一站式論文代寫,英国、美国、澳洲留学生Essay代寫—FreePass代写

數學代寫 - ECON6008: International Money & Finance
時間:2020-11-14
1 The model (equations and variables) 1.1 The model in brief The model you will analyze is a simpli ed 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 1 + hh hbit Etbt+1i + g^t (1) Goods-market clearing condition: byt = (1 )bct + ybt + (2 )Sbt (2) The link between terms of trade and real exchange rate: bqt = (1 )Sbt (3) Changes (growth rate) of the terms of trade: Sbt Sbt 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 ) H cmct (5) The real marginal cost: cmct = 'ybt + Sbt + bct + ^"s;t (6) The wedge between CPI- and PPI-in ation: bt = bH;t + Sbt Sbt 1 (7) The uncovered interest-parity (UIP) condition: bit bit = Etebct+1  bat + Etbt+1 (8) The net-foreign-assets position (the current account): byt bct = bat 1bat 1 + (1 )qbt (9) Imported-good in ation (based on the law of one price): bF;t = ebct + bt (10) Monetary-policy (Taylor) rule: bit = ibit 1 + bt + ybyt + yybt + eebct "m;t (11) Evolution of risk premium: bt = bt 1 + ";t (12) Evolution of foreign output: byt = y ybt 1 + "y;t (13) Evolution of foreign in ation: bt =  bt 1 + ";t (14) Evolution of foreign interest rate: bit = ibit 1 + "i;t (15) Evolution of preference shock: ^gt = gg^t 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 for bit, bt, bH;t, bF;t, bt , and bit , which are in terms of level deviation from the steady state (e.g. bit  it 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) qbt real exchange rate bH;t domestic-goods (PPI) in ation bF;t imported-goods in ation cmct real marginal cost bat domestic-households' holding of foreign assets bect domestic-currency depreciation rate (% change in the exchange rate) byt foreign output bt foreign in ation bit foreign interest rate bt 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;t foreign-output shock (i.i.d.) ";t foreign-in ation shock (i.i.d.) "i;t foreign interest-rate shock (i.i.d.) "g;t preference shock (i.i.d.) s;t labor-supply shock (i.i.d.) 3 4 De nition of parameters and their calibration Parameters De nition Value  inverse intertemporal elasticity of substitution 1 openness parameter 0.25  elasticity of substitution between domestic and imported goods 0.80 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 0.25 consumption elasticity of preference shock 0.12 H degree of price indexation 0.20 i Taylor-rule interest smoothness 0.75  Taylor-rule response to in ation 1.90 y Taylor-rule response to output 0.08 y Taylor-rule response to output growth 0.67 e Taylor-rule response to exchange-rate uctuations 0  AR(1) coecient of risk-premium shock 0.95 y AR(1) coecient of foreign-output shock 0.55  AR(1) coecient of foreign-in ation shock 0.50 i AR(1) coecient of foreign interest-rate shock 0.50 g AR(1) coecient of preference shock 0.65 s AR(1) coecient of labor-supply shock 0.70 m, , y ,  , i , g; s standard deviations of shocks 1 The Questions 1. 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 output ("y;t). Analyze (i.e. explain the dynamics) and plot the e ect of each of these shocks to domestic output (ybt), consumption (bct), interest rate (bit), in ation (bt), domestic-currency nominal depreciation (ebct ), and the "shocked" variable (e.g. if it's a foreign output shock, plot ybt ). 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? [Extra points: plot the evolution of the level of nominal exchange rate and the current account in a separate gure and explain the dynamics.] 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, the COVID-19 pandemic "shocks" are proxied by a combination of negative labor supply and negative preference shocks. The preference (or consumer-spending) shock in the model is a type of demand 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. A negative labor supply shock captures an aggregate supply reduction due to supply-chain disruptions and large-scale social and economic restrictions (lockdowns). In particular, assume that the economy starts at period 0 (2019.Q4) at the steady state. Assume that the pandemic "shocks" occur for 4 periods or quarters, from periods 1-4 (2020.Q1-2020.Q4) with the following magnitudes: Period (Quarter) 1 (2020.Q1) 2 (2020.Q2) 3 (2020.Q3) 4 (2020.Q4) Labor supply (s;t) 5% 7% 3% 2% Preference ("g;t) 3% 3% 2% 3% 5 There are positive labor supply and preference shocks in period 4, perhaps in response to the expectations that an e ective COVID-19 vaccine is imminent and about to be approved and rolled out to the public. (a) Analyze the e ect of these pandemic shocks under the current policy rule with i = 0:75,  = 1:9, y = 0:08, y = 0:67, and e = 0. Plot the responses of ybt, bct, bit, bt, ebct in one (3x2) gure. Explain their dynamics. In another (2x1) gure, plot the evolution of exogenous labor supply variable ^"s;t and consumer preference variable bgt. Is this combination of shocks a realistic representation of the COVID-19 pandemic shocks? Why? (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 = 0:65 > 0 The rest of policy rule coecients are unchanged. Analyze the e ect of the pandemic shocks under this new assumption, in comparison to the e ect in part (a). Plot the responses of byt, bct, bit, bt, ebct in one (3x2) gure. Is this policy more e ective in terms of mitigating the e ect of the pandemic shocks on byt, bt , and bect ? 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: bect = 0 This policy rule e ectively (and credibly) xes the nominal exchange rate at a speci- ed level. Redo questions 2(a). Your answer and analysis should be in comparison to the oating exchange-rate regime (both when e = 0 and e = 0:65). [Notes: (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 = bit under the xed-exchange rate regime, unless  = 0)]. [Extra points: plot the variables under the three policies in one gure, e.g. the plot for ybt 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.

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