I use Svennson's (1997) dynamic macroeconomic model to study the impact of cross-country differences in structure and preferences on the choice of inflation target. Following Svensson (1997), I assume that the objective of the political authority is to stabilize inflation around the long-run inflation target π∗ and the surrounding output gap. In this section, I use the results derived above to establish the relationship between economic structure, policy preferences, and the magnitude of the optimal interest rate response when inflation is low.
Concerns about the constraint posed by a zero interest rate have arisen when economies have reached low levels of inflation. To be successful, inflation targeting policies must be consistent with the long-run characteristics of the underlying economy. Equation (1) shows that inflation is more responsive to changes in the output gap, the larger α2 is.
For an inflation target to be sustainable in the long term, it must be consistent with the underlying economic structure. In the context of the model used here, such long-term consistency results in the appropriate inflation target being fully determined by the structural parameters α0 and α1.
4.Estimation of the Structural Equations
It is this empirical question that is central to the remainder of this article. For Italy, the quality of the estimation results steadily deteriorated as the sample was expanded after 1992. Moreover, for European countries, the financial turmoil surrounding the ratification of the Maastricht Treaty at the end of 1992 appears to have caused some temporary changes in structural relations.
The likelihood that the results obtained here may be sensitive to the construction of the output gap was assessed by applying the Wald test on the slope coefficient obtained by regressing the standardized gap of the linear trend on the standardized HP gap. Details of variable definitions, unit root tests, and estimation results are available in Appendix 3. For most of the countries in this study, the 1980s was a transitional period in which countries struggled with the effects of oil price increases.
Perron's (1989) Model A captures the impact of the oil price shocks in the form of a shift in the mean of the inflation and/or interest rate processes in France, Italy, Great Britain and the United States. For European countries such as France and Italy, German output, prices and interest rates, and the value of the domestic currency relative to the Dmark were in the initial variable set. There are undoubtedly many ways one might think of making an empirical assessment of the practical significance of the zero interest rate limit.
Ericsson and Irons (1995) illustrate a method for testing the empirical significance of the Lucas critique. The first step involves carefully modeling the individual processes that generate the variables included in the estimation equation. The results obtained by applying this test to each of the countries included in this study indicate that all parameters estimated from (1) and (2) are statistically invariant for Canada, France, the United Kingdom and the United States. .
Details of the estimated marginal processes and the invariance test results are provided in Appendix 3.
5.A Counter-Factual Empirical Assessment
One way to obtain an empirical assessment of the practical significance of the zero interest rate peg is through simulations.15 Another option is to conduct a counterfactual experiment in which we ask what would have happened in some past period if interest rates had were as low as they are now. In this section, I estimate the annual levels of interest rates that would have been optimal for six countries over the period 1976 to 1996 if the inflation rate had been stable at 2% over that period. I also provide an estimate of the maximum annual contractionary gap that could be eliminated through the use of interest rate policy alone.
It is clear that in addition to parameter estimates of all the structural coefficients, the calculation of the optimal interest rate involves the choice of specific values for the discount factor δ, the preference parameter λ, the inflatin target π∗ and the long-run equilibrium interest rate r∗.16 There the calculated optimal interest rate levels were found to be insensitive to variations in δ over the range 0.75 ≤ δ ≤ 099, so I followed common practice and set δ= 0.99. Stuart (1996) provides evidence that the average long-term real interest rate level in the industrialized countries is close to 3.5% for the period studied here. 15For simulations of the impact of low inflation rates on the effectiveness of US monetary policy, see, for example, Fuhrer and Madigan (1997), Orphanides and Wieland (1998), and Reifschneider, Williams, Sims, and Taylor (2000).
Whether the zero interest rate is likely to constrain expansionary monetary policy depends on the magnitude of business cycle contractions. To determine which countries are more likely than others to face conditions in which a zero interest rate is a binding constraint, I use (17) to obtain a measure of the output gap that would have accompanied a 0% interest. It is clear that there are three countries - Canada, France and Great Britain - for which the zero interest rate level may have represented a binding constraint on monetary policy during the sample period.
