equilibrium. For instance, public consumption goods such as education and health care would also improve the utility of residents. Another possibility is the impact on productivity. The infrastructure that the government invests in can work as the public input of private production. Moreover, government measures against environmental pollution might ultimately stimulate labor productivity, which this paper treats as a stochastic exogenous variable. In either case, government expenditure is likely to fall in the domestic market, and thus, it might produce an additional mechanism in which cooperation alters the inflation.
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Appendix A A.1 Proof of Lemma 1 To compare the left-hand sides of Eqs. (13) and (14), subtract the latter from the former. In essence, the difference reflects the change in foreign consumption and work effort.
nε
r
¼
nε
r
þ1n
ð1 nÞε
r
þ
1s
Q
ð1 nÞε
r
ε
r
nε
r
1s ð1 nÞε 1 s þ1n ð1 nÞ
1 s ð1 nÞ
r 1 s ð1 nÞε 1 1 ¼ r Q ε
Q
r
Q
Q
If 1 > ð1 r=εÞð1 s Þ=Q, this value is negative, and thus, the value of L is greater under cooperation (Q.E.D.). A.2 Proof of Lemma 2 Define MhEflnmg.
vL vL vEflnmg ¼ vm vM vm o1 n 2 vE C 1r U0 þ mU00 m m þ E C 1r ¼ E C 1r vm Since this expression applies for any realization of m, vL=vM ¼ EfvL=vMg must hold for all m. Therefore, we obtain
o1 n vL E m U0 þ mU00 : ¼ E C 1r vM Given that U0 þ mU00 > 0 and m > 0, the right-hand side of this equation is always positive. Therefore, L is increasing in the value of E{lnm} (Q.E.D.). References Adolfson, Malin, Laseen, Stefan, Linde, Jesper, Villani, Mattias, 2007. Bayesian estimation of an open economy DSGE model with incomplete pass-through. Journal of International Economics 72 (2), 481–511. Benigno, Gianluca, Benigno, Pierpaolo, 2003. Price stability in open economies. Review of Economic Studies 70, 743–764. Benigno, Pierpaolo, Woodford, Michael, 2005. Inflation stabilization and welfare: the case of a distorted steady state. Journal of the European Economic Association 3 (6), 1185–1236. Betts, Caroline, Devereux, Michael, 2000. Competitive depreciation and monetary policy coordination: a reevaluation. Journal of Money, Credit and Banking 32 (4), 722–745. Braun, R. Anton, 1994. Tax disturbances and real economic activity in the postwar United States. Journal of Monetary Economics 33 (3), 441–462. Canzoneri, Matthew B., Gray, Jo Anna, 1985. Monetary policy games and the consequences of non-cooperative behavior. International Economic Review 26 (3), 547–564. Çenesiz, M. Alper, Pierdzioch, Christian, 2009. Efficiency wages, financial market integration, and the fiscal multiplier. Journal of International Money and Finance 28 (5), 853–867. Clarida, Richard, Galí, Jordi, Gertler, Mark, 2002. A simple framework for international monetary policy analysis. Journal of Monetary Economics 49 (5), 879–904. Corsetti, Giancarlo, Pesenti, Paolo, 2005. International dimensions of optimal monetary policy. Journal of Monetary Economics 52 (2), 281–305. Corsetti, Giancarlo, Pesenti, Paolo, Roubini, Nouriel, Tille, Cédric, 2000. Competitive devaluations: toward a welfare-based approach. Journal of International Economics 51 (1), 217–241. Darius, Reginald, 2010. The macroeconomic effects of monetary and fiscal policy in a small open economy: does the exchange rate regime matter? Journal of International Money and Finance 29 (8), 1508–1528.
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Díaz, Antonia, Josep, Pijoan-Mas, José-Victor, Ríos-Rull, 2003. Precautionary savings and wealth distribution under habit formation preferences. Journal of Monetary Economics 50, 1257–1291. Dornbusch, Rudiger, 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Flemming, J. Marcus, 1962. Domestic financial policies under fixed and floating exchange rates. IMF Staff Papers 9, 369–379. Heathcote, Jonathan, Storesletten, Kjetil, Violante, Giovanni L., 2010. The macroeconomic implications of rising wage inequality in the United States. Journal of Political Economy 118 (4), 681–722. Jensen, Henrik, 1997. Monetary policy cooperation may not be counterproductive. Scandinavian Journal of Economics 99 (1), 73–80. Lucas, Robert E., 1988. Money demand in the United states: a quantitative review. Carnegie-Rochester Conference Series on Public Policy 29 (1), 137–167. Mundell, Robert A., 1963. Capital mobility and stabilization policy under fixed and flexible exchange rates. Canadian Journal of Economics and Political Science 29, 475–485. Mundell, Robert A., 1964. A reply: capital mobility and size. Canadian Journal of Economics and Political Science 30, 421–431. Obstfeld, Maurice, Rogoff, Kenneth, 1995. Exchange rate economics redux. Journal of Political Economy 103 (3), 624–660. Obstfeld, Maurice, Rogoff, Kenneth, 1996. Foundations of International Macroeconomics. MIT Press. Obstfeld, Maurice, Rogoff, Kenneth, 2000. New directions for stochastic open economy models. Journal of International Economics 50 (1), 117–153. Rogoff, Kenneth, 1985. Can international monetary cooperation be counterproductive? Journal of International Economics 18, 199–217. Rotemberg, Julio J., Woodford, Michael, 1995. Dynamic general equilibrium models with imperfectly competitive product markets. In: Cooley, T., Prescott, E. (Eds.), Frontiers of Business Cycle Research. Princeton University Press, Princetson, pp. 243–293. Smets, Frank, Wouters, Raf, 2003. An estimated dynamic stochastic general equilibrium model of the euro area. Journal of the European Economic Association 1 (5), 1123–1175. Smets, Frank, Wouters, Rafael, 2007. Shocks and frictions in US business cycles: a Bayesian DSGE approach. American Economic Review 97 (3), 586–606. Svensson, Lars E.O., van Wijnbergen, Sweder, 1989. Excess capacity, monopolistic competition, and international transmission of monetary disturbances. Economic Journal 99, 785–805. Tille, Cédric, 2001. The role of consumption stability in the international transmission of monetary shocks. Journal of International Economics 53 (2), 421–444.
