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 0i. 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
O Senay, A Sutherland Joumal of International Economics 117(2019)196-208 Table 2 Results for the benchmark Trade elasticity, e 0.75 Optimal Policy rule 3.066 00020 portfolio(bond holdings) 16.2 PPI Inflation (inf tar St Dev rer gap 0430 0.33 (inf tar) Autarky 0085 0003 difference 00000 Pl Inflation 0.124 0.394 Welfare difference 00008 00000 St Dev ppl inflation St Dev rEr gap (optimal) 1267 f steady-state consumption Standard deviations are measured in percentages Portfolio holdings are measured relative to steady state cup o red in terms of the equivalent percent& Note: For each e and financial structure the table shows the optimal value of &p, the welfare difference between optimal policy and inflation targeting. standard deviations for optim policy and inflation targeting and ( for the two-bond case)equilibrium portfolios for optimal policy and inflation targeting. Welfare is measur (2010, 2018) by showing that non-trivial differences between optimal Now consider the two-bond case. The results in table 2 show that policy and inflation targeting are not strictly associated with low values again there is a deviation between optimal policy and strict inflation of 0. It is more correct to say that they arise at values of e close to 1/2. The targeting. But now the pattern of results is quite different to that found significance of 6= 1/2 is easily explained. Given the values of other pa- in the autarky and single-bond cases. In the two-bond case the welfare tution effects of the terms of trade on the trade balance almost cancel trivial for all values of 0. There are also relatively large differences be- ach other out. It follows therefore that at 6= 1/2 the trade balance is tween optimal policy and inflation targeting in terms of the variances very insensitive to the terms of trade. In this case, the absence of finan- of the real exchange rate and the output gap. In particular, optimal policy cial trade ( or the highly restricted nature of financial trade)has signifi- implies very significant stabilisation of the real exchange rate gap com- cant implications for welfare because the terms of trade and real pared to strict inflation targeting regardless of the value of 0. exchange rate become very sensitive to shocks(as can be seen in It is clear, therefore, that there is a significant qualitative and quanti- Table 2). 1 There is therefore a strong incentive for the policymaker to tative difference between the two bond case and the other financial mar- deviate from inflation targeting. At other values of e(either above or ket structures shown in Table 2. This is somewhat surprising. In terms of below 1/2) the trade balance is more sensitive to changes in the terms the degree of market incompleteness it would be natural to assume that of trade so the terms of trade and real exchange rate are less volatile the two-bond case is closer to complete markets than the autarky and nd the absence of financial trade(or the limited nature of financial single-bond cases. One would therefore naturally predict that the optimal trade) is less significant for welfare. In this case the incentive to deviate policy rule in the two bond case would be closer to the optimal policy from inflation targeting is much reduced rule in the complete market case(ie strict inflation targeting)than it is The general message from Table 2 is that our basic model reproduces in the autarky and single-bond cases. However, the results in Table 2 con- the results of Corsetti et al. (2010, 2018)for the autarky and single-bond tradict this intuition. It appears from the results in Table 2 that trade in cases, ieoptimal policy does deviate from inflation targeting, but this two bonds pushes optimal policy further away from strict inflation appears to be quantitatively important only for a restricted range of targeting(at least for values of e different from 1/2)than in the autark values of e(ie. close to 1/2). 3 and single-bond case. What is causing this counter-intuitive result? The key to understanding the answer to this question is to consider 12 When the trade balance is relatively insensitive to changes in the terms of trade an in detail the role of portfolio allocation. In the autarky and single-bond 14 Notice in Table 2 that. for th case, the divergence between optimal policy and work effort. So, in the vicinity of e fort are highly ve and inflation targeting centive for the policymaker to stal se the terms of trade and 0.5. This contrasts with th cases where the divergence is real exchange rate. This effect is less acute, but still present, when there is trade in a single largest at 0=0.5. This contras to the fact that the income and substitution bond. See Bodenstein(2010)and Rabitsch(2012)for further discussion of how a number effects of terms of trade changes almost perfectly cancel in the vicinity of ep= 1. This in reversed at particularly low values generated by TFP shocks. Another way to view this is that(as shown by Cole and Obstfeld 3 Note that the standard deviations of the real exchange rate gap and the output gap (1991)). in the vicinity of ep= 1, movements in the terms of trade provie ninian d other variables)are all quite sensitive to the degree of persistence ofTFP and taste degree of hedging against TFP shocks. This allows portfolio allocation hocks. However, the persistence of shocks has no significant implications for the optimal to be more focused on hedging of taste shocks. with the combination of the tems of trade olicy rule or the difference between optimal policy and inflation targeting equilibria for movements and bond portfolios providing significant risk sharing in the vicinity of p=1 either the autarky or single-bond cases. there is less need for optimal monetary policy to deviate from inflation stabilisation
