辅导 ECON6008 International Money & Finance Semester 2讲解留学生SQL 程序

Quantitative Group Project ECON6008 International Money & Finance Semester 2 (Int. August-September) 2025

Due date: Sunday 19 October, 11:59pm

1 The model (equations and variables) 1.1 The model in brief The model that you need to analyse is a modiÖed version of the New-Keynesian small open-economy (SOE) model in Justiniano and Preston (2010, henceforth JP), which in turn is based on the model in Monacelli (2005) and Gali and Monacelli (2005). Compared to the JP model, our modiÖed 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 foreign economy is also modeled di§erently than in the paper (see below for further details), although we still assume that the foreign economy is essentially a closed economy. There is also a cost-push shock that enters the domestic-price Phillips curve. Aggregate áuctuations in the model are driven by 7 exogenous shocks. Four of these shocks are domestic shocks: preference (consumer spending), risk premium, monetary policy (interest rate), and cost-push shocks. Three of the shocks are foreign or external shocks: foreign output, foreign ináation, and foreign interest rate shocks. These shocks a§ect the domestic economy through their ináuence on the foreign economyís output, ináation, and nominal interest rate. The model can be derived from the ground up with micro-foundations, based on optimizing households, domestic Örms and importers, etc., resulting in a set of non-linear equations. We will instead work directly with the log linearized equilibrium equations, listed below. 1.2 The log-linearized equations Consumption Euler-equation (the IS equation):

Goods-market clearing condition:

The link between terms of trade and real exchange rate:

Changes (growth rate) of the terms of trade:

Domestic-price ináation (the "Phillips curve"):

The real marginal cost:

The wedge between CPI- and PPI-ináation:

The uncovered interest-parity (UIP) condition:

The net-foreign-assets position (the current account):

Imported-good ináation (based on the law of one price):

Monetary-policy (Taylor) rule:

Evolution of risk premium:

Evolution of preference shock:

Evolution of cost-push shock:

The monetary policy (interest rate) shock ^"m;t is assumed to be i.i.d. (with zero mean and a constant variance). ;t, z;t, and H;t are i.i.d. risk-premium shock, preference shock, and cost-push shock, respectively.

The foreign economy We will treat the foreign economy as essentially a closed economy, i.e. we can think of it as the "rest of the world" and as a large economy, much larger in size compared to the domestic economy. In the benchmark speciÖcation, letís assume an exogenous foreign economy, in a sense that each of foreign output, foreign ináation, and foreign nominal interest rate is assumed to follow an AR(1) process:

where y ;t, ;t, and i ;t are i.i.d. foreign-output shock, foreign-ináation shock, and foreign interest-rate shock, respectively. In the alternative speciÖcation, letís assume that the foreign economy is represented by a standard closed-economy New Keynesian model (in its log-linearized form):

Under this specÖcation, i now denotes the degree of interest-rate smoothing in the foreign economyís monetary policy (Taylor) rule. Also, "y ;t, " ;t, and "i ;t can be interpreted as a foreign preference (consumer spending) shock, foreign cost-push shock, and foreign monetary policy shock, respectively, assumed to follow

Here, as in the benchmark speciÖcation, y ;t, ;t, and i ;t are i.i.d. shocks.

DeÖnition of variables and shocks NOTE: all hatted variables are in terms of log or percentage deviation from the steady-state value, except for b it , b t , b H;t , b F;t , b t , and b i t , which are in terms of level deviation from the steady state (e.g. bit it

