Joumal of International Economics 117(2019)196-208 Contents lists available at Science Direct Journal of International economics ELSEVIER journalhomepagewww.elsevier.com/locate/jie Optimal monetary policy, exchange rate misalignments and incomplete financial markets☆ Ozge Senay a *, Alan Sutherland b Universiry of St Andrews, School of Economics and Finance, St Andrews, KY169AL, UK CEPR University of St Andrews. St Andrews, KY16, UK ARTICLE O A BSTRACT Recent literature shows that, when international financial trade is restricted to autarky or a single bond, there are Received 13 February 2017 Received in revised form 18 November 2018 internal and external welfare trade-offs that imply optimal monetary policy, in principle, deviates from inflation targeting in order to offset real exchange rate misalignments. This paper develops a more realistic model of in- Available online 27 December 2018 mplete markets, where there is international trade in multiple assets. The analysis shows that the presence f multiple assets creates a potentially powerful interaction between monetary policy and household portfolio location. This interaction is, by definition, not present when there is financial autarky or a single tradeable bond and this paper shows that the interaction with portfolio allocation can imply that optimal monetary policy aerates a quantitatively much more significant stabilisation of the real exchange rate gap than implied by sim- pler models of financial market incompleteness. O 2019 Elsevier B V. All rights reserved. rket structure Country portfolios 1 Introduction Benigno and Benigno(2003)showed that optimal cooperative mone- tary policy should focus on targeting the rate of inflation of producer To what extent should the design of monetary policy rules explic- prices. These authors demonstrate that a policy of inflation targeting itly account for open economy factors such as current account imbal- is sufficient to close all internal and external welfare gaps. There is ances or exchange rate misalignments? Recent literature has therefore no trade-off between internal and external policy objectives. emphasised the key role of imperfections in international financial This early open economy literature, however, focused on models where arkets in creating a trade-off between internal and extemal objec- international financial markets are complete. Households can therefore tives of monetary policy. The aim of this paper is to extend the anal- fully hedge against country specific income shocks. More recent litera- ysis of this question to a model with international trade in multiple ture has begun to analyse monetary policy in open economy models assets but where there are insufficient assets to hedge against all where financial markets are incomplete. For instance, Corsetti et al sources of shocks simultaneously. We show that monetary policy(2010, 2018)analyse cooperative monetary policy in a context where can have a significant effect on welfare via its impact on portfolio al- international financial trade is absent or is restricted to a single non- location. This provides a strong incentive to direct monetary policy contingent bond. They show that, in contrast to the previous literature, away from internal objectives (i.e. inflation stabilisation)and towards when international financial markets are incomplete there an external objective (i.e. stabilisation of the real exchange rate around its first-best level) This paper is a contributi monetary policy in open economies. The early literature emphasised that open economy factors need have no explicit role in the design of optimal cooperative monetary policy rules. For instance, a world level in order to maximize world welfare. In some special cases, see for instance Clarida et al. (2002)and Gali and Monacelli(2005), optimal cooperative policy is identical to non-cooperative policy, but this is not true in general ny helpful comments on an earlier draft of this paper. This basic closed economy results of woodford (2003)and Benigno and woodford (2005). research is supported by ESRC Award Number ES/1024174/1 The only difference between the closed and open economy results is in the choice of price index for the inflation target- consumer prices for a closed economy and producer prices E-mail address: os12@st-andac uk(O Senay). for an open economy. ttps: //doiorg/10. 1016/jinteco 2018. 12.001 0022-1996/6 2019 Elsevier B V. All rights reserved
Optimal monetary policy, exchange rate misalignments and incomplete financial markets☆ Ozge Senay a, ⁎, Alan Sutherland b a University of St Andrews, School of Economics and Finance, St Andrews, KY16 9AL, UK b CEPR, University of St Andrews, St Andrews, KY16 9AL, UK article info abstract Article history: Received 13 February 2017 Received in revised form 18 November 2018 Accepted 5 December 2018 Available online 27 December 2018 JEL: E52 E58 F41 Recent literature shows that, when international financial trade is restricted to autarky or a single bond, there are internal and external welfare trade-offs that imply optimal monetary policy, in principle, deviates from inflation targeting in order to offset real exchange rate misalignments. This paper develops a more realistic model of incomplete markets, where there is international trade in multiple assets. The analysis shows that the presence of multiple assets creates a potentially powerful interaction between monetary policy and household portfolio allocation. This interaction is, by definition, not present when there is financial autarky or a single tradeable bond and this paper shows that the interaction with portfolio allocation can imply that optimal monetary policy generates a quantitatively much more significant stabilisation of the real exchange rate gap than implied by simpler models of financial market incompleteness. © 2019 Elsevier B.V. All rights reserved. Keywords: Optimal monetary policy Financial market structure Country portfolios 1. Introduction To what extent should the design of monetary policy rules explicitly account for open economy factors such as current account imbalances or exchange rate misalignments? Recent literature has emphasised the key role of imperfections in international financial markets in creating a trade-off between internal and external objectives of monetary policy. The aim of this paper is to extend the analysis of this question to a model with international trade in multiple assets but where there are insufficient assets to hedge against all sources of shocks simultaneously. We show that monetary policy can have a significant effect on welfare via its impact on portfolio allocation. This provides a strong incentive to direct monetary policy away from internal objectives (i.e. inflation stabilisation) and towards an external objective (i.e. stabilisation of the real exchange rate around its first-best level). This paper is a contribution to a long-running literature on optimal monetary policy in open economies. The early literature emphasised that open economy factors need have no explicit role in the design of optimal cooperative monetary policy rules. For instance, Benigno and Benigno (2003) showed that optimal cooperative monetary policy should focus on targeting the rate of inflation of producer prices.1 These authors demonstrate that a policy of inflation targeting is sufficient to close all internal and external welfare gaps. There is therefore no trade-off between internal and external policy objectives.2 This early open economy literature, however, focused on models where international financial markets are complete. Households can therefore fully hedge against country specific income shocks. More recent literature has begun to analyse monetary policy in open economy models where financial markets are incomplete. For instance, Corsetti et al. (2010, 2018) analyse cooperative monetary policy in a context where international financial trade is absent or is restricted to a single noncontingent bond. They show that, in contrast to the previous literature, when international financial markets are incomplete there are Journal of International Economics 117 (2019) 196–208 ☆ We are grateful to Giancarlo Corsetti, Charles Engel, Oliver de Groot, Kemal Ozhan and two anonymous referees for many helpful comments on an earlier draft of this paper. This research is supported by ESRC Award Number ES/I024174/1. ⁎ Corresponding author. E-mail address: os12@st-and.ac.uk (O. Senay). 1 In this paper we focus on optimal cooperative policy, i.e. a world where policy is set at a world level in order to maximize world welfare. In some special cases, see for instance Clarida et al. (2002) and Gali and Monacelli (2005), optimal cooperative policy is identical to non-cooperative policy, but this is not true in general. 2 This early literature is in effect a direct extension to an open economy setting of the basic closed economy results of Woodford (2003) and Benigno and Woodford (2005). The only difference between the closed and open economy results is in the choice of price index for the inflation target - consumer prices for a closed economy and producer prices for an open economy. https://doi.org/10.1016/j.jinteco.2018.12.001 0022-1996/© 2019 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Journal of International Economics journal homepage: www.elsevier.com/locate/jie