Contents lists available at SciVerse ScienceDirect
Journal of International Money and Finance journal homepage: www.elsevier.com/locate/jimf
Competitive depreciation and the role of distorting taxes in an interdependent economyq Satoko Takamatsu* School of Political Science and Economics, Waseda University, 1-6-1 Nishiwaseda, Shinjyuku-ku, Tokyo 169-8050, Japan
a b s t r a c t JEL classification: E52 E63 F42 Keywords: Competitive depreciation Inflation Welfare spillover Monetary policy International cooperation
This paper investigates the manners in which international cooperation in monetary policies affects the rate of inflation in a twocountry sticky-price model. Within reasonable parameter values, international monetary coordination increases the steady-state inflation for given tax policies. When the tax regime is endogenously chosen, however, self-oriented monetary policies can engage in competitive depreciation and induce a higher average inflation than the first best inflation rate. 2012 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, there have been calls for Japan and China to alter their exchange-rate policies. While Japan’s efforts to weaken the yen and China’s implicit peg to the U.S. dollar may be good for domestic employments in these economies, the policies can trigger competitive depreciations and systematic inflation. China has begun to pose concerns about inflation and is often thought to signal the upcoming revaluation. Are these policies good for Japan and China but bad for the rest of the world? Would Japan, China, and the rest of the world achieve a better management of inflation with increased international cooperation on exchange-rate policies?
q The author would like to thank R. Anton Braun, Shin-ichi Fukuda, Masahiro Kawai, Hiroshi Ohashi, Maskoto Saito, Yasuyuki Sawada, and a referee for their comments. In addition, the author also acknowledges the financial support from Grants-in-Aid for Scientific Research. * Tel.: þ81 3 3202 4240. 0261-5606/$ – see front matter 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jimonfin.2012.05.022
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Rogoff (1985) provides one answer to these questions. He argues that increased international monetary cooperation may raise the rate of inflation. Using a sophisticated modern framework, Obstfeld and Rogoff (1995) also show that the surprise monetary expansion has a positive welfare spillover. In light of these prominent papers, has the Mundell–Fleming–Dornbusch result of competitive devaluation become outdated? More recent literature suggests that this is not the case. Some studies (Betts and Devereux (2000) and Jensen (1997), among others) show that monetary expansion can produce a negative welfare spillover under enriched environments. In considering these pros and cons, the literature thus far assumes that no distorting taxes are present or that taxes merely play secondary roles in supporting the monetary policy. In reality, taxes distort decision making in the private sector, and it is interesting to discover what happens if we relax these assumptions. This paper addresses this question and finds that, in the absence of an endogenous choice of tax policies, international monetary cooperation raises the rate of inflation. On the other hand, if taxes are set in accordance with the monetary regime, competitive depreciation is possible. Our model considers a two-country economy similar to that of Obstfeld and Rogoff (1995, 2000), except for the presence of distorting taxes. Goods markets are under monopolistic competition and the prices in producers’ currencies are set before the technology shock occurs. Prices are inefficiently high due to monopoly markups and price setting under uncertainty, which potentially motivates governments to correct. Since the tax policy is chosen by collective opinions within a country, it has an implementation lag and cannot react to ex-post productivity shocks. The monetary policy, on the other hand, is implemented by a delegated decision-maker such as the central bank and can be determined under discretion. Prices are sticky and hence do not respond to policy shocks in the short run. Once prices are set and all shocks have been revealed, each monetary authority supplies money. We examine how the optimal rate of money growth changes with cooperation between monetary authorities. This paper assumes that governments monitor utility from consumption and the disutility of work effort. Owing to the law of one price and unit intratemporal elasticity,1 consumptions are equated and produce no conflict between nations. However, since there are no markets to trade the risks of country-specific fluctuations in production, labor is a source of conflict between the objectives of different countries. Each monetary authority has the incentive to use contractions to reduce work efforts in favor of their own country and expansions to increase consumption. By cooperating, countries endogenize the exchange rate externality that improves the purchasing power of foreign residents. Other things being equal, each central bank depends on the other to expand its money supply and to benefit overseas consumers, at the cost of reducing their own residents’ leisure. This positive welfare spillover can be overturned, however, when distorting taxes are endogenously determined. If a fiscal authority switches its objective in accordance with the international cooperation regime, the Pigouvian subsidy is optimal under cooperation and the coordinated monetary policy produces no inflation or deflation. On the other hand, under reasonable parameter values, the self-oriented tax policy can be less likely to boost the aggregate demand compared to the monetary policy, which gives the monetary policy an incentive to engage in competitive depreciation. One of the most notable results on the international welfare spillover of monetary policy is the “beggar-thy-neighbor” effect indicated by Mundell (1963, 1964), Flemming (1962), and Dornbusch (1976). In contrast to these works, Rogoff (1985) analyzes a reduced-form model and argues that inflation might be systematically higher under monetary cooperation than under monetary noncooperation. Obstfeld and Rogoff (1995) further develop a model using micro-foundation, which analyzes the short-run deviation from the steady state and demonstrates that monetary
1 In order to insulate the effect of monetary expansion on the current account when extending the analysis to a multiperiod setting, the intratemporal elasticity is set to unity so that the expenditure-switching effect and the change in the real price of products directly offset each other.
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surprise has a positive welfare spillover. Such a property of monetary expansion, that is, the beggar-thy-self effect, corresponds to the case of exogenous tax determination in this paper.2 Under enriched environments, however, it became apparent that monetary cooperation can be welfare improving. Jensen (1997) qualifies Rogoff’s result (1985) by arguing that if wage-setters are non-atomistic and inflation averse, cooperation leads to higher employment and possibly lower inflation. Betts and Devereux (2000) consider the pricing-to-market model in which the relative risk aversion is limited to unity. They show that a monetary authority has an incentive to engage in competitive depreciation for a high degree of pricing-to-market. In addition, although the interest of their paper is not necessarily policy coordination, Corsetti et al. (2000) develop a center-periphery model and show that devaluation can be the optimal strategy for neighboring countries. Tille (2001) also demonstrates that positive monetary shocks have a beggar-thy-neighbor effect if home and foreign goods are close substitutes. This paper contributes to this body of literature by demonstrating the case in which monetary cooperation can produce a lower inflation with the generalized specification of tax schemes. Clarida et al. (2002) design the production subsidy such that the steady-state inflation is zero a priori and analyze how well the monetary policy can offset unanticipated disturbances. Benigno and Benigno (2003) show the importance of sales tax in controlling the inflationary bias of the monetary policy. They derive the condition in which price stability is efficient in a two-country model, but the behavior of a biased monetary policy is not fully articulated. It is important to note, however, that a more detailed policy implication can be obtained in an environment in which distorting taxes affect the private sector’s behaviors as in the real world. Braun (1994) argues that personal and corporate income tax rates have significant effects on postwar US business cycle fluctuations. Benigno and Woodford (2005) suggest that assuming an output subsidy that attains the zeroinflation steady state is not realistic, and propose to analyze the steady state in which output is inefficient owing to the distorting taxes on sales revenues or labor income, in addition to the monopoly markups. In light of these observations, our producer–consumer economy analyzes the systematic inflation/deflation, that is, how the monetary policy behaves in the distorted steady state, by considering two cases: one with constant sales taxes and the other with sales taxes synchronized with monetary regimes. Our framework that the monetary policy can have a negative welfare spillover is consistent with Svensson and Wijnbergen (1989). Using a multi-period model, they show that monetary spillover effects may be either positive or negative, depending upon whether the intertemporal elasticity of substitution exceeds the intratemporal elasticity of substitution. In their model, goods markets open before asset markets, and monetary policy affects the economy of tomorrow. In our model, since money transfer occurs before goods trading, the monetary policy works today. The inverse of the consumption elasticity of money demand in the present paper corresponds to their intertemporal elasticity. We clarify that, even without savings devices, monetary expansion can have either a positive or a negative international spillover. This paper is organized as follows. Section 2 outlines the analytical framework. In Section 3, we derive a closed-form solution for the private sector’s equilibrium. Section 4 discusses the monetary policy and provides the numerical implications. Section 5 discusses the effects of a tax policy. Section 6 concludes the paper.