(2010, 2018) by showing that non-trivial differences between optimal policy and inflation targeting are not strictly associated with low values of θ. It is more correct to say that they arise at values of θ close to 1/2. The significance of θ = 1/2 is easily explained. Given the values of other parameters (in particular the value of ρ) at θ = 1/2 the income and substitution effects of the terms of trade on the trade balance almost cancel each other out. It follows therefore that at θ = 1/2 the trade balance is very insensitive to the terms of trade. In this case, the absence of financial trade (or the highly restricted nature of financial trade) has signifi- cant implications for welfare because the terms of trade and real exchange rate become very sensitive to shocks (as can be seen in Table 2).12 There is therefore a strong incentive for the policymaker to deviate from inflation targeting. At other values of θ (either above or below 1/2) the trade balance is more sensitive to changes in the terms of trade so the terms of trade and real exchange rate are less volatile and the absence of financial trade (or the limited nature of financial trade) is less significant for welfare. In this case the incentive to deviate from inflation targeting is much reduced. The general message from Table 2 is that our basic model reproduces the results of Corsetti et al. (2010, 2018) for the autarky and single-bond cases, i.e. optimal policy does deviate from inflation targeting, but this appears to be quantitatively important only for a restricted range of values of θ (i.e. close to 1/2).13 Now consider the two-bond case. The results in Table 2 show that again there is a deviation between optimal policy and strict inflation targeting. But now the pattern of results is quite different to that found in the autarky and single-bond cases. In the two-bond case the welfare difference between optimal policy and inflation targeting is now nontrivial for all values of θ. There are also relatively large differences between optimal policy and inflation targeting in terms of the variances of the real exchange rate and the output gap. In particular, optimal policy implies very significant stabilisation of the real exchange rate gap compared to strict inflation targeting, regardless of the value of θ. 14 It is clear, therefore, that there is a significant qualitative and quantitative difference between the two-bond case and the other financial market structures shown in Table 2. This is somewhat surprising. In terms of the degree of market incompleteness it would be natural to assume that the two-bond case is closer to complete markets than the autarky and single-bond cases. One would therefore naturally predict that the optimal policy rule in the two-bond case would be closer to the optimal policy rule in the complete market case (i.e. strict inflation targeting) than it is in the autarky and single-bond cases. However, the results in Table 2 contradict this intuition. It appears from the results in Table 2 that trade in two bonds pushes optimal policy further away from strict inflation targeting (at least for values of θ different from 1/2) than in the autarky and single-bond case. What is causing this counter-intuitive result? The key to understanding the answer to this question is to consider in detail the role of portfolio allocation. In the autarky and single-bond Table 2 Results for the benchmark case. Trade elasticity, θ 0.25 0.5 0.75 1.5 3 Two Bonds Optimal Policy rule δD 3.066 5.663 −6.281 −1.686 −0.94 Welfare difference 0.0023 0.0020 0.0029 0.0036 0.0041 Portfolio (bond holdings) (optimal) −10.7 −4.4 5.8 30.7 79.5 (inf tar) −16.2 −8.4 −0.6 22.8 69.6 St Dev PPI Inflation (optimal) 0.017 0.044 0.029 0.010 0.008 St Dev Output gap (optimal) 0.011 0.072 0.045 0.049 0.042 (inf tar) 0.014 0.080 0.119 0.184 0.237 St Dev RER gap (optimal) 1.29 0.90 0.61 0.27 0.10 (inf tar) 2.99 2.20 1.76 1.13 0.67 St Dev D (optimal) 0.88 0.69 0.55 0.33 0.19 (inf tar) 2.04 1.74 1.59 1.39 1.27 Autarky Policy rule δD 0.017 −0.085 −0.010 −0.003 0.00 Welfare difference 0.0003 0.0291 0.0000 0.0000 0.0000 St Dev PPI Inflation (optimal) 0.026 0.217 0.007 0.002 0.000 St Dev RER gap (optimal) 8.45 16.91 1.88 1.58 1.18 (inf tar) 8.52 18.91 1.90 1.58 1.18 Single Bond Policy rule δD 0.124 −0.394 −0.018 0.027 0.037 Welfare difference 0.0008 0.0430 0.0000 0.0000 0.0000 St Dev PPI Inflation (optimal) 0.043 0.287 0.001 0.003 0.005 St Dev RER gap (optimal) 12.67 22.18 1.84 1.57 1.13 (inf tar) 12.86 24.65 1.84 1.57 1.13 Note: For each θ and financial structure the table shows the optimal value of δD, the welfare difference between optimal policy and inflation targeting, standard deviations for optimal policy and inflation targeting and (for the two-bond case) equilibrium portfolios for optimal policy and inflation targeting. Welfare is measured in terms of the equivalent percentage of steady-state consumption. Standard deviations are measured in percentages. Portfolio holdings are measured relative to steady state GDP. 12 When the trade balance is relatively insensitive to changes in the terms of trade and there is no financial market (i.e. there is financial autarky), any shock which causes a change in the trade balance must cause a large change in the terms of trade in order to bring the trade balance back to zero. In turn, this causes large fluctuations in consumption and work effort. So, in the vicinity of θ = 1/2, consumption and work effort are highly volatile. This creates a strong incentive for the policymaker to stabilise the terms of trade and real exchange rate. This effect is less acute, but still present, when there is trade in a single bond. See Bodenstein (2010) and Rabitsch (2012) for further discussion of how a number of key welfare and equilibrium results can be reversed at particularly low values of the trade elasticity in models similar to the one analysed here. 13 Note that the standard deviations of the real exchange rate gap and the output gap (and other variables) are all quite sensitive to the degree of persistence of TFP and taste shocks. However, the persistence of shocks has no significant implications for the optimal policy rule or the difference between optimal policy and inflation targeting equilibria for either the autarky or single-bond cases. 14 Notice in Table 2 that, for the two-bond case, the divergence between optimal policy and inflation targeting is at its smallest at θ = 0.5 and rises for values of θ away from 0.5. This contrasts with the autarky and single-bond cases where the divergence is at it largest at θ = 0.5. This contrast is again due to the fact that the income and substitution effects of terms of trade changes almost perfectly cancel in the vicinity of θρ = 1. This in turn implies that the trade balance is relatively insensitive to changes in the terms of trade generated by TFP shocks. Another way to view this is that (as shown by Cole and Obstfeld (1991)), in the vicinity of θρ = 1, movements in the terms of trade provide a significant degree of hedging against TFP shocks. This allows portfolio allocation across the two bonds to be more focused on hedging of taste shocks. With the combination of the terms of trade movements and bond portfolios providing significant risk sharing in the vicinity of θρ = 1, there is less need for optimal monetary policy to deviate from inflation stabilisation. O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208 201
