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External Shocks, Banks and Monetary Policy in an Open Economy Yasin Mimir* Enes Sunel Central Bank of the Republic of Turkey CBRT and BOE Joint Workshop on International Monetary and Financial System: short-term challenges, long-term solutions June 14, 2015 The ideas in this talk are solely authors’ and do not reflect the official views or the policies of the Central Bank of the Republic of Turkey. Macroeconomic dynamics in EMEs around 2007-09 crisis EMBI Spreads Capital Flows to Emerging Economies (Million $) 25,000 Real Economic Activity 500 4 20,000 8 Gross Domestic Product Private Consumption Investment (right axis) 3 15,000 400 10,000 5,000 300 0 -5,000 200 -10,000 4 1 2 0 0 -1 -2 -2 -4 -3 -15,000 100 I II III IV I II 2007 III IV I II 2008 III IV I II 2009 III IV I 2010 II III IV I II III IV I 2007 II III IV I 2008 Lending Spreads II III IV I 2009 II III IV I 2010 II III Lending Spread (Domestic) Lending Spread (Foreign) 900 4 1.6 2 1.2 0 0.8 -2 -4 0.0 -6 -0.4 600 500 -8 400 300 Change in REER C.A. Balance to GDP Ratio (right axis) -10 I II III IV 2008 I II III IV 2009 III IV I I II III IV 2010 I II III 2011 II III IV I 2008 II III IV I 2009 II III IV I 2010 II III 2011 Policy Instruments 9 11 Policy Rate Avg. Reserve Req. Ratio (right axis) 8 10 7 9 6 8 5 7 0.4 700 II III IV 2007 II 2007 800 I -8 I 2011 External Side 1,100 1,000 -6 -4 2011 6 2 I II III IV 2007 I II III IV 2008 I II III IV 2009 I II III IV 2010 I II III 2011 -0.8 -1.2 4 6 3 5 I II III IV 2007 I II III IV 2008 I II III IV 2009 I Cross-country means of 20 EMEs. I Sources: BIS, Bloomberg, EPFR, IFS, country central banks. I II III IV 2010 I II III 2011 Research Questions I What are the macroeconomic and financial effects (transmission channels) of external shocks on EMEs? I We consider four types of external shocks observed: I I Country risk premium ⇒ Lehman Brothers (September 2008), Taper tantrum (May 2013) I US interest rate ⇒ FED’s policy normalization (expected late(?) 2015) I Policy uncertainty ⇒ Magnitude of FED’s interest rate hike I Export demand ⇒ Exogenous disturbance in the income of the rest of the world Should monetary policy respond to financial variables over and above their effect on inflation in an open economy? Theoretical Framework I A New Keynesian small open economy with banking. I Workers consume, supply labor and save in domestic currency deposits. I Bankers collect domestic and foreign funds, and lend to production firms. I I Financial frictions à la Gertler and Kiyotaki (2011) between bankers and depositors ⇒ countercyclical lending spreads. I Frictions are asymmetrically more intense on foreign investors ⇒ differentiation in domestic/foreign lending spreads. Costly price adjustment framework à la Rotemberg (1982). I Imperfect exchange rate pass through due to sticky import prices. Methodology I Quantitatively investigate how alternative Taylor type monetary policy rules might perform in terms of I I I Macroeconomic stability ⇒ inflation and output Domestic financial stability ⇒ inflation and credit