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3.2  The steady-state solution

Like the fit of a regression model, the steady-state solution gives us an indication of how well the data fits the model. In practice, the steady-state solution should not be too far away from the actual data; otherwise convergence problems may arise when using the dynamic version of the model for forecasting. The difference between the actual values and the steady-state values can be interpreted as measures of disequilibrium. In this section, we focus on explaining the steady state solution of two key endogenous variables, namely output and the real exchange rate.

3.2.1  Potential Output

In recent years, many central banks have favoured a demand-pull framework for modelling inflation. Usually, some measure of the output gap is used to measure future inflationary pressures. The output gap is the difference between actual output and potential output. The production block of the model provides a measure of potential output of the private business sector.

Although private sector production (PNA10) accounts for about 68% of total production, almost all the variability in total production can be attributed to PNA10. Figure 12 shows the output gaps for total GDP (NA10) and private sector production (PNA10). Both measures of potential output are estimated using the HP filter with λ=1600.

The other components of total GDP (NA10) besides PNA10 are housing consumption (CONH), government employment (C5000*NGG) and consumption tax (C5001*CONO). The following identity defines NA10 as:


where PNA10 =YD+TEXPS-IM.

In NZTM, the output gap measure is based on the private business sector production rather than total production. The main reason for using the private business sector production is that the output gap is used to determine the inflation rate of the domestic good but not the general inflation rate in the dynamic model. Therefore, it is more appropriate to use the private sector output gap.

Figure 13 compares the output gap derived from the model with the output gap estimated from the HP filter. The steady-state solution is very similar to the potential output estimated from the HP filter over the estimation period. The main advantage of using the production function approach is that one can analyse the impact of changes in the economic structure on potential output.

3.2.2  Real Exchange Rate

Like potential output, the level of the long-run equilibrium real exchange rate is unobservable and various techniques have been developed to estimate it. In this model, the steady-state solution of the real exchange rate is the level at which both internal and external balance is simultaneously attained. External equilibrium is attained when the current account balances are compatible with the underlying capital inflows. Internal equilibrium means that the market for the domestic good and the factors of production are in equilibrium. The resultant estimates of the real exchange rate from the steady-state model are, therefore, consistent with the definition of the long-run equilibrium exchange rate developed by Williamson (1985).

The real exchange rate is defined as the relative price of importables to non-tradables (RPM) or exportables to non-tradables (RPTEX). An appreciation of the real exchange rate is represented by a decrease of RPM or RPTEX. Figure 14 charts the inverse of the steady-state solution of RPM with that of the actual RPM. The extent of real exchange rate misalignment is plotted in Figure 15, which plots the difference between the actual real exchange rate and its long-run equilibrium. The results suggest that the real exchange rate overshot its long-run equilibrium level over the period 1996 to 2000.

Although the nominal exchange rate has dropped sharply since 1997, the real exchange rate remained overvalued for a long period of time after the initial fall in the nominal exchange rate started in 1997. Our results suggest that the fall in the nominal exchange rate has been offset by a sharp fall in the world prices during the Asian crisis. As a result, the real exchange rate remained overvalued substantially at the beginning of 1999.

By the beginning of 2001, the real exchange rate had fallen to the point where the model estimates that it was undervalued by about 6%. Assuming all else being equal, the equilibrium nominal value for the NZD at that time was around 53 on a Trade Weighted Index (TWI) basis.

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