ions is a measure of the conflict be- cks. So, if the shadow portfolio al- cy is a figu
cases there is, by definition, no portfolio decision for agents to make. In the autarky case there are no traded assets so there is no portfolio. In the single-bond case there is only one traded asset so portfolio composition is fixed. But in the two-bond case there are two traded assets so there is a portfolio allocation decision. The existence of the portfolio allocation decision gives the policymaker a qualitatively different channel by which to influence the equilibrium degree of risk sharing and this new channel has a qualitatively and quantitatively important effect on the optimal policy rule. In the two-bond case the policymaker can implicitly use monetary policy to alter the risk sharing properties of the two bonds, and can therefore influence the equilibrium portfolio, in such a way that the equilibrium portfolio provides a significantly higher degree of risk sharing compared to an inflation targeting equilibrium. This can be a powerful incentive for the policymaker to deviate from strict inflation targeting. This portfolio allocation incentive, by definition, does not exist in the autarky or single-bond cases and this explains the significant differences between the two-bond case and the autarky and single-bond cases. This process is illustrated in more detail in Fig. 1. This figure is based on the benchmark parameter set given in Table 1 with the international trade elasticity, θ, set equal to 1.5. It therefore corresponds to one of the cases reported in Table 2. So it can be noted from Table 2 that the optimal value of δD is approximately −1.686. Panel (a) in Fig. 1 plots welfare against δD and shows that welfare at the optimal value of δD is approximately 0.0036% above welfare at strict inflation targeting (δD ¼ 0 ) (which again corresponds to the number reported in Table 2).15 Panel (b) shows the standard deviation of PPI inflation at the optimal value of δD is approximately 0.01% while Panel (c) shows that the standard deviation of Dis reduced by optimal policy by a factor of 4 when compared to strict inflation targeting (i.e. from 1.39% to 0.33%). Panel (c) also shows that optimal policy implies a very significant reduction in the volatility of the real exchange rate gap compared to strict inflation targeting (i.e. from 1.13% for strict inflation targeting to 0.27% for optimal policy). The main mechanism behind these effects is illustrated in relation to portfolio allocations and asset returns in Panels (d) and (e) of Fig. 1. Panel (d) shows how equilibrium portfolio allocation depends on the choice of the parameter δD: Panel (d) shows that this portfolio position rises from approximately 23 times steady state GDP at δD ¼ 0 (strict in- flation targeting) to approximately 31 times steady state GDP at δD ¼ − 1:686 (optimal policy), so monetary policy has a significant impact on portfolio holdings. This is clearly an important part of the mechanism which allows optimal policy to reduce deviations from perfect risk sharing. But the role played by portfolio allocation can be understood more clearly if one considers the nature of imperfect risk sharing in this simple model. There are two independent sources of risk faced by households - TFP shocks and taste shocks. But there is only one degree of freedom in portfolio choices to allow hedging against these two sources of risk. The equilibrium portfolio is therefore a compromise between hedging the two different sources of risk. The degree of compromise can be illustrated by comparing two alternative ‘shadow worlds’ - one where there are only TFP shocks and one where there are only taste shocks. In each of these worlds there is a ‘shadow portfolio allocation’ which maximises welfare.16 The divergence between these two alternative shadow portfolio allocations is a measure of the conflict between hedging the two sources of shocks. So, if the shadow portfolio allocations are very different, one can say that there is a significant ‘hedging conflict’ in the choice of a portfolio designed to hedge both shocks simultaneously, i.e. the compromise portfolio is likely to offer limited hedging against one or other (or both) shocks. While, if the shadow portfolios are very similar, one can say that the ‘hedging con- flict’ is less severe - i.e. a compromise portfolio is likely to be a good hedge against both shocks. Panel (d) illustrates how these two shadow portfolio allocations depend on the policy parameter δD:In particular, these plots show that the degree of divergence between the two shadow portfolio allocations, and thus the degree of conflict between hedging the two sources of shocks, depends on δD: Panel (d) shows how the policy maker can ease the con- flict between hedging TFP shocks and hedging taste shocks by making an appropriate choice of the policy parameter δD: It is apparent from Panel (d) that the optimal choice of δD (δD ¼ −1:686) significantly reduces the divergence between the shadow portfolio allocations and thus allows the equilibrium portfolio allocation to become simultaneously a good hedge against both sources of risk. It is this that allows optimal policy to generate a significant reduction in deviations for perfect risk sharing.17 Note, of course, that any deviation of policy from strict inflation targeting generates inflation volatility, which (given sticky nominal prices) has a negative effect on welfare, so optimal policy is a compromise between inflation volatility and deviations from risk sharing. Panel (d) illustrates the impact of policy on portfolio and shadow portfolio allocations. But further insight into the effects of policy on portfolio allocations can be found in