The Role of Financial Market Structure and the Trade Elasticity for Monetary Policy in Open Economies ∗ Katrin Rabitsch
†
August 31, 2011
Abstract Imperfect international risk sharing and exchange rate volatility matter for how monetary policy should optimally be conducted in an open economy: these features lead to optimal deviations from the inward-looking behavior of solely stabilizing domestic inflation and affect terms of trade considerations of policymakers. I study these motives for a classical and long-standing question in international monetary economics: the size of potential gains from international policy coordination. In a standard two-country model with monopolistic competition and nominal rigidities I allow for various degrees of risk sharing by considering different assumptions on international financial markets – complete markets, financial autarky and a bond economy – and a large region for the crucial parameter of the trade elasticity. The incentive of terms of trade manipulation, that is, the attempt of policymakers to influence international relative prices in their own favor, is shown to be particularly strong when international prices are very volatile. When incomplete markets give rise to high exchange rate volatility and poor risk sharing – such as in Corsetti et al. (2008)–, gains from policy coordination are shown to be an order of magnitude larger than previous studies, working under the assumptions of complete financial markets, suggest. Keywords: Monetary Policy, Risk Sharing, Price Stability, Policy Coordination, Financial Market Structure, Trade Elasticity JEL-Codes: E52, E58, F42
∗ This paper has benefited from discussion with or comments from P´ eter Bencz´ ur, Giancarlo Corsetti, Robert Kollmann, Margarita Rubio, as well as participants at the MNB-CEPR Workshop 2009, the Vienna Macroeconomics Workshop 2009, ASSET 2009, and EEA 2010. † Central European University and Magyar Nemzeti Bank, e-mail:
[email protected]
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1
Introduction
This paper studies the role of international risk sharing and exchange rate volatility in shaping optimal monetary policy in open economies, and their role for the magnitude of gains from an international coordination of national policies – a classical and much discussed question in the open economy literature on monetary economics. Under perfect international risk sharing the international relative price of consumption is efficient, such that a country’s consumption is high relative to consumption abroad when its relative price is low. Lack of international risk sharing – for which there is ample evidence in the data – adds an additional distortion that policymakers in open economies have to take into account in their design of policies. Given the empirical evidence of poor international risk sharing and high exchange rate volatility in the data, it can be argued that incorporating these fact into our tools of analysis should be an integral element when addressing questions on optimal policies in an international setting. I analyze how this changes the prescriptions of (producer) price stability as the optimal policy, and, in particular, re-examine how strategic interactions between policymakers and the role for international policy coordination are affected. When poor risk sharing is included as a feature in an otherwise standard model, gains from policy coordination become an order of magnitude larger than previous studies – working under the assumptions of complete financial markets – suggest. This is because the incentive of a country’s policymaker to manipulate international relative prices in one’s favor has much more detrimental consequences once price swings are large and, because of an incomplete asset market structure, lead to large inefficient wealth effects of country specific shocks. As shown by Corsetti et al. (2008), this is precisely the case under which standard open economy models can be reconciled with the observed low international risk sharing. The questions of this paper connect to a large literature on optimal monetary policy in open economies, pioneered by Obstfeld and Rogoff (2002), Corsetti and Pesenti (2001, 2005), Clarida et al. (2001, 2002), Devereux and Engel (2003), Benigno and Benigno (2003, 2006), Gal´ı and Monacelli (2005), to name just a few. These contributions established that in some cases the policy in an open economy may be ’isomorphic’ to that in a closed economy and established circumstances under which it is not. Other international dimensions of optimal policy studied thoroughly in this literature concern, e.g., the currency denomination of exports, and whether or not flexible exchange rates are desirable. The literature has also suggested that an international coordination of monetary policies can eliminate strategic behavior of countries to manipulate international prices, but that the size of such welfare gains may be rather small. Nevertheless, most of the above papers have worked under the setting of perfect international risk sharing, and only very few authors have analyzed the role of international financial market inefficiencies, which add an open economy distortion of crucial importance. Noteworthy exceptions are Sutherland (2004), De Paoli (2009), Benigno (2009), and Corsetti et al. (2010a). Corsetti et al. (2010b) provide an excellent discussion of the literature and identify new directions for research on monetary policy in open economies as coming from ’inefficiencies unrelated to nominal rigidities, stemming from arguably deeper and potentially more consequential distortions’, namely from frictions in international asset market. A relatively unexplored area, even among the above contributions, is a re-evaluation of the size of potential benefits from a coordination of monetary policies when the traditional distortions considered in the literature interact with imperfect international risk sharing and exchange rate volatility. This paper aims to fill this gap. The framework used to address these issues is a relatively standard two-country imperfectlycompetitive sticky-price model of the open economy, yet it puts imperfect risk sharing at center stage. In such a setup, a number of imperfections characterize the economy that typically exert influence on the way monetary policy should optimally be conducted. In addition to the two internal distortions of monopolistic competition and rigidities in price setting (assumed to be set in 2
producer currency), there is an external distortion which stems from a country’s monopoly power on the relative price of its exports to imports, that is, on its terms of trade (T OT ).1 Monopoly power over the terms of trade may create cross-border monetary spillovers when national policymakers act non-cooperatively, as each country aims to achieve a more favorable international relative price. The failure to internalize international spillovers then leads to inefficient outcomes through distorted prices and quantities, which gives rise to potential welfare gains from a coordination of policies. This paper shows that the size and direction in which movements in the terms of trade enter into the consideration of monetary policy, crucially depend on and interact with the degree of international risk sharing. The degree of risk sharing in turn, is determined by the structure of international financial markets assumed, as well as by the precise parameterization of the trade elasticity. For this purpose, I contrast three stylized assumptions on the international financial market structure – namely, complete markets (CM), financial autarky (FA) and an incomplete markets-bond economy (IM) – and consider a wide range of the trade elasticity. The latter is of importance as it governs the strength in which relative wealth is affected in response to country specific shocks. In the special case of a unitary elasticity (combined with log-utility) movements in the terms of trade provide full automatic risk sharing independent of the financial market structure assumed.2 An analysis of the role of the degree of risk sharing for optimal monetary policy can therefore only be addressed at values of the elasticity away from unity. In the previous literature there has been no consensus on the choice of the value of the trade elasticity – it has been all over the place. Therefore, I choose not to calibrate this parameter to a specific fixed value, but consider instead a large range for it, where domestic and foreign consumption goods are allowed to be either substitutes or complements. Most importantly, I consider also very low elasticities in my analysis which have been shown to be necessary to reproduce – together with an incomplete financial market structure – the empirically observed low degrees of international risk sharing (see Corsetti et al. (2008)) and will give these scenarios particular emphasis. The main results are summarized as follows: First, to understand the policy tradeoffs that motivate and generate a role for policy coordination, I study the transmission and international spillovers of productivity shocks. I provide a precise characterization of when, depending on financial market structure and the trade elasticity, these tradeoffs lead to an optimal policy that deviates from the replication of flexible prices, in what direction the policy deviates, and how large these differences are quantitatively. For almost all cases of financial market assumptions and policy regimes considered the implications are that full stabilization of inflation is not the optimal monetary policy. By full stabilization I refer to a policy of achieving fully stable producer prices, such that the terms of trade behave exactly as in the world without nominal rigidities and the flexible price allocation is replicated (fully closing the output gap). Only in the case of CM under coordination and in the case of the unit-elasticity-’automatic perfect risk sharing’ producer prices should be kept fully stabilized.3 With imperfect risk sharing policymakers face an additional distortion and – as a direct consequence of addressing multiple distortions with only one instrument – will find it optimal to trade off some inflation for achieving a more efficient international relative price. An interesting result is that the optimal policy is found to be exactly the opposite under CM and FA: when it is optimal for an independently acting policymaker to understabilize the economy under CM (full risk sharing), he finds it optimal to overstabilize the 1 Throughout the paper, I refer to the terms of trade when talking about the influence of international prices on policy decisions. However, it should be noted that, equivalently, I could have referred to the real exchange rate as the relevant international price to consider (which in this model always moves proportionally to the terms of trade). 2 In this case any income effects from shocks are offset by proportional movements in the international relative price (see, Cole and Obstfeld (1991), Corsetti and Pesenti (2001)). 3 This is the ’isomorphism’ and ’inward-looking’ result of early contributions: if everyone ’keeps their own house in order’ the optimal policy is implemented by ’divine coincidence’ (see, e.g., Clarida et al. (2001), Gal´ı and Monacelli (2005), or Corsetti and Pesenti (2001), Benigno and Benigno (2003)).