growth External financial stability ⇒ inflation and RER depreciation. I Construct optimized monetary policy rules based on alternative policy mandates using loss function approach. I Impulse-response experiments that intend to reflect on the impact of “Taper tantrum” and “(uncertain) policy normalization” shocks. Main Findings Literature Review I Risk premium shocks have more explanatory power than TFP, world interest, and export demand shocks for most macro aggregates. I Negative external shocks trigger an adverse feedback loop of real depreciation, capital flow reversal, tightening in credit conditions and reduced real economic activity, alongside inflation. I The credit-augmented IT rule outperforms classical and RER augmented IT rules in minimizing losses that depend on price, output and/or credit growth (or real exchange rate) stability. I I monetary policy can lean against the wind to reduce the procyclicality in the financial system. Augmenting a strict IT rule with a RER stabilization objective does not contribute to macroeconomic stabilization. Bankers I Banker j borrows from worker i 6= j and foreigners to finance loans. ∗ Qt ljt = (1 − rrt )Bjt+1 + (1 − rrt )St Bjt+1 + Njt , I For R̂t+1 = njt+1 Rt+1 −rrt 1−rrt ; net worth evolution i h ∗ ∗ bjt+1 + R̂t+1 njt = Rkt+1 − R̂t+1 qt ljt + Rt+1 − Rt+1 b∗ I For Ψt = F ( yt+1 )ψt , F 0 (.) > 0; t Pt ∗ ∗ St+1 Pt Rt = Et (1 + rnt ) Rt = Et Ψt (1 + rnt ) Pt+1 St Pt+1 I External shocks are assumed to follow AR(1) processes: Country risk premium: U.S. interest rate: U.S. policy uncertainty: ln(ψt+1 ) = ρψ ln(ψt ) + ψ t+1 ∗ ∗ ∗ ∗ ln(Rt+1 ) = ρR ln(Rt∗ ) + σtR Rt+1 ∗ R∗ ∗ R∗ ∗ R∗ R σt+1 = (1−ρσ )σ R +ρσ σtR +σt+1 Workers Bankers’ profit maximization Vjt = max ∗ ljt+i ,bjt+1+i Et ∞ X Optimization Problem (1 − θ)θi Λt,t+1+i njt+1+i (1) i=0 I Bankers survive with a likelihood of 0 < θ < 1 and are subject to Vjt ≥ λ qt ljt − ωl bjt+1 (2) I Financial frictions, λ > 0 and ωl = 0 reduce the magnitude of intermediated funds I I Loan-deposit spreads emerge due to limited external finance. Domestic and foreign debt are perfect substitutes. b∗ b+b ∗ I In the data, = 40% in Turkey between 2002-2010. I If domestic depositors have a comparative advantage in monitoring banks, i.e. 0 < ωl < 1 a fraction of domestic debt becomes non-divertable Asymmetry in financial frictions Spreads I λ > 0 and ωl = 0 reduce the magnitude of intermediated funds ⇒ n o ∗ Et {Λt,t+i+1 Rkt+i+1 } > Et Λt,t+i+1 R̂t+i+1 = Et Λt,t+i+1 Rt+i+1 I If domestic lenders monitor better, i.e. 0 < ωl < 1, part of domestic debt is non-divertable ⇒ n o ∗ Et {Λt,t+i+1 Rkt+i+1 } > Et Λt,t+i+1 R̂t+i+1 > Et Λt,t+i+1 Rt+i+1 I Competition for funds in the domestic deposit market bids up real deposit rates. I The credit spread over real deposit rates becomes smaller. I Can pick 0 < ωl < 1 to hit b∗ b+b ∗ in the data. Symmetric equilibrium Capital Producers qt ljt − ωl bjt+1 = Final-Goods Producers Intermediate-Goods Producers νt − νt∗ njt = κjt njt λ − ζt (3) where ζt = νtl + νt∗ . I Divertable assets cannot exceed an endogenous multiple of bank capital, i.e., qt