O Senay, A Sutherland Joumal of International Economics 117(2019)196-208 significant internal and external trade-offs that prevent optimal cooper- Because our model allows for international trade in multiple assets it ative policy from simultaneously closing all welfare relevant gaps. is obviously necessary to compute equilibrium gross portfolios. As just The basic intuition for the Corsetti et al. (2010, 2018 )results is sim- explained, a crucial mechanism at work in our model is that the size ple to explain a policy of producer price inflation targeting reproduces and composition of these portfolios depend on the properties of the the flexible price outcome and therefore eliminates the welfare costs as- monetary rule. There is therefore an interaction between policy choice sociated with staggered price setting. But the flexible price equilibrium and portfolio choice. Equilibrium portfolios are computed using tech- is not fully optimal because international financial markets are imper- niques developed in recent literature(see Devereux and Sutherland fect and thus cross-country income risks are not optimally shared A(2010a, 2011a)and Tille and van wincoop(2010). The combining of corollary of this is that the real exchange rate and trade balance will de- these techniques with the analysis of optimal policy is an important in viate from their first best outcomes. Corsetti et al.(2010, 2018)show novation of this paper. that optimal cooperative policy deviates from inflation targeting and The paper proceeds as follows. The model is presented in Section 2. takes account of external welfare gaps and acts to offset exchange rat ur definition of welfare and the characterisation of monetary poli misalignments. is described in Section 3 and our methodology for deriving optimal pol- The results in Corsetti et al. (2010, 2018 )clearly point to a poten- icy rules in the presence of endogenous portfolio choice is described in tially important deviation from the standard policy prescription of infla- Section 4. The main results of the paper are presented in Section 5 and tion targeting. There is however a significant limitation to Corsetti et als the results from an extended version of the model are described in work In Corsetti et al. ( 2010)the analysis of imperfect international fi- Section 6. Section 7 concludes the paper. nancial markets is restricted to a model with financial autarky, while in Corsetti et al. (2018)the analysis of imperfect financial markets is rep- 2. The model resented by a single-bond economy. These structures provide important insights into the implications of imperfect financial trade but they are Our main analysis is based on a model of two countries with two obviously not a good representation of modern international financial main sources of shocks. In later sections we consider an extended ver- sion of the model with a number of other sources of shocks. The The main objective of the current paper is to analyse optimal mone. model shares many of the same basic features of the closed economy tary policy in more general models of imperfect international financial models developed by Christiano et al. (2005)and Smets and Wouters trade than those considered in Corsetti et al. ( 2010, 2018). Our analy 2003). It is based on the open economy model developed in begins with a simple model which adds one extra asset compared Devereux et al. (2014). Corsetti et al (2010, 2018), so there is trade in two nominal bonds. De- Households consume a basket of home and foreign produced final spite the additional asset our model continues to be one where financial goods. Final goods are produced by monopolistically competitive firms markets are incomplete( because there are not sufficient assets to hedge which use intermediate goods as their only input. Final goods prices against all shocks). We show that this small change in financial market are subject to Calvo-style contracts. Intermediate goods are produced structure has an important qualitative and a potentially large quantita- by perfectly competitive firms using labour and real capital as inputs. tive effect on optimal cooperative policy compared to Corsetti et al. Intermediate goods prices are perfectly flexible. The capital stock is (2010, 2018). Corsetti et al.'s(2010, 2018)analysis shows that optimal fixed Households supply homogeneous labour to perfectly competitive cooperative policy deviates from inflation targeting most significantly firms producing intermediate goods. for small values of the international trade elasticity and when prices In the benchmark version of the model we allow for shocks to home are set in the currency of the consumer (local currency pricing, LCI nd foreign TFP and home and foreign household preferences and there At higher values of the trade elasticity the deviations from inflation is intemational trade in nominal bonds denominated in the currency of targeting are quantitatively small. In contrast, our results show that, each country. Given the range of shocks, trade in two bonds is sufficient with international trade in two bonds, there are quantitatively large de- to provide full risk sharing. This is therefore a model of incomplete viations from inflation targeting for a wide range of values of the trade financial markets. This is a key feature of the model elasticity. These large deviations arise in terms of welfare, the optimal The following sections describe the home country in detail. The for- policy rule and variances of critical variables. In particular, we show eign country is identical. An asterisk indicates a foreign variable or a that optimal cooperative policy implies a significant stabilisation the real exchange rate gap relative to inflation targeting. We are further able to show that the critical difference between the 21 households single-bond case and the two-bond case arises specifically because, in the two-bond case, monetary policy is able to change portfolio returns Household z in the home country ma a utility function of the and the composition of the equilibrium portfolio. In effect monetary form policy achieves a significant amount of leverage on risk sharing through its influence on portfolio returns and portfolio allocation. This is a mech- anism which does not exist in the single-bond case. U,=E2B(2)-4H4+(2) Having demonstrated the basic result in a simple model with a lim ited range of stochastic shocks, two nominal bonds and a very simple policy rule, we extend the analysis in a number of directions We add where p>0, d>0, 4>0, C(z) is the consumption of household z, H(z)is further sources of shocks, we allow for trade in equities as well as nom- labour supply. B is the discount factor and y, are stochastic shocks inal bonds and we consider a more general version of the policy rule. which affect consumption preferences. We assume ,=Y exp(i I and Ey r is a zero-mean normally arries over to these more general cases. nyYt-1+Evr.0 distributed iid shock with Var E=o Taste shocks in the form of yr are emphasised by Corsetti et al. (2010, 2018)because they create a strong role for current account 3 Corsetti et al. (2010, 2018)focus on optimal monetary policy creditor countries. De Paoli(2010) analyses monetary policy for a small open economo icy can be analysed along ricted case, strict inflation targeting reproduces the full risk sharing outcom and shows how optimal policy depends on the degree of financial integration no trade-off between intemal and extemal policy objectives in that very res