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economy under FA (no risk sharing).4,5 The above outlined policy motives, stemming from the presence of the various distortions, and the precise way in which they interact with the incentive to move the TOT, imply that welfare gains from policy coordination depend on the degree of risk sharing. I study optimal monetary policy using a Ramsey approach and assuming that policymakers can commit. The two-country setup allows for an explicit consideration of Nash versus coordinated optimal policies, which allows to also draw conclusions about the gains from policy cooperation. These are found increasing for elasticities of substitution away from unity and are substantially larger in the case of complementarity between domestic and foreign goods, particularly when risk sharing is low (FA and IM). In addition, contrasting the optimal policies across financial market structures, I find that welfare gains from coordination are larger under complete markets when goods are substitutes, as previously found by Sutherland (2004), however, they turn out to be larger, by an order of magnitude, under incomplete markets when goods are complements. The intuition for this result is simple: when international price swings are large for any given size of a fundamental shock, the policymakers’ power over influencing the price becomes strong, which translate into higher welfare losses of acting uncoordinated. Since, the terms of trade are more volatile under complete markets when goods are substitutes, but (substantially) more volatile under FA/IM when goods are complements, the above result evolves. In the aforementioned model specification that allows the model to be reconciled with the documented low degree of international risk sharing in the data (FA/IM paired with a low trade elasticity), welfare gains from international policy coordination are an order of magnitude larger than previous studies suggested. The rest of the paper is organized as follows. Section 2 describes the model, section 3 discusses the model’s parameterization. Section 4 discusses the role of monetary policy in a world with various degrees of international risk sharing, discussing in detail the relevant distortions, their implications for deviating from price stability and their consequences for the size of gains from policy coordination. Section 5 concludes.
2
The Model
The world economy consists of a Home country (H) and a Foreign country (F ), each of which is specialized in the production of one type of tradable good. Households and firms are defined over a continuum of unit mass. Home and Foreign households are indexed by j ϵ [0, 1] and j ∗ ϵ [0, 1] respectively. Each good is produced by firms in a number of varieties, indexed by h in the Home country and by f in the Foreign country. Firms act under monopolistic competition, face quadratic adjustment costs in their price setting decision, and are assumed to set the price in the foreign market in their own currency (producer currency pricing). I abstract from modeling monetary frictions by considering a cashless economy. Unless necessary otherwise, in the following I only discuss the problem of Home agents, with an understanding that the problem for Foreign agents is symmetric – variables of Foreign agents are marked with an asterisk. Since the model is relatively standard, I keep the exposition of the model structure to a minimum, and refer the more interested reader to a technical appendix that accompanies this paper, which can be found on the author’s website.6 4 This finding is summarized graphically in Figure 1, which plots the impact responses (to a productivity shock) of optimal producer price inflation as a function of the trade elasticity, for the various financial market structures and policy regimes. 5 In a recent contribution De Paoli (2009) documents a related result. She studies the role of financial market structure on optimal monetary policy in a small open economy in the form of comparing different targeting rules and finds that the welfare based ranking of these rules is in opposite order for the case of CM and FA. The simple rules she considers are producer price inflation targeting, consumer price inflation targeting, and a fixed exchange rate regime. 6 http://www.personal.ceu.hu/departs/personal/Katrin Rabitsch
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2.1
Households
Household j maximizes her lifetime expected utility: E0
∞ ∑
β t U (Ct , Lt ) = E0
t=0
∞ ∑
{ βt
t=0
ξC,t Ct1−σ (j) L1+κ (j) −χ t 1−σ 1+κ
} ,
(1)
where β is the discount factor, C (j) is consumption, L (j) is labor effort, and ξC,t is a consumption preference shock whose mean is normalized to 1. Consumption C (j) is a constant-elasticityof-substitution (CES) basket over domestic and foreign goods: ω [ 1 ω−1 ] ω−1 ω−1 1 ω Ct (j) = γ ω CH,t (j) + (1 − γ) ω CF,tω (j) ,
(2)
where ω denotes the trade elasticity, that is, the intratemporal elasticity of substitution between domestic and foreign goods, and where parameter γ ≥ 12 determines the degree of home bias in consumption. For each household j the consumption indices of Home and Foreign goods are defined by a CES basket over home varieties, h, and foreign varieties, f , as:
CH,t
θ θ 1 θ−1 1 θ−1 ∫ ∫ θ−1 θ−1 = Ct (h, j) θ dh , CF,t = Ct (f, j) θ df ,
0
(3)
0
Household j maximizes equation (1) subject to the budget constraint. Each period household j receives wage income, Wt Lt (j), and dividends from the monopolistic firms they own, Πt (j), and has consumption expenditure Pt Ct (j). The availability of any assets of domestic household j depends on the assumptions of the structure of international financial markets. Throughout the paper, I consider three possible scenarios: complete markets (CM), financial autarky (FA) and an incomplete markets-bond economy (IM). Under complete markets the household has access to a full set of state-contingent (ArrowDebreu) securities. Let Q (st+1 |st ) denote the price, common to all individuals, of one unit of Home currency delivered in period t + 1 contingent on the state of nature at t + 1 being st+1 . Let BH,t (j, st+1 ) denote the claim to BH,t units of Home currency at time t + 1 in the state of nature st+1 , that household j buys at time t and brings into time t + 1. Q∗ (st+1 |st ) and BF,t (j, st+1 ) are defined similarly in The nominal interest rates can be ∑ ∑terms of units of Foreign currency. expressed as Rt∗ = 1/ st+1 Q∗ (st+1 |st ) and Rt = 1/ st+1 Q (st+1 |st ). εt denotes the nominal exchange rate (units of Home currency per unit of Foreign currency). The budget constraint under complete markets is then given by: ∑ ∑ Q (st+1 |st ) BH,t (j, st+1 ) + Q∗ (st+1 |st ) εt BF,t (j, st+1 ) (4) st+1
st+1
≤ BH,t−1 (j, st ) + εt BF,t−1 (j, st ) + Wt Lt (j) + Πt (j) − Pt Ct (j) . If the two economies are in financial autarky no assets can be traded internationally. Domestic agents have available a bond denominated in either domestic currency, BH,t , which can be traded ∗ only domestically. Equivalently, foreign agents can trade a foreign currency bond, BF,t , but also only within their country. The budget constraint of domestic household j under financial autarky then becomes: BH,t (j) = BH,t−1 (j) + Wt Lt (j) + Πt (j) − Pt Ct (j) . (5) Rt Finally, I consider the case of the incomplete markets-bond economy. I now assume that both countries can engage in financial trade through one of the one-period nominal bonds. In particular, I assume that the foreign currency denominated bond, BF,t , can be traded internationally (and
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net foreign wealth is initially zero).7 While this assumption introduces a small asymmetry into the otherwise symmetric setup, I do so because the domestic and foreign currency bond holdings are not separately identified. Following Schmitt-Groh´e and Uribe (2003), to render the incomplete markets economy stationary, I assume that domestic agents face a quadratic adjustment cost when taking on an international asset position different from their long-run (zero) position. The budget constraint under the assumption of the incomplete markets-bond economy is: ( )2 BH,t (j) εt BF,t (j) ψ εt BF,t (j) + + Pt (6) Rt Rt∗ 2 Pt ≤ BH,t−1 (j) + εt BF,t−1 (j) + Wt Lt (j) + Πt (j) − Pt Ct (j) .