2. Model We consider a two-period model and refer to these periods as time 0 and 1. There are two symmetrical countries, the home and foreign countries. All households are consumer–producers called yeomen. Each yeoman specializes in the production of a differentiated good using his or her own labor
2 It is known in the literature that new open economy macroeconomics (NOEM) models can produce implications that run contrary to the textbook results of the Mundell-Fleming model. For instance, Çenesiz and Pierdzioch (2009) incorporate efficiency wages into an NOEM model and find that financial market integration increases the fiscal multiplier. In addition, Darius (2010) suggests that a government expenditure shock depreciates the nominal exchange rate and generates real effects under the fixed rate system.
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and is the only producer of that good. Individuals are indexed by intervals such that h˛[0,n], and f˛(n,1]. Goods are produced under monopolistic competition, and their prices are inefficiently high. Expost prices can be further inefficient because yeomen are supposed to set their product prices one period in advance. Yeomen inelastically supply labor and therefore products. All goods are tradable. At time 0, fiscal authorities announce the time 1 tax rates, and yeomen pre-set product prices in the domestic market, Ph or Pf. At the beginning of time 1, productivities are revealed. At time 1, monetary authorities inject money, the exchange rate is determined, yeomen produce output and consume, and fiscal authorities levy sales and lump-sum taxes. 2.1. Household The preference for a home yeoman of type h is defined over consumption Ch, the real balance Mh/P, and the work effort from production Yh.
Uhh
Ch
1r
1r
þc
1ε M h =P 1ε
k
Yh
n ;
n
where r > 0, r s 1, c > 0, ε > 0, ε s 1, k > 0, and n > 1. M represents the money holdings at the beginning of time 1 and reduces transaction costs. The coefficient c is constant. A home economic agent of type h produces one unit of a single differentiated good h by using one unit of their own labor input, which yields the disutility from work effort. k is a country-specific productivity shock. A decline in k represents technological progress, which economizes on inputs. The consumption comprises two types of composites, CH and CF, each of which constitutes the differentiated brand of home Ch0 or foreign goods Cf, respectively.
Chh
CHh n
!n
CFh
!1n
1n
0 B1 ; CHh hB @ 1q n
Z
1
q q1
q 0 1q1 Z 1 q1 C 1 q q dh0 C ; C h h@ Cfh df A ; 1 F A ð1 nÞq n
n h q1 0
Ch0
where 0 < n < 1 and q > 1. Price indexes are defined as the minimal cost of purchasing one of the corresponding consumption composites.
0 P ¼ PHn PF1n ; PH
1 ¼ @ n
Z
111 q
n
0
q dh0 A ; P ¼ @ 1 Ph1 0 F 1n 0
Z
1 n
111 q Pf1q df A
P represents the consumer price index; PH, the price of home consumption composite; and PF, the price of foreign consumption composite. Ph0 represents the price of the home brand h0 in the home currency, and Pf, the price of the foreign brand f in the home currency. Given these assumptions, it is easy h or C h : to derive an individual h’s demand function for good h0 or f and the corresponding composites CH F
CHh ¼ nðPH =PÞ1 C h ; Chh0
CFh ¼ ð1 nÞðPF =PÞ1 C h ; q ¼ n1 ðPh0 =PH Þq CHh ; Cfh ¼ ð1 nÞ1 Pf =PF CFh :
The home yeoman’s budget constraint is given by
0 1 Z n Z 1 0 f M h þ PC h þ T ¼ M0h þ ð1 sÞ@ Ph Chh dh0 þ Ph Ch df A; 0
(1)
n
where T represents a nominal lump-sum tax per capita imposed by the domestic government, s < 1 is the tax rate on the nominal income derived from yeoman h’s production activity, and Ph is the price of the home brand h in a foreign currency.
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Foreign economic agents have identical preferences; however, the realization of the foreign shock, namely, k , might differ from k ex-post. The process fk; k g follows the Markov process and has a unique stationary distribution. Other parameters are the same in both countries. An “*” is used to represent foreign variables. All home yeomen are symmetric and have the same preferences and budget constraints. Consequently, we omit the superscript h. The same applies for foreign agents. 2.2. Fiscal and monetary authorities The fiscal authority in the home country levies an output tax on its residents at the rate of s, for eliminating factors that distort the level of output, including monopolistic distortions. It also collects lump-sum taxes T and receives transfer of the seigniorage from the central bank TM. The home government’s budget constraint is given by
0 1 Z n Z 1 h0 0 f @ s Ph Ch dh þ Ph Ch df A þ T þ T M ¼ 0: 0
(2)
n
The monetary authority earns seigniorage from the private sector and transfers it to the fiscal authority.