significant internal and external trade-offs that prevent optimal cooperative policy from simultaneously closing all welfare relevant gaps.3 The basic intuition for the Corsetti et al. (2010, 2018) results is simple to explain. A policy of producer price inflation targeting reproduces the flexible price outcome and therefore eliminates the welfare costs associated with staggered price setting. But the flexible price equilibrium is not fully optimal because international financial markets are imperfect and thus cross-country income risks are not optimally shared. A corollary of this is that the real exchange rate and trade balance will deviate from their first best outcomes. Corsetti et al. (2010, 2018) show that optimal cooperative policy deviates from inflation targeting and takes account of external welfare gaps and acts to offset exchange rate misalignments. The results in Corsetti et al. (2010, 2018) clearly point to a potentially important deviation from the standard policy prescription of inflation targeting. There is however a significant limitation to Corsetti et al's work. In Corsetti et al. (2010) the analysis of imperfect international fi- nancial markets is restricted to a model with financial autarky, while in Corsetti et al. (2018) the analysis of imperfect financial markets is represented by a single-bond economy. These structures provide important insights into the implications of imperfect financial trade but they are obviously not a good representation of modern international financial markets. The main objective of the current paper is to analyse optimal monetary policy in more general models of imperfect international financial trade than those considered in Corsetti et al. (2010, 2018). Our analysis begins with a simple model which adds one extra asset compared to Corsetti et al. (2010, 2018), so there is trade in two nominal bonds. Despite the additional asset our model continues to be one where financial markets are incomplete (because there are not sufficient assets to hedge against all shocks). We show that this small change in financial market structure has an important qualitative and a potentially large quantitative effect on optimal cooperative policy compared to Corsetti et al. (2010, 2018). Corsetti et al.'s (2010, 2018) analysis shows that optimal cooperative policy deviates from inflation targeting most significantly for small values of the international trade elasticity and when prices are set in the currency of the consumer (local currency pricing, LCP). At higher values of the trade elasticity the deviations from inflation targeting are quantitatively small. In contrast, our results show that, with international trade in two bonds, there are quantitatively large deviations from inflation targeting for a wide range of values of the trade elasticity. These large deviations arise in terms of welfare, the optimal policy rule and variances of critical variables. In particular, we show that optimal cooperative policy implies a significant stabilisation of the real exchange rate gap relative to inflation targeting. We are further able to show that the critical difference between the single-bond case and the two-bond case arises specifically because, in the two-bond case, monetary policy is able to change portfolio returns and the composition of the equilibrium portfolio. In effect monetary policy achieves a significant amount of leverage on risk sharing through its influence on portfolio returns and portfolio allocation. This is a mechanism which does not exist in the single-bond case. Having demonstrated the basic result in a simple model with a limited range of stochastic shocks, two nominal bonds and a very simple policy rule, we extend the analysis in a number of directions. We add further sources of shocks, we allow for trade in equities as well as nominal bonds and we consider a more general version of the policy rule. We also consider local currency pricing. We show that our basic result carries over to these more general cases. Because our model allows for international trade in multiple assets it is obviously necessary to compute equilibrium gross portfolios. As just explained, a crucial mechanism at work in our model is that the size and composition of these portfolios depend on the properties of the monetary rule. There is therefore an interaction between policy choice and portfolio choice. Equilibrium portfolios are computed using techniques developed in recent literature (see Devereux and Sutherland (2010a, 2011a) and Tille and van Wincoop (2010)). The combining of these techniques with the analysis of optimal policy is an important innovation of this paper.4 The paper proceeds as follows. The model is presented in Section 2. Our definition of welfare and the characterisation of monetary policy is described in Section 3 and our methodology for deriving optimal policy rules in the presence of endogenous portfolio choice is described in Section 4. The main results of the paper are presented in Section 5 and the results from an extended version of the model are described in Section 6. Section 7 concludes the paper. 2. The model Our main analysis is based on a model of two countries with two main sources of shocks. In later sections we consider an extended version of the model with a number of other sources of shocks. The model shares many of the same basic features of the closed economy models developed by Christiano et al. (2005) and Smets and Wouters (2003). It is based on the open economy model developed in Devereux et al. (2014). Households consume a basket of home and foreign produced final goods. Final goods are produced by monopolistically competitive firms which use intermediate goods as their only input. Final goods prices are subject to Calvo-style contracts. Intermediate goods are produced by perfectly competitive firms using labour and real capital as inputs. Intermediate goods prices are perfectly flexible. The capital stock is fixed. Households supply homogeneous labour to perfectly competitive firms producing intermediate goods. In the benchmark version of the model we allow for shocks to home and foreign TFP and home and foreign household preferences and there is international trade in nominal bonds denominated in the currency of each country. Given the range of shocks, trade in two bonds is sufficient to provide full risk sharing. This is therefore a model of incomplete financial markets. This is a key feature of the model. The following sections describe the home country in detail. The foreign country is identical. An asterisk indicates a foreign variable or a price in foreign currency. 2.1. Households Household z in the home country maximises a utility function of the form Ut ¼ Et X∞ i¼0 βi Ψtþi C1−ρ tþi ð Þz 1−ρ −Δ H1þϕ tþi ð Þz 1 þ ϕ ( ) ð1Þ where ρ N 0, ϕ N 0, Δ N 0, C(z) is the consumption of household z, H(z) is labour supply, β is the discount factor and Ψt are stochastic shocks which affect consumption preferences. We assume Ψt ¼ Ψ expðΨ^ tÞ where Ψ^ t ¼ ηΨΨ^ t−1 þ εΨ;t; 0 ≤ ηΨ b 1 and εΨ, t is a zero-mean normally distributed i.i.d. shock with Var[εΨ] = σΨ 2 . Taste shocks in the form of Ψt are emphasised by Corsetti et al. (2010, 2018) because they create a strong role for current account 3 Corsetti et al. (2010, 2018) focus on optimal monetary policy in a symmetric twocountry world. Benigno (2009) analyses an asymmetric world with incomplete financial markets and shows how optimal monetary policy differs between net-debtor and netcreditor countries. De Paoli (2010) analyses monetary policy for a small open economy and shows how optimal policy depends on the degree of financial integration. 4 Devereux and Sutherland (2008) consider a simple case where optimal monetary policy can be analysed alongside endogenous portfolio choice. They show that, in a special restricted case, strict inflation targeting reproduces the full risk sharing outcome, so there is no trade-off between internal and external policy objectives in that very restricted case. O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208 197
