2.2 Dynamic path
If prices and wages were fully flexible and all factors of production, such as capital and labour, could move instantaneously, the economy would always operate at steady state (ie, the values of all variables would always be at their steady-state value).
However, the economy is one where frictions exist (for example, adjustment costs and imperfect information). As a result, prices are sticky (ie, do not adjust instantaneously) and resources are not fully mobile and therefore it takes time (in the absence of further shocks) for the economy to get to steady state. These frictions are modelled in NZTM by variables seeking to adjust partially (as opposed to full adjustment in a frictionless world) towards steady-state values (xss). NZTM also introduces frictions through partial adjustment towards medium-run values (xmr), representing profit or utility maximising values in the medium run, as well as the use of lags of dependent variables. The medium-run profit maximising values are determined by the first order conditions for profit maximisation of the dynamic production block of the business sector, which will be described further in Section 3.
In general, the dynamic equations in NZTM have the following structure:
That is, the dynamic value of a generic variable xt is a function of its lag(s), its steady-state value, its medium-run value and a vector of relative prices (z; for example, interest and exchange rates). Note that not all equations contain all the elements stated above. We discuss the components of equation (2.3.1) in turn below:
(i) Feedback from the steady state
The steady state of the model gives long-run values of the following variables which are used in the dynamic part of the model:
- Private sector potential output and, given government spending is exogenous, economy-wide potential output. These variables are private sector and economy-wide output in the steady state
- Real hourly wage
- Real exchange rate
- Inventory levels
- The relative price of residential investment
- Equilibrium housing stock
- Equilibrium volumes of non-commodity export goods and export services, and
- The relative price of both non-commodity export goods and export services.
When the economy is not in equilibrium, the current levels of some (if not all) variables are different from their steady-state levels. The deviation of the above variables from their steady-state level is a key driver in restoring the economy to long-run equilibrium and is therefore also a key driver of dynamics in some equations. The parameter λ measures the speed of adjustment towards achieving that steady state value.
For some equations, the dynamic value of xt is a function of its steady-state stock variable rather than its steady-state flow variable. If the actual value of the relevant steady-state stock variable (Xt) falls short of, or exceeds, its required steady-state level (Xss), flows must adjust to ensure that in the long run the gap is closed. For example, if the housing stock is currently below its steady-state value, all else equal, growth in residential investment will need to be faster (compared to steady-state growth). Over time, this increased investment will see the difference between the housing stock and the steady-state housing stock fall, until (all else equal) the housing stock is at its steady-state level and therefore the current rate and the steady-state rate of residential investment are equal. Table 1 presents some of the key stocks in the model and the flows which adjust to achieve the steady-state values.
| Steady-state variable | Steady-state value is achieved through adjusting… | |
|---|---|---|
| Households | Desired level of the housing stock | Residential investment |
| Government | Optimal level of gross debt consistent with the government's fiscal strategy | The personal tax rate |
| External balance | Households have a desired level of net financial wealth which in turn determines the desired level of net foreign asset position. | The real exchange rate (see section 2.1.1) |
| Internal balance | Target level of unemployment (the non-accelerating inflation rate of unemployment, NAIRU[6]) | Wages, inflation and monetary policy |
(ii) Feedback from medium-run values
In the dynamic model, as in the steady state, there is a production block (discussed in more detail in Section 3) that determines the firms' profit-maximising input and output mixes. However, the presence of adjustment costs means adjustment towards the input and output mixes that maximise profit in the dynamic version of the production block is not instantaneous. Examples of adjustment costs include the costs of hiring and firing labour and changing the production mix. Therefore, equations that are dependent on production-block decisions (for example, labour market decisions and exporting and importing decisions) feature a partial adjustment towards these dynamic production block values (which we call medium-run values, xMR). Private consumption also adjusts towards a medium-run value, which can be (informally)[7] thought of as the utility-maximising level of consumption in the Permanent Income Hypothesis sense. We will discuss this in more detail in Section 4.6.
(iii) Persistence
Lags serve two functions in the model. The first is to introduce momentum. A positive coefficient on a lag term ensures that strong growth in the previous quarter flows through to the next quarter. Lags also provide another way of introducing frictions and lags also mean the adjustment to shocks in the economy takes time to flow through.
(iv) Relative prices
Relative prices are a key driver of decision making in NZTM. The relative price of inputs determines the amounts of different inputs used in production, and the relative price of outputs determines the output mix. In demand equations, an increase in the real exchange rate (the relative price of New Zealand goods and services to foreign goods and services) will encourage more importing, while an increase in interest rates (the relative price of current spending as opposed to saving) will discourage expenditure. Note, with the obvious exception of interest rates, relative prices are typically expressed relative to the price of “other goods” (pydo) which includes all non-commodity goods and services produced by the private sector.