2.2
Firms
The production function is assumed to be linear in labor: Yt (h) = Zt Lt (h) ,
(7)
where Zt is the level of productivity, which is given by a country-specific AR(1) process with persistence parameter ρZ and standard deviation σZ . Firms operate under conditions of monopolistic competition taking into account the downward-sloping demand for their product and set prices to maximize their profit. They are assumed to set the prices in the foreign market in their own currency, that is, I consider the scenario of producer currency pricing (PCP). When firms set their prices they have to take into consideration a quadratic adjustment cost ´a la Rotemberg (1982), which makes the firms’ price setting decision dynamic:8 ( )2 α pt (h) ϕt (h) = −1 , (8) 2 pt−1 (h) where parameter α measures the degree of price stickiness. Under producer currency pricing the law of one price holds, such that for each variety h we have εt p∗t (h) = pt (h). Each producer chooses its price pt (h) such as to maximize its total market value: {∞ ] [ ] [( )−θ ( )2 } ∑ ( ) pt (h) M Ct (h) pt (h) α p (h) t ∗ E0 Ω0,t (1 + τ ) − CH,t + CH,t − −1 , P P P 2 pt−1 (h) H,t H,t H,t t=0 (9) where M Ct is the marginal cost that minimizes labor input, which is equal to all firms, M Ct (h) = M Ct = Wt /Zt , Ω0,t is the household’s stochastic discount factor between time 0 and t, and τ stands for a production subsidy which is chosen such as to offset the distortion from ) monopolistic competition at the non-stochastic steady state, that is, Φ ≡ (θ−1)(1+τ = 1. θ I focus attention on a symmetric equilibrium where all domestic producers charge the same price, adopt the same technology and therefore choose the same demand for labor. This implies ∗ pt (h) = PH,t , p∗t (h) = PH,t , Lt (h) = Lt , Πt (j) = Πt .
2.3
Resource Constraints
The resource constraint for each variety h and each variety f are given by: ∫1 Yt (h) =
∫1 ct (h, j)dj +
0 7 As
∫1 0
∗
∫1
∗
ct (h, j )dj + 0
∗ ϕt (j) dj = CH,t + CH,t + ϕt ,
bonds are in zero net-supply worldwide, the asset market clearing conditions imply
∗ (j ∗ ) dj ∗ = 0 under FA, and BF,t
∫1
(10)
0
BH,t (j) dj = 0 and
0
∫1 0
BF,t (j) dj +
∫1 0
∫1
BH,t (j) dj = 0 and
0 ∗ (j ∗ ) dj ∗ = 0 under the IM-bond BF,t
economy. 8 The assumption of price adjustment costs instead of the more standard Calvo price setting mechanism is mainly for convenience, as it keeps model size to a minimum by avoiding the need to introduce auxiliary variables when the model is solved by a second-order approximation.
6
Yt∗
∫1 (f ) =
∫1 ct (f, j)dj +
0
∗
∗
∫1
ct (f, j )dj + 0
∗ ϕ∗t (j ∗ ) dj ∗ = CF,t + CF,t + ϕ∗t ,
(11)
0
where the last step follows from imposing symmetry across all households, which implies that indices j can be dropped, and Ct (j) = Ct , Lt (j) = Lt , λt (j) = λt .
2.4
Relative Prices and The Terms of Trade
The terms of trade is defined as the price of imports to exports,
PF,t , ∗ εt PH,t
which given the law of
PF,t PH,t .
one price can be written as T OTt = Using the optimal consumer price level resulting from the optimal intratemporal allocation, it is possible to express all relative prices as a function of the terms of trade only. In particular, the real exchange rate, which is the price of a foreign consumption bundle relative to the domestic consumption bundle, that is, RERt = (εt Pt∗ ) /Pt , is related to the terms of trade by: ] 1 [ ∗ γ + (1 − γ ∗ ) T OTt1−ω 1−ω RER RERt = f (T OTt ) = [ (12) ] 1 . γ + (1 − γ) T OTt1−ω 1−ω ∗ The PPI-to-CPI ratios are defined as pH,t ≡ PH,t /Pt and p∗F,t ≡ PF,t /Pt∗ and can also be written as functions of the terms of trade only: [ ]− 1 pH,t = f pH (T OTt ) = γ + (1 − γ) T OTt1−ω 1−ω , (13) 1 [ ] ∗ − p∗F,t = f pF (T OTt ) = γ ∗ T OTtω−1 + (1 − γ ∗ ) 1−ω .
2.5
Definition of Equilibrium, Constraints for Ramsey Policy Problems and Model Solution
An equilibrium requires that households and firms behave optimally, markets for labor, goods, and assets clear and that the economies’ resource constraints are satisfied. The model’s equilibrium conditions are summarized in Table 1. Equations (RC1)-(RC2) are the two Euler equations, equations (RC3)-(RC4) the two price setting equations, equations (RC5)-(RC6) the two resource constraints, and equations (RC7-CM), (RC7-FA), or (RC7a-IM)-(RC7b-IM) are the relevant conditions that hold under complete markets, financial autarky or the bond economy respectively. p∗ p F,t−1 ∗ ∗ Making use of the fact that πt = H,t−1 πF,t , and by using the functional relationpH,t πH,t , πt = p∗ F,t
ships between the real exchange rate and the terms of trade (equation (12)) and the PPI-to-CPI ratio and the terms of trade (equation (13)), the system in Table 1 fully determines the equilib∗ rium dynamics of Ct , Ct∗ , Lt , L∗t , πH,t , πF,t , and T OTt (and bF,t in the IM economy) – for given ∗ ∗ exogenous processes for Zt and Zt (together with ξC,t and ξC,t ), and for a policy for Rt and Rt∗ . The above conditions also correspond to the private sector constraints a Ramsey policymaker has to take into account when deciding on the welfare maximizing policy. I assume throughout that policymakers can credibly commit in the sense that they can choose the entire future (statecontingent) evolution of the control variables, once and for all, at date zero. The assumption of commitment is important, as private sector expectations about the evolution of prices affect the forward looking terms in the dynamic pricing equations. I study these issues by employing a Ramsey type approach, following closely the steps outlined in Schmitt-Groh´e and Uribe (2009) to obtain the steady state and dynamics implied by the Ramsey equilibrium.9,10 In particular, 9 This builds on previous work on the study of optimal policy in dynamic economies, see e.g., (Ramsey (1927)), Atkinson and Stiglitz (1976), Lucas and Stokey (1983), Chari et al. (1991). 10 While most studies of optimal monetary policy in the recent literature build on a linear-quadratic approximation approach in the spirit of Rotemberg and Woodford (1997), Woodford (2003), and Benigno and Woodford (2005), recently, the Ramsey type approach has been employed in an increasing number of dynamic equilibrium models with monopolistic competition and nominal rigidities. Examples include, among others, Khan et al. (2003), SchmittGroh´ e and Uribe (2005, 2007), and Faia and Monacelli (2004, 2008).