M ¼ M0 þ T M :
(3)
The foreign authorities have similar constraints. 3. Market equilibrium Since the goods markets are monopolistically competitive, each yeoman in the home country faces the aggregate demand curve ChW hnCh þ ð1 nÞCh . The goods market clears when Y ¼ ChW . The pricing rule Ph is determined in the currency of the producer at the end of time 0. The representative home agent chooses the pricing rule Ph by maximizing the expected utility E{U}, subject to the aggregate demand and the budget constraint (5). E{.} denotes the mathematical expectation conditional on the information available at time 0. An optimally chosen product price relates to the expected utility from consumption and the expected disutility from work effort:
EfkY n g ¼
1s n W o E C UC ;
Q
where
q Qh ; q1
C W hnC þ ð1 nÞC;
and UC ¼ C r :
(4)
Given the goods market clearing condition, the first-order necessary conditions are rearranged as follows in a symmetric equilibrium:
Ph ¼
n !1
n QE k PC W : W ð1 sÞE C UC
(5)
The markups Q are imposed owing to monopolistic distortion. We consider an environment in which the law of one price applies. Denote the exchange rate, that is, the home currency price of foreign currency, as S. Foreign currency prices Ph are set so that Ph ¼ Ph =S, once S is revealed at time 1. Though Ph cannot be changed at time 1, the exchange rate uncertainty makes Ph , and therefore P*, unknown a priori. Analogous expressions apply to foreign goods. When the foreign tax rate is s ,
0
n 11n
QE k P C W A ; Pf ¼ @ ð1 s ÞE C W UC Pf ¼ Pf S:
where
UC ¼ ðC Þr ; (6)
At time 1, individuals choose the consumption level C and nominal money balances M. A home agent maximizes the utility subject to the budget constraint (5) and the nonnegativity constraints C 0 and M 0. The first-order necessary condition for the money holdings is as follows:
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C r ¼ cðM=PÞε :
467
(7)
Eq. (7) is a money-demand function in which the consumption elasticity of money demand is r/ε. Given the productivities, government policies, and initial values, the market equilibrium is defined as a set of allocations and prices that satisfy the yeoman’s optimization problems; the cost minimization of purchasing goods; the budget constraints (1)–(3); and the goods market clearing conditions and their foreign counterparts. The unitary elasticity of substitution between home goods composite CH and foreign goods composite CF imply that PhY ¼ P(nC þ (1 n)C*). Combined with this relation and budget constraints (2) and (3), the private sector’s budget constraint is reduced to C ¼ C*. Since there is no home bias in the consumption of goods and because all goods are tradable, the law of one price implies that S ¼ P/P*. Thus, S ¼ M/M*. Given this exchange rate, the consumption per capita and individual work effort can be written as the function of exogenous and predetermined variables. The decomposition of utilities into two factors shows the policymakers’ objectives: average utility and short-run deviation. 3
ð1rÞ3
1r r M E C 1r C 1r C 9; 8 W ¼ ¼ 1r 1r 1r > > > > > > r ð1 Þ 3 = < r E MW > > > > > > ; : 0 3
k
1
1n
r A k@MMW
Yn
¼
n
1 s n 1r o 8 0 E C 1 n 9; nQ 3 < = 1 r E k@MMW A : ; 0 3
n
(9)
1n
r1 A
k @M MW 1 s n 1r o 8 0 k ¼ E C 1 n 9; n nQ 3 < = 1 r E k @M MW A : ; Y
(8)
(10)
1n 0 11n 1 1r 0 0 n1þr B C B C C B B C B C C B B C B C C B1B 1r 1s 1 s C C C B B 8 B where E C ¼ B B 0 1n 9C B 8 0 1n 9C C BQB < B < C 3 3 =C =C 1 1 C C C B B B @ @E k@MMr A A @E k @M Mr A A A W W : : ; ; 8 9 n > >n1þr > < ð1rÞ3 > = 1n r E MW ; MW hMn M : > > > > : ;
3 This money demand does not depend on the interest rate, simply because there is no next period. The multi-period extension of our model produces the money-demand function that depends positively on consumption and negatively on the interest rate.
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Observe that a positive productivity shock in the home country merely reduces labor disutility in the home country. No other allocation is affected in the absence of active policy intervention. Then, consider the effects of monetary expansion. In response to the monetary shock, the exchange rate depreciates and consumer price index (CPI) increases by the share of foreign goods, whereas the producer-currency prices are predetermined. Accordingly, the real balance increases only by the fraction of n. Given the consumption elasticity of money demand r/ε (Eq. (7)), domestic consumption increases by nε/r. We refer to this effect as the expenditure-changing effect. In a foreign country, the depreciation increases the real value of foreign currency, thereby also increasing foreign consumption with the elasticity of nε/r. Regarding labor disutility, home residents only engage in the production of home goods, whose demand (Ph/P)1(nC þ (1 n)C*) is determined by the relative price and the aggregate demand. Monetary expansion has two effects on this. First, the depreciation of the home currency reduces the relative price of the home goods. Given the unitary intratemporal elasticity of substitution, the world expenditure shifts to home goods with the elasticity of 1 n, which is known as the expenditureswitching effect. Second, the expenditure-changing effect increases the world consumption with the elasticity of nε/r. Overall, the world’s demands for home goods increase with the elasticity of nε/r þ 1 n. There is a spillover effect on the overseas production, too. First, the depreciation of home currency weakens the price competitiveness of foreign goods by the fraction of n. On the other hand, the expenditure-changing effects that are already described boost consumption by nε/r in both countries. On balance, the demand for foreign goods increases by nε/r n. When r/ε > 1, the expenditureswitching effect dominates the expenditure-changing effect, and thus, monetary policy has a negative spillover on production. If r/ε < 1, that is, if the consumption elasticity of money demand is less than the intratemporal elasticity, the expenditure-changing effect dominates. 4. Monetary policy This section describes the monetary authority’s problems and optimal policies. The monetary authority chooses the rate of money growth mhM=M0 . We consider the situation in which no technology dictates that monetary authorities maintain their previously announced policies for some future period. 4.1. Policymakers’ objectives Policymakers care about the utilities of residents. Following the convention, we assume that the authority determines its policy by taking account of household utility relating to consumption and leisure. Real balances are neglected in the social welfare function because the coefficient c is quantitatively small. In this model, the cost of the sort-run nominal instability is already reflected in the household utility as a gap between the average utility and the short-run deviation in Eqs. (8)–(10). Without a further nominal anchor, the rational expectation equilibrium is available only when there is no inflationary bias. In order to have a finite inflation in equilibrium, we assume that the authority faces some cost U(m) in changing money supply. This cost can be interpreted as the administrative (non-budgetary) cost of adjusting money in circulation, or alternatively, the steady-state inflation/deflation averse.4 The cost function satisfies U(1) ¼ 0, U0 ð1Þ ¼ 0, U00 > 0, limm/0 U0 ¼ N, limm/N U0 ¼ N, and U0 þ mU00 > 0. The last three
4 The existing studies also consider the policy objectives different from those of the residents. Canzoneri and Gray (1985) incorporate the money growth into the policy maker’s utility by assuming that the government takes care of the cost of the steady-state inflation. In NOEM frameworks, Obstfeld and Rogoff (1996, p. 714) and Betts and Devereux (2000) introduce the inflation cost into welfare. Their specification, however, is not applicable to the nominal indeterminacy problem in our twoperiod model, because their cost function is minimized at zero CPI, not zero inflation. Moreover, introducing the inflation into the policy objective itself produces additional strategic interactions to manipulate the other country’s inflation cost. To avoid unnecessary complication, we modify their specification by simply assuming the cost of changing money.