O Senay, A Sutherland /Joumal of International Economic 117(2019)196-208 dynamics and thus potentially create a strong welfare trade-off for mon- steady state net foreign asset position is zero. This outcome is implied tary policy when financial markets are incomplete. These taste shocks by the assumed endogeneity of the discount factor given in(2) will likewise play an important role in our analysis. The discount factor, B is endogenous and is determined as follows 22. Firms Within each country firms are divided between final and intermedi- ate sectors. Intermediate goods firms use labour and real capital. There is a unit mass of firms in both the final and intermediate levels where 0<n<p 0<B<l, CA is aggregate home consumption and CA is a 2.2. 1. Final goods We define Cr to be a consumption basket which aggregates home Each firm in the final goods sector produces a single differentiated and foreign goods according to product. Sticky prices are modelled in the form of Calvo(1983)style contracts with a probability of re-setting price given by 1-K. In the C:={y+(1-y割 basic version of the model we assume producer currency pricing(PCP (3) If firms use the discount factor n, to evaluate future profits, then firm z chooses its prices for home and foreign buyers, PH Hr(z)and pH Ed(z). where CH and C are baskets of individual home and foreign produced in home currency to maximize oods. The elasticity of substitution across individual goods within these baskets is x>i. The parameter @in(3)is the elasticity of substitu- Et ZOrnIyHH/*(z)h paul+ yH.E 1 +( 2) H.r(2)-qil tion between home and foreign goods. The parameter y measures the importance of consumption of the home good in preferences. For (6) The price index associated with the consumption basket Cr is where is the demand for home good z from home buyers and yH F(z) demand for home good z from foreign buyers and q i y+(1-y) (4) the pric where Ph H is the price index of home goods for home consumers and The representative firm in the intermediate goods sector combines PE, H is the price index of foreign goods for home consumers. The corre- labour, L, and capital, K, to produce output Y using a standard Cobb- sponding price indices for foreign consumers are PH. F and pe. s Douglas technology Y,=ArK-HLH We assume that the capital stock The flow budget constraint of the home country household is is fixed and that total factor productivity(TFP), Ar, is determined by Ar =nAAr-1+ EA, t where na >0 and EA r are zero mean normally distrib- PrCt+PrFt=WHr+Prnt+Pt2akr-1'kt uted iid shocks The representative firm chooses Lr to maximize the real discounted value of dividends, given by where Fr denotes home country net external assets in terms of the home asset k(defined in terms of the home consumption basket)purchased subject to the production function where q is the price of intermediate at the end of period t-1 and rk represents the gross real return on goods. n, is assumed to be the stochastic discount factor of shareholders sset k In our analysis, we initially allow for trade in N=2 assets of the firm Equilibrium in the labour market implies Lt=H, home and foreign nominal bonds. Note that F:= KnO, t Nominal bonds are assumed to be perpetuities, so for instance. 3. Monetary policy and wellare home nominal bonds represent a claim on a unit of home currency in each period into the infinite future. The real price of the home The particular welfare measure on which we focus is the uncondi bond is denoted ZB, t. The gross real rate of return on a home bond is tional expectation of aggregate period utility For the home economy thus rBr +1=(1 /P+1+ZB, I+1)/ZB, r For the foreign nominal bond. this is defined as follows the real return on foreign bonds, in terms of home consumption, is 8+1=(Q+1/Q-)(1/Pi+1+ZB +1)/ZE. where Q=S,P:/Pr is the real U-Ey cl-p Hl+o) exchange rate(where S is the price of the foreign currency in terms of the home currency For the purposes of comparison, we also consider a financial autarky where time subscripts are omitted to indicate that this is a n of ersion of the model, which implies N=0, and a single bond version, unconditional expectation Damjanovic et al.(2008)argue that uncon i.e.N=1, where the only internationally traded asset is a single real ditionally expected utility provides a useful alternative to woodford's bond. For all financial structures we impose the assumption that the (2003)timeless perspective when analysing optimal policy problem For the purposes of this paper, unconditional expected utility provides Following Schmitt-Grohe and Uribe(2003). B is assumed to be taken as exogenous by dividual decision makers. The impact of individual consumption on the discount factor 7 In the basic model, where intermational asset trade is restricted to nominal bonds, all herefore not internalized. Note that this externality in principle creates a distortion in equity is owned within each country, so the relevant discount factor for home and foreign has no significant implication for the analysis presented below. average of home and household discount factors, with the weight being deter- assumption that bonds are perpetuities has no particular sig sults. We have experimented with of the model with single-period bonds and, (which has trivial qt hile there are some quantitative implications, there is no systematic qualitative differ- is intemational trade in equities we impose the assumption that the firm discount factor ences compared to the results reported below in each country corresponds to the household discount factor in each country
dynamics and thus potentially create a strong welfare trade-off for monetary policy when financial markets are incomplete. These taste shocks will likewise play an important role in our analysis. The discount factor, βi, is endogenous and is determined as follows βiþ1 ¼ ββi CA;i CA −η ; β0 ¼ 1 ð2Þ where 0 b η b ρ, 0bβb1, CA is aggregate home consumption and CA is a constant.5 We define Ct to be a consumption basket which aggregates home and foreign goods according to: Ct ¼ γ 1 θC θ−1 θ H;t þ ð Þ 1−γ 1 θC θ−1 θ F;t h i θ θ−1 ð3Þ where CH and CF are baskets of individual home and foreign produced goods. The elasticity of substitution across individual goods within these baskets is λ N 1. The parameter θ in (3) is the elasticity of substitution between home and foreign goods. The parameter γ measures the importance of consumption of the home good in preferences. For γ N 1/2, we have ‘home bias’ in preferences. The price index associated with the consumption basket Ct is Pt ¼ γP1−θ H;H;t þ ð Þ 1−γ P1−θ F;H;t h i 1 1−θ ð4Þ where PH, H is the price index of home goods for home consumers and PF, H is the price index of foreign goods for home consumers. The corresponding price indices for foreign consumers are PH, F and PF, F. The flow budget constraint of the home country household is PtCt þ Pt Ft ¼ wtHt þ PtΠt þ Pt XN k¼1 αk;t−1rkt ð5Þ where Ft denotes home country net external assets in terms of the home consumption basket, wt is the home nominal wage and Πt is profits of all home firms. The final term represents the total return on the home country portfolio where αk, t−1 represents the real external holdings of asset k (defined in terms of the home consumption basket) purchased at the end of period t − 1 and rk, t represents the gross real return on asset k. In our analysis, we initially allow for trade in N = 2 assets; home and foreign nominal bonds. Note that Ft = ∑k=1Nαk, t. Nominal bonds are assumed to be perpetuities, so for instance, home nominal bonds represent a claim on a unit of home currency in each period into the infinite future. The real price of the home bond is denoted ZB, t. The gross real rate of return on a home bond is thus rBt+1 = (1/Pt+1 + ZB, t+1)/ZB, t. For the foreign nominal bond, the real return on foreign bonds, in terms of home consumption, is rB∗ t+1 = (Qt+1/Qt)(1/Pt+1 ∗ + ZB, t+1 ∗ )/ZB, t ∗ , where Qt = StPt ∗ /Pt is the real exchange rate (where S is the price of the foreign currency in terms of the home currency).6 For the purposes of comparison, we also consider a financial autarky version of the model, which implies N = 0, and a single bond version, i.e. N = 1, where the only internationally traded asset is a single real bond. For all financial structures we impose the assumption that the steady state net foreign asset position is zero. This outcome is implied by the assumed endogeneity of the discount factor given in (2). 2.2. Firms Within each country firms are divided between final and intermediate sectors. Intermediate goods firms use labour and real capital. There is a unit mass of firms in both the final and intermediate levels. 