2 A small model of the New Zealand economy

There are a number of ways in which to develop a model of the economy, the suitability of which depends upon its intended use. One type of modelling method is the DSGE approach, referred to above. Such models, often used by central banks, are typically quite large and strictly adhere to the prescriptions of their microeconomic foundations. That is to say that, whether it's a model with three equations or twenty, the laws of motion of the economy are governed by the optimising behaviour of agents operating within it. DSGE models tend to fall into two categories - real business cycle models, which treat all deviations from steady state as optimal responses to shocks, and, so-called, New Keynesian models, which attribute some of the deviation to nominal rigidities. The model presented here can be considered a reduced-form version of the latter.

The strength of micro-founded models is that the equations are based on optimising behaviour and so should be robust to changes in policy - the dynamics of the model are driven by 'deep' or structural parameters.[2] However, models featuring forward-looking equations tend to underperform simple autoregressive models and, quite often, little empirical support is found for the hypothesised underlying relationships.[3] This is partly because many of the variables move with a degree of inertia that is inconsistent with the adjustment paths implied by forward-looking, rational expectations models. In these models, it is the rational but immediate adjustment of households' expectations to innovations which implies jump responses, which are rarely seen in the data. To overcome this problem, many DSGE models feature adjustment costs and other mechanisms introduced with the intention of replicating the inertial responses of the data.

All economic models are misspecified, since they represent a simplification of reality. And while the model presented in this paper is deliberately small, with the objective of parsimony and tractability in mind, it is also likely to be particularly prone to misspecification. Recognising this, I attach structural interpretations only loosely to the parameters of the reduced-form model, since many of them capture broader influences on the variables to which they pertain.

The four key variables of interest are the output gap, bank rate, the inflation rate and the real exchange rate; given by the investment-saving (IS), Taylor, Phillips and real uncovered interest parity (RUIP) relations respectively. In what follows, I present the baseline functional forms adopted for the core equations and identify where the assumptions are consistent with the microeconomic theory upon which they are founded and how that translates into the functional form of the reduced-form model. For reference, a complete set of the equations that constitute the model can be found at the end of this section and descriptions of the data used to estimate are presented in the annex.