According to Table 4, France would have found its ability to implement expansionary interest rate policy limited for two-thirds of the sample period. For Canada, the calculated optimal interest rates are negative for the period 1993 to 1995.17 For the remaining three countries, the actual output gap (shown in the row labeled 'GDP gap') is well above the maximum output gap that monetary policy could handle without breaching the zero interest rate bound. The regression results indicate that the Canadian output gap was positively related to the real interest rate in 1981 and 1982.
Because of the positive relationship between the real interest rate, a decrease in the interest rate would have been required to stabilize output even though the output gap was positive.
6.Model and Parameter Variation
The size of the output gap that would have been associated with an interest rate of 0% can be derived directly from (36) by setting it to 0 and then solving for yt. The measures of the optimal interest rate and the maximum output gap consistent with (36) are shown in Table 5. A comparison of the estimated counterfactuals in Tables 4 and 5 indicates some sensitivity to model variations with respect to the size of the maximum output gap and the timing of negative optimal interest rates.
Orphanides and Wieland provide annual estimates of α2, β1 and β2 for the eurozone and the United States over the period 1976-1998. Averaging the parameter estimates in Tables 1 and 2 for France, Germany and Italy yields α2 = 0.38, β1 = 0.75 and β2 = 0.56, all of which are close to the values obtained by Orphanides and Wieland for the eurozone as a whole. In Table 5, I have recalculated the optimal interest rate and maximum output gap values for the United States using the Orphanides and Wieland estimates.19 The results are shown in Table 6.
There are several obvious differences between the US counterfactuals given in Tables 5 and 6. First, the estimated maximum output gap is significantly smaller when using the Orphanides and Wieland parameter estimates. Second, according to Table 6, the optimal U.S. interest rate would be negative in 1982 and 1983 if the 2% inflation target was achieved in those two years.
Finally, the variability of the optimal interest rate is somewhat higher in Table 6 than in Table 5. Considering the magnitude of the variation in α2 and β2 estimates used in this sensitivity analysis, the qualitative results are remarkably robust. It seems fairly safe to say that from a 2% inflation target it would not have resulted in US monetary policy being constrained by the zero interest rate limit.
It is for this reason that I use the values given for the US in Table 5 rather than those given in Table 4 to assess the impact of parameter variation on the estimated US counterfactuals.
7.Conclusion
Using (6) to substitute V(πt+2|t+1) into (5) and taking the derivative of the expression in parentheses with respect to πt+1|t gives A.3) Differentiation of the assumed solution for V(πt+1|t), given by (6), with respect to πt+1|t yields.
The variables ∆Yus and ∆eus respectively indicate the change in the natural logarithm of US real GDP and the change in the natural log of the average Germany/US nominal exchange rate (IFS line rf). The invariance tests performed using the procedure described in Section 4.2 of the main text are summarized in Tables A2.1 and A2.2. Variables used as regressors for more than one country are specified in the section relating to their country of origin if used for domestic estimation or, if used only for foreign countries, in the section relating to the first country for which the variable is used .
The calculated values of the test statistic and the distributions of the statistic under the null hypothesis are reported. An asterisk added to the test statistic in Table A2.2 indicates that the null hypothesis that the estimated parameter value is invariant at the 5% significance level has been rejected. In particular, Platforms Model A was used to allow for a shift in the unit root process or time trend.
Perron has shown that the critical values of the test statistic depend on the time period in which the structural break occurs. The year of the break and the shareλof the total number of observations that occurred before the break are given in the third column of Table B2.3. The absence of an entry in this column indicates that no apparent break in the data occurred during the sampling period.
The test statistics obtained on the basis of the Augmented Dickey-Fuller test and Perron's test procedure are given in the last column of the table under the heading ADF/ADFP. It is clear from the reported results that all the variables used to estimate (1) and (2) are I(0) at a significance level of at least 10%. In Table A2.3, the significance of the test statistic at the 1% and 5% level is indicated by ** and *, respectively.
The presence of a deterministic time trend was rejected at the 5% level of significance for all variables.