2.2.1. Final goods Each firm in the final goods sector produces a single differentiated product. Sticky prices are modelled in the form of Calvo (1983) style contracts with a probability of re-setting price given by 1 − κ. In the basic version of the model we assume producer currency pricing (PCP). If firms use the discount factor Ωtto evaluate future profits, then firm z chooses its prices for home and foreign buyers, pH, H, t(z) and pH, F, t(z), in home currency to maximize Et X∞ i¼0 Ωtþiκi yH;H;tþið Þz pH;H;tð Þz −qtþi Ptþi þ yH; F;tþið Þz pH; F;tð Þz −qtþi Ptþi ( ) ð6Þ where yH, H(z) is the demand for home good z from home buyers and yH, F(z) is the demand for home good z from foreign buyers and q is the price of the intermediate good.7 2.2.2. Intermediate goods The representative firm in the intermediate goods sector combines labour, L, and capital, K, to produce output Y using a standard CobbDouglas technology, Yt = AtK1−μ Lt μ . We assume that the capital stock is fixed and that total factor productivity (TFP), At, is determined by At = ηAAt−1 + εA, t where ηA N 0 and εA, t are zero mean normally distributed i.i.d. shocks. The representative firm chooses Lt to maximize the real discounted value of dividends, given by Et X∞ i¼0 Ωtþi qtþi Ptþi Ytþi− wtþi Ptþi Ltþi subject to the production function where q is the price of intermediate goods. Ωt is assumed to be the stochastic discount factor of shareholders of the firm. Equilibrium in the labour market implies Lt = Ht. 3. Monetary policy and welfare The particular welfare measure on which we focus is the unconditional expectation of aggregate period utility. For the home economy this is defined as follows U ¼ E Ψ C1−ρ 1−ρ −Δ H1þϕ 1 þ ϕ ( ) ð7Þ where time subscripts are omitted to indicate that this is a measure of unconditional expectation. Damjanovic et al. (2008) argue that unconditionally expected utility provides a useful alternative to Woodford's (2003) ‘timeless perspective’ when analysing optimal policy problems. For the purposes of this paper, unconditional expected utility provides 5 Following Schmitt-Grohe and Uribe (2003), βi is assumed to be taken as exogenous by individual decision makers. The impact of individual consumption on the discount factor is therefore not internalized. Note that this externality in principle creates a distortion in portfolio choice (in the sense that market equilibrium portfolios will differ from the welfare maximising portfolio) - but in practice this distortion is quantitively very small and has no significant implication for the analysis presented below. 6 The assumption that bonds are perpetuities has no particular significance for our results. We have experimented with a version of the model with single-period bonds and, while there are some quantitative implications, there is no systematic qualitative differences compared to the results reported below. 7 In the basic model, where international asset trade is restricted to nominal bonds, all equity is owned within each country, so the relevant discount factor for home and foreign firms is, respectively, the discount factor for home and foreign households. When there is international trade in equities the discount factor for firms will in principle be a weighted average of home and foreign household discount factors, with the weight being determined by relative portfolio holdings of equity. However, as a convenience simplification (which has trivial quantitative implications for equilibrium outcomes), even when there is international trade in equities we impose the assumption that the firm discount factor in each country corresponds to the household discount factor in each country. 198 O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208
O Senay, A Sutherland Joumal of International Economics 117(2019)196-208 a simple and convenient way to compute welfare in a context where or in terms of log-deviations portfolio allocation is endogenous. The next section provides a more de- caned tas of ane complications tnat nse n tne simutaneous -(y-p)-p(GC)+2=0 In common with Corsetti et al. (2010, 2018)we focus on co-opera tive policy in the sense that policy rules for each country are simulta- This is the well-known risk sharing condition that is standard in neously chosen to maximize global welfare, ie the sum of the home open-economy models with complete financial markets. It is thus and foreign welfare measures. Note that, for simplicity. throughout the clear that d in( 8)is a measure of deviations from full risk sharing. remainder of this paper we refer to optimal policy' or the optimal pol- And it is clear that this term in the monetary policy rule captures the ex icy rule. This should be understood to imply optimal cooperative policy. tent to which monetary policy is adjusted in order to achieve greater eral the optimal targeting rule is model dependent. Corsetti et al. The simple targeting rule in 8) is sufficient to capture the key trade- 010, 2018)show that the optimal targeting rule for a model similar off in monetary policy between inflation stabilisation and deviations to ours includes measures of inflation and a number of welfare gaps. from risk sharing. There is just one parameter in this rule, Sp, so the Because of the complicated interaction between policy and portfolio policy optimisation problem is to choose the value of op to maximize choice we do not derive the fully optimal policy rule for our model. welfare(as measured by (7 Instead we use the form of the optimal rule derived by corsetti et al Before proceeding to a discussion of the solution and optimisation (2010, 2018)as an approximation for optimal policy in our model. procedure, it is worth noting that the characterisation of policy as a In fact, we start our analysis with the following very restricted fo targeting rule is(as argued by Woodford (2003))a convenient way to of targeting rule capture the welfare trade-offs faced by policy makers without the need explicitly to model policy in terms of the optimal setting of a policy (P-Py-1)+o(D-D-1)=0 nstrument(such as the nominal interest rate). In cases where a instru- (8) ment rule is of interest it is, in principle, easy to derive such a rule once the optimal targeting rule has been derived. But note that it is often the case(as is true in the present model) that the optimal targeting rule in- where a hat over a vanable represents its log deviation from the non- volves' gap variables'-ie the difference between the actual and the first-best level of a variable. This raises a practical problem for translat- ing the targeting rule into an implementable rule for monetary policy since the optimal instrument rule would then require full knowledge by the policymaker of the exogenous shocks that affect the first-best level of variables In the case of the model described above this would imply that TFP and taste shocks are directly observable by policymakers. (8)is the home-country targeting rule. There is a corresponding We acknowledge that this is a practical problem that makes is difficult targeting rule for the foreign country. Given that the model is symmet ic, the coefficient of the of the foreign monetary rule is assumed to be to translate the results presented below into an implementable policy identical to the coefficient of the home rule, with appropriate changes significant proportion of the monetary policy literature following the The targeting rule in( 8)contains two terms. The first term repre approach of Woodford(2003) so our approach is not especially limited sents producer price(PPl) inflation. The central role of inflation in this respect. A separate point regarding implementation (which is again common known consequence of staggered price setting. In essence, staggered to the majority of the literature on optimal monetary policy)is that op- terms of the rate of inflation and the rate of change in gap variables between goods Inflation is thus(other things equal) welfare reducing. (in our case the distance from perfect risk sharing). There is an implicit It is also well-known that, in the presence of PCP, the weltare-relevant assumption that the optimal policy rule has been in place for many pe- measure of inflation is PPI inflation. This is captured by the first term riods and the objective of policy is to respond to stochastic shocks in(8) The second term in the targeting rule is referred to by Corsetti et al. that is often faced by policymakers is how to set policy in an environ- (2010, 2018)as a measure of 'demand imbalances. It measures devia- ons from full risk sharing. This captures the welfare reducing effects ment where past policy may have been far from optimal. The main of incomplete financial markets. To understand this term note that, if policy issue is theretore