## OPEN-ECONOMY MARKET: Price Adjustment 2

McCallum and Nelson (1998) show that rearrangement of equation (5.7) establishes that the aggregate price behavior implied by problem (5.5) is the same as that associated with the “P-baf ’ model of price adjustment (e.g., McCallum [1994]). They additionally show that solving the Euler equation (5.7) produces the following decision rule for pt:

While this analysis pertains to the individual household’s pricing decision, in a symmetric equilibrium equation (5.9) will also apply to the economy-wide aggregate output gap. Therefore, from now on we use the notation у h у h exh and pt to refer to the aggregates of the corresponding individual-household variables. It should be mentioned that equation (5.9) permits a “one-line proof’ that the strict version of the natural rate hypothesis, due to Lucas (1972), is valid in the P-bar model: simply apply the unconditional expectations operator to both sides of (5.9) and note the resulting implication that E[y t] = 0, regardless of the monetary policy in place. This is important because most models with gradual price adjustment (i.e., sticky prices) do not satisfy the strict natural rate hypothesis.

Calculation of Y-bar

where со = 5i / {(1 – vj) (1 – 5i)}. Equation (5.15) indicates that the flexible price level of log output, у h is a function of both the technology shock and the real exchange rate. This relation displays the route by which exchange rate changes affect the price of domestic goods. Since the P-bar model implies that pt is set in response to EM ph changes in s, that affect qt lead to rapid changes in pt. Electronic Payday Loans Online

Log-Linearization and Solution of the Model

Let lower case letters denote logarithms of the corresponding upper-case variables. Loglinearizing (4.7), we then have (neglecting constants)