The Questions ___ 1. Solve the model described above using Dynare, assuming the benchmark foreign economy speciÖcation (equations (16.A)-(18.A)). Obtain the impulse response for 12 peri ods to a one-time positive 1% shock to (a) money supply or the domestic interest-rate shock ("m;t); (b) preference shock ( z;t); (c) risk premium shock ( ;t); (d) foreign interest rate shock ( i ;t). Analyse (i.e. explain the dynamics) and plot the e§ect of each of these shocks to domestic output (yb t ), consumption (bct), interest rate ( b it), ináation (b t ), domestic-currency nominal depreciation (eb c t ), the "shocked" variable (e.g. if itís a foreign interest rate shock, plot b t ), the level of the nominal exchange rate, and the current account. Plot these eight variables in one 4x2 Ögure (with 4 rows and 2 columns). Relate your analysis to what you have learned in the Örst half of the course on the qualitative AA-DD model (e.g. how are they the same and/or di§erent). For the money supply or the domestic interest-rate shock, do you observe an overshooting of the nominal exchange rate? Explain your answer. 2. Now assume that the foreign economy is represented by a closed-economy New Keynesian model, i.e. equations (16.B)-(18.B) and (19)-(21). Redo question 1(d), i.e. a one-time 1% foreign-interest rate shock. Relate and compare your responses to both that under the qualitative AA-DD model and the responses under 1(c) (where the foreign interest rate follows an AR(1) process). How and why are they di§erent (or the same)? 3. GFC-like shocks and exchange rate policies Letís analyse the impact of a GFC-like shock in the foreign economy on the domestic economy. For simplicity, assume that the foreign economy follows the benchmark speciÖ- cation in (16.A)-(18.A). First, letís assume that there is a GFC-like event in the foreign economy at time t = 0 that decreases the level of foreign output by 5%, i.e. assuming an AR(1) process for foreign output, we have a negative 5% foreign output shock y ;t at t = 0. After this period, there is no more shock and yb t simply follows an AR(1) process in (16.A). E§ectively, under this assumption, we assume that the exposure of the GFC-like event in the foreign economy to the domestic economy is through its e§ect on the cur rent account (since yb t in the model directly ináuences the foreign economyís demand for domestic products, i.e. domestic economyís exports).

(a) Analyze the e§ect of this GFC-like shock under the current policy rule with i = 0:75, = 1:90, y = 0:05, y = 0:55, and e = 0. Plot the responses of yb t , bct , b it , b t , b e c t , b yt , the level of nominal exchange, and the current account in one (4x2) Ögure for the Örst 12 periods. Explain their dynamics and relate your analysis to that under the qualitative AA-DD model. Now assume that in addition to the exposure to the domestic economy through the current account, there is an added exposure through domestic householdsíholding of foreign assets. In our model, this can be represented by a further negative consumer-spending shock (just like the how we incorporate the spillover e§ect of the GFC in the AA-DD model in class). Letís assume that this added exposure is equivalent to a negative 3% consumer preference shock ( z;t) at t = 0; after this period, there is no more shock and the preference level (^"z;t) simply follows an AR(1) process in equation (13). Hence, at t = 0, we have two shocks: a negative 5% foreign output shock ( y ;t) and a negative 3% consumer preference or spending shock ( z;t). (b) Redo part (a) above under this two-shock assumption. How and why they are di§er ent (or the same) compared to part (a)? (c) In part (a) and (b) above, we assume a fully-áexible (áoating) exchange rate regime. Suppose that the domestic central bank also directly intervenes in the foreign ex change market, i.e. itís operating under a managed áoating exchange rate regime. This policy can be analyzed within our model by assuming that e = 0:80 > 0 The rest of policy rule coe¢ cients are unchanged. Redo part (b) above, where we assume that the spillover from the GFC-like event in the foreign economy is repre sented by two combined shocks (negative y ;t and z;t shocks). Analyze the e§ect in comparison to the e§ect in part (b) (under the fully-áexible, áoating exchange rate regime). Plot the same (4x2) Ögure as in part (b). Is this policy more e§ective in terms of mitigating the e§ect of the spillover of the GFC-like shocks on yb t , b t , and eb c t than the fully-áoating exchange rate policy? Explain. (d) Now assume that the central bank is operating under a Öxed exchange-rate regime. SpeciÖcally, the monetary policy rule in equation (11) is replaced with the following policy rule: eb c t = 0 This policy rule e§ectively (and credibly) Öxes the nominal exchange rate at a spec iÖed level. Redo question 3(b) (GFC event with two shocks). Your answer and analysis should be in comparison to the freely-áoating exchange-rate regime ( e = 0 under the original policy rule) and managed-áoating regime ( e = 0:85 under 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 Önd bit = bi t under the Öxed-exchange rate regime, unless = 0), (iii) to solve the model under the Öxed regime in 2(d), you should remove monetary-policy shock "m;t from the list of shocks in your .mod Öle, as this shock now does not enter any of the equations.] [Extra points: plot the variables under the three policies in the two-shock case (parts (b), (c), (d)) in one (4x2) Ögure as described above, e.g. the plot for yb t in the (4x2) Ögure should include three di§erent impulse responses.]

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.

辅导 ECON6008 International Money & Finance Semester 2讲解 留学生SQL 程序

辅导 ECON6008 International Money & Finance Semester 2讲解留学生SQL 程序