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5  Dynamic structure

The dynamic structure of the model evolves or fluctuates around the steady state structure and attempts to replicate the actual cycles in macroeconomic data. While the steady-state version of the model is particularly important in determining the steady-state values for the key endogenous variables, the dynamic model also has an important role in shaping the path of the economy following a shock as it adjusts over the medium term to the long run equilibrium steady-state path. The specification of the dynamic model is therefore critical in determining short- to medium- term economic forecasts. Dynamic equations are specified to capture both short to medium-term data movements and partial adjustment to equilibrium steady-state values.

While parts of the model have been estimated, for example the production block, the dynamic component of the model has been calibrated[7]. A noted example of a calibrated New Zealand macroeconomic model is the FPS model developed by the Reserve Bank of New Zealand (See Black et al, 1997). The results from previous estimation work to develop the earlier NZM model (Murphy, 1998) have been used to inform the calibration of this new model.

The dynamic structure of the model has been kept as parsimonious as possible while still replicating the dynamic properties of the data. One of the motivations for this parsimonious specification is the ability to trace back and understand what is driving a model forecast. Applying over-specified dynamic models to actual data, which in New Zealand’s case is normally quite volatile, can lead to model forecasts that are difficult to understand.

This section will focus on the components of GDP and discuss the inflation process and the monetary and fiscal rules. The equations comprising the dynamic model are listed in Appendix 5.

5.1  Private consumption

Many models of consumption are based on individual optimisation of utility, where an individual makes consumption decisions over some period, based upon their earnings and wealth, and preferences for present and future consumption. The long-run structure of the private consumption sector has been detailed in the previous section. The dynamic specification of private consumption is intended to capture the idea that private consumption is modelled in a partial adjustment process.

The dynamic consumption equation is shown by equation (16). It specifies current consumption (CON) as a function of the equilibrium level of consumption (COND), the yield curve (YCURVE) and the relative price of imports (RPM). The equilibrium level of consumption is determined by labour income and wealth. The yield curve reflects the fact that households will decrease (increase) consumption when interest rates rise (fall) and the return on savings increases (decreases).

As mentioned before, all imports are intermediate goods in the production function. The last two terms in the equation capture the impact of import prices on consumption goods. If the relative price of imports (RPM) is above its long-run equilibrium (ERPM), real consumption is reduced.

(16)      LOG(CON) = C0401*LOG(COND) + (1-C0401)*LOG(CON(-1)*GR) +C0402*(YCURVE(-2)) +C0403*(RPM(-1)-ERPM(-1))+C404*(RPM(-2)-ERPM(-2))+Z_CON

GR-1 is the sustainable growth rate of real output. We assume that the rate of potential growth of the economy (GR-1) is 2.75% per annum. This growth rate is composed of population growth of 1.25% per annum, labour productivity growth of 1.5% per annum and other technological change parameters of the production block.

If our view changes around any of these determinants of growth then the assumptions can be changed to reflect that revised view. Section 6.5 for example examines the consequences of changing our view on the labour productivity growth assumption on the properties of the model.

5.2  Residential Investment

A Tobin-q style (Tobin, 1969) model of housing investment is used in which the rate of investment is above or below a benchmark rate, according to whether the actual rate of return on housing investment is above or below a required rate of return. This requires measures of the benchmark rate of housing investment and of the actual and required rates of return on housing investment.

In the long run, the stock of housing will increase in line with the natural rate of growth of the economy, GR-1. Thus the benchmark rate of housing investment (IH) needs to cover both natural growth in the stock of housing and depreciation which is set at 1% per quarter, as shown by equation (17).

(17)     IH = (GR - 1 + DRRB_EQ)*KH

The required rate of return on housing (RRH) is defined by equation (18). It includes depreciation, the equilibrium real interest rate, RI_EQ, and a risk premium, RP, where each of these is expressed as a proportionate rate per quarter.

(18)    RRH=DRRB_EQ + RI_EQ + RP

The rate of housing investment adjusts partially to the benchmark rate, and is influenced by the Tobin q-effect (the difference between the actual and required rates of return) lagged one quarter. The slope of the yield curve, YCURVE, also appears as a second interest rate effect on housing investment. The adjustment process is captured by equation (19).

(19)     IH/KH=C0501*(IH(-1)/KH(-1))+(1-C0501)*(GR(-4)+DRRB_EQ-1)+C0502*(KSRATIO*(RPCONH(-1)-POL7_EQ(-1))-(DRRB_EQ+RI_EQ+RP)) +C0503*YCURVE(-2) + C0504*YCURVE(-3) +Z_IH,

The housing stock is calculated through a perpetual inventories approach where housing investment, net of depreciation, adds to the housing stock, which is carried over to the next quarter. These are captured by equations (20) and (21).

(20)    KH1 = (1 – DRRB_EQ).KH + IH

(21)    KH = KH1(-1)

5.3  Business investment

A Tobin-q style model is used for private business investment, the same approach that was used for housing investment. Thus the rate of investment is above or below a benchmark rate, according to whether the actual rate of return on business investment is above or below a required rate of return. This approach incorporates the main factors commonly believed to influence business investment. In this approach, higher real wages reduce business investment by reducing the actual rate of return, while higher real interest rates reduce business investment by increasing the required rate of return.

In the long run, the stock of business capital (KBF) will increase in line with the natural rate of growth of the economy, GR-1. Thus the benchmark rate of business investment (IBF) needs to cover both natural growth in the stock of business capital and depreciation (DR_EQ), as shown by equation (22).

(22)    IBF = (GR - 1 + (DR_EQ)).KBF

In the business investment equation the ratio of business investment to capital is driven by its own lag, prospective profitability and the tightness of monetary policy. Profitability is measured through the gap between actual and required rates of return. The required rate of return on investment includes the depreciation rate, the real interest rate and a risk premium (RP1), as shown in equation (23).

(23)    DR_EQ + RI_EQ + RP1

The actual rates of return on capital is increased through higher prices for outputs and lowered through higher prices for inputs. Although the dynamic structure is calibrated, the parameter values for the equation are close to those of their estimated values. The dynamic specification of the business investment equation is represented by equation (24).

(24)     IBF/KBF=C1301*(IBF(-1)/KBF(-1))+(1-C1301)*(GR(-4)+DR_EQ-1)+C1302*(AR(-1)-(DR_EQ+RI_EQ+RP1))+C1303*YCURVE(-2)+ ))+C1304*YCURVE(-3)+Z_IBF,

Net business investment adds to the business capital stock carried over to the next quarter.

(25)    KBF1 = (1 – DR_EQ).KBF + IBF

(26)    KBF = KBF1(-1)

5.4  Inventories

There are two types of inventories in the model: those for domestic consumption (IINR) and those for export (IIE). Domestic inventories are modelled as a function of YD and a deviation of the level of inventories from their equilibrium value.

(27)    IINR=EXP(LOG(YD*SSRATIO_EQ)-LOG(KINR(-1)/EKINR(-1)))+Z_IINR,

Export inventories are simply a residual and represent the difference between the domestic supply of commodity exports (CEXPS) and the foreign demand for commodity exports (CEXP).

Notes

  • [7]This is an area of ongoing development as the model is “fine tuned.”
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