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 con￾text 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 pol￾icy 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 argu￾ment of Corsetti et al. (2010, 2018) there does not appear to be a signif￾icant 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 opti￾mal 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 two￾bonds-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 ef￾fect 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 illus￾trated in the simple model carry over to a more general structure. Note however, in the context of the simple model, the mechanism that gen￾erated 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. Port￾folio 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 hold￾ings 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 equi￾ties. 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 strat￾egies, 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 alloca￾tion to focus on taste shocks. The general model illustrated in Tables 4 and 5 contains mul￾tiple 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