Panel (e). This panel shows the impact effect of each shock on the return differential between the two bonds. The size and sign of these effects are key determinants of the equilibrium and shadow portfolio allocations. Panel (e) shows that the policy parameter has a significant influence on the impact effects of shocks on the return differential so it is evident that this link is an important part of the mechanism that allows monetary policy to affect portfolio allocations.18 Fig. 1 shows clearly how portfolio allocation plays an important role in the policy transmission mechanism. In particular, these results show that policy has a potentially important role in easing the hedging con- flict that arises when there are more sources of risk than degrees of freedom in portfolio allocation. However, it should be clear from this explanation, that this mechanism can only be important if a hedging conflict exists in the first place. The example illustrated in our simple benchmark model is one where TFP shocks and taste shocks create a significant hedging conflict. We will show below that these two sources of shocks continue to create a hedging conflict in a more general model. But we also show that other combinations of shocks may not give rise to such a significant hedging conflict. In these cases, the optimal policy rule is much closer to strict inflation targeting - so it will become clear 15 Where welfare is measured as a percentage of steady state equivalent consumption. In Figure 1 Panel (a) this is normalised to be zero at inflation targeting. 16 Note that, for any single shock or combination of shocks, the welfare maximising portfolio is not necessarily equal to the market equilibrium portfolio (as yielded by the Devereux and Sutherland (2011a) approach). This is because the endogenous discount factor defined in (2) implies an externality in portfolio selection. Individual households treat aggregate consumption as exogenous when selecting their portfolio position while a welfare maximising policymaker would internalise this effect. The shadow portfolios shown in the figure are based on maximising welfare and therefore differ from the portfolios that would be selected by households in the presence of each shock. The welfare maximising shadow portfolios are relevant here because, in this exercise, we are illustrating the incentives faced by the policymaker in choosing the policy rule. The shadow portfolios are computed using a search algorithm that maximises welfare (as measured by (7)) in the presence of each individual source of shock and for each value of the policy parameter, δD. 17 Note that the externality contained within the endogenous discount factors (which generates a difference between the equilibrium portfolio allocation and the welfare maximising portfolio allocation) implies that it is not possible for policy to achieve perfect risk sharing by choice of δD: Note also that this same externality also implies that the market equilibrium portfolio will not yield full risk sharing even in a case where there are suf- ficient assets to span the space of shocks. In principle in the two-bond model this implies that there would be a policy trade-off between inflation stabilisation and risk sharing even if there is only one source of shocks (and thus no hedging conflict). Numerical experiments with the basic model show that this effect is quantitively extremely small and therefore has no significant quantitive implications for the main focus of analysis in this paper. 18 The hedging properties of a portfolio position depend on how the return differential (i.e. the difference between the return on the home bond and the foreign bond) responds on impact to the two shocks. Note, however, that there are a number of interacting factors which determine the equilibrium and shadow portfolios, so it is not possible to draw a simple link between the effects of the policy parameter on return differentials in Panel (e) and the shadow portfolio allocations shown in Panel (d). 202 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) Welfare(% of steady state consumption (b)Standard deviation of PPl inflation (% 0.03 0.02 0.01 c)Standard deviations of D and the real exchange rate gap(%) 15 2.5 =0.5 (d)shadow oldings(relative Both shocks 30 20 TFP shocks 0.5 (e)Impact effect of shocks on the rate of return diffential (%) TFP shocks -2.5 5 The policy parameter, 8, is plotted on the horizontal axis in each panel Fig. 1. Portfolio Allocation and the Monetary Policy Rule. that the particular combination of shocks chosen in our benchmark shocks, news shocks, government spending shocks and price nodel is a critical factor in the results illustrated in Table 2 and Fig. 1. mark-up shocks We add more assets and consider a more general policy 6. A more general model pricing. Note that as in the basic model, the number of assets in the extended model is insufficient to provide hedging against In this section we generalise the basic model in a number of di- the full range of shocks, so financial markets continue to be rections. We add four additional sources of risk: labour supply incomplete
that the particular combination of shocks chosen in our benchmark model is a critical factor in the results illustrated in Table 2 and Fig. 1. 6. A more general model In this section we generalise the basic model in a number of directions. We add four additional sources of risk: labour supply shocks, news shocks, government spending shocks and price mark-up shocks. We add more assets and consider a more general policy rule. We also consider the effects of local currency pricing. Note that as in the basic model, the number of assets in the extended model is insufficient to provide hedging against the full range of shocks, so financial markets continue to be incomplete. Fig. 1. Portfolio Allocation and the Monetary Policy Rule. O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208 203