one of choosing an optimal path from anon-op- a complete set of financial instruments were available for international trade, equilibrium in financial markets would imply that the ratio of respect a targeting rule(such as(8)which specifies policy in terms of marginal utilities across countries would equal the relative price of con- sharing may be quite misleading as a guide to policy when the initial umption baskets, i.e position of the economy is far from its optimal steady state. In such a sit- uation the policy maker should be concerned about the level deviation YC from the perfect risk sharing-not the rate of divergence (as implied by( 8)). This is an interesting question for further research, but a full analysis of this issue is well beyond the scope of this paper. Recently, Fanelli(2017)has developed proach which allows a 4. Model solution, country portfolios and policy optimisation rgeting rule which is very sin Our objective in this paper is to analyse optimal monetary policy off between a term which measures the output gap and price dispersion and a term which the above specified model. The key distinguishing feature of the above olicy on portfolio allocation and argues that there isa role for capital controls. Fanelli's an- model, that sets it apart from much of the existing literature on optimal tical approach is useful for the analysis of simple models but is unlikely to be easily gen- monetary policy in open economies, is that it allows for international eralised to more complex models of the type analysed in the later sections of this paper trade in multiple assets
a simple and convenient way to compute welfare in a context where portfolio allocation is endogenous. The next section provides a more detailed discussion of the complications that arise in the simultaneous computation of welfare and equilibrium portfolios. In common with Corsetti et al. (2010, 2018) we focus on co-operative policy in the sense that policy rules for each country are simultaneously chosen to maximize global welfare, i.e. the sum of the home and foreign welfare measures. Note that, for simplicity, throughout the remainder of this paper we refer to ‘optimal policy’ or the ‘optimal policy rule’. This should be understood to imply optimal cooperative policy. We model monetary policy in the form of a ‘targeting rule’. In general the optimal targeting rule is model dependent. Corsetti et al. (2010, 2018) show that the optimal targeting rule for a model similar to ours includes measures of inflation and a number of welfare gaps. Because of the complicated interaction between policy and portfolio choice we do not derive the fully optimal policy rule for our model. Instead we use the form of the optimal rule derived by Corsetti et al. (2010, 2018) as an approximation for optimal policy in our model.8 In fact, we start our analysis with the following very restricted form of targeting rule ^ PY;t−^ PY;t−1 þ δDð Þ¼ Dt−Dt−1 0 ð8Þ where a hat over a variable represents its log deviation from the nonstochastic steady state and D is defined as D ¼ −ρ ^ C−^ C þ Q^− Ψ^ −Ψ^ (8) is the home-country targeting rule. There is a corresponding targeting rule for the foreign country. Given that the model is symmetric, the coefficient of the of the foreign monetary rule is assumed to be identical to the coefficient of the home rule, with appropriate changes of sign. The targeting rule in (8) contains two terms. The first term represents producer price (PPI) inflation. The central role of inflation stabilisation in optimal policy in New Keynesian models is a wellknown consequence of staggered price setting. In essence, staggered price setting implies that inflation causes distortions in relative prices between goods. Inflation is thus (other things equal) welfare reducing. It is also well-known that, in the presence of PCP, the welfare-relevant measure of inflation is PPI inflation. This is captured by the first term in (8). The second term in the targeting rule is referred to by Corsetti et al. (2010, 2018) as a measure of ‘demand imbalances’. It measures deviations from full risk sharing. This captures the welfare reducing effects of incomplete financial markets. To understand this term note that, if a complete set of financial instruments were available for international trade, equilibrium in financial markets would imply that the ratio of marginal utilities across countries would equal the relative price of consumption baskets, i.e. Ψ t C−ρ t ΨtC−ρ t ¼ Qt or in terms of log-deviations − Ψ^ −Ψ^ −ρ ^ C−^ C þ Q^ ¼ 0 This is the well-known risk sharing condition that is standard in open-economy models with complete financial markets. It is thus clear that D in (8) is a measure of deviations from full risk sharing. And it is clear that this term in the monetary policy rule captures the extent to which monetary policy is adjusted in order to achieve greater risk sharing. The simple targeting rule in (8) is sufficient to capture the key tradeoff in monetary policy between inflation stabilisation and deviations from risk sharing. There is just one parameter in this rule, δD; so the policy optimisation problem is to choose the value of δD to maximize welfare (as measured by (7)). Before proceeding to a discussion of the solution and optimisation procedure, it is worth noting that the characterisation of policy as a targeting rule is (as argued by Woodford (2003)) a convenient way to capture the welfare trade-offs faced by policy makers without the need explicitly to model policy in terms of the optimal setting of a policy instrument (such as the nominal interest rate). In cases where a instrument rule is of interest it is, in principle, easy to derive such a rule once the optimal targeting rule has been derived. But note that it is often the case (as is true in the present model) that the optimal targeting rule involves ‘gap variables’ - i.e. the difference between the actual and the first-best level of a variable. This raises a practical problem for translating the targeting rule into an implementable rule for monetary policy since the optimal instrument rule would then require full knowledge by the policymaker of the exogenous shocks that affect the first-best level of variables. In the case of the model described above this would imply that TFP and taste shocks are directly observable by policymakers. We acknowledge that this is a practical problem that makes is difficult to translate the results presented below into an implementable policy rule. This is a problem which (except for special cases) also exists in a significant proportion of the monetary policy literature following the approach of Woodford (2003) so our approach is not especially limited in this respect. A separate point regarding implementation (which is again common to the majority of the literature on optimal monetary policy) is that optimal policy is here being characterised as rule which is specified in terms of the rate of inflation and the rate of change in gap variables (in our case the distance from perfect risk sharing). There is an implicit assumption that the optimal policy rule has been in place for many periods and the objective of policy is to respond to stochastic shocks around an optimal (stochastic) steady state. But the policy problem that is often faced by policymakers is how to set policy in an environment where past policy may have been far from optimal. The main policy issue is therefore one of choosing an optimal path from a non-optimal initial point back to the optimal (stochastic) steady state. In this respect a targeting rule (such as (8)) which specifies policy in terms of the rate of inflation and the change in deviations from perfect risk sharing may be quite misleading as a guide to policy when the initial position of the economy is far from its optimal steady state. In such a situation the policy maker should be concerned about the level deviation from the perfect risk sharing - not the rate of divergence (as implied by (8)). This is an interesting question for further research, but a full analysis of this issue is well beyond the scope of this paper. 4. Model solution, country portfolios and policy optimisation Our objective in this paper is to analyse optimal monetary policy in the above specified model. The key distinguishing feature of the above model, that sets it apart from much of the existing literature on optimal monetary policy in open economies, is that it allows for international trade in multiple assets. 8 Recently, Fanelli (2017) has developed an approximation approach which allows a combined analysis of portfolio allocation and optimal monetary policy in a simple theoretical framework which allows monetary policy to be characterised as a fully optimal targeting rule which is very similar to (8). Fanelli shows that optimal policy is a tradeoff between a term which measures the output gap and price dispersion and a term which measures risk sharing. Fanelli uses this framework to investigate the impact of optimal policy on portfolio allocation and argues that there is a role for capital controls. Fanelli's analytical approach is useful for the analysis of simple models but is unlikely to be easily generalised to more complex models of the type analysed in the later sections of this paper. O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208 199
