Quantitative Group Project
ECON6008 International Money & Finance, Semester 2 2024
Due date: Friday 8 November, 11:59pm
1 The model (equations and variables)
1.1 The model in brief
The model that you need to analyse is a modified 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 modified 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 differently than in the paper (see below for further details), although we still assume that the foreign economy is essentially a closed economy. The model is also extended to include a labor-supply shock, which could be used as a proxy for the supply-side disruption of the COVID-19 pandemic. There is also a cost-push shock that enters the domestic-price Phillips curve.
Aggregate fluctuations in the model are driven by 8 exogenous shocks. Five of these shocks are domestic shocks: preference (consumer spending), risk premium, monetary pol-icy (interest rate), cost-push, and labor supply shocks. Three of the shocks are foreign or external shocks: foreign output, foreign infiation, and foreign interest rate shocks. These shocks affect the domestic economy through their ináuence on the foreign economy's out-put, infiation, and nominal interest rate. The model can be derived from the ground up with micro-foundations, based on optimizing households, domestic firms 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 inflation (based on the law of one price):
Monetary-policy (Taylor) rule:
Evolution of risk premium:
Evolution of preference shock:
Evolution of labor-supply shock:
Evolution of cost-push shock:
The unsystematic monetary policy (interest rate) shock ^"m;t is assumed to be i.i.d. (with zero mean and a constant variance). η φ;t , η z;t , η s;t, and η H;t are i.i.d. risk-premium shock, preference shock, labor-supply 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 specification, 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 ηy* ;t , ηπ* ;t, and ηi* ;t are i.i.d. foreign-output shock, foreign-ináation shock, and foreign interest-rate shock, respectively.
In the alternative specification, letís assume that the foreign economy is represented by a standard closed-economy New Keynesian model (in its log-linearized form):
Under this specfication, pi* now denotes the degree of interest-rate smoothing in the foreign economyís monetary policy (Taylor) rule. Also, εy* ;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 specification, ηy* ;t , ηπ* ;t, and ηi* ;t are i.i.d. shocks.