O Senay, A Sutherland /Joumal of International Economic 117(2019)196-208 The household utility function is modified as follows ble 3 Parameter values in the extended model. 4=△2 Share of government spending in output Share of profit taxes in total taxes TFP and news shocks =0.9.5=0.025 h=0.0.=0.0015 We assume△=△exp(△t) where Ar=n△△-1+E△r,0≤7T, and Ev, r and eu, r are zero mean normally distributed i.i.d. +6(Tcx-7c-1)+6(x-t-1)=0 hocks with varE = o and varel= o. This structure oncept of news shocks as in Beaudry and Portier(2006). We add a government sector where total government expenditur Dand Pyt-PYr-1 again capture PPlinflation and deviations from assumed to be exogenous and subject to stochastic shocks In partic t risk sharing. The additional terms are based on YG, Tc and A we assume that Gr=G exp(Gr) is government spending where are defined as follows Gr=nd Gr-1+EGr, 0<nG<I and EG, t is a zero-mean normally distrib- ted i d shock with VarEc= o. All government spending is assumed YG=f-p/b to be financed via lump sum taxes on households, TD, and firms, Tc. The G=7-÷b government budget constraint is PG, Gr= PTD, t PTc, r where it is ssumed that P TD=(1-p)PG, rG and PrTc=pPG, iG where p is a xed parameter which determines the share of profit taxes in the over where the superscript fb indicates the first best value of a variable all tax take Pc, t is the price index of government purchased goods. It is and T is the terms of trade. Thus Yc is a measure of the output gap, TG assumed that government spending is on domestically produced goods is a measure of the terms of trade gap and is a measure of the devia o P.=PH Hr the household budget constraint is modified to tion from the law of one price. There is an analogous targeting rule for include tp the foreign economy Monopoly power in the final goods sector impl The targeting rule in(10) now contains six terms. The first two prices are subject to a mark-up given by ur=A/(r-1). In the bench- terms represent a weighted average of producer price(PPl)and con- mark model the mark-up is assumed to be fixed In the extended model sumer e( Cpi)inflation. This captures the result shown by Corsetti the mark-up is assumed to be subject to stochastic shocks such that t et al. (2010, 2018)that, for general parameter combinations, in the T exp(i,)where i=nit-1+Eur, 0 sn. <1 and E, r is a zero-mean case of LCP the welfare-relevant measure of inflation is effectively a normally distributed i.i.d. shock with VarE J =C2 weighted average of PPI and CPi inflation. In the extended analysis of the model we allow for local currency The fourth term in(10)measures the welfare-relevant output gap home currency and PH, Et(z)in foreign currency to maximize(6) models is well-known and needs no further explanatlon w Keynesian ricing(LCP). In the LCP case final good firm z chooses pH. H. (z)in The role of the output gap in optimal targeting rules in where pH. E rz) is replaced by pi.E t(z)St+- The fifth term in the targeting rule measures the welfare-relevant The extended model allows for trade in equities. Home equities rep- terms-of-trade gap. As Corsetti et al. (2010, 2018)explain in detail, in resent a claim on aggregate profits of all firms in the home final and in- anopeneconomy, because there are different baskets of goods produced termediate sectors. The real payoff to a unit of the home equity in different countries, shocks may have distortionary effects on the rela- purchased in period t is defined to be [,+1+ZE. t+1. where ZE. t+1 is tive price of these different baskets. These distortions are welfare reduc the real price of home equity and nlt +1 is real aggregate profits. Thus ingin the same way as the within-country price distortions generated by the gross real rate of return on the home equity is TE. +1=(n+1+ inflation are welfare reducing. The terms of trade gap therefore plays the ZE, t+1)/ZE, t. Foreign equities are similarly defined. Total dividends ag- same role in the monetary policy rule as the CPI and PPl inflation terms gregated across al intermediate and final goods firms are given by fects of deviations from the law of one price. Such deviations are a direct consequence of (and only arise from)local currency pricing In a similar It=pYrplr-ic way to the price distortions caused by staggered pricing, deviations from the law of one price are a form of price distortion which potentially requires a monetary policy response. The benchmark parameter values assumed for the additional param- Note that policy rule(10)contains strict CPI and PPI inflation eters in the extended model are shown in Table 3. Again these param targeting as special cases. Strict CPI inflation targeting is given by 5m ter values are based on Corsetti et al.(2010, 2018)and Smets and or =6,=6p=%=0 and strict PPI inflation targeting is given by =1,y=6x=6p=6=0. Given the generalised rule, there are now five policy coefficients to In the absence of shocks to V this structure yields TFP shocks of exactly the same form be chosen by the policymaker. Our policy optimisation problem now in inthe simple model so u captures contemporaneous innovations in T P. News shocks volves a grid search across these five coefficients, ie. 6m,0y., 6, p and 6. a positive realisation of e,, t raises the expected future time path of TEP for t+1 on- in order to identify the parameter combination which maximises the ards(ie Ev, t contains news about future TFP) but has no impact on TFP in period t. unconditional expectation of period welfare(as defined in (7))
The household utility function is modified as follows Ut ¼ Et X∞ i¼0 βi Ψtþi C1−ρ tþi ð Þz 1−ρ −Δtþi H1þϕ tþi ð Þz 1 þ ϕ ( ) ð9Þ where Δt are stochastic preference shocks which affect labour supply. We assume Δt ¼ Δ expðΔ^tÞ where Δ^t ¼ ηΔΔ^t−1 þ εΔ;t; 0 ≤ ηΔ b 1 and εΔ, t is a zero-mean normally distributed i.i.d. shock with Var[εΔ] = σΔ 2 . Total factor productivity, At, is now defined as follows: At ¼ Ut−Vt where Ut ¼ ηuUt−1 þ εu;t þ εν;t Vt ¼ ηνVt−1 þ εν;t where ηu N ην and εν, t and εu, t are zero mean normally distributed i.i.d. shocks with Var[εν] = σν 2 and Var[εu] = σu 2 . This structure captures the concept of news shocks as in Beaudry and Portier (2006). 