On discretion versus commitment and the role of the direct exchange rate channel in a forward-looking open economy model

¹For a detailed exposition of the closed economy New Keynesian framework, see Clarida et al.'s Citation(1999) survey article.

²This list is by no means exhaustive. Early contributions that highlight the real exchange rate effects on aggregate supply are by Marston Citation(1985) and Turnovsky Citation(1983).

³While writing this paper, I became aware of the existence of an unpublished paper by Walsh Citation(1999). He examines the conduct of monetary policy in the open economy from a similar perspective after extending Calvo's Citation(1983) staggered price setting model to the open economy.

⁴Employing a backward-looking framework, Ball Citation(1999) motivates the direct real exchange rate effect on the rate of inflation by assuming that foreign producers care only about goods prices expressed in their home currency. McCallum & Nelson Citation(1999) and Froyen & Guender Citation(2000) assume that a foreign resource input enters as an intermediate input in production. Walsh Citation(1999) introduces a real exchange rate channel by assuming that real wage demands are based on the CPI.

⁵This is a simplified version of the IS relation for the open economy in McCallum & Nelson Citation(1999), Svensson Citation(2000) or Guender Citation(2003) that is derived from first principles. The IS relation presented in Guender Citation(2003) differs from the one above in that the expectation of the real exchange rate for period t + 1, the current foreign output gap as well as the expectation of the foreign output gap for period t + 1 enter. The simplified IS relation suffices for the purpose of the current paper as, for instance, it yields the same optimizing condition under discretion as the more elaborate IS specification. There is no LM relation as the policymaker uses the nominal interest rate as the policy instrument.

⁶This is evident once the UIP condition is solved for R _t and the resulting expression is inserted into the IS curve. For a similar view on why the loss function contains only real output and the domestic rate of inflation, see Clarida et al. Citation(2001). Adopting Equationequation (4) as the welfare criterion ignores the effects on welfare of changes in the real exchange rate in the open economy framework. Ignoring these potential effects is rather inconsequential in the current context as there is no imported intermediate input in production.

⁷Woodford Citation(1999a) derives an endogenous loss function based on the utility-maximizing framework. According to this analysis, the policymaker ought to be concerned with the variability of the output gap (and not the level of output) and the stability in the general price level.

⁸There is a third characteristic of discretionary policymaking that applies to the Barro-Gordon framework but not to the forward-looking framework: the target for the level of real output exceeds the potential level of real output. This feature gives rise to the inflationary bias in the model of Barro & Gordon Citation(1983).

⁹Here we adopt the convention of describing the conduct of discretionary policy along the lines of Clarida et al. Citation(1999).

¹⁰Future values of y _t and π _t are not affected by policy today as the effect of policy is contemporaneous and because of the absence of persistence in the endogenous variables.

¹¹This method simply states that a trial solution for the endogenous variables should include all stochastic disturbances. If the model features any predetermined variables or constants, then they should appear in the trial solution as well. For further details on how this method is applied, see McCallum Citation(1983) or McCallum & Nelson Citation(2004).

¹²Throughout the analysis, the coefficient on is identical to that on ϵ _t . For the sake of brevity, we report only the latter.

¹³Here we will abstract from the notion of conducting monetary policy from a timeless perspective as discussed by Woodford Citation(1999b) and McCallum & Nelson Citation(2004).

¹⁴To simplify things, we assume that the autoregressive parameter is the same for each disturbance. Imposing this condition has the advantage of allowing us to derive an analytical solution to the problem of determining optimal policy under commitment.

¹⁵Here we follow Clarida et al. Citation(1999). Also recall that θ y _t  = −π _t .

¹⁶The points made earlier about the properties of the optimality condition under discretion in an open as opposed to a closed economy also apply with minor modifications under commitment. For instance, if the exchange rate channel is absent from the Phillips Curve then the optimality condition is the same for both open and closed economies and is given by .

¹⁷This assumes that the disturbances are positively correlated.

¹⁸The bar over the expectation of inflation next period implies that the policymaker treats the expectation as given, i.e. as a constant.

¹⁹A separate appendix, which is available upon request, provides a detailed explanation of this result.

²⁰It should be borne in mind, however, that the autoregressive parameter φ has a far more important role to play in an open economy than in a closed economy. This is made evident by 1-φ being attached not only to the preference parameter of the policymaker but also to structural parameters such as b and a ₁ .

²¹Intuitively, a conservative central banker responds more vigorously to deviations of inflation from its target than society would if it conducted monetary policy.

²²To obtain this result, simply equate the optimizing conditions under discretion and commitment and solve for μ ^CB (which is the μ that appears in the optimizing condition under discretion). Alternatively, set the denominators of the coefficients of the rate of inflation (or output) on a given shock under both policy regimes equal to each other and solve for μ ^CB .

²³Numerical evaluations are typically based on loss functions that consist of unconditional variances. It can be shown that equals the weighted sum of the unconditional variances of the variables in question. On this point see Svensson Citation(2000).

²⁴Recall that under discretion the autoregressive parameter appears only in the denominator of the coefficients in the reduced form equation. But the denominators cancel in the process of calculating the ratio of the variances, thus accounting for the absence of a relationship between the variances of real output and inflation under discretion and the size of φ.

²⁵Here a slight anomaly ought to be pointed out. Closer inspection of column 7 in Table 4 reveals that for extremely high values of φ, such as 0.99, the variance of inflation is actually less than for smaller values of φ. This is clearly attributable to the particular parameter values chosen for the purpose of the comparisons. If the current parameter values are replaced with those chosen by Leitemo et al. Citation(2002), the variance of inflation under commitment increases throughout as φ increases. Nevertheless, the essential characteristic of Figure 2, the downward sloping curve, also materializes in this alternative scenario.

²⁶Precise calculations of the relative loss functions appear in Table 5A in the separate appendix.

²⁷Lower case letters denote the logarithms of variables.

²⁸Within a general equilibrium framework where labour is the only variable labour input, the co-movement between marginal cost and economic activity can be established by combining the labour supply and demand relations with the market clearing condition in the goods market. On this point see Clarida et al. Citation(2001). Gali & Monacelli Citation(1999) derive a similar relation that stresses the positive relation between real marginal cost and domestic consumption. The positive link between output and marginal cost is also characteristic of earlier models of monopolistic competition such as Blanchard & Kiyotaki Citation(1987).

²⁹In a general equilibrium setting, for the pricing decision of domestic firms to be sensitive to the prevailing price charged by foreign competitors, it is necessary to drop the assumption of constant elasticity of substitution in the utility function. Bergin & Feenstra Citation(2000) and Taylor Citation(2000) show how a translog specification for preferences or a linear demand relation yields an optimal pricing rule that responds to competitors' prices in addition to marginal cost. EquationEquation (A3) embodies this idea.

³⁰It can be shown that the Calvo Citation(1983) framework, where price adjustment occurs randomly, can be extended to an open economy too. The extension produces a Phillips curve for the open economy that also includes the real exchange rate.