2.1 The Open Economy NCM Model
We employ the following six-equation model for the open economy NCM model.
1 The symbols have the following meaning:
a0, d0, and
e0 are constants;
Yg is the domestic output gap (the difference between actual and trend output; the latter is the output that prevails when prices are perfectly flexible, and as such it is a long-run variable, determined by the supply-side of the economy);
is world output gap,
R is nominal rate of interest,
Rw the world nominal interest rate, p is the rate of domestic inflation,
pw the world inflation rate, and
pT is the target inflation rate to be achieved by the independent Central Bank.
RR* is the âequilibriumâ real rate of interest, that is the rate of interest consistent with zero output gap, which implies from Eq. (
2) a constant rate of inflation; (
rer) stands for the real exchange rate, and (
er) for the nominal exchange rate, defined as in Eq. (
6) and expressed as foreign currency units per domestic currency unit.
CA is the current account of the balance of payments,
si (with
i = 1, 2, 3, 4, 5) represents stochastic shocks, and
Et refers to expectations held at time
t.
Pw and
P (both in logarithms) are world and domestic price levels, respectively. The change in the nominal exchange rate can be derived from Eq. (
6) as in
.
Equation (1) is the aggregate demand equation with the current output gap determined by past and expected future output gap, the real rate of interest and the real exchange rate (through effects on the demand for exports and imports). Equation (1) emanates from intertemporal optimisation of expected lifetime utility of the representative agent who never defaults on debts, and under the assumption of short-run wage and price rigidities or frictions of the Calvo (1983) type. This optimisation reflects optimal consumption smoothing subject to a budget constraint, and based on the transversality condition that all debts are ultimately paid in full. The latter condition means that all economic agents with their rational expectations are perfectly credit worthy, and agents would never default. There is, thus, no need for a specific monetary asset. Under such circumstances, no individual economic agent or firm is liquidity constrained, which implies that there is no need for financial intermediaries (commercial/investment banks or other non-bank financial intermediaries) and money (see also, Goodhart 2004, 2007, 2009).
The non-appearance of money in the model is justified on the assumption that the Central Bank allows the money stock to be a residual to achieve the desired real rate of interest (Woodford 2008). Thereby money plays no role other than being a unit of account (GalĂ and Gertler 2007). Furthermore, there is the question of the role for investment, introduced in terms of the expansion of the capital stock that is required to underpin the growth of income. There is then by assumption, no independent investment function that arises from firmsâ decisions (Woodford 2003, Chapter 4).
Equation (2) is a Phillips curve, derived from the intertemporal-optimising representative firm in a model of staggered price setting as, for example, in Calvo (1983). Inflation in Eq. (2) is based on the current output gap, past and future inflation, expected changes in the nominal exchange rate, and expected world prices; the latter accounts for imported inflation. The model allows for sticky prices in the short run, the lagged price level in this relationship, and full price flexibility in the long run. It is assumed that b2 + b3 + b4 = 1, thereby implying a vertical Phillips curve in the long run at the point of the Non-Accelerating Inflation Rate of Unemployment (NAIRU). The term Et(pt+1) captures the forward-looking aspect of inflation determination. It implies that the Central Bankâs success to achieve its inflation target not only does it depend on its current policy stance but also on what economic agents perceive that stance to be in the future. The assumption of rational expectations is important in this respect. Agents are in a position to know the consequences of current policy actions on the future inflation rate. Consequently, the term Et(pt+1) is viewed to reflect Central Bank credibility. If the Central Bank can achieve its inflation target, then expectations of inflation are contained. Expected changes in import prices and in the nominal exchange rate are another two important determinants of inflation as shown in Eq. (2).
Equation (3) is a monetary policy rule of the Taylor (1993, 1999, 2001) type. It is derived from the optimisation of the monetary authoritiesâ loss function subject to the model utilised. The nominal interest rate, thereby derived, is related to the equilibrium rate of interest (RR*), defined as the âequilibrium real rate of return when prices are fully flexibleâ (Woodford 2003, p. 248), expected inflation, output gap, deviation of inflation from target, and with the lagged interest rate representing the monetary authoritiesâ interest rate âsmoothingâ. The exchange rate is assumed to play no role in the setting of interest rates (except in s...