19 We add a government sector where total government expenditure is assumed to be exogenous and subject to stochastic shocks. In particular we assume that Gt ¼ G expðG^tÞ is government spending where G^t ¼ ηGG^t−1 þ εG;t, 0 ≤ ηG b 1 and εG, t is a zero-mean normally distributed i.i.d. shock with Var[εG] = σG 2 . All government spending is assumed to be financed via lump sum taxes on households, TD, and firms, TC. The government budget constraint is PG, tGt = PtTD, t + PtTC, t where it is assumed that PtTD = (1 − ρ)PG, tG and PtTC = ρPG, tG where ρ is a fixed parameter which determines the share of profit taxes in the overall tax take. PG, t is the price index of government purchased goods. It is assumed that government spending is on domestically produced goods so PG, t = PH, H, t. The household budget constraint is modified to include TD. Monopoly power in the final goods sector implies that final goods prices are subject to a mark-up given by υt = λt/(λt − 1). In the benchmark model the mark-up is assumed to be fixed. In the extended model the mark-up is assumed to be subject to stochastic shocks such that υt ¼ υ expðυ^tÞ where υ^t ¼ ηυυ^t−1 þ ευ;t, 0 ≤ ηυ b 1 and ευ, t is a zero-mean normally distributed i.i.d. shock with Var[ευ] = συ 2 . In the extended analysis of the model we allow for local currency pricing (LCP). In the LCP case final good firm z chooses pH, H, t(z) in home currency and pH, F, t ∗ (z) in foreign currency to maximize (6) where pH, F, t(z) is replaced by pH, F, t ∗ (z)St+i. The extended model allows for trade in equities. Home equities represent a claim on aggregate profits of all firms in the home final and intermediate sectors. The real payoff to a unit of the home equity purchased in period t is defined to be Πt+1 + ZE, t+1, where ZE, t+1 is the real price of home equity and Πt+1 is real aggregate profits. Thus the gross real rate of return on the home equity is rE, t+1 = (Πt+1 + ZE, t+1)/ZE, t. Foreign equities are similarly defined. Total dividends aggregated across al intermediate and final goods firms are given by Πt ¼ PY;t Pt Yt− wt Pt Lt−TC The benchmark parameter values assumed for the additional parameters in the extended model are shown in Table 3. Again these parameter values are based on Corsetti et al. (2010, 2018) and Smets and Wouters (2003, 2005, 2007). 6.1. A general policy rule We extend the simple policy rule used in the simple model to include a number of terms which capture additional welfare gaps. The generalised rule takes the following form: δπ ^ PY;t−^ PY;t−1 þ ð Þ 1−δπ ^ Pt−^ Pt−1 þ δDð Þþ Dt−Dt−1 δY YG;t−YG;t−1 þδτ τG;t−τG;t−1 þ δℒð Þ¼ ℒt−ℒt−1 0 ð10Þ where Dand ^ PY;t−^ PY;t−1 again capture PPI inflation and deviations from perfect risk sharing. The additional terms are based on YG, τG and ℒ. These are defined as follows YG ¼ ^ Y−^ Y fb τG ¼ τ^−τ^fb ℒ ¼ ^ PH;H−^S−^ P H; F where the superscript fb indicates the first best value of a variable and τ is the terms of trade. Thus YG is a measure of the output gap, τG is a measure of the terms of trade gap and ℒ is a measure of the deviation from the law of one price. There is an analogous targeting rule for the foreign economy. The targeting rule in (10) now contains six terms. The first two terms represent a weighted average of producer price (PPI) and consumer price (CPI) inflation. This captures the result shown by Corsetti et al. (2010, 2018) that, for general parameter combinations, in the case of LCP the welfare-relevant measure of inflation is effectively a weighted average of PPI and CPI inflation. The fourth term in (10) measures the welfare-relevant output gap. The role of the output gap in optimal targeting rules in New Keynesian models is well-known and needs no further explanation. The fifth term in the targeting rule measures the welfare-relevant terms-of-trade gap. As Corsetti et al. (2010, 2018) explain in detail, in an open economy, because there are different baskets of goods produced in different countries, shocks may have distortionary effects on the relative price of these different baskets. These distortions are welfare reducing in the same way as the within-country price distortions generated by inflation are welfare reducing. The terms of trade gap therefore plays the same role in the monetary policy rule as the CPI and PPI inflation terms. The final term in the targeting rule captures the welfare reducing effects of deviations from the law of one price. Such deviations are a direct consequence of (and only arise from) local currency pricing. In a similar way to the price distortions caused by staggered pricing, deviations from the law of one price are a form of price distortion which potentially requires a monetary policy response. Note that policy rule (10) contains strict CPI and PPI inflation targeting as special cases. Strict CPI inflation targeting is given by δπ ¼ δY ¼ δτ ¼ δD ¼ δℒ ¼ 0 and strict PPI inflation targeting is given by δπ = 1, δY ¼ δτ ¼ δD ¼ δℒ ¼ 0:. Given the generalised rule, there are now five policy coefficients to be chosen by the policymaker. Our policy optimisation problem now involves a grid search across these five coefficients, i.e. δπ, δY, δτ, δD and δℒ, in order to identify the parameter combination which maximises the unconditional expectation of period welfare (as defined in (7)). Table 3 Parameter values in the extended model. Share of government spending in output g = 0.2 Share of profit taxes in total taxes ϱ = 0.15 TFP and news shocks ην = 0.9, σν = 0.019 ηu = 0.95, σu = 0.006 Labour supply shocks ηΔ = 0.9, σΔ = 0.025 Mark-up shocks ηυ = 0.0, συ = 0.0015 Government spending shocks ηG = 0.9, σG = 0.003 19 In the absence of shocks to V this structure yields TFP shocks of exactly the same form as in the simple model, so εu, t captures contemporaneous innovations in TFP. News shocks on the other hand are represented by εv, t. So, for instance, given the assumption that ηu N ηv, a positive realisation of εv, t raises the expected future time path of TFP for t + 1 onwards (i.e. εv, t contains news about future TFP) but has no impact on TFP in period t. 204 O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208
