RDP 8802: Var Forecasting Models of the Australian Economy: A Preliminary Analysis 1. Introduction

A difficulty regularly faced by economists, particularly in policy making and advisory roles, is the production of reliable forecasts of important macroeconomic variables. Forecasting may involve the development of complex and expensive macroeconomic models, and often relies heavily on the judgment of the forecaster in prescribing future paths of exogenous variables or in adjusting model-generated forecasts in line with his subjective expectations.

This paper investigates whether extremely cheap and relatively simple vector autoregressive models (VARs) produce sensible forecasts of major Australian macroeconomic variables. In particular, we examine the accuracy of ex-ante forecasts produced by some representative VARs, relative to the accuracy of other publically available forecasts. The forecasting accuracy of similar VAR models (eg. Litterman, 1986b) has been examined in the United States over the last decade, with encouraging results – they tend to do no worse than much more complex and expensive macroeconometric models of the economy and private forecasting services.

In any model building exercise, certain decisions about the structure of the model need to be made. For a VAR forecasting model these decisions concern the list of variables to be included in the model, the lag length of the model and the detrending procedure to be used for detrending data^[1]. The choice of detrending procedure is likely to be particularly important for forecasting horizons of more than a few periods. VAR (and other econometric) models are based on an assumption of stationarity in the data-generating mechanism. If a series displays non-stationarity, that is, if it has no fixed long-term stochastic distribution, then we cannot expect to determine stable econometric relationships from the data, especially of the sort needed for useful forecasting. A study by Nelson and Plosser (1982) produced evidence that the non-stationarity of some historical time series for the U.S. was of a type which could not be corrected by simple procedures. More recent work on co-integration (Engle and Granger, 1987 and Hendry, 1986), stochastic trends (Harvey, Henry, Peters and Wren-Lewis, 1986 and Watson, 1986) and common trends (Fernandez-Macho, Harvey and Stock, 1986 and Stock and Watson, 1986) has emphasised the potential importance of using appropriate detrending methods.^[2]

To partially accommodate these results, three different VAR models (each with a different detrending scheme) are considered. One model uses a first-difference detrending process, another uses a first-order deterministic process and the third is estimated under Bayesian-like priors which lean heavily towards random walk models.^[3] We also, unsuccessfully, consider a fairly general stochastic trend procedure. No allowance is made for common trends at this stage of our research as they often involve complex estimation strategies.

In each case, we apply the techniques in a relatively mechanical fashion to generate estimates and forecasts from data as they existed at the time of the release of the December 1985 Quarterly Estimates of the National Accounts. Although we believe that there are large potential gains in accuracy to be realised, we have not used our technical expertise or the tracking performance of the models to undertake any fine-tuning. In essence, our three VAR models (and their forecasts) could have been obtained in early 1986 by any relatively unsophisticated user of commercially available personal computer or mainframe software.

Forecasts over a six-quarter horizon (i.e. till June 1987) are generated from each of the three VAR models. These ex-ante forecasts are evaluated by comparing them with publicly available forecasts and actual outcomes (as at the release of the June 1987 Quarterly Estimates of the National Accounts).

Section 2 surveys some of the literature on VAR forecasting models. Section 3 details the VAR models estimated here, the data and estimation techniques employed. Section 4 sets out our results and Section 5 our conclusions and views on how the models may be improved.

Footnotes

When a VAR model is being used to interpret intertemporal relationships between variables, one also has to make decisions about contemporaneous causality. See, for instance, Trevor and Donald (1986). [1]

