4 The firm and the rest of the model

4.1  Business investment

The steady-state level of capital (kbf) comes from the production block. As implied by the balanced growth path, the growth rate of the capital stock is equal to population plus productivity growth (gr_1). Business investment (ibfr) is such that capital grows at this rate and any depreciated capital is replaced. dr_eq is the steady-state depreciation rate.

where exp is the exponential operator.

In the dynamic part of the model, business investment will adjust to close the gap between the current capital stock and the steady-state capital stock. In the model, this adjustment occurs using the gap between the actual rate of return and the required rate of return. If the current level of capital is below the steady-state stock of capital, then the actual rate of return on capital (ar, determined in the production block) will exceed the required rate of return, meaning firms will invest more (relative to steady-state investment). Eventually, the actual rate of return converges on the required rate of return as the higher level of business investment means the dynamic value of the capital stock converges to the steady-state capital stock. The required rate of return is the rate that covers depreciation (dr_eq) plus the opportunity cost of capital (the steady-state real interest rate, ri_eq, plus a risk premium, rp1).

In the dynamic model, business investment also depends on the cost of borrowing to fund investment (as captured by the yield curve, ycurve), the relative price of capital imports (rpmca) and its lag (ibfr (-1)), which introduces frictions into the adjustment process.

4.2  Capital and intermediate imports

The capital goods import equations determine the share of capital imports (imca) relative to the sum of business investment and government investment (ggifr_eq). In the steady state (4.2.1) and dynamic model (4.2.2), the share of capital imports depends on the relative price of capital (rpmca). The relative price of capital is the exogenous foreign price of capital goods converted into New Zealand dollar terms by the nominal exchange rate (see Section 5) deflated by “other goods” prices (Section 6).

Steady-state equations

Dynamic equations

Another flow we want to model is the amount of intermediate goods imported (imo). This is mainly dependent on the firms' demand for intermediate imports from the production block (imsr). In steady state, firms' demand for imported intermediates is identical to firms' demand from the steady-state production block.

In the dynamic part of the model, imports of intermediates partially adjust towards firms' demand for intermediate imports from the dynamic production block (imsr), that is the profit-maximising medium-run value. The partial adjustment (rather than a full adjustment) towards the medium-run value of intermediate imports reflects that firms cannot achieve their profit-maximising level of intermediate imports straight away as it takes time to change the amount of goods imported (for example, due to contractual arrangements and transport lags). The lag,imo(-1), also induces frictions in this adjustment. The parameter beta2 is introduced to allow for the real share of imports to increase over time as the economy becomes more open.[10]

4.3  Commodity exports

Analogous to the imported intermediate equation, in steady state commodity exports (cexps) equals its profit-maximising value from the steady-state production block (exrsr).

In the dynamic model, analogous to the intermediate imports equation, commodity exports (cexps) adjust towards the medium-run profit-maximising level of exports from the dynamic production block (exrsr). The extent to which commodity production can be varied is restricted by biological limits,[11] and therefore the adjustment parameter towards the profit-maximising level of commodity exports (pa5_1) has quite a low value (currently 0.1). In the absence of further shocks and any other adjustments, it takes about 7 quarters to make half of the adjustment. A lagged term is also used to introduce slow adjustment (cexps(-1)). Beta1 allows for the real share of commodity exports to change but the new estimate of this parameter is close to zero suggesting that the real share of commodity exports as a percentage of total private sector output is rather constant.

4.4  Non-commodity exports

The following equations determine how the composition of the “other good” (from the production block) is split between goods and services supplied to the domestic economy and exports of non-commodity goods and services.

4.4.1  Non-commodity goods exports

In steady state, the representative firm decides the ratio of non-commodity goods exports (ncexpg) to the production of “other goods” (ydo) based on the price received for exports of non-commodity goods relative to the price of ydo. The relative price of ncexgg (rpexncg) is an exogenous foreign price (pexncgf) multiplied by the nominal exchange rate (e) and deflated by pydo.

In the dynamic model, the supply of non-commodity goods exports (ncexpg) adjusts towards its steady-state value (encexpg). A relative price term, the deviation of the relative price (rpexncg) from its steady-state relative price(erpenxcg), also drives dynamics, reflecting the fact that when the New Zealand dollar price of exports is higher than the price received domestically, firms will prefer to supply the export market (note that the relative prices enter with a lag reflecting that the supply response to higher prices takes time). The closing of the gap between the current relative price and the steady-state value is a key mechanism to get the dynamic values of these variables to converge to their steady-state values over time. If the relative price is currently higher than its steady-state value, this will increase the supply of the non-commodity goods exports (relative to its steady-state value), decreasing our external indebtedness and increasing the associated real exchange rate. A higher real exchange rate will decrease the relative price of exports in New Zealand dollar terms, meaning the relative price moves towards the steady-state relative price and thus helps ensure non-commodity goods exports converge to their steady-state value.

4.4.2  Services exports

In steady state, the ratio of services exports to production for domestic demand is dependent on the relative price of export services to pydo (rpexncs) and a trend factor (TF). The trend factor reflects that travel services, which make up around half of services exports, have generally been increasing over time owing to rising global incomes promoting more spending on luxury goods such as travel. In the forecasting environment, the trend factor continues to operate for the first five years of the forecasting period. As with the exports of non-commodity goods equation, the relative price of export services is an exogenous foreign price (pexncsf) multiplied by the nominal exchange rate (e) and deflated by pydo.

The relative price term in equations (4.4.3) plays a similar role as in the other export equations.

In the dynamic equation, as with the exports of non-commodity goods equation, the closing of the gap between current relative prices(rpexncs) and their steady-state (erpexncs) values is a key mechanism to get the dynamic values of these variables to converge to their steady-state values over time. Also like the exports of non-commodity goods equation, the services exports equation also features an adjustment towards its steady-state value (encexps).