O Senay, A Sutherland /Joumal of International Economic 117(2019)196-208 Combining the analysis of optimal policy and endogenous portfolio Table 1 choice presents some new technical challenges. These challenges arise Benchmark parameter values. because there is an interaction between policy choices and portfolio Discount factor B=0.99,n=0.005 choice. Monetary policy affects the stochastic behaviour of income and Elasticity of substitution: individual goods the hedging properties of assets and therefore affects optimal portfolio Elasticity of labour supply choice. In turn, the equilibrium portfolio affects consumption and labour Risk aversion supply choices and thus affects macroeconomic outcomes and welfare. Share of home goods in consumption basket Elasticity of substitution: home and foreign goods hus, in addition to the standard routes via which policy affects the Share of labour in production ====三 count of the welfare effects of policy that occur via the effects of policy TP shan setting macro economy, the optimal choice of monetary policy must take ad Calvo 095,A=0006 on portfolio allocation As will be demonstrated below, this mechanism turns out to play a key role.g Our solution approach follows the recent portfolio literature based on Devereux and Sutherland (201la)in computing equilibrium portfo. taste shock processes are based on Corsetti et al. (2010, 2018)and lios using a second order approximation to the portfolio selection equa Smets and Wouters(2003, 2005, 2007). tions for the home and foreign country in conjunction with a first order In this section we focus on optimal policy based on the simple policy approximation to the home and foreign budget constraints and the ve rule given in(8). This allows us to illustrate in detail the economic mechanism behind the effects we wish to emphasise. Given the As already explained, we model monetary policy as a simple targeting simplithed policy rule, the only policy parameter that needs to be tor of excess returns. ule(8). We optimise the choice of coefficient in the targeting rule by ferent values of 8p on welfare, portfolio allocation and the variances of value for op in the targeting rule and for each grid point there is an equi- key variables. librium portfolio allocation and a corresponding general macroeconomic Table 2 presents some key results for a range of values of the inter- equilibrium and level of welfare. We use the devereux and Sutherland national trade elasticity, 0. For comparison, this table shows the results 011b) portfolio solution approach to evaluate the equilibrium portfolio for the two-bond case together with the financial autarky and single at each grid point. This equilibrium portfolio is then used to compute real-bond version of the model For each value of e and for each financial macroeconomic equilibrium and evaluate welfare at each grid point. In conducting this analysis it necessary to be mindful of orders of al difference between optimal policy and strict inflation targeting, the derstood in the literature, this requires that the overall model must also icy and inflation targeting and for the two-bond case)equilibrium principles outlined in Samuelson(1970), an order n approximation of utility(in our case welfare)depends only on the order n-2 behaviour sumption Standard deviations are reported in percentage terms And of portfolios. Thus, in computing a second order approximation of wel- portfolio holdings are measured relative to steady state GDP. Given that, in this simple model, there are just two assets that can be traded fare, we only require the zero-order(or steady state)equilibrium porto- internationally, it is possible to represent portfolio positions in terms lio. Hence the technique outlined in Devereux and Sutherland(2011a) of a single number. In this case we focus on the home country's portfolio for computing the zero-order portfolio is sufficient for our purposes. position in the foreign nominal bond. As in Devereux and Sutherland 5. Optimal monetary policy in the basic model (2011a), we compute the zero-order(i.e. steady state) portfolio hold ing In the steady state it is assumed that net foreign assets are zero, so a positive holding of foreign bonds must be matched by an equivalent The benchmark parameter values used in the following analysis are negative(external )holding of home bonds. I isted in Table 1. Many of these parameter values are taken directly from First consider the autarky and single-bond cases. These two cases Corsetti et al (2010, 2018). The values ofA(the elasticity of substitution correspond to the financial market structures considered by Corsetti between individual final goods)and u( the Cobb-Douglas coefficient on et al. 2010, 2018). For both these cases, and for all the values of e labour in the production function of intermediate goods)are chosen to shown, the optimal value of p( derived numerically using the search yield a steady state monopoly mark-up of 11% and share of capital in procedure outlined above)differs from zero. This indicates a deviation output of.33. The implied steady state share of dividends in GDP is ap- from strict inflation targeting(which corresponds to 6p=O). But notice proximately 0. 15. The Calvo parameter for price setting, K, is Chosen to that the difference between the welfare level yielded by optimal policy imply an average period between price changes of 4 quarters. The and the welfare level yielded by strict inflation targetingis very small for values of (inverse labour elasticity) and p (risk aversion )are consi all values of e, except for 0=1/2. The variance of the real exchang tent with the estimates of Smets and Wouters(2003, 2005, 2007). The gap and the variance of PPl inflation are also only marginally different parameters of the endogenous discount factor, B and n, are chosen to between the optimal policy and strict inflation targeting equilibria for yield a steady state rate of return of approximately 4%. The TFP and all values of 0, except for 0=1/2 These results broadly match the results emphasised by Corsetti et al policy choices are made in advance of(2010, 2018)who find that the differences between the optimal rule mane ta y sei ry rule fn ano tme pes eh. senay and su herland s oea. w a sh emphasise and inflation targeting are likely to be very small except for low values how monetary policy can interact with portfolio choice. But in that earlier paper we ana lyse non-cooperative policy in a world where financial markets are complete. The inter tion that occurs there is an explicitly distortionary effect that is quite different to the n Note that, for all values of e, gross portfolio positions are very large ote, t der realisation of asset retum differentials. These terms. however, drop the expectations operator is applied and therefore do not enter the exp nd taxation ancial regulation issues which go wusts.informa- nd-order approximation of expected utility. See Devereux and Sutherland(2010b)for a scope of the analysis in this paper. Note that throughout our analysis (again for the pur- more detailed discussion of orders of approximation in the analysis of portfoli poses of simplification) we also abstract from short selling constraints