O Senay, A Sutherland Joumal of International Economics 117(2019)196-208 Table 4 General model: PCp Trade elasticity, e 0.5 1.5 Policy rule 0.129 0068 0204 0.007 0584 0635 0 0.770 1.020 0.542 Welfare difference 0.0030 00033 00038 00043 Portfolio(optimal 5 (inf tar) St Dev ppl infiation 00065 0.0082 00074 00043 St Dev Output gap 0019 St Dev rer gap 1.77 1.28 027 (inf tar) 132 Note: For each e the table shows the optimal policy rule coefficients, the welfare difference between optimal policy and inflation targeting, standard deviations and equilibrium portfolios optimal policy and inflation targeting Welfare is measured in terms of the equivalent percentage of steady-state consumption. Standard deviations are meas percentages. Port- folio holdings are measured relative to steady state GDI It should be noted that, while this rule is a significant generalisation The lower half of Tables 4 and 5 show the implications of optimal of the simple ruled used in our basic analysis, we do not claim that this policy and inflation targeting for the volatility of a number of variables. methodology necessarily computes fully optimal policy for our model. As emphasised in the context of the simple model, optimal policy Our optimal rule is simply the optimal rule within the restricted class implies quite significant stabilisation of the output gap and the real of rules defined by (10) exchange rate gap relative to strict inflation targeting. Again this is true in both the pcp and lcp cases The cases analysed in Tables 4 and 5 are based on trade in both 62. Optimal policy in the general model: PCP and LCP equities and bonds. It is useful to compare the results yielded by Results relating to the generalised model are presented in Tables 4 market structures. To do this we concentrate on the impact of opti- and 5. Table 4 shows the PCP case and Table 5 shows the LCP case. mal policy on the volatility of the real exchange rate and we focus Both tables show results for a range of values of the international on the PCP case. This is sufficient to illustrate the difference between trade elasticity, 0, from 0. 25 to 3. financial market structures. Table 6 compares results for the two- Tables 4 and 5 report the coefficients of the optimal policy rule. It is bonds-two-equites case with autarky and a single non-contingent clear that, as in the case of the simple model considered above, optimal bond. The numbers shown in this table are the ratio of the standard policy implies quite a significant departure from inflation targeting in deviation of the real exchange rate yielded by optimal policy relative terms of the policy rule coefficients. Recall that strict PPI inflation to the standard deviation yielded by inflation targeting. The lower targeting implies On= 1, Sy OD=6%=0 and strict CPI inflation the reported number the more stabilising optimal policy is relative rgeting implies an=6y=8=0p=6/=0. Tables 4 and 5 show to inflation targeting, while a reported number close to unity implies that optimal policy implies relatively large values(in absolute terms) almost no stabilising effect of optimal policy relative to inflation for the coefficient on the risk sharing gap, op, so as emphasised in the con- targeting. text of the simplified model, optimal policy requires a strong response t It is apparent that, for values of 0 not close to 1/2, the stabilising ef- the departures from full risk sharing that arise because of the incomplet fect of optimal policy is very small in the autarky and single-bond market structure Tables 4 and 5 show the difference in welfare between optimal po cases. Itis only when 0 is close to 1/2 that the stabilising effect of optimal policy is non-trivial. By contrast, in the two-bonds-two-equites case the cy and a policy ofinflation targeting. This difference is of the same order stabilising effect of optimal policy is significant at all values of 0.These of magnitude as in the simple modeL. Notice that, contrary to the argu- results match the results derived in the simple model and they confirm ment of Corsetti et aL.(2010, 2018)there does not appear to be a signif- that the basic mechanism illustrated in Fig 1 the welfare benefit of optimal policy 2 1 more general model.22 6.3. Different combinations of shocks As before. welfare is in terms percentage of steady sta d relative to steady state GDP. In a symmetric equilibrium( with zero The results reported in Tables 4 and 5 confirm that the results illus- eign bonds is matched by a trated in the simple model carry over to a more general structure. Note egative(external)position in home bonds and a positive holding of foreign equities is however, in the context of the simple model, the mechanism that gen- by a negative(external) holding o erated large differences between optimal policy and inflation targeting es. The foreigncountry portfolio is the mirror image of the home portfolio. Note that inthe depended on the trade-off between choosing a portfolio that could LCP case we compare optimal policy to CPl inflation targeting. Engel (2011)shows that, with LCP and perfect risk sharing, strict CPI inflation targeting is the optimal policy, st LCP case in 2 LCP plays a significant role in Corsettiet al(2010, 2018)because their welfare results of p= 1. The special rol the simple model in Table 2 because there are most significant when the trade balance is insensitive to changes in the terms of trade of shocks. As explained above, in the vicinity of ep= 1, the terms r when the terms of trade are insensitive to change in the nominal exchange rate(ie the of trade provide hedging against TFP shocks and, in the simple model, allows bond alloca- LCP case). Our results are driven by the link be policy. This link is relatively independent of whether firms are following PCP or LCP strat- monetary tion to focus on taste shocks. The general model illustrated in Tables 4 and 5 contains mt iple sources of risk so the hedging properties of the terms of trade in the vicinity of ep egies. hence there are no significant differences between the results in Tables 4 and 5. are much less significant
It should be noted that, while this rule is a significant generalisation of the simple ruled used in our basic analysis, we do not claim that this methodology necessarily computes fully optimal policy for our model. Our optimal rule is simply the optimal rule within the restricted class of rules defined by (10). 