lt − ωl bt+1 = κt nt I I Substitute (4) into (7), we get n o ∗ ∗ net+1 = θ Rkt+1 − Rt+1 κt + Rt+1 nt New entrants are endowed with assets 1−θ nnt+1 = (1 − θ) (4) (5) fraction of exiting bankers’ qt lt = qt lt 1−θ nt+1 = net+1 + nnt+1 . (6) (7) Monetary authority I log log 1 + rnt 1 + rn 1 + rnt 1 + rn log Central bank conducts monetary policy using three types of Taylor rule configurations and discretionary changes in reserve requirements. = ρrn log 1 + rnt 1 + rn = ρrn log 1 + rnt−1 1 + πt+1 qt lt +(1−ρrn ) ϕπ Et log + ϕl log 1 + rn 1+π qt−1 lt−1 = ρrn log H yt 1 + rnt−1 1 + πt+1 + ϕy log +(1−ρrn ) ϕπ Et log 1 + rn 1+π y 1 + rnt−1 1 + πt+1 st +(1−ρrn ) ϕπ Et log + ϕs log 1 + rn 1+π st−1 log(1 + rrt ) = (1 − ρrr ) log(1 + rr ) + ρrr log(1 + rrt−1 ) + rr Parametrization and calibration Description Parameter Value Target Financial Intermediaries Fraction of the revenues that can be diverted Fraction of domestic deposits that cannot be diverted Survival probability of the bankers Proportional transfer to the entering bankers λ ωl θb b 0.598 0.822 0.925 0.0015 Commercial loan/domestic deposits spread Banks’ liability composition (foreign funds) Leverage ratio of 7.5 for commercial banks 1.33% of aggregate net worth rr ϕy ϕl ϕs gH 0.06 2.2564 0.2280 1.4268 0.1 Required reserve ratio for 2002 - 2013 Estimated from the Turkish data Estimated from the Turkish data Estimated from the Turkish data average share of government spending in GDP ρΨ σΨ ρRn∗ σRn∗ 0.9628 0.0032 0.977 0.00097 Estimated Estimated Estimated Estimated Monetary Authority and Government Domestic and foreign currency required reserve ratios Reaction parameter to output gap in Taylor rule Reaction parameter to credit growth in Taylor rule Reaction parameter to change in RER in Taylor rule Steady state government expenditure to GDP ratio Shock Processes Persistence of risk premium process Standard deviation of risk premium shocks Persistence of U.S interest rate process Standard deviation of U.S. interest rate shocks R∗ Persistence of U.S policy uncertainty process ρσ Standard deviation of U.S. policy uncertainty shocks σσ Other R∗ 0.15 0.0015 from from from from the the the the Turkish EMBI data Turkish EMBI data US data US data N/A Estimated from the US data Inefficiencies and external shocks I Monopolistic competition → Higher mark-up → Lower employment and output I Price rigidity → Increased import prices due to ER pass through and higher price dispersion → Higher inflation → Increased menu costs → lower output I Financial friction (λ > 0) → Insufficient substitution of foreign debt with domestic deposits → Less intermediated funds → Larger credit ∗ spreads Et [Rkt+1 − Rt+1 ], Et [Rkt+1 − Rt+1 ] ↑ → Reduced investment and output I Asymmetry in the financial friction (ω > 0) → Differentiates domestic and foreign funding rate, and partly eliminates the arbitrage between loan-domestic deposit rates i.e., ∗ Et [Rkt+1 − Rt+1 ] > Et [Rkt+1 − Rt+1 ] > 0. Variance decomposition (%) TFP Country Risk Premium U.S. Interest Rate Export Demand 49.31 21.11 8.14 28.41 65.48 76.92 4.92 10.99 