2 Model

The model is composed of 4 main blocks, namely potential output, inflation, unemployment and capacity utilisation. In the equations that follow, a bar over a variable denotes the equilibrium value of the variable and ε represents the error term for each transition equation. In this paper, the model is called SMM (small macro model).

2.1  The model

2.1.1   Potential output

      (1)

      (2)

where Υ_t=100*log(gdp), is potential output, γ_t is the output gap and θ is the labour share of income.

In the long run, the growth rate of potential GDP is mainly determined by the medium-term growth of potential . Changes in the NAIRU may cause the short- and medium-term growth of potential output to differ from and θ is the labour share of a Cobb-Douglas production function (see Appendix 1 for the derivation).

      (3)

Equation (3) states that is a function of its past value and the steady-state growth rate . The model incorporates a fairly flexible stochastic process - allowing for permanent changes in the underlying estimates of the equilibrium values for potential output and temporary changes in the medium-term growth rate of potential output .

As monetary conditions are not modelled in the model, the deviation of the lagged core inflation rate (π_τ) from its expectations is used as a proxy of the movement of the short-term real interest rate. Therefore, the output gap equation is specified as follows:

      (4)

In order to capture richer dynamics of GDP growth in New Zealand, we add two lags of the output gap in the above equation instead of one lag in the original model.

Inflation expectations are modelled as follows:

      (5)

where inflation expectations are determined by their lag and the steady-state rate of inflation π_ss.

We augment the inflation expectations equation from the original model by adding the steady-state inflation π_ss variable. The rationale of adding π_ss is to reflect the current monetary policy framework of keeping the inflation rate between 1 and 3 percent over the medium run and the fact that inflation expectations were relatively well anchored over the observation period.

2.1.2  Inflation

      (6)

As shown in the above equation, the core inflation rate, π_τ, is not only driven by the level of the output gap as specified in the New Zealand Treasury model (see Ryan and Szeto 2009) but also by the change in the gap. The reason for including the change in the gap in the inflation equation is to capture rigidities in the adjustment of the economy. The equation also includes the lagged inflation rate and inflation expectations.

2.1.3  Unemployment

The unemployment gap (u_t) is defined as the difference between the equilibrium unemployment rate or NAIRU, and the actual unemployment rate (U_t). The dynamics of the labour market are mainly determined by the Okun's law. As shown in the following equation, the unemployment gap is a function of the output gap and the lag of the unemployment gap:

      (7)

The equilibrium unemployment rate depends on the steady state of the unemployment rate (U^ss) as well as the level of output gap, which captures a partial hysteresis effect from economy-wide demand fluctuations:

      (8)

The inclusion of a persistent shock in the above equation allows for a persistent deviation of the NAIRU from the steady-state level of unemployment. The persistent shocks to the NAIRU follow a damped autoregressive process.

2.1.4  Capacity utilisation

As in the preceding equation, the equilibrium capacity utilisation includes transitory shocks as well as more persistent shocks. Similarly, the persistent shock also follows a damped autoregressive process and the capacity utilisation gap is a function of the output gap and its own lag:

      (9)

      (10)

2.2  Steady-state assumptions

There are four key steady-state assumptions in the model. The values of these variables are shown as follows:

Table 2 - Steady-state assumptions

Labour share θ	55%
Steady-state growth rate	2.5%
Steady-state unemployment rate Uss	5.0%
Steady-state inflation πss	2.0%

In New Zealand, the labour share fell from 60% in 1988 to a low of 53% in 2002. According to the latest data, the labour share rose to 58% in the March 2012 year.[1] As a result, the steady-state labour share is set at 55%, as the average of the low and the latest value of the labour share.

The steady-state growth rate is set at 2.5% per year, which implies labour input and labour productivity are assumed to contribute 1% and 1.5% to annual GDP growth in steady state respectively.

The steady-state unemployment rate was assumed to be 4.5% in the 2012 Budget Economic and Fiscal Update (BEFU 2012). Since BEFU 2012, the unemployment rate rose unexpectedly to 7.3% in the September quarter 2012. In the context of the recent weakness in the labour market, the steady-state unemployment rate is set at 5% in the baseline model.

Although annual inflation averaged around 2.7% over the past 10 years, the steady-state inflation rate is set at 2.0%, which is the target midpoint of the Policy Targets Agreement 2012.