RDP 2000-07: The Effect of Uncertainty on Monetary Policy: How Good are the Brakes? 4. Model and Methodology
October 2000
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To investigate the impact of the various forms of uncertainty described in Section 3, we use as our benchmark the path of interest rates that results from the optimisation of a small macroeconomic model of the Australian economy.^{[8]} The model is a slightly simpler version of the model described in Beechey et al (2000), although the impact of interest rate changes on output and inflation are comparable with that paper and the estimates in Table 2.
The objective function for monetary policy is the standard weighted average of squared deviations of inflation from target, and output from potential.^{[9]} The transmission of monetary policy occurs through two channels: directly through the impact of short-term interest rates on output,^{[10]} and indirectly through the impact of exchange rate changes on imported goods prices.
In the model, short-term interest rates affect output with a two-quarter lag. In more fully specified models of Australian GDP, the lag tends to be between two and six quarters (Gruen, Romalis and Chandra 1999). The output gap, in turn, affects inflation directly one quarter later, and indirectly through its impact on unit labour costs in a wage Phillips curve. The effect of the output gap on unit labour costs is larger than that directly on inflation, so that the effect of the output gap on unit labour costs is the main channel through which monetary policy can have a permanent effect on the inflation rate.
The exchange rate responds to a change in interest rates with a lag of one quarter. This then causes a contemporaneous movement in imported goods prices that feeds into inflation a further quarter later. Imported goods account for around 40 per cent of the consumer price basket. A 10 per cent depreciation of the exchange rate leads to about a one percentage point increase in the year-ended inflation rate after one year.
To introduce multiplicative and additive uncertainty into the model, we need distributions for the parameters in the model and the shocks to each equation, respectively. The parameter distributions were formed from the parameter variance-covariance matrix for each equation.^{[11]} The distribution of the shocks for each equation were derived from the residuals obtained from estimating each equation over the sample period 1985–1998, allowing for covariance in the residuals across equations.
The optimal policy response could, in theory, be calculated at this stage. However, as this was not analytically tractable, we derived numerical solutions. To examine the effect of parameter uncertainty, a set of 50 parameter draws was taken from a normal distribution for each of the parameters of interest.^{[12]} Then the economy was subjected to an additive shock in each equation, every period for a total of 50 periods. Using the approach outlined in Shuetrim and Thompson (1999), the optimal stance of policy was calculated every period under the assumption that there were no future shocks.^{[13]} This procedure was then repeated for another 49 sets of additive shocks, thereby generating 50 simulated paths for the policy interest rate, each 50 periods long.
To summarise the smoothness of policy interest rates, we are interested in the average absolute change in short-term interest rates in each path. The variability of interest rates is measured by the standard deviation of the absolute change in the short-term policy interest rate. The distribution of this statistic is not symmetric, hence we report the median absolute change in the interest rates, in addition to the average absolute change.
Footnotes
A full description of the model is provided in Appendix A. [8]
In adopting this as the objective function, we are assuming that the paths of policy interest rates described in Section 2 were set by policy-makers with such an objective function in mind. [9]
Empirical work has generally been unable to uncover any significant link between long-term interest rates and activity in Australia. Hence, the rationale for smoothing discussed by Goodfriend (1991) and Woodford (1999) is not captured in this model. [10]
We did not allow for covariance across equations in the parameter distributions, so the system variance-covariance matrix of the parameters is block-diagonal. [11]
We do not allow for learning by the policy-maker about the parameters of the model. [12]
The zero-bound on nominal interest rates was not enforced during the simulations. Orphanides and Wieland (1998) investigate the implications of such a constraint. [13]