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restrictions are regulatory conditions for the interior solution. It is assumed that each monetary authority maximizes the private agent’s welfare net of such a cost of changing money. We refer to the situation as “noncooperation,” when each authority cares only about the welfare of its own residents:
C 1r Yn Vh k UðmÞ; n 1r
1r
n
C Y V h k Uðm Þ: n 1r
Another situation that we consider is “cooperation” in which all the authorities jointly maximize the objective function, wV þ (1 w)V*.
4.2. Monetary authority’s optimization problem Monetary authorities choose optimal policies at time 1, using information available after the shocks have been observed. In each case, the monetary authority solves the maximization problem, taking tax policies as given. When there is no cooperation between the authorities, each monetary authority separately maximizes V subject to (8) and (9) or V* subject to (8) and (10), taking tax policies as given. The firstorder condition to the problem of monetary authority in the home country is given by the following equation:
0
ð1rÞε
nε
mW r
8
r > <
9
ð1rÞε > =
r E mW > :
> ;
1n ε r1 A
k@mmW mU0 1n 1s 8 0 9 ¼ 0: where mW hmn m : þ1n 1 n > E C 1r r Q > ε < = r1 E k@mmW A > > : ;
nε
(11) The first term captures the consideration on the effects on consumption, the second term, the effects on production, and the third term, the effects on the cost of changing money. In principle, the monetary policy has two roles: stabilization and stimulation. First, it stabilizes the domestic labor disutility so that the pre-set prices are ex-post efficient. ð1rÞε=r ð1rÞε=r ε=r1 ε=r1 =EfmW Accordingly, mW g and kðmmW Þn =EfkðmmW Þn g fluctuate around one depending on the realization of productivities, in which the reaction function of each monetary authority has interdependence. Aside from these stabilization motives, there are four factors that induce the systematic inflation/deflation biasdn, r, Q, and s. The n captures the home bias in consumption.5 Since the monetary policy can control the entire domestic production but only the fraction n of consumption, policymakers are less motivated to implement the expansionary policy as compared to in a closed economy. According to the consumption elasticity of money demand r/ε, the effect on consumption is mitigated as nε/r. In the second term, the labor disutility is controlled by the elasticity of nε/r þ 1 n through the demand for home goods (See Section 3). Further, monetary policy offsets the markup and fiscal taxes, which distort the efficient price-setting that balances the expected utility from consumption and work effort. Since both the markup Q arising from monopolistic competition and distorting sales taxes lowers production, they are corrected by the monetary expansion. Considering all of these factors, monetary authority balances the benefit of changing money to the marginal cost of adjusting money, which is reflected in the third term. In the case of cooperation, monetary authorities maximize wV þ (1 w)V* subject to (8)–(10), taking the tax policies as given. The solution to the optimization problem of the monetary authority in the home country is described as follows:
5 Corsetti and Pesenti (2005) analyze the model that allows the equilibrium of non-rational expectation and find that the same type of bias might arise in the case of noncooperation.
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0
1n ε1 r k@m mA
ð1rÞε
W nε 1s 9w 8 8 0 þ1n 1n 9 r > r Q > > > > > = < ð1rÞε > < B ε1 C > = r r B C E mW E k@mW mA > > > > > > > > ; : : ; 0 1n
mW r
nε
ε
(12)
1 k @mr m A
W mU0 nε 1 s 8 0 9w ¼ 0: ð1 wÞ n 1 n r Q > E C 1r > > > ε 1 < = B r C E k @mW m A > > > > : ;
The first term captures the effects on consumption; the second and third terms, the effects on production; and the fourth term, the effects on the cost of change in money. Unlike under noncooperation, the additional term, w, appears in Eq. (12) under cooperation. The term w indicates the home country’s weight for labor disutility in the global objective of the policymakers. This explains the expansionary incentive. In addition, the optimality condition includes foreign productivity. For the foreign country’s policies, the mechanism through which the monetary policy affects the real economy is similar to that through which the home country’s policies operate. By cooperating, each monetary authority conducts a monetary expansion. The unilateral monetary expansion in the home country increases the aggregate demand and depreciates the exchange rate. When r/ε > 1, since the expenditure-switching effect exceeds the increase in the aggregate demand, the production disutility increases in the home country and decreases in the foreign country. Therefore, the benefit of monetary expansion is partially transferred to foreign residents at the cost of home labor disutility. In the case of mutual monetary expansion, on the other hand, the appreciation is ameliorated and the production of foreign goods also increases. Thus, when there is cooperation, each country can further benefit from mutually altruistic expansion. The comparison of these two regimes provides a proposition about the inflation; for reasonable parameter values (ex., 1 s < Q), cooperation yields a higher growth rate of money on average. To see this, take the expectation of Eqs. (11) and (12), respectively:
nε
r
ε
r
0 E mU 1s þ1n ¼ 1r ; r Q E C
nε
E mU0 1s ð1 nÞε 1 s : þ1n ð1 nÞ ¼ Q r r Q E C 1r
nε
(13)
(14)
The second equation uses the assumption w ¼ n. Let us define the right-hand side of each equation as LhEfmU0 g=EfC 1r g. Lemma 1.
L is greater under cooperation than under noncooperation when ð1 r=εÞð1 s Þ=Q < 1.