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Table 1: Model Equilibrium Equations and Ramsey Constraints (’RC’) { (RC1):
1 = βEt
(RC2):
1 = βEt
{
−σ Ct+1 ξC,t+1 Rt Ct−σ ξC,t πt+1
}
∗−σ ∗ Ct+1 ξC,t+1 Rt∗ ∗ ∗−σ ∗ Ct ξC,t πt+1
}
(RC4):
] [ −σ σ Ct+1 ξC,t+1 χLκ t Ct − Φ + αβEt C −σ (πH,t+1 − 1) πH,t+1 α (πH,t − 1) πH,t = θZt Lt Zt pH,t ξC,t ξ πt+1 C,t t ] [ ∗ ∗κ ∗σ ∗−σ ∗ ) ∗ ( ∗ ) ∗ ( ∗ C ξ χ L C t+1 C,t+1 πF,t+1 − 1 πF,t+1 α πF,t − 1 πF,t = θZt∗ L∗t Z ∗ p∗t ξ∗t − Φ∗ + αβEt C ∗−σ ξ∗ π∗
(RC5): (RC6):
Zt Lt = (pH,t ) [Ct + RERtω Ct∗ ] − ϕt ( )−ω [ ] RERt−ω Ct + Ct∗ − ϕ∗t Zt∗ L∗t = p∗F,t
(RC7-CM):
RERt =
(RC7-FA):
pH,t (Zt Lt ) − ϕt = Ct
(RC7-IM):
(1 + ψRERt bF,t ) = βEt
(RC8-IM):
RERt bF,t Rt∗
(RC3):
t
−ω
F,t C,t
t
C,t
t+1
∗ Ct∗−σ ξC,t
Ct−σ ξC,t
+
ψ 2
{ 2
−σ Ct+1 ξC,t+1 Rt∗ RERt+1 ∗ Ct−σ ξC,t πt+1 RERt
(RERt bF,t ) =
RERt bF t−1 πt∗
}
+ pH,t (Zt Lt ) − Ct − ϕt
the system of optimality conditions to the respective (nonlinear) Ramsey policy problem is solved by a second-order perturbation method. In the welfare computations in section 4.4, the welfare measures are thus based on a second-order approximation, while the first-order approximated solutions have been used when deriving the impulse responses in section 4.3. The Ramsey problem under cooperation is obtained from a benevolent world social planner that maximizes the country size-weighted average welfare, subject to the equilibrium allocations and prices, and subject to the policy instruments, Rt and Rt∗ .11 If monetary authorities act uncoordinated, the home and foreign policymaker each maximize their respective national welfare, taking as given the entire path of the other country’s choice of policy instrument, that is, either (the entire path of) interest rates Rt or Rt∗ . A detailed description of the setups of the Ramsey problems for the various model economies and regimes (Coordination versus Nash) is available in the online technical appendix.
3
Parameterization
The baseline parameterization of the model is as follows. The discount factor β is taken to be 0.99, implying an annual interest rate of about 4 percent. Parameter θ is taken to be 6, which implies a markup over marginal cost of about 20 percent. The weight on domestic good in the domestic (foreign) consumption basket, is set to reflect positive home bias, γ = 0.8 (γ ∗ = 0.2). The parameter of the quadratic price adjustment cost, α, is set such that it corresponds, together with the chosen value for θ, to a parameter of about 0.75 in a Calvo style price setting or a price stickiness of about four quarters.12 The degree of risk aversion, σ, is considered to be 1 (implying log utility). The relative utility weight on labor, χ is set to obtain a steady state value of L = 1/3. The inverse Frisch elasticity of labor supply, κ, is equal to 3, a value that lies well in the region used 11 In this dynamic economy it is not possible to solve in closed form the decentralized economy as a function of policy instruments only. Different from Chari and Kehoe (1999) the Ramsey problem is therefore set up by carrying the model’s equilibrium conditions as constraints, that implicitly define the economy’s allocation as a functions of the instruments, Rt and Rt∗ . 12 This equivalence is based on the slope coefficient in the linearized pricing equations (see, e.g. Faia and Monacelli
(2008)). Here, α =
αCalvo (θ−1)(1+τ )Y
(1−αCalvo )(1−βαCalvo )
.
8
in the literature (e.g. Rotemberg and Woodford (1997) suggest a value of 0.47, while micro data on (low) estimated Frisch elasticities suggest values as high as 5, which is chosen e.g. by Benigno (2009). In order to focus on the external dimension of monetary policy, and to isolate the influence of terms of trade considerations for the conduct of monetary policy, I follow much of the literature in considering a setup in which the presence of a production subsidy fully offsets the distortion from monopolistic competition, that is, τ , is set equal to 1/ (θ − 1). 13 In the IM economy, the portfolio adjustment cost parameter is set to ψ = 0.005. Turning to the exogenous processes, I consider a baseline case of productivity shocks only. In line with most of the international business cycle literature, a rather persistent technology shock with autocorrelation coefficient of ρ∗ = 0.95, and with standard deviation of the shock of σε , σε∗ = 0.01. In the sensitivity case that includes preference shocks, they are assumed to follow the same autocorrelation and standard deviation parameters as the productivity shock. Finally, I consider a wide range for the value of the trade elasticity, ranging from goods being very complementary in consumption to goods being very substitutable. As I show, the value of the trade elasticity is a most crucial parameter in determining the influence of terms of trade considerations in shaping optimal monetary policy in an open economy. Also, there is no consensus on the choice for this parameter in the literature. In the trade literature, Lai and Trefler (2002) estimate, for individual goods, trade elasticities of around 5 and higher. In the business cycle literature, the trade elasticity is typically taken to be lower. Backus et al. (1995) use elasticities between 0 and 5, Chari et al. (2002) assume a value of 1.5. A number of recent contributions have also emphasized the role of a low elasticity of intratemporal substitution (well in the complementarity region) together with an incomplete financial markets structure in the transmission of productivity shocks across countries, in particular in addressing stylized facts on international relative prices and the low degrees of international risk sharing observed in the data (see e.g., Heathcote and Perri (2002), Corsetti et al. (2008), Thoenissen (2008), Enders and Mueller (2009)). In particular, as Corsetti et al. (2008) show, the volatility of the terms of trade or the exchange rate becomes particularly high around a threshold of the trade elasticity that is related to the degree of home 1 14 bias and lies at 1 − 2γ . An analysis of the effects of low risk sharing and high exchange rate volatility on optimal monetary policy should therefore put particular emphasis on this region of low elasticities.