Combining the analysis of optimal policy and endogenous portfolio choice presents some new technical challenges. These challenges arise because there is an interaction between policy choices and portfolio choice. Monetary policy affects the stochastic behaviour of income and the hedging properties of assets and therefore affects optimal portfolio choice. In turn, the equilibrium portfolio affects consumption and labour supply choices and thus affects macroeconomic outcomes and welfare. Thus, in addition to the standard routes via which policy affects the macro economy, the optimal choice of monetary policy must take account of the welfare effects of policy that occur via the effects of policy on portfolio allocation. As will be demonstrated below, this mechanism turns out to play a key role.9 Our solution approach follows the recent portfolio literature based on Devereux and Sutherland (2011a) in computing equilibrium portfolios using a second order approximation to the portfolio selection equations for the home and foreign country in conjunction with a first order approximation to the home and foreign budget constraints and the vector of excess returns. As already explained, we model monetary policy as a simple targeting rule (8). We optimise the choice of coefficient in the targeting rule by means of a grid search algorithm. Each grid point represents a different value for δD in the targeting rule and for each grid point there is an equilibrium portfolio allocation and a corresponding general macroeconomic equilibrium and level of welfare. We use the Devereux and Sutherland (2011b) portfolio solution approach to evaluate the equilibrium portfolio at each grid point. This equilibrium portfolio is then used to compute macroeconomic equilibrium and evaluate welfare at each grid point. In conducting this analysis it necessary to be mindful of orders of approximation. We approximate welfare up to second order. As is well-understood in the literature, this requires that the overall model must also be solved up to second-order accuracy. But note that, according to the principles outlined in Samuelson (1970), an order n approximation of utility (in our case welfare) depends only on the order n − 2 behaviour of portfolios. Thus, in computing a second order approximation of welfare, we only require the zero-order (or steady state) equilibrium portfolio. Hence the technique outlined in Devereux and Sutherland (2011a) for computing the zero-order portfolio is sufficient for our purposes.10 5. Optimal monetary policy in the basic model The benchmark parameter values used in the following analysis are listed in Table 1. Many of these parameter values are taken directly from Corsetti et al. (2010, 2018). The values of λ (the elasticity of substitution between individual final goods) and μ (the Cobb-Douglas coefficient on labour in the production function of intermediate goods) are chosen to yield a steady state monopoly mark-up of 11% and share of capital in output of 0.33. The implied steady state share of dividends in GDP is approximately 0.15. The Calvo parameter for price setting, κ, is chosen to imply an average period between price changes of 4 quarters. The values of ϕ (inverse labour elasticity) and ρ (risk aversion) are consistent with the estimates of Smets and Wouters (2003, 2005, 2007). The parameters of the endogenous discount factor, β and η, are chosen to yield a steady state rate of return of approximately 4%. The TFP and taste shock processes are based on Corsetti et al. (2010, 2018) and Smets and Wouters (2003, 2005, 2007). In this section we focus on optimal policy based on the simple policy rule given in (8). This allows us to illustrate in detail the economic mechanism behind the effects we wish to emphasise. Given the simplified policy rule, the only policy parameter that needs to be determined is δD: It is therefore simple to investigate the effects of different values of δD on welfare, portfolio allocation and the variances of key variables. Table 2 presents some key results for a range of values of the international trade elasticity, θ. For comparison, this table shows the results for the two-bond case together with the financial autarky and singlereal-bond version of the model. For each value of θ and for each financial market structure the table shows the optimal value of δD; the welfare difference between optimal policy and strict inflation targeting, the standard deviations of a number of variables in the case of optimal policy and inflation targeting and (for the two-bond case) equilibrium portfolios for the case of optimal policy and inflation targeting. Welfare is measured in terms of the equivalent percentage of steady state consumption. Standard deviations are reported in percentage terms. And portfolio holdings are measured relative to steady state GDP. Given that, in this simple model, there are just two assets that can be traded internationally, it is possible to represent portfolio positions in terms of a single number. In this case we focus on the home country's portfolio position in the foreign nominal bond. As in Devereux and Sutherland (2011a), we compute the zero-order (i.e. steady state) portfolio holding. In the steady state it is assumed that net foreign assets are zero, so a positive holding of foreign bonds must be matched by an equivalent negative (external) holding of home bonds.11 First consider the autarky and single-bond cases. These two cases correspond to the financial market structures considered by Corsetti et al. (2010, 2018). For both these cases, and for all the values of θ shown, the optimal value of δD (derived numerically using the search procedure outlined above) differs from zero. This indicates a deviation from strict inflation targeting (which corresponds to δD ¼ 0). But notice that the difference between the welfare level yielded by optimal policy and the welfare level yielded by strict inflation targeting is very small for all values of θ, except for θ = 1/2. The variance of the real exchange rate gap and the variance of PPI inflation are also only marginally different between the optimal policy and strict inflation targeting equilibria for all values of θ, except for θ = 1/2. These results broadly match the results emphasised by Corsetti et al. (2010, 2018) who find that the differences between the optimal rule and inflation targeting are likely to be very small except for low values of θ. The results in Table 2 go somewhat further than Corsetti et al. Table 1 Benchmark parameter values. Discount factor β ¼ 0:99; η = 0.005 Elasticity of substitution: individual goods λ = 6 Elasticity of labour supply 1/ϕ = 0.5 Risk aversion ρ = 2 Share of home goods in consumption basket γ = 0.875 Elasticity of substitution: home and foreign goods θ = 0.25 - 6.00 Share of labour in production μ = 0.67 Calvo price setting κ = 0.75 TFP shocks ηA = 0.95, σA = 0.006 Taste shocks ηΨ = 0.9, σΨ = 0.01 9 In this paper we are making an assumption that policy choices are made in advance of trade in asset markets. This implies that equilibrium portfolios depend on the choice of monetary policy rule. In another paper, Senay and Sutherland (2013), we also emphasise how monetary policy can interact with portfolio choice. But in that earlier paper we analyse non-cooperative policy in a world where financial markets are complete. The interaction that occurs there is an explicitly distortionary effect that is quite different to the mechanism being analysed in this paper. 10 Note, the fact that welfare is based on expected utility is crucial in allowing us to focus on the zero-order portfolio. A second-order approximation of realised utility may include terms that depend on the first-order behaviour of portfolio holdings multiplied by the first-order realisation of asset return differentials. These terms, however, drop out when the expectations operator is applied and therefore do not enter the expression for the second-order approximation of expected utility. See Devereux and Sutherland (2010b) for a more detailed discussion of orders of approximation in the analysis of portfolios. 11 Note that, for all values of θ, gross portfolio positions are very large relative to steady state GDP. Portfolio positions of this magnitude are obviously very unrealistic. It is only for very few countries (usually tax havens) where external portfolio positions exceed 4 or 5 times GDP. It is not the purpose of this analysis to match the data on international portfolio positions. Such an exercise is likely to require consideration of transaction costs, informational asymmetries, and taxation and financial regulation issues which go well beyond the scope of the analysis in this paper. Note that throughout our analysis (again for the purposes of simplification) we also abstract from short selling constraints. 200 O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208