RDP 2008-03: Monetary Transmission and the Yield Curve in a Small Open Economy 3. Estimation

For estimation purposes, the discount factor, β, is set at 0.99 which, at a quarterly frequency, corresponds to a steady-state real rate of interest of 4.1 per cent. The degree of openness, α, is set at 0.2, consistent with the value of the share of foreign goods in the Australian consumption basket.^[7]

The rest of the model's parameters are estimated with Bayesian techniques, as discussed in Lubik and Schorfheide (2006), An and Schorfheide (2007) and Griffoli (2007).^[8] We do so in two steps: in the first, we estimate the large economy's parameters; and in the second, we estimate the remaining small economy's parameters, taking the posterior mean values of the common parameters as given from the first step.^[9]

Since our focus is on the cross-correlations of domestic interest rates with their US counterparts, we take the US to be the large economy. We use quarterly HP-filtered data on real US GDP per capita, US consumer price inflation and a US 3-month nominal interest rate for the sample period 1993:Q1–2007:Q2.^[10] Table 1 summarises results for this first step of the estimation.

Since the large economy is exogenous to the small economy, we take the smoothed estimates for and from the first step of the estimation and use these as additional series in the estimation of the small economy's parameters. This differs from much of the relevant literature on small open economies which typically adopts an unrestricted reduced-form VAR process for foreign variables. Such a reduced-form process may or may not be consistent with the theory at hand. However, to the extent that an arbitrarily imposed reduced-form specification for the dynamics of foreign variables differs from that of the theory, the structural equations for the small economy will be invalid. As noted by Justiniano and Preston (2006), the structural equations of the domestic economy depend on the assumption that the large economy is populated with households and firms with identical preferences and technology. Therefore, the assumption of an arbitrary reduced-form process will not generally be consistent with the structural equations of the small economy.

We take the estimated posterior mean parameter values as given from the first step and estimate the remaining small open economy parameters on Australian data. For the small economy we use quarterly HP-filtered data on real GDP per capita, consumer price inflation and a 3-month nominal interest rate for the sample period 1993:Q1–2007:Q2.^[11] Table 2 below summarises results for this second step of the estimation.

Footnotes

In preliminary attempts to estimate the model, we found that α would invariably tend towards zero for a range of prior distributions. Nimark (2007) follows a similar strategy to calibrate these two parameters. [7]

We used the MATLAB package Dynare for the estimation of the model; the relevant files are available upon request. [8]

As noted before, because the small economy is open, the definitions of both potential output and CPI inflation are different from those of the large economy. Hence, the choice of prior distributions for the two economies need not be the same. [9]

Using the same priors, we have also estimated the model using linearly detrended output and demeaned inflation and interest rates. Although the posterior density changes, our key findings and main conclusions remain the same. In the interest of space, we do not report these results; they are available upon request. [10]

Appendix A contains a description of the data sources. We take the inflation-targeting period for the estimation of the small economy's parameters because the assumption of a symmetric steady state, which entails relatively similar rates of steady-state inflation, does not appear valid before then. [11]