4
Optimal Monetary Policy and International Risk Sharing
Having completed the description of the model economy, I now turn to studying the optimal monetary policy in this two-country imperfectly competitive sticky price economy. The particular focus will lie on how the degree of international risk sharing affects the scope and goals of monetary policy and if the predictions for optimal monetary policy in this otherwise standard model are altered. For this reason, it is useful to first reflect on the distortions that characterize the economy, starting with the distortions that are common to all model economies, independently of the financial market assumption. As in the closed economy both countries are characterized by two internal distortions: price stickiness and monopolistic competition. The latter generally produces an inefficient level of output, which however was assumed to be offset by the production subsidy. The other internal distortion, price stickiness, prevents efficient adjustment to the disturbances that affect the economy and opens up a gap of output relative to the flexible price allocation. The consensus result of the closed economy literature on optimal monetary policy is that a procyclical 13 Note that this assumption is not necessary. In particular, the working paper version of this paper (Rabitsch (2010)) performs sensitivity analysis in which, among others things, the distortion from monopolistic has not been offset. 14 Moreover, they show that for values of the trade elasticity below the threshold, the T OT appreciate in response to a home productivity increase which leads to a decrease in foreign consumption (which is in line with empirical response for the case of the US), whereas above the threshold the T OT depreciate and transmission to the other country is positive.
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policy can remove the sticky-price distortion by making production supply-determined and can restore the flex-price equilibrium (see, e.g. Woodford (2003) or Gal´ı (2008)). In addition to the two internal distortions, there is an external distortion present in all the financial market structures, which stems from countries’ monopoly power on the international relative price, that is, on their terms of trade. While a coordinated policymaker fully takes into account the effect of movements in the terms of trade on world welfare, a non-coordinated policymaker will seek to use his monopoly power to maximize his own country’s welfare, ignoring the effect of such a strategy on the other country. This open economy distortion has been the focus of a large literature (see, e.g., Corsetti and Pesenti (2005), Benigno and Benigno (2006, 2008), Pappa (2004), Faia and Monacelli (2004, 2008), De Paoli (2009))), however, mostly in the framework of models with complete risk sharing. The strength and direction in which terms of trade considerations enter monetary policy crucially depends on and interacts with the amount of international risk sharing, which in turn depends on a) the assumptions on asset markets and b) the degree of substitutability between domestic and foreign goods. With the production subsidy eliminating the distortion from monopolistic competition, a policymaker acting under the setup of complete financial markets, therefore only faces the distortion of sticky prices and the fact that he has monopoly power over the terms of trade. Under incomplete markets (FA or IM) there is yet another distortion present, in addition to the three distortions outlined above: policymakers also face a situation in which the degree of international risk sharing is too low. This means that even for an uncoordinated policymaker there are now multiple distortions to address, but the policymaker only has available one instrument. On the one hand, as before, he aims at making demand supply-determined, on the other hand, at improving international risk sharing (see Corsetti et al. (2010a)). Therefore a coordinated policymaker will aim at using his instrument to trade off some inflation for a more efficient international relative price. A non-coordinated policymaker’s terms of trade considerations in an incomplete markets world are now influenced by both his desire to tilt the terms of trade in his favor, but also by improving risk sharing properties to some degree.
4.1
Ramsey Steady State
To determine the long-run inflation rate associated to the optimal policy problems above, one needs to solve the steady-state versions of the system of equations of first order conditions derived from the appropriate Ramsey problem. In all economies and regimes considered, the steady state (gross) inflation rate associated to the optimal policy problem is found to be equal to 1, as, under commitment, the planner cannot systematically affect the economy through monetary surprises. The planner therefore aims at choosing a long-run inflation rate that minimizes the cost of adjusting prices, which is summarized by the quadratic term. The above outlined openness dimensions of the desire of adjusting the terms of trade can, therefore, drive the planner’s behavior only in the presence of equilibrium fluctuations (as induced by country-specific shocks) around the same long-run steady state.
4.2
Shock Transmission under Flexible Prices – a Benchmark
To facilitate the analysis of optimal monetary policy, and to evaluate the significance of the distortion of imperfect international risk sharing for optimal policy, I first examine a useful benchmark in which price adjustment is flexible. In this flexible price environment, there is no scope for monetary policy. I study this case in detail however, as the flexible price allocation is a natural reference case, to which I will, in the following, relate the optimal monetary policy to. To illustrate the international transmission, I take, throughout, the example of a domestic productivity increase. Under flexible prices the productivity increase in the domestic economy leads to a higher abundance of domestic goods. This translates into a decrease in the price of domestic goods, resulting in a depreciation of the domestic terms of trade, and channeling world demand towards domestic goods – with the strength of the TOT depreciation depending on the trade elasticity
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(whether goods are complementary, substitutable or unit-elastic) and financial market structure (CM, FA, IM). Let’s focus first on the case of a high trade elasticity, when goods are substitutes and let’s consider the scenario of CM. The increase in domestic productivity leads to a domestic consumption increase, labor effort rises as the home economy gets more productive and the terms of trade deteriorate. Enjoying a more favorable price and because it is easy to substitute to the now more abundant domestic good the foreign country also benefits from the domestic productivity shock. In particular, under CM, the terms of trade depreciate just enough to equalize the marginal utility of consumption across countries with its relative price, the real exchange rate, as dictated by the risk sharing equation. When financial markets are incomplete (FA or the IM-bond), however, the response of the terms of trade is somewhat less pronounced. While the terms of trade still depreciate as an equilibrium response to the now more abundant domestic goods, it does so to a much lesser extent than in the case where marginal utility had to be equalized across countries. As no state-contingent assets have been traded promising the Foreign country part of the benefits, Home labor effort does not increase, the expansion in domestic output is therefore lower than in the CM case, and the fall in the price of domestic goods relative to foreign goods (that is, the terms of trade deterioration) in turn less pronounced. When goods are substitutes the TOT and labor move too little under incomplete financial markets relative to the efficient allocation of CM. The transmission of the productivity shock is somewhat different when goods are complements. Generally speaking, a lower elasticity of substitution implies that for any given change in quantities, higher movements in the price are necessary to bring about these movements in quantities. That is, under all financial market structures, the terms of trade responses are now much stronger than in the case where goods are substitutes. In addition, the TOT now depreciates more in the case of incomplete financial markets than under complete markets. Because home and foreign goods are complementary in utility from consumption, the (productivity-induced) higher abundance of domestic goods also leads to a higher demand for foreign goods. If markets are complete the foreign country is therefore bound to expand its output by increasing its labor effort which tends to take some of the pressure from the terms of trade to increase. Under FA such an increase in foreign output is absent, as a result the increased demand for the foreign goods without a counterbalancing increase in supply for it leads to a deterioration of the terms of trade that is even stronger. The lower the trade elasticity, the stronger is the terms of trade depreciation, and the foreign country increasingly benefits from the domestic productivity increase. Summarizing, now, when goods are complements the TOT move too much under incomplete markets relative to the perfect international risk sharing case of CM. Finally, let’s turn to the case in which goods are unit-elastic. If the elasticity is unity then relative price changes are completely offset by changes in output volumes. In this knife-edge case, the income effect of the required terms of trade depreciation (given the relatively higher productivity in Home) balances the incentive to switch expenditure towards Home goods: relative wealth is always unaffected in response to country specific shocks and complete risk sharing is always obtained independent of the financial market structure assumed.15
4.3
Transmission under Sticky Prices and Optimal Stabilization
Under sticky prices, it is costly for firms to change their prices which as a result don’t adjust instantaneously. In the above example of a domestic productivity increase domestic goods prices would be too high, its output too low. However, by following a procyclical policy –lowering the nominal interest rate– a policymaker can initiate a fall in domestic prices and the home terms of trade, that mimics the behavior under flexible prices. As is well known in the literature, a policy of full stabilization of producer price inflation would lead to an exact replication of the flexible price allocation. 15 See Cole and Obstfeld (1991), Corsetti and Pesenti (2001). Strictly speaking, the threshold where relative price changes are completely offset by changes in output volumes lies only at unity because of my assumption of log-utility. More generally this threshold is given by ω = (2γ − 1 + σ)/(2γσ).