12.60 17.35 2.42 2.33 37.38 30.51 18.28 17.21 2.90 9.73 51.53 41.30 46.38 49.46 82.56 47.00 7.92 6.81 7.38 7.95 11.78 7.70 3.17 21.37 27.97 25.39 2.77 35.56 52.08 52.27 38.90 39.71 6.24 6.14 2.78 1.87 Real Variables Output Consumption Investment Financial and External Variables Credit Liability Composition (Foreign) Domestic lending spread Foreign Lending spread Real Exchange Rate C.A. Balance to GDP ratio Nominal Variables CPI inflation rate Policy Rate Loss function values for alternative policies and mandates 2 σπ + σy2 TFP Risk prem. US int. rate Export dem. All Loss TR1 ϕπ ϕy Loss TR2 ϕπ ϕl Loss TR3 ϕπ ϕs 1.428e-05 4.551e-06 5.358e-07 3.149e-06 2.357e-05 1.51 1.01 1.01 1.26 2.01 1 2.5 2.5 2.5 2.5 9.782e-06 4.695e-06 5.123e-07 5.497e-06 2.237e-05 1.76 2.26 2.01 1.01 2.01 2 2.25 2 1.75 2.25 2.7695e-05 6.4040e-06 7.262e-07 7.234e-06 3.875e-05 1.01 1.01 1.01 1.01 1.01 0 0 0 0 0 7.478e-05 2.735e-05 2.791e-06 8.666e-06 1.994e-04 4.76 1.01 1.01 1.26 4.76 1.5 2.5 2.5 0.25 2.25 7.928e-05 2.275e-05 2.596e-06 7.174e-06 1.259e-04 3.26 1.01 1.01 1.01 2.51 2.5 1.75 1.50 2.00 2.5 1.314e-04 2.783e-05 2.965e-06 9.789e-06 1.999e-04 2.01 1.01 1.01 1.01 1.26 0 0.25 0 0 0 1.544e-04 0.0025 2.360e-04 1.284e-04 0.0028 1.01 4.76 4.76 4.76 4.26 0 0 0 0 0.25 1.212e-04 0.0024 2.286e-04 1.258e-04 0.0026 3.51 4.76 4.76 4.76 4.76 2.5 0.75 0.75 0.50 1.5 1.544e-04 0.0025 2.360e-04 1.284e-04 0.0028 1.01 4.76 4.76 4.76 3.51 0 0 0 0 0 2 2 σπ + σy2 + σql TFP Risk prem. US int. rate Export dem. All 2 σπ + σy2 + σs2 TFP Risk prem. US int. Export dem. All Taper tantrum shock (100 bp increase in risk premium) Current Account Balance−to−GDP Real Exchange Rate 4 %Ch. 0.2 3 0.15 2 0.1 1 0.05 2 4 6 8 10 12 0 14 2 4 Nominal Depreciation Rate 4 3 %Ch. 6 8 10 12 14 10 12 14 8 10 Quarters 12 14 Liability Structure 0 −1 2 −2 1 0 2 4 6 8 10 12 −3 14 2 4 6 0.6 0.4 0.2 0 2 4 6 8 10 Quarters 8 Policy Rate Ann. Bs. Pt. Ch. Ann. % Pt. Ch. CPI Inflation 12 14 Taylor 30 20 10 2 Credit augmented 4 6 Taper tantrum shock ctd. (100 bp increase in risk premium) Output Consumption %Ch. 0.02 0 −0.02 Investment −0.05 −0.2 −0.1 −0.4 −0.15 −0.6 −0.2 −0.04 5 10 15 Credit 10 15 5 Bank Net Worth 0 1 −0.1 −0.2 0 −0.2 −0.3 −1 −0.3 −0.4 −2 5 10 15 5 Loan−Foreign Deposits Spread 10 15 Asset Price 0 2 −0.1 %Ch. −0.8 5 10 15 −0.4 Loan−Domestic Deposits Spread 5 10 15 Country Risk Premium Ann. Bs. Pt. Ch. 100 80 10 60 80 40 5 60 20 0 5 10 Quarters 15 0 5 Taylor 10 Quarters 15 Credit augmented 40 5 10 Quarters 15 US interest rate shock (25 bp increase) Current Account Balance−to−GDP Real Exchange Rate 0.08 1 %Ch. 0.06 0.04 0.5 0.02 0 2 4 6 8 10 12 0 14 2 4 Nominal Depreciation Rate 6 8 10 12 14 10 12 14 8 10 Quarters 12 14 Liability Structure 0 %Ch. 1 −0.5 0.5 0 −1 2 4 6 8 10 12 14 2 4 6 0.2 0.15 0.1 0.05 0 2 4 6 8 10 Quarters 8 Policy Rate Ann. Bs. Pt. Ch. Ann. % Pt. Ch. CPI Inflation 12 14 Taylor 12 10 8 6 4 2 2 4 Credit augmented 6 US interest rate shock ctd. Output (25 bp increase) Consumption Investment 0.01 %Ch. −0.02 0 −0.04 −0.01 −0.02 −0.05 −0.1 −0.15 −0.2 −0.25 −0.06 5 10 15 −0.08 Credit 5 10 15 5 Bank Net