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≤7<1 and Government spending shocks k=09.c=0003 EA,t is a zero-mean normally distributed ii.d. shock with VarEA=oX Total factor productivity, At, is now defined as follows 6.1 A general policy rule We extend the simple policy rule used in the simple model to in- where clude a number of terms which capture additional welfare gaps. The generalised rule takes the following form: Ur=nuUt-1+Eur +Evr Vr=n, Vt-1+Ert 4(P4-P)+(1-(P--)+6(2--)+6(a-a-) where Thu >T, 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 distrib￾uted 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 over￾all 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 bench￾mark 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 rep￾resent a claim on aggregate profits of all firms in the home final and in￾termediate 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 ag￾gregated 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 param￾eters in the extended model are shown in Table 3. Again these parame￾ter 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 in￾clude 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 devia￾tion 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 con￾sumer 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 rela￾tive price of these different baskets. These distortions are welfare reduc￾ing 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 ef￾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 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 in￾volves 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 on￾wards (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