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While the replication of the flex-price allocation is possible, it depends on the distortions that characterize the economy if it is also the optimal policy. Additional open economy distortions such as imperfect risk sharing or non-coordinated policymaking will generally have an influence on the degree of optimal stabilization that monetary policy should provide. As outlined previously these considerations do not influence the steady state level of inflation, and can drive the planner’s behavior only in the presence of equilibrium fluctuations around the long-run steady state that derive from country-specific shocks. Therefore, the optimal policy is studied here in the sense of optimal stabilization in response to shocks – I continue to consider a 1% increase in domestic productivity throughout this section. Figure 1: Impact responses of optimal domestic and foreign producer price inflation to a domestic 1 % productivity shock πH, impact responses to domestic 1% prod. shock
πF*, impact responses to domestic 1% prod. shock
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Figure 1 provides an informative graphical summary of the optimal degree of stabilization under the various market structures (CM, FA, IM) and regimes (Nash vs. Coordination). It captures the optimal responses of annualized producer price inflation on impact of a the productivity shock. That is, the time dimension of the impulse response is ignored, and the first-period responses are depicted instead as a function of the trade elasticity, which is given on the horizontal axis and which covers a wide range, where domestic and foreign goods are complements (ω < 1), unit-elastic, or substitutes (ω > 1) in consumption. A central result, which becomes immediately apparent upon inspecting Figure 1 is that, for all cases but the one of coordinated policy under CM, and the special case of a unit elasticity, the implications are that deviating from full price stability is optimal. To better understand why this is the case I also study the responses of other variables of interest. Figures 2 and 3 therefore display the behavior of the terms of trade, the consumption and labor responses in the domestic economy under the various scenarios, by looking at differences of the responses of these variables to the responses that would occur in a flexible price version.16 A number of authors has previously made the point that deviations from price stability and inward-lookingness can arise as optimal when the trade elasticity differs from unity (see references on page 13). These contributions, however, have generally focused their attention on an environment of complete financial markets, thereby ignoring imperfect risk sharing as a source or contributing factor for these optimal deviations. The focus of the present paper goes beyond these findings, and aims to understand the precise patterns of optimal deviation from price stability, depending on financial market structure. In laying out the mechanism of optimal monetary policies under the various scenarios, I start by reviewing the findings of the literature under complete markets, and then continue to discuss how the distortion of imperfect risk sharing affects these results. 16 Alternatively, for the case of FA or IM, one could also study the differences of the responses of these variables with respect to the first best allocation.
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Figure 2: Differences of optimal TOT impact responses over flexible price TOT impact responses (to a domestic 1 % productivity shock), depending on the trade elasticity TOT
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The intuition for the pattern in Figure 1 is as follows: under complete markets, when risk sharing is perfect and price stickiness is the only distortion in the economy, a coordinated policymaker that maximizes world welfare will always find it optimal to replicate the efficient flexible price allocation (as seen by the firm black line from Figure 1). However, when acting uncoordinated, the policymaker of each country fails to take into account the effect of his policy choice on the other country’s welfare, and tries to make use of his monopoly power over the T OT . With domestic and foreign goods being substitutes in consumption, the uncoordinated home authority’s optimal policy falls short of achieving the full required drop in domestic prices that would bring about full stabilization and replication of the efficient allocation. Producer price inflation is too low (the dashed line corresponding to the CM Nash case in Figure 1 is negative, below the efficient zero inflation). Similarly, the T OT is somewhat less depreciated relative to the flexible price (impact) response to the productivity increase, as shown in Figure 2. As consumption risk is shared and domestic goods can easily be substituted by foreign goods, the less pronounced T OT response aims at having to increase employment by a little less, thereby raising welfare, as this is done with the prospect of keeping the same utility from consumption. In a Nash equilibrium, however, this attempt is unsuccessful, as both policymakers have the incentive to let the terms of trade (or the real exchange rate) fluctuate less than what would be dictated by perfect risk sharing. As a result the T OT do not move ’enough’, and while the uncoordinated planner succeeds in generating a lower volatility of labor effort, consumption volatility increases, which worsens overall welfare.17 When goods are complements, the incentive for the home policymaker to contract the employment response and push some of the work effort to the foreign economy is absent, as foreign goods consumption cannot substitute consumption of domestic goods. On the contrary, the incentive is to render foreign goods even cheaper. As a result, when goods are complements, producer price inflation is positive following the domestic productivity increase, and the T OT is more depreciated relative to its flexible price response. Only in the case of a unit elasticity of intratemporal substitution the economies are insular with respect to T OT movements and the Nash outcome and coordination deliver the same result of a prescription of price stability as the optimal policy. While this basic incentive of influencing the relative price in one’s favor is present under any financial market structure, whenever a policymaker acts non-cooperatively and fails to take into account spillovers of his policy on the other country, in a world with incomplete international financial market yet an other distortion comes into play. With incomplete financial markets (financial autarky or the bond economy), the terms of trade provide inefficient risk sharing in a 17 It should be stressed that the result documented is in terms of volatilities. In particular, for a negative productivity shock the optimal T OT response under the optimal policy of an uncoordinated policymaker would be to generate a T OT appreciation that is less pronounced than under flexible prices. A policymaker under commitment cannot resort to ex-post terms of trade appreciation.
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Figure 3: Differences of optimal consumption and labor impact responses over flexible price impact responses (to a domestic 1 % productivity shock), depending on the trade elasticity C
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world of flexible prices: as shown in section 4.2, in response to shocks the terms of trade vary too little when goods are substitutes, but vary too much when goods are complements to achieve the efficient equalization of cross-country marginal utilities of consumption with their relative price. Thus, a policymaker now also has an incentive to use monetary policy to improve the risk sharing properties by pushing the terms of trade behavior closer to the way they would behave under complete markets. This important international inefficiency has been largely ignored by the literature as a source of optimal deviations from price stability and welfare gains. Only recently Corsetti et al. (2010a,b) identify international relative price distortions as an important new direction in the study of monetary policy in an open economy, and show that their consideration can be quantitatively important for optimal monetary policy.18 Here I provide, again, a precise characterization of how this international distortion shapes the optimal policy and the optimal degree of inflation stabilization. Moreover, over and above the previous contributions, I provide a characterization of not only the cooperative solution, but also the Nash policy, thereby enabling me to identify the relative strength of the international price distortions (monopoly power versus imperfect risk sharing), their interaction with each other, and, following in section 4.4, the welfare gains of coordination. Figure 2 shows that, under FA, the optimal inflation response is positive when goods are substitutes – the planner finds it optimal to reduce prices by more than they would fall under flexible prices. The T OT is found to be more depreciated (compared to a flexible price scenario): the planner improves risk sharing by pushing the T OT response somewhat closer towards how it would respond in a complete markets-perfect risk sharing world. The higher T OT volatility therefore translates into a lower consumption volatility which improves welfare relative to flexible prices. The direction in which to deviate from price stability again flips when turning to the region 18 Other
notable contributions in this direction are Sutherland (2004), Benigno (2009), De Paoli (2009), a discussion of which, together with a discussion of their relation to the present paper, is deferred to section 4.4.