Worth 10 15 Asset Price 0 0 −0.05 0 −0.1 −0.5 5 10 15 −0.1 5 Loan−Foreign Deposits Spread Ann. Bs. Pt. Ch. %Ch. 0.5 −0.05 10 15 5 Loan−Domestic Deposits Spread 30 10 15 Country Risk Premium 0 3 −2 20 2 −4 10 1 −6 0 5 10 Quarters 15 0 5 Taylor 10 Quarters 15 Credit augmented 5 10 Quarters 15 Policy uncertainty shock (59 bp variation in FOMC 2015 projections) Current Account Balance−to−GDP Real Exchange Rate 0.3 %Ch. 3 0.2 2 0.1 0 1 2 4 6 8 10 12 0 14 2 4 %Ch. Nominal Depreciation Rate 6 8 10 12 14 10 12 14 8 10 Quarters 12 14 Liability Structure 3 0 2 −1 −2 1 −3 0 2 4 6 8 10 12 −4 14 2 4 6 CPI Inflation Ann. Bs. Pt. Ch. Ann. % Pt. Ch. 0.6 0.4 0.2 0 2 4 6 8 10 Quarters 8 Policy Rate 0.8 12 14 Taylor 40 30 20 10 2 4 Credit augmented 6 Policy uncertainty shock ctd. Output (59 bp variation in FOMC 2015 projections) Consumption Investment 0.02 0 −0.05 −0.1 −0.15 −0.2 −0.25 %Ch. 0 −0.02 −0.04 −0.06 −0.08 5 10 15 −0.5 −1 5 Credit 10 15 5 Bank Net Worth 10 15 Asset Price %Ch. 0 −0.1 −0.2 −0.3 −0.4 −0.5 2 −0.2 0 −0.3 5 10 15 −2 Loan−Foreign Deposits Spread Ann. Bs. Pt. Ch. −0.1 5 10 15 12 80 −0.4 Loan−Domestic Deposits Spread 10 −5 60 8 −10 40 6 −15 4 −20 20 5 10 Quarters 15 2 5 10 15 Country Risk Premium 0 −25 5 Taylor 10 Quarters 15 Credit augmented 5 10 Quarters 15 Conclusion I A New Keynesian small open economy model with financial frictions is able to generate the adverse macroeconomic and financial repercussions of external shocks that EMEs face. I The credit-augmented IT rule outperforms classical and RER augmented IT rules in minimizing losses that depend on price, output and/or credit growth (or real exchange rate) stability. I I Augmenting IT rules with external financial stability objective might overwhelm monetary policy. I I monetary policy can lean against the wind to reduce the procyclicality in the financial system. A strict IT rule with a RER stabilization objective does not contribute to macroeconomic stabilization. Further research calls for determining (Ramsey) optimal and implementable rules and conducting the normative comparison of policy rules, accordingly. THANK YOU Discretionary increase in reserve requirements Current Account Balance−to−GDP (1 % point) Real Exchange Rate 1.5 %Ch. 0 1 0.5 −0.5 0 −1 −0.5 2 4 6 8 10 12 14 2 4 %Ch. Nominal Depreciation Rate 6 1.5 1 1 0.5 0.5 0 0 −0.5 10 12 14 10 12 14 8 10 Quarters 12 14 −1 −0.5 2 4 6 8 10 12 14 2 4 6 0.2 0.1 0 2 4 6 8 10 Quarters 8 Policy Rate Ann. Bs. Pt. Ch. CPI Inflation Ann. % Pt. Ch. 8 Liability Structure 12 14 Taylor 30 20 10 0 2 4 Credit augmented 6 Discretionary increase in reserve requirements ctd. Output Consumption Investment 0 0 0.02 −0.1 %Ch. −0.02 −0.2 0 −0.04 −0.02 10 15 −0.4 5 Credit 10 15 5 Bank Net Worth 0.2 %Ch. −0.3 −0.06 5 0.1 2 0.2 0 0.1 −2 0 −0.1 −4 −0.1 −6 5 10 15 5 10 15 20 0 −0.2 Loan−Domestic Deposits Spread Loan−Foreign Deposits Spread 10 15 Asset Price 0 −0.2 Ann. Bs. Pt. Ch. (1 % point) 5 10 15 Country Risk Premium 10 0 −20 −200 5 −40 −400 −60 −600 5 10 Quarters 15 −80 5 Taylor 10 Quarters 15 Credit augmented 0 5 10 Quarters 15 Literature review I