Lemma 2. L is increasing in the value of E{lnm}. The proofs of Lemmas 1 and 2 are given in the Appendix. These lemmas enable us to state the following proposition: Preposition 1. When the sales tax is invariant across the monetary regime, cooperation increases the average rate of inflation in the logarithm for reasonable parameter values ðð1 r=εÞð1 s Þ=Q < 1Þ. This condition is supported, for instance, when the foreign tax rate is positive or at least the subsidy does not exceed the markup ð1 s < QÞ, or if the money demand is sufficiently elastic (r/ε > 1) and
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1 s* > 0. Intuitively, policy cooperation reduces overseas labor disutility. When r/ε > 1, the expenditure-switching effect dominantly works, and the cooperative monetary expansion reduces foreign work effort and increases consumption. On the other hand, when r/ε < 1, an expansive monetary policy leads to higher work effort in the foreign country because the increase in the aggregate demand dominates. In this case, cooperation works to limit the monetary expansion. Unless the foreign tax is strongly negative, the benefit of cooperative monetary expansion on foreign consumption nε/r exceeds the foreign work effort ðnε=r nÞð1 s Þ=Q. 4.3. Calibration This section illustrates the numerical example of the optimal monetary policy under each regime. The parameter values in the baseline case are chosen as follows. Since the import share in consumption are about 10% in industrialized countries, we set n ¼ 0.9. Following Díaz et al. (2003), the coefficient of the relative risk aversion is set as r ¼ 2. Later in this section, we examine the sensitivity of the result to this parameter. As per the US micro data study by Heathcote et al. (2010), the household elasticity of labor disutility is assumed to be about 0.7 and n ¼ 2.4. These values for r and n are also consistent with the recent Bayesian estimations of the utility separable between consumption and leisure. Smets and Wouters (2003) introduce habit persistence in consumption and report slightly smaller estimations of risk aversion and elasticity of labor supply in the euro area. However, Smets and Wouters (2007) estimate values similar to ours for US data in the case of low habit persistence. In terms of the scale elasticity of money demand, the typical estimates are about unity, as indicated by Lucas (1988), among others. Therefore, the baseline case assumes r/ε to be unity, and we set ε ¼ 2. We focus on the steady state in which the productivity k is 20.25, so that individuals work for 1/3rd of the time endowment. The elasticity of substitution between goods is q ¼ 6 to produce the 20% monopoly markup. This markup is slightly smaller than that in Smets and Wouters (2003, 2007), but well within the ranges suggested by Rotemberg and Woodford (1995) for US data and by Adolfson et al. (2007) in their Bayesian estimation for the euro area. The rate of sales tax ranges from 5% to 20% among G7 countries. In the baseline case, the sales tax is set s ¼ s* ¼ 0.1. The adjustment cost function is specified as U(m) ¼ k[(m1 r 1)/(1 r) (m1 s 1)/(1 s)]. For any set of k > 0, r < 0, and s > 1 (and s / 1), this specification of U(m) satisfies the restrictions imposed in Section 4.1. To obtain the closed-form solution, we set r ¼ 1 and s/1. k ¼ 11 is chosen to produce the average annual money growth rate of about 2% under noncooperation. For these parameters, cooperation produces the 3.353% money growth, and noncooperation yields 2.025% money growth in the steady state, which verifies Proposition 1. Next, we examine the sensitivity. Fig. 1A)–1C) show how the optimized money growth in the home country changes with r. The tax rates are 20% in Fig. 1A), 10% (baseline) in Fig. 1B), and 20% in Fig. 1C). The dashed line represents the cooperative policy and the solid line represents the noncooperative policy. These figures demonstrate Proposition 1 that, for any value of r, cooperation yields a higher inflation. To understand the mechanism underling these figures, it is useful to rewrite the optimal policies. When s ¼ s ¼ s, the cooperative policy in Eq. (14) is reduced to
ε
r
1
1s
Q
E mU0 ¼ 1r : E C
(15)
The first term captures the expenditure-changing effect on consumption and the second term that on production. Because the work efforts in both countries are considered, consumption and work effort are equally weighted. As r increases, the marginal utility from consumption Cr increases, because consumption is less than one, and stimulates the monetary policy. At the same time, the increase in r weakens the expenditure-changing effects and makes the large monetary change unnecessary. The graphs show the balance of these conflicting motives. Fig. 1A) and 1B) demonstrate that the optimal money growth is positive as long as ð1 sÞ=Q > 1. If the tax completely offsets the markup, as in Fig. 1C), the money growth is zero. Note that, in this cooperative policy, expenditure-switching effects
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A
C
B
D
Fig. 1. Growth rate of money. The graphs in Fig. 1 compare the steady-state money growth mhM=M0 under noncooperation and cooperation. The vertical axis indicates the money growth. The horizontal axis represents the coefficient of the relative risk aversion r. The solid line represents the noncooperative policy in Eq. (13): ðnε=rÞð1 ð1 sÞ=QÞ ð1 nÞð1 sÞ=Q ¼ EfmU0 g=EfC 1r g; and the dashed line represents the cooperative policy in Eq. (14): ðε=rÞð1 nð1 sÞ=Q ð1 nÞð1 s Þ=QÞ ð1 nÞ 0 0 ðð1 sÞ=Q ð1 s Þ=QÞ ¼ EfmU g=EfC 1r g; where U(m) ¼ k[(m2 1)/2 lnm]. In this case, EfmU g ¼ kðEfm2 g 1Þ. As Eq. (8) implies, E{C1r} is calculated by ½ðð1 sÞ=kÞn ðð1 s Þ=k Þ1n =Q1=ðn=ð1rÞ1Þ . The tax rates in both countries are 20% in A), 10% (baseline) in B), and 20% in C). In D), noncooperative taxes are given by sN and s*N in Eq. (18), and cooperative taxes are given by sC and s*C in Eq. (19). Other parameters are n ¼ 0.9, ε ¼ 2, Q ¼ 1:2, n ¼ 2.4, and k ¼ 11. The productivity parameters k and k are set so that individuals work the 1/3rd of the time endowment in the steady state in the baseline case ðs ¼ s ¼ s ¼ 0:1; r ¼ r ¼ 2Þ : k ¼ k ¼ ð1 sÞ=Q=ð1=3Þv1þr ¼ 20:25:
are mutually canceled out. Since the depreciation of one currency implies the appreciation of the other, the expenditure switching produces a zero-sum benefit from the global perspective. When s ¼ s*, the consideration of the expenditure-switching effects on home production and foreign production completely cancel out each other. The noncooperative policy in Eq. (13) can be rewritten as follows.