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where goods are complementary in consumption. Because the flexible price incomplete markets allocation was characterized by too much T OT volatility, domestic agents have an incentive to let their terms of trade depreciate somewhat less (appreciate relative to a flex price world) and to contract output relative to the flexible price outcome. It is interesting to note that, given the additional open economy distortion under FA, the direction in which to deviate from producer price targeting is exactly the opposite under CM compared to FA. Figure 4: Impact responses of optimal domestic and foreign producer price inflation to a domestic 1 % productivity shock π , impact responses to domestic 1% prod. shock
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Contrasting the two regimes of Nash versus Coordination in the FA case, we can again observe that, by failing to incorporate the effect of his policy choice on world welfare, the non-coordinated policymaker chooses a comparably more appreciated T OT . Nevertheless, under FA, the policy incentive to improve international risk sharing is strong, therefore the optimal policy behaves qualitatively the same in both the coordinated and the Nash policy regime. This is different when we turn to the third financial market structure considered. In the bond economy case, a coordinated planner’s incentive to improve risk sharing dominates and the coordinated policy is closer to the optimal policy under FA, however, the Nash policy under IM is dominated by the desire to achieve more favorable T OT and, consequently, is closer to the Nash policy under CM. While the discussion so far has focused on the qualitative characterization of optimal deviations from price stability under the various market structures and policy regimes, I now turn to discussing their quantitative significance. Figure 1 suggests that optimal deviations from price stability are found when moving away from the unit-elasticity, and that they are particulary important in the region where the volatility of international relative prices increases. The stronger the T OT move in response to shocks, the more consequential will be a policymaker’s desire to influence this price. While the optimal policies are relatively close to the case of price stability in the region where domestic and foreign goods can be easily substituted in consumption, the magnitude of optimal deviations from inflation targeting increases drastically when the trade elasticity is relatively low, especially when coupled with incomplete financial markets – the parameterization that is necessary to reconcile the model with the empirical stylized fact of a low degree of international risk sharing. In fact, to be able to see this, Figure 1, depicting the optimal inflation responses, is reproduced in Figure 4, plotted on a larger scale on the vertical axis.19 In addition 1 figures could be obtained for the other macro variables. The vertical line at ω = 1 − 2γ refers to the asymptotic threshold at which the sign of transmission switches and at which the volatility of the terms of trade is infinite, as discussed in section 3. It is important to note that this asymptotic threshold is generally present in this model class, even in absence of nominal rigidities. In particular, it is not the case that optimality of the Ramsey policy is compromised in this parameter region. This has been confirmed, by explicitly checking that the second order conditions for a (local) maximum of the policy problem are satisfied. I am grateful to Vasco C´ urdia 19 Similar
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Table 2: Volatilities of Macro Variables under the Optimal Policy
Policy Regime, i i f lex σ(y ( i )− y ( i )) σ (c ) /σ ( y ) σ li /σ y i i ) H ) ( i) ( σ(π i σ rer /σ y Welfare gains over price stability
Policy Regime, i i f lex σ(y ( i )− y ( i )) σ (c ) /σ ( y ) σ li /σ y i i ( σ(π ) H ) ( i) i σ rer /σ y Welfare gains over price stability
low trade elasticity ω = 0.35 CM-C CM-N FA-C FA-N 0.000 0.032 0.632 0.502 1.011 1.012 1.212 3.175 0.114 0.083 0.952 0.728 0.000 0.003 0.218 0.096 1.316 1.353 1.873 8.243 −9 × e−5 4.40 3.07
FA-flex 7.742 0.000 21.014 -
IM-C 0.240 2.129 0.169 0.027 2.532 0.07
IM-N 0.061 2.185 0.042 0.007 2.949 −0.07
IM-flex 2.193 0.092 3.122 -
high trade elasticity ω = 1.5 CM-C CM-N FA-C FA-N 0.000 0.008 0.011 0.006 0.764 0.766 0.896 0.896 0.044 0.037 0.012 0.006 0.000 0.001 0.001 0.001 0.657 0.653 0.470 0.469 −5 × e−6 9 × e−6 7 × e−6
FA-flex 0.897 0.000 0.467 -
IM-C 0.005 0.804 0.034 0.001 0.594 9 × e−7
IM-N 0.005 0.807 0.024 0.000 0.589 −3 × e−6
IM-flex 0.805 0.029 0.591 -
Table 2 presents some second moments of interest, under the various financial market structures and policy regimes, for a high parameter choice of the trade elasticity (ω > 1, substitutes) and a low parameter choice (ω < 1, complements).20 In line with the findings of the impact impulse responses, Table 2 reveals that in the case where goods are substitutes (high trade elasticity) exchange rate volatility under incomplete markets is increased under the optimal policy, at the cost of accepting some inflation. Also, exchange rate volatility in the Nash policy is consistently found lower than in the cooperative case. The quantitative differences are small however. In stark contrast to this, in the low elasticity environment, a planner under incomplete markets attaches a strong weight to fighting highly volatile and inefficient exchange rate movements, achieving a substantially lower amount of volatility by in turn accepting much higher degrees of inflation. In line with the findings by Corsetti et al. (2010a), this difference in the quantitative importance is also reflected in the size of welfare gains (expressed in terms of steady state consumption) of following the optimal policy over a policy of price stabilization. Even though deviating from price stability was found to be, in principle, optimal with imperfect risk sharing, these welfare gains are virtually zero when goods are substitutes. For the case of complements, welfare gains of following the optimal policy instead are substantially larger, an approximate 0.07% in the bond economy (’IM-C’), where exchange rate volatility is in line with its empirical counterpart. Finally, Table 2 reveals that, in a similar fashion, the difference between Coordination and Nash, and as a consequence, the potential for welfare gains from coordination, become much more amplified when risk sharing is low. The remainder of the paper is devoted to the implications for gains from an international coordination of monetary policies. for sharing his codes (documented in Altissimo et al. (2005)), that implement an LQ-approximation to optimal policy and that specifically check the second order conditions. 20 Parameter ω in the low elasticity case was chosen such as to obtain a volatility of the real exchange rate (relative to that of output) that is close to the values found in the data.