6.2. Optimal policy in the general model: PCP and LCP Results relating to the generalised model are presented in Tables 4 and 5. Table 4 shows the PCP case and Table 5 shows the LCP case. Both tables show results for a range of values of the international trade elasticity, θ, from 0.25 to 3.20 Tables 4 and 5 report the coefficients of the optimal policy rule. It is clear that, as in the case of the simple model considered above, optimal policy implies quite a significant departure from inflation targeting in terms of the policy rule coefficients. Recall that strict PPI inflation targeting implies δπ = 1, δY ¼ δτ ¼ δD ¼ δℒ ¼ 0 and strict CPI inflation targeting implies δπ ¼ δY ¼ δτ ¼ δD ¼ δℒ ¼ 0 . Tables 4 and 5 show that optimal policy implies relatively large values (in absolute terms) for the coefficient on the risk sharing gap, δD;so as emphasised in the context of the simplified model, optimal policy requires a strong response to the departures from full risk sharing that arise because of the incomplete market structure. Tables 4 and 5 show the difference in welfare between optimal policy and a policy of inflation targeting. This difference is of the same order of magnitude as in the simple model. Notice that, contrary to the argument of Corsetti et al. (2010, 2018) there does not appear to be a significant difference between the PCP and LCP cases in terms of the size of the welfare benefit of optimal policy.21 The lower half of Tables 4 and 5 show the implications of optimal policy and inflation targeting for the volatility of a number of variables. As emphasised in the context of the simple model, optimal policy implies quite significant stabilisation of the output gap and the real exchange rate gap relative to strict inflation targeting. Again this is true in both the PCP and LCP cases. The cases analysed in Tables 4 and 5 are based on trade in both equities and bonds. It is useful to compare the results yielded by the two-bond-two-equity case to those yielded by other financial market structures. To do this we concentrate on the impact of optimal policy on the volatility of the real exchange rate and we focus on the PCP case. This is sufficient to illustrate the difference between financial market structures. Table 6 compares results for the twobonds-two-equites case with autarky and a single non-contingent bond. The numbers shown in this table are the ratio of the standard deviation of the real exchange rate yielded by optimal policy relative to the standard deviation yielded by inflation targeting. The lower the reported number the more stabilising optimal policy is relative to inflation targeting, while a reported number close to unity implies almost no stabilising effect of optimal policy relative to inflation targeting. It is apparent that, for values of θ not close to 1/2, the stabilising effect of optimal policy is very small in the autarky and single-bond cases. It is only when θ is close to 1/2 that the stabilising effect of optimal policy is non-trivial. By contrast, in the two-bonds-two-equites case the stabilising effect of optimal policy is significant at all values of θ. These results match the results derived in the simple model and they confirm that the basic mechanism illustrated in Fig. 1 continues to operate in the more general model.22 6.3. Different combinations of shocks The results reported in Tables 4 and 5 confirm that the results illustrated in the simple model carry over to a more general structure. Note however, in the context of the simple model, the mechanism that generated large differences between optimal policy and inflation targeting depended on the trade-off between choosing a portfolio that could Table 4 General model: PCP. Trade elasticity, θ 0.25 0.5 0.75 1.5 3 Policy rule δY 0.129 0.129 0.129 0.129 0.129 δτ −0.021 −0.068 −0.204 −0.007 −0.003 δD 0.584 −0.635 −0.770 −1.020 −0.542 δℒ 00000 δπ 1.002 0.996 0.997 0.998 0.998 Welfare difference 0.0025 0.0030 0.0033 0.0038 0.0043 Portfolio (optimal) ðbondsÞ ðequitiesÞ −23:0 15:2 −42:7 50:1 −33:3 53:5 23:8 5:8 68:4 −4:5 (inf tar) ðbondsÞ ðequitiesÞ −14:4 0:3 −7:3 0:3 −0:2 0:3 21:1 0:3 63:7 0:3 St Dev PPI Inflation (optimal) 0.0065 0.0082 0.0104 0.0074 0.0043 St Dev Output gap (optimal) 0.019 0.060 0.080 0.095 0.089 (inf tar) 0.028 0.093 0.134 0.196 0.245 St Dev RER gap (optimal) 2.68 1.77 1.28 0.64 0.27 (inf tar) 3.83 2.75 2.16 1.32 0.76 Note: For each θ the table shows the optimal policy rule coefficients, the welfare difference between optimal policy and inflation targeting, standard deviations and equilibrium portfolios for optimal policy and inflation targeting. Welfare is measured in terms of the equivalent percentage of steady-state consumption. Standard deviations are measured in percentages. Portfolio holdings are measured relative to steady state GDP. 20 As before, welfare is measured in terms of the equivalent percentage of steady state consumption and standard deviations are measured in percentage terms. Portfolio holdings are measured relative to steady state GDP. In a symmetric equilibrium (with zero net foreign assets in the steady state) a positive holding of foreign bonds is matched by a negative (external) position in home bonds and a positive holding of foreign equities is matched by a negative (external) holding on home equities. Hence the portfolio position can be summarised by home holdings of foreign bonds and home holdings of foreign equities. The foreign country portfoliois the mirror image of the home portfolio. Note that in the LCP case we compare optimal policy to CPI inflation targeting. Engel (2011) shows that, with LCP and perfect risk sharing, strict CPI inflation targeting is the optimal policy, so CPI inflation targeting is the natural benchmark for comparison in the LCP case in Table 5. 21 LCP plays a significant role in Corsetti et al. (2010, 2018) because their welfare results are most significant when the trade balance is insensitive to changes in the terms of trade or when the terms of trade are insensitive to change in the nominal exchange rate (i.e. the LCP case). Our results are driven by the link between portfolio allocation and monetary policy. This link is relatively independent of whether firms are following PCP or LCP strategies, hence there are no significant differences between the results in Tables 4 and 5. 22 Notice in Tables 4 and 5 that, unlike in the two-bond case in Table 2, the divergence between optimal policy and inflation targeting does not appear to decline in the vicinity of θρ = 1. The special role of θρ = 1 arises in the simple model in Table 2 because there are only two sources of shocks. As explained above, in the vicinity of θρ = 1, the terms of trade provide hedging against TFP shocks and, in the simple model, allows bond allocation to focus on taste shocks. The general model illustrated in Tables 4 and 5 contains multiple sources of risk so the hedging properties of the terms of trade in the vicinity of θρ = 1 are much less significant. O. Senay, A. Sutherland / Journal of International Economics 117 (2019) 196–208 205