nε
r
1
1s
Q
ð1 nÞ
1s
Q
0 E mU ¼ 1r : E C
(16)
The first term captures the expenditure-changing effects on consumption and work effort, and the second term represents the expenditure-switching effect that increases the home production for overseas sales. For larger tax rates (Fig. 1A), any effects on work effort are less considered and the expenditure-changing effect on consumption is relatively important. When the tax rate is intermediate as in Fig. 1B), the expenditure-switching effect on work effort is stronger, and the authority is more motivated to deflate compared to Fig. 1A). In both cases, the deflation is more likely for a sufficiently large r, which works to reduce the weight given to consumption. If the tax rate completely offsets the markup, the expenditure-changing effects on consumption and work effort cancel out each other. In this case, the left-hand side of the noncooperative policy function (13) is independent of r. Fig. 1C) shows this case. The curvature of optimized m only reflects the expenditure-switching effect. 5. Endogenous tax policies and implications for inflation So far, this paper has assumed tax policies that are invariant across monetary regimes. They are determined independently of monetary authorities cooperating or not. In the course of the ongoing
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globalization, however, it is also possible that international monetary cooperation occurs as a part of a policy coordination package that includes tax policies.6 To gauge the impact of such a possibility, this section examines one plausible case in which both fiscal and monetary authorities in the same country share the same objective function and where tax rates are optimally chosen under each regime. We assume full commitment to the tax policy. This is justified if, for instance, there is a one-period lag in the implementation of the fiscal policy. Tax rates are usually legislated for, which is a time consuming process. Fiscal policymakers choose tax rates using the information available at time 0. The fiscal authorities act as Stackelberg leaders of the private sector, taking the monetary base as given. Under noncooperation, each fiscal authority determines its tax rule independently to maximize the expected welfare of its own country, E{V} or E{V*}, given the private sector’s allocation and pricing rules. In this case, sN and s*N satisfy the following:
2
3
3
2
n n 7 1 6 7 1 6 þ 1 n5 ¼ 0; 4 4 5 1 r n 1 sN 1r nQ 1 1 n n 3 3 2 2
(17)
1n 7 1 6 1n 7 1 6 þ n5 ¼ 0: 5 4 4 1 r n 1 sN 1r nQ 1 1
n
n
In each equation, the first term captures the effects on consumption, and the second term, the effects on production. In the first equation, the fiscal authority considers two effects of the tax cut in the home country: increasing consumption by n/[1 (1 r)/n] and deteriorating terms of trade Ph/Pf(¼[(1 s*)/(1 s)]1/n) by 1/n. As a result, production in the home country increases by [n/[1 (1 r)/n] þ (1 n)]/n. Thus, the change in the tax rate has a smaller impact on consumption than in the case of an autarky. Therefore, each government desires to retain the monopoly power in both markets, so that its residents produce less than that in an autarky, in order to avoid indulging in excessive work efforts. This is the reason why the fiscal authority limit decreases in the tax rate. Note also that producers require higher prices for their production as r increases, which decreases the expected value of income E{CWUC}, or as n increases, which increases work effort. Since the change in terms of trade is independent of these parameters, the impact of tax reduction on work effort is larger than that on consumption under a large r or n. This motivates the fiscal authority to discourage production by raising sales taxes. As seen in the second term, governments also offset the markup Q, and this term plays the role of decreasing the tax rate. Rearranging these conditions, we obtain the following optimal tax rates:
1 sN ¼
Q
; 1r 1n 1 þ1 n n
1 sN ¼
Q
1
1r
n
n þ1 1n
:
(18)
Note that when r/1, the producers’ pricing becomes independent of the expected value of income before tax E{CWUC}, which is evaluated using marginal utility from consumption. In this case, the fiscal authority’s incentive to limit the tax cut is ameliorated as compared to the case where r > 1. When fiscal authorities cooperate, they jointly maximize the expected world welfare E {wV þ (1 w)V*}, subject to (8)–(10). In this case, each government sets the tax rate under cooperation, sC or s*C, so that
6 The analysis in this section can also be considered as the cooperative framework toward regional integration or, alternatively, the first-best policies by a central planner in the integrated global system.
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2
2 0
3
1
0
1
3
C n n n 6 B C B C 1s 7 1 6 7 1 4w@ þ 1 nA þ ð1 wÞ@ nA ¼ 0; 4 5 5 1 r 1 sC 1r 1r 1 sC Q 1 1 1 n n n 2 0 1 0 13 3 2 C 6 B 1n C 1s B 1n C7 1 6 1n 7 1 4w@ ð1 nÞA þ ð1 wÞ@ þ nA5 ¼ 0: 5 4 C C 1r 1s 1r 1r Q 1s 1 1 1
n
n
n
Unlike fiscal noncooperation, an additional term w appears in the second term, and the domestic policy becomes dependent on the foreign policy. This additional term w reflects the fiscal authority’s reduced care about the disutility from production in its own country, and it has a greater incentive to stimulate production. When the weight of social welfare is equal to country sizes, that is, w ¼ n, these optimal policies are reduced in equilibrium as follows:
1 sC ¼ Q;
1 sC ¼ Q:
(19)
In this case, the central planner chooses the efficient allocation by fully eliminating the monopoly distortion. 5.1. Implications for the inflation and exchange rates Suppose that each fiscal authority knows the monetary regime and maximizes the same objective that the monetary authority in the same country engages in. Under such an assumption, the left-hand side of the noncooperative policy (13) with s ¼ sN becomes
0 B nε þ1n B @ r
1 C 1 1 C: 1 nr 1n 1r A 1þ 1 1þ n ε n n
This is positive when r/ε < 1 (1 r)/n. Lemma 2 in Section 4 implies that, the noncooperative monetary policy has an incentive to inflate on average. Intuitively, either policy equally weights the deterioration of terms of trade with 1 n (See Eqs. (13) and (17)). On the other hand, consumption responds to monetary shock by nε/r, but to tax policy by n/[1 (1 r)/n]. When r/ε < 1 (1 r)/n, a monetary policy maker evaluates the benefit on consumption (net of the cost of increased labor disutility) higher than a tax policy maker does. In other words, the monetary policy not only offsets the increased tax but also creates inflation in equilibrium. When r/ε > 1 (1 r)/n, the opposite is true. The exceptional case with no inflationary/deflationary incentive (the left-hand side of Eq. (13) is zero) is obtained only when r/ε ¼ 1 (1 r)/n. On the other hand, s ¼ sC and s* ¼ s*C under cooperation brings the equilibrium monetary policy to a neutral stance regardless of the value of r. To summarize, we offer the following proposition: Preposition 2. When the sales tax is set to maximize for the same monetary objective in each regime, cooperation increases the rate of inflation on average when r/ε > 1 (1 r)/n and decreases it when r/ε < 1 (1 r)/n. Cooperation does not alter the rate of inflation when r/ ε ¼ 1 (1 r)/n. This phenomenon is depicted in Fig. 1D). Except for taxes, the parameter values are the same as those explained in Section 4.3. The difference between the roles of monetary and tax policies is based on the mechanism through which they control the consumer prices. Origin-based tax controls the prices Ph and Pf in the producer’s currency, while monetary surprise affects overseas consumer prices Ph ð ¼ Ph =SÞ and Pf ð ¼ Pf SÞ through the exchange rate. Under a noncooperative regime, in estimating the policy impact on consumption, both policies consider the marginal utility from consumption, but the tax policy also considers the feedback from labor disutility, which increases Ph and decreases consumption. Thus, the value of r has less importance in the tax policy than in the monetary policy, and
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the monetary policy is less (more) motivated to contract the economy than the tax policy when r/ε<(>) 1 (1 r)/n. Under cooperation, both policies offset any disproportionate effects on consumption and labor disutility, thus yielding no inflation bias regardless of the value of r. Therefore, the noncooperative regime results in competitive depreciation when r/ε < 1 (1 r)/n. Under our parameterization, the neighborhood around r ¼ 2, which yields the unitary consumption elasticity of money demand, supports the competitive depreciation story. Admittedly, the tax policies examined in this section should be subject to cautious examination. First, the fiscal authority may have other objectives, such as the provision of public goods and revenue requirements. In addition, if fiscal instruments are available only for the domestic objectives, tax policies should be interpreted independent of monetary regime, and the results in Section 4 are retained. However, independent countries can also coordinate the policy mix. For instance, regional integration can begin with the establishment of a comprehensive cooperative framework among participating countries. When we examine the potential costs and benefits of economic integration, the joint analysis of monetary and fiscal cooperation in this section applies.