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4.4
The Role of Risk Sharing for Gains from Policy Coordination
This section turns to studying the welfare consequences of the conclusions obtained from the last section, of potentially large optimal deviations from price stability and a of consideration of international prices in the optimal policy. I focus the interest on the novel results, namely, on how welfare gains from an international coordination of monetary policies are affected by the distortion of frictions in international financial markets. We have seen that a policymaker that decides on its optimal policy in isolation generally aims to strategically influence the terms of trade in his own favor, and that the resulting international spillovers lead to a Nash policy that generally is worse than the optimal policy under cooperation. The finding that the degree of international risk sharing and exchange rate volatility are important determinants for the way open economy motives shape the optimal policy implies that the welfare gains from policy coordination similarly depend on these factors. The interest in the size of potential gains from an international policy coordination has a long history in international monetary economics; the so-called first generation policy coordination models date back to the late 1970s.21 Interest in these questions resurged after Obstfeld and Rogoff (1995) and the new generation of microfounded open economy macromodels allowed to measure welfare gains based on a more precise, utility-based welfare criterium. The findings of this second generation policy coordination models were that –in a standard open economy model with price rigidities and complete international financial markets– an non-coordinated policymaker may find it optimal to deviate from strict price stability (when the trade elasticity is different from unity), but the found welfare gains from an international policy coordination appear to be rather small (a non-exhaustive list of references includes Obstfeld and Rogoff (2000), Corsetti and Pesenti (2005), Benigno and Benigno (2006, 2008), Pappa (2004), Faia and Monacelli (2004, 2008). This view was challenged by some authors (see e.g. Canzoneri et al. (2005), Tchakarov (2004)), who showed that when considering richer models, that incorporated multiple sources of distortions, welfare gains can be quantitatively more important. A distortion that has been relatively unexplored in the literature is that of frictions in international financial markets. This is despite the fact that low degrees of international risk sharing and high exchange rate volatility are firm characteristics of open economies in the data and, as a result, should be an important model feature in the study of monetary policy in an international setting. As mentioned before, there are a couple of recent contribution that make progress in this important direction, which I discuss in the following. Nevertheless, these contribution typically look at a coordinated policymaker or a small open economy setup, which does not allow for an analysis of welfare gains from coordination. Most related, Corsetti et al. (2010a) and Corsetti et al. (2010b) consider an incomplete market bond economy setting and show that there can be substantial welfare gains of a world social planner following the optimal policy that includes international variables over following a policy of stabilizing inflation. Benigno (2009) also studies a bond economy and shows that non-zero asset and liability positions can amplify welfare gains over a policy of price stability, as the exchange rate affects the valuation of these positions. De Paoli (2009) studies the performance of standard policy rules (PPI targeting, CPI targeting, exchange rate peg) in a small open economy setting, and documents that asset market structure can be consequential for what rule to optimally follow. With respect to these contributions, the present paper presents a more detailed consideration of the policy regime and therefore allows to analyze the consequences for potential welfare gains from policy coordination under the various financial market structures. While this issue has been studied by Sutherland (2004), and to some degree by Tchakarov (2004), novel results are obtained by including a model specification that allows exchange rate volatility and imperfect risk sharing to be in line with the evidence in the data.22 21 See
Hamada (1974, 1979), Oudiz and Sachs (1984) and Canzoneri and Gray (1985). Sutherland (2004) considers a purely static model, and focuses on the extreme financial market assumptions of CM and FA only (that imply full or no international risk sharing). In contrast, I consider an economy in which nominal rigidities are dynamic, which seems more appropriate when interpreting the results quantitatively, and also specifically consider case of the more plausible intermediate degree of risk sharing of the IM-bond economy. 22 Furthermore,
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Table 3: Welfare gains from monetary policy coordination, in % of st.st. consumption ω 0.15 0.25 0.30 0.35 0.50 0.55 0.65 0.85 1.00 1.50 2.00 3.00 5.00
1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2* 1e-2*
productivity shock CM FA IM 0.0280 0.3789 0.1548 0.0163 2.1555 0.3959 0.0124 8.7991 1.0698 0.0093 127.8308 13.7017 0.0038 0.8447 3.0716 0.0027 0.0190 0.0849 0.0013 0.0043 0.0052 0.0002 0.0003 0.0002 0 0 0 0.0005 0.0002 0.0004 0.0007 0.0002 0.0006 0.0005 0.0001 0.0006 0.0000 0.0000 0.0000
prod. and preference shock CM FA IM 0.0294 0.3957 0.1720 0.0164 2.1616 0.4047 0.0124 8.8539 1.0199 0.0096 132.2962 12.5610 0.0060 0.8975 16.1006 0.0059 0.1378 0.5379 0.0066 0.0802 0.0927 0.0101 0.0268 0.0234 0.0135 0.0147 0.0139 0.0251 0.0043 0.0063 0.0345 0.0021 0.0044 0.0479 0.0008 0.0027 0.0637 0.0003 0.0008
Table 3 presents welfare gains from policy coordination, for the three financial market scenarios considered (CM, FA, IM-bond), and for a large range of the trade elasticity. Also, I present welfare gains for the case when the economy is driven by productivity shocks only, and for a scenario in which it is driven by shocks to preferences in addition to productivity shocks. For the sake of space, I abstract from sensitivity analysis w.r.t. to specific parameter values, and refer the interested reader to the working paper version. The welfare measures computed are conditional welfare, measured in terms of consumption equivalents. While it should be noted that, as the steady state level of inflation is non-distorted, welfare gains are generally found to be small, Table 3 shows that the welfare gains are found to be increasing for elasticities of substitution away from unity and are substantially larger in the case of complementarity between domestic and foreign goods, particularly when financial markets are incomplete (FA and IM). In addition, I find that welfare gains from coordination are larger under CM when goods are substitutes, as previously found by Sutherland (2004). However, they turn out to be larger, and substantially so, under incomplete markets when goods are complements. The intuition for this result has been hinted at previously: when the volatility of international relative prices is inefficiently high, this not only becomes the dominant distortion for a coordinated policymaker under incomplete markets to offset or alleviate. Also the non-coordinated policymaker’s incentive to aim for a more favorable T OT in this case has more detrimental consequences. Table 3 shows that, with ω = 0.35 (as used previously in Table 2) welfare gains from coordination amount to about 0.14% of steady state consumption in the IM-bond economy, and are even higher in the case of FA. 23 Arguably, in studying the effects of the open economy distortions of low risk sharing and high exchange rate volatility for monetary policy, it is of particular importance to include the region of the trade elasticity which is able to reconcile model and empirical stylized facts. The conclusion in such case of low risk sharing is, therefore, that welfare gains from an international policy coordination are an order of magnitude larger than previous studies may have suggested. 23 It
can be argued that in the case of more general incomplete market models with multiple assets, the welfare gains from coordination may again be more modest – at least when, as common in the literature, the economy is driven by only relatively few shocks. For example, following the recent methodological advantages by Devereux and Sutherland (2011) in solving for country portfolios in incomplete market models, Devereux and Sutherland (2008) show that the multiple asset case may be closer to complete markets.
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5
Conclusion
The analysis of this paper has emphasized that the elasticity of intratemporal substitution and assumptions on the international financial market structure are important determinants of optimal monetary policy in the open economy. In particular, section 4.3 documented how optimal monetary policy is shaped by the open economy distortions of potentially inefficient and volatile international relative price swings, and by strategic manipulation of international prices that result from non-coordinated policymaking. A re-evaluation of the size of potential welfare gains from an international coordination of countries’ monetary policies suggests that under imperfect international financial markets these gains may be substantially higher than previous studies, working under the assumption of complete markets, have concluded.
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