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 ressignificant internal and external trade-offs that prevent optimal cooper￾ative policy from simultaneously closing all welfare relevant gaps.3 The basic intuition for the Corsetti et al. (2010, 2018) results is sim￾ple to explain. A policy of producer price inflation targeting reproduces the flexible price outcome and therefore eliminates the welfare costs as￾sociated with staggered price setting. But the flexible price equilibrium is not fully optimal because international financial markets are imper￾fect and thus cross-country income risks are not optimally shared. A corollary of this is that the real exchange rate and trade balance will de￾viate 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 poten￾tially important deviation from the standard policy prescription of infla￾tion 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 rep￾resented 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 mone￾tary 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. De￾spite 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 quantita￾tive 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 de￾viations 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 mech￾anism which does not exist in the single-bond case. 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 further sources of shocks, we allow for trade in equities as well as nom￾inal 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 tech￾niques 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 in￾novation 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 pol￾icy 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 ver￾sion 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 for￾eign 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 two￾country world. Benigno (2009) analyses an asymmetric world with incomplete financial markets and shows how optimal monetary policy differs between net-debtor and net￾creditor 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 pol￾icy can be analysed alongside endogenous portfolio choice. They show that, in a special re￾stricted 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