6. Concluding remarks This paper has analyzed how the international cooperation of monetary policies alters the inflation rate in a simple sticky-price model. We have examined whether the traditional analysis of the beggar-thy-neighbor incentive of monetary policy, and thereby, competitive depreciation, exists or not. For the given tax rates, international monetary policy cooperation increases the average inflation rate. This result arises irrespective of whether or not the fiscal tax eliminates the monopoly distortions. When tax rates are set optimally to maximize the welfare in each regime, monetary cooperation can eliminate the inflation bias under noncooperation if the expenditure-changing effect of monetary policy is sufficiently strong, restoring the competitive depreciation story. Under the small expenditurechanging effect, on the other hand, cooperation prevents the deflation that would emerge under a noncooperative regime. One caveat is that the examined alternative setup assumes that the fiscal and monetary authorities share the same functional form of the objective. It is also interesting to examine the cases in which the fiscal and monetary authorities have separate policy objectives. For instance, we can consider the provision of public goods in the fiscal objective. For future research, we plan to relax the assumption of the law of one price and introduce local currency pricing into the environment of endogenous tax. Since the existing literature indicates that pricing-to-market itself can produce competitive depreciation, it is meaningful to see whether the combination of these two elements overturns the traditional beggar-thy-neighbor property again. Another possible extension is a multi-period model. While we focused on the two-period setting for the purpose of insulating intratemporal issues from intertemporal ones, the introduction of asset trading would provide an additional element with which policymakers evaluate welfare effects. When we consider repeated games, the time-consistency features may also arise. Further, it is worth examining the equivalence of a sales tax and other types of distorting taxes, such as a consumption tax. Although this is beyond the scope of this paper, considering government expenditure in addition to distorting taxes would also provide insightful results. Government spending increases the supplier’s income and hours worked and can further alter the equilibrium. For instance, public consumption goods such as education and health care would also improve the utility of residents. Another possibility is the impact on productivity. The infrastructure that the government invests in can work as the public input of private production. Moreover, government measures against environmental pollution might ultimately stimulate labor productivity, which this paper treats as a stochastic exogenous variable. In either case, government expenditure is likely to fall in the domestic market, and thus, it might produce an additional mechanism in which cooperation alters the inflation.
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Appendix A A.1 Proof of Lemma 1 To compare the left-hand sides of Eqs. (13) and (14), subtract the latter from the former. In essence, the difference reflects the change in foreign consumption and work effort.
nε
r
¼
nε
r
þ1n
ð1 nÞε
r
þ
1s
Q
ð1 nÞε
r
ε
r
nε
r
1s ð1 nÞε 1 s þ1n ð1 nÞ
1 s ð1 nÞ
r 1 s ð1 nÞε 1 1 ¼ r Q ε
Q
r
Q
Q
If 1 > ð1 r=εÞð1 s Þ=Q, this value is negative, and thus, the value of L is greater under cooperation (Q.E.D.). A.2 Proof of Lemma 2 Define MhEflnmg.
vL vL vEflnmg ¼ vm vM vm o1 n 2 vE C 1r U0 þ mU00 m m þ E C 1r ¼ E C 1r vm Since this expression applies for any realization of m, vL=vM ¼ EfvL=vMg must hold for all m. Therefore, we obtain
o1 n vL E m U0 þ mU00 : ¼ E C 1r vM Given that U0 þ mU00 > 0 and m > 0, the right-hand side of this equation is always positive. Therefore, L is increasing in the value of E{lnm} (Q.E.D.). References Adolfson, Malin, Laseen, Stefan, Linde, Jesper, Villani, Mattias, 2007. Bayesian estimation of an open economy DSGE model with incomplete pass-through. Journal of International Economics 72 (2), 481–511. Benigno, Gianluca, Benigno, Pierpaolo, 2003. Price stability in open economies. Review of Economic Studies 70, 743–764. Benigno, Pierpaolo, Woodford, Michael, 2005. Inflation stabilization and welfare: the case of a distorted steady state. Journal of the European Economic Association 3 (6), 1185–1236. Betts, Caroline, Devereux, Michael, 2000. Competitive depreciation and monetary policy coordination: a reevaluation. Journal of Money, Credit and Banking 32 (4), 722–745. Braun, R. Anton, 1994. Tax disturbances and real economic activity in the postwar United States. Journal of Monetary Economics 33 (3), 441–462. Canzoneri, Matthew B., Gray, Jo Anna, 1985. Monetary policy games and the consequences of non-cooperative behavior. International Economic Review 26 (3), 547–564. Çenesiz, M. Alper, Pierdzioch, Christian, 2009. Efficiency wages, financial market integration, and the fiscal multiplier. Journal of International Money and Finance 28 (5), 853–867. Clarida, Richard, Galí, Jordi, Gertler, Mark, 2002. A simple framework for international monetary policy analysis. Journal of Monetary Economics 49 (5), 879–904. Corsetti, Giancarlo, Pesenti, Paolo, 2005. International dimensions of optimal monetary policy. Journal of Monetary Economics 52 (2), 281–305. Corsetti, Giancarlo, Pesenti, Paolo, Roubini, Nouriel, Tille, Cédric, 2000. Competitive devaluations: toward a welfare-based approach. Journal of International Economics 51 (1), 217–241. Darius, Reginald, 2010. The macroeconomic effects of monetary and fiscal policy in a small open economy: does the exchange rate regime matter? Journal of International Money and Finance 29 (8), 1508–1528.
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