Recent global financial crisis has brought up the issue of macroeconomic and macroprudential policy coordination. I I Angeloni and Faia (2009), Angelini et al. (2012), Alpanda et al. (2014) and others. Additional policy tools are explored in order to target financial stability. I I Back Christensen et al. (2011), Glocker and Towbin (2012), Mimir et al. (2013). Financial frictions in emerging economies bring additional burden on monetary authorities. I I Transmission of country borrowing premium shocks to business cycles and domestic deposit and lending rates. Uribe and Yue (2006) and Akinci (2013). Adjusting short term policy rates triggers fear of appreciation/depreciation. Workers max ct ,ht ,Bt+1 ,mt I Back E0 ∞ X t=0 β (ct − hc ct−1 ) 1−σ 1−σ −1 χ 1+ξ − h + υ log 1+ξ t Mt Pt # Mt Wt (1 + rnt−1 )Bt Mt−1 Tt Bt+1 + = ht + + + Πt − Pt Pt Pt Pt Pt Pt c is a CES aggregate of home and foreign goods consumption, γ h 1 i γ−1 γ−1 γ−1 1 ct = ω γ (ctH ) γ + (1 − ω) γ (ctF ) γ I Workers save only in domestic currency deposits and hold cash. ct + I " t Leading to the domestic CPI, 1 h i 1−γ Pt = ω(PtH )1−γ + (1 − ω)(PtF )1−γ Optimality conditions of workers’ problem Back Lagrange multiplier of the BC: −σ ϕt = (ct − hc ct−1 ) −σ − βhc Et (ct+1 − hc ct ) CS optimality condition: Pt ϕt = βEt ϕt+1 (1 + rnt ) Pt+1 H-F goods optimal consumption demand: H −γ ctH ω Pt = 1 − ω PtF ctF CL optimality condition: Wt χhtξ = Pt ϕt CM optimality condition: υ/mt rnt = ϕt 1 + rnt Financial frictions and spreads Back Bankers’ profit maximization I Back ∗ + ν n and solve the Lagrangian Conjecture Vjt = νtl qt ljt + νt∗ bjt+1 t jt with the multiplier µt s.t. Vjt ≥ λ qt ljt − ωl bjt+1 to obtain n h io νtl = Et Ξt,t+1 Rkt+1 − R̂t+1 o n νt = Et Ξt,t+1 R̂t+1 and n o ∗ νt∗ = Et Ξt,t+1 Rt+1 − Rt+1 ∗ where Ξt,t+1 = Λt,t+1 [1 − θ + θ(ζt+1 κt+1 + νt+1 − νt+1 )] and Λt,t+1+i = β i+1 Uct+1+i Uct . I λ, µt , ωl > 0 ⇒ νt∗ > 0. Solution to bankers’ problem ∗ max L = νtl qt ljt + νt∗ bjt+1 + νt njt ∗ ljt ,bjt+1 qt ljt − njt ∗ l ∗ ∗ − bjt+1 +µt νt qt ljt + νt bjt+1 + νt njt − λ qt ljt − ωl 1 − rrt First Order Conditions: νtl (1 + µt ) = λµt 1 − ljt : b∗jt+1 : µt : νtl qt ljt + νt∗ ωl 1 − rrt νt∗ (1 + µt ) = λµt ωl qt ljt − njt − bt+1 + νt njt − λ(qt ljt − ωl bjt+1 ) ≥ 0 1 − rrt Capital goods producers I Buy the deprecited capital at production firms at qt , Back PI ,t Pt , repair it, and sell it to the ∞ X n h PI ,t io it t qt it − it max E0 β Λt,t+1 qt it − Φ it it−1 Pt t=0 I subject to the evolution of physical capital it kt+1 = (1 − δt )kt + 1 − Φ it it−1 Q-investment Condition for Capital Goods: h h 0 0 it it it i it+1 it+1 i PI ,t = qt 1−Φ −Φ +βEt Λt,t+1 qt+1 Φ Pt it−1 it−1 it−1 it it Home - Foreign Goods Optimal Investment Demand: H −γi itH Pt ωi = 1 − ωi PtF itF Final goods producers I Back Repackage a continuum of intermediate goods in a competitive market. 1−1 1 Z 1 j j 1− 1 di yt = yt (i) . 0 where j denotes Home (H) and Foreign (F) intermediate goods. max ytj (i) Ptj Z 1 1 ytj (i)1− di 0 1−1 1 Z − 1 Ptj (i)ytj (i)di 0 Iso-elastic demand for each good i of type j: !− Ptj (i) j ytj , yt (i) = Ptj Price of each good i of type j: 1 Z 1 1− j j 1− Pt = Pt (i) di . 0 Intermediate goods producers (Home) Foreign Back I They use capital and labor in the production of intermediate goods and they can vary capital utilization. α ytH (i) = At ut (i)kt (i) ht (i)1−α (8) I Total factor productivity follows an AR(1) process: ln(At+1 ) = ρA ln(At ) + At+1 I (9) They incur convex price adjustment costs as in Rotemberg (1982). Pt 2 ϕH PtH (i) − 1 H (i) 2 Pt−1 (10) Intermediate goods producers (Home) ctd. max Et PtH (i) H Dt+j (i) ptH ∞ X " Λt,t+j j=0 H (i) Dt+j Pt+j # (11) I They maximize real profits by choosing the sales price: = H H H∗ H∗ Pt+j (i)yt+j (i)+St+j Pt+j ct+j (i)−MCt+j yt+j (i)−Pt+j I Optimal sales price is given by ϕH πtH (πtH − 1) ϕH rmct − Et = + H −1 −1 −1 yt I " #2 H (i) ϕH Pt+j −1 H 2 Pt+j−1 (i) (12) π H (π H − 1) Λt,t+1 t+1 t+1 ytH ϕH → 0 ⇒ home goods prices are flexible and reflect a constant markup of −1 over the marginal cost. (13) Intermediate goods producers (Home) ctd. I Factor demands are determined by their marginal products, pI ,t δ 0 (ut )kt = α α Rkt = ytH kt t ut rmct (14) rmct − pi,t δ(ut ) + qt (15) qt−1 wt = (1 − α) with δ(ut ) = δ + and δ, d, % > 0. yH yH t rmct (16) d u 1+% 1+% t (17) ht Intermediate goods producers (Foreign) Back I Importers of foreign goods incur similar rigidities with MCtF = St PtF ∗ . F F (πt+1 − 1) πt+1 ϕF πtF (πtF − 1) ϕF F pt = st − Et Λt,t+1 + −1 −1 −1 ytF ytF (18) I Exporters do not have monopoly power, i.e., " −Γ #ν H PtH∗ H∗ H∗ 1−ν H ct = yt∗ (ct−1 ) Pt∗ with PtH∗ = Pt∗ = 1, and yt∗ taken as given. (19) Parametrization and calibration ctd. Description Parameter Value Target Preferences Quarterly discount factor Relative risk aversion Habit persistence Labor supply elasticity Relative utility weight of labor Relative utility weight of money Relative weight of domestic goods in consumption basket Intra-temporal elasticity of substitution for consumption composite Intra-temporal elasticity of substitution for investment composite β σ hc ξ χ υ ω γ γi 0.9821 2 0.7 5 4x103 0.35 0.4 1 1 Average annualized real deposit rate (7.48%) Literature Literature Literature steady state hours worked of 0.33 M2 to GDP ratio. average consumption to GDP ratio Gertler et al. (2007) Gertler et al. (2007) α ωi δ u % ψ ϕH ϕF 0.4 0.87 0.035 1 1 11 4 120 120 Labor share of output (0.6) average share of investment in GDP (0.15) Average annual ratio of investment to capital (14.8%) Literature Gertler et al. (2007) Steady state mark-up of 1.1 Elasticity of price of capital w.r.t. investment-capital ratio Frequency of price change per quarter Frequency of price change per quarter Firms Share of capital in output Share of domestic goods in the investment composite Depreciation rate of capital Steady-state utilization rate Elasticity of marginal depreciation with respect to the utilization rate Elasticity of substitution between varieties Investment adjustment cost parameter Price adjustment cost for domestic intermediate goods producers Price adjustment cost for domestic intermediate goods producers Back