ECON6008 International Money and Finance - Quantitative Group Project: New-Keynesian small open- economy (SOE) model
Quantitative Group Project
Due date: Friday 2 June, 11:59pm
1 The model (equations and variables) 1.1 The model in brief The model you will analyze is a simplied version of the New-Keynesian small open- economy (SOE) model in Justiniano and Preston (2010), which in turn is based on the model in Monacelli (2005) and Gali and Monacelli (2005). Compared to Justiniano and Preston s model, our simpli ed model assumes that the law of one price (LoP) holds for all imported retail goods and there is no price indexation for these imported goods. The model is also extended to include labor-supply shocks, which could be used as a proxy for the supply-side disruption of the COVID-19 pandemic. Aggregate uctuations in our model model are driven by 7 exogenous shocks: risk premium, monetary policy (money supply), preference (consumer spending), labor supply, foreign in ation, foreign output, and foreign interest rate.
The model can be derived from the ground up with micro-foundations, based on op- timizing households, domestic rms and importers, etc., resulting in a set of non-linear equations. We will instead work directly with the log-linearized equilibrium equa- tions , listed below. 1.2 The log-linearized equations Consumption Euler-equation (the IS equation): bct=h 1 +h bct 1+1 1 +h Etbct+1 1 1 h 1 +hh bit Etbt+1i + ^gt (1) Goods-market clearing condition: byt= (1 )bct+ by t+ (2 )bSt (2) The link between terms of trade and real exchange rate: bqt= (1 )bSt (3) Changes (growth rate) of the terms of trade: bSt bSt 1=bF;t bH;t (4) 1 Domestic-price in ation (the "Phillips curve"): (bH;t H^H;t 1) = Et(bH;t+1 H^H;t) +(1 H)(1 H ) Hcmct (5) The real marginal cost: cmct='byt+ bSt+bct ^"s;t (6) The wedge between CPI- and PPI-in ation: bt=bH;t+ bSt bSt 1 (7) The uncovered interest-parity (UIP) condition: bit bi t=Etbec t+1 bat+Etb t+1 (8) The net-foreign-assets position (the current account): byt bct=bat 1bat 1+ (1 )bqt (9) Imported-good in ation (based on the law of one price): bF;t=bec t+b t (10) Monetary-policy (Taylor) rule: bit=ibit 1+ bt+ ybyt+ ybyt+ ebec t "m;t (11) Evolution of risk premium: b t= b t 1+" ;t (12) Evolution of foreign output: by t=yby t 1+"y;t (13) Evolution of foreign in ation: b t=b t 1+";t (14) Evolution of foreign interest rate: bi t=ibi t 1+"i;t (15) Evolution of preference shock: ^gt=g^gt 1+"g;t (16) Evolution of labor-supply shock: ^"s;t=s^"s;t 1+s;t (17) 2 De nition of variables and shocks NOTE: all hatted variables are in terms of log or percentage deviation from the steady-state value, except forbit,bt,bH;t,bF;t,b t, and bit, which are in terms of level deviation from the steady state (e.g. bitit i). bct consumption (per capita) bit nominal interest rate bt CPI in ation byt output bSt terms of trade (price of exports in terms of imports) bqt real exchange rate bH;t domestic-goods (PPI) in ation bF;t imported-goods in ation cmctreal marginal cost bat domestic-householdsholding of foreign assets bec t domestic-currency depreciation rate (% change in the exchange rate) by t foreign output b t foreign in ation bi t foreign interest rate b t relative risk premium bgt consumer preference ^"s;t exogenous labor-supply disruption "m;t monetary-policy shock (i.i.d.) " ;t risk-premium shock (i.i.d.) "y;tforeign-output shock (i.i.d.) ";tforeign-in ation shock (i.i.d.) "i;tforeign interest-rate shock (i.i.d.) "g;t preference shock (i.i.d.) s;t labor-supply shock (i.i.d.) 3 De nition of parameters and their calibration Parameters De nition Value inverse intertemporal elasticity of substitution 1 openness parameter 0.22 elasticity of substitution between domestic and imported goods 0.85 subjective discount factor 0.99 H probability of price xity for domestic goods 0.70 risk-premium parameter 0.01 ' inverse Frisch labor-supply elasticity 1.26 h degree of habit formation 0.30
consumption elasticity of preference shock 0.12 H degree of price indexation 0.25 i Taylor-rule interest smoothness 0.75 Taylor-rule response to in ation 1.85 y Taylor-rule response to output 0.05 y Taylor-rule response to output growth 0.70 e Taylor-rule response to exchange-rate uctuations 0 AR(1) coe¢ cient of risk-premium shock 0.95 y AR(1) coe¢ cient of foreign-output shock 0.55 AR(1) coe¢ cient of foreign-in ation shock 0.50 i AR(1) coe¢ cient of foreign interest-rate shock 0.50 g AR(1) coe¢ cient of preference shock 0.70 s AR(1) coe¢ cient of labor-supply shock 0.65 m, ,y,,i,g;sstandard deviations of shocks 1 4 The Questions
- Solve the model described above using Dynare. Obtain the impulse response for 10 periods to a one-time 1% shock to (a) money supply or the domestic interest-rate shock ( "m;t); (b) preference ( "g;t); (c) labor supply ( s;t); (d) foreign interest rate shock ( "i;t). Analyze (i.e. explain the dynamics) and plot the e¤ect of each of these shocks to domestic output ( byt), consumption ( bct), interest rate ( bit), in ation ( bt), domestic-currency nominal depreciation (bec t), and the "shocked" variable (e.g. if it s a foreign output shock, plotby t).Plot these six variables in one 3x2 gure or plot (with 3 rows and 2 columns) . Relate your analysis to what you have learned in the rst half of the course (the qualitative AA-DD model). For the money supply or the domestic interest-rate shock, do you observe an overshooting of the nominal exchange rate?
2.COVID-19 pandemic and monetary and exchange-rate policies . Let s analyze the economic impact of the COVID-19 pandemic using this model, with several di¤erent assumptions on the central bank s monetary and exchange-rate policies. Here, assume that the COVID-19 pandemic "shock" is simply proxied by a one-time 15% negative preference (consumer-spending) shock at period 1 (2020.Q1): Period (Quarter)1 (2020.Q1) Preference shock ( "g;t) 15% Note that this simple representation cannot fully capture the e¤ect of the COVID-19 pandemic as the actual pandemic shocks a¤ect both the supply-side and the demand-side of the economy. The preference shock considered here is a demand shock hence, we can only capture the demand-side e¤ect of the pandemic.1Nevertheless, we could still analyze 1The preference shock in the model is a shock that in uences household intertemporal consumption- saving decisions. A negative preference shock thus serves as a proxy for a reduction in aggregate demand during the pandemic, e.g. due to lost labor income or an increase in household income uncertainty which leads to a precautionary saving behaviour. 5 the impact of the pandemic on several key macroeconomic variables under several di¤erent central bank policies. (a) Analyze the e¤ect of this pandemic shock under the current policy rule with i= 0:75, = 1:85, y= 0:05, y= 0:70, and e= 0. Plot the responses of byt,bct,bit,bt, bec t, and bgtin one ( 3x2) gure. Explain their dynamics. In another ( 2x1) gure, plot the evolution of the level of nominal exchange rate and the current account. How are the responses here di¤erent (or the same) compared to question 1(b) (where the shock size is 1%)? (b) In the model above, we assume a fully- exible ( oating) exchange rate regime. Sup- pose that the central bank also directly intervenes in the foreign exchange market, i.e. it s operating under a managed oating exchange rate. This policy can be analyzed within our model by assuming that e= 0:75>0 The rest of policy rule coe¢ cients are unchanged. Analyze the e¤ect of the pandemic shock under this new assumption, in comparison to the e¤ect in part (a) . Plot the same ( 3x2) gure and ( 2x1) gure as in part (a) above. Is this policy more e¤ective in terms of mitigating the e¤ect of the pandemic shock on byt,bt, and bec t than the fully- oating exchange rate policy? Explain. (c) Now assume that the central bank is operating under a xed exchange-rate regime. Speci cally, the monetary policy rule in equation (11) is replaced with the following policy rule: bec t= 0 This policy rule e¤ectively (and credibly) xes the nominal exchange rate at a speci- ed level. Redo question 2(b) . Your answer and analysis should be in comparison to the freely- oating exchange-rate regime ( e= 0 under the original policy rule ) and managed- oating regime ( e= 0:75under the original policy rule ). [Notes/tips :(i)Dynare does not plot the impulse response of a variable if that variable is always constant (zero deviation from the steady state), (ii)since the foreign-debt holding, bat, enters the UIP condition in equation (8), you will generally not nd bit=bi tunder the xed-exchange rate regime , unless = 0),(iii) to solve the model under the xed regime in 2(c), you should remove monetary-policy shock "m;tfrom the list of shocks in your .mod le, as this shock now does not enter any of the equations.] [Extra points : plot the variables under the three policies in one ( 3x2) gure and one (2x1) gure as described above, e.g. the plot for bytin the (3x2) gure should include three di¤erent impulse responses.] 6 References [1] Gali, J. and T. Monacelli. 2005. "Monetary policy and exchange rate volatility in a small open economy". Review of Economic Studies 72: 707-734. [2] Justiniano, A. and B. Preston. 2010. "Monetary policy and uncertainty in an empirical small open-economy model". Journal of Applied Econometrics 25: 93-128. [3] Monacelli, T. 2005. "Monetary policy in a low pass-through environment". Journal of Money, Credit, and Banking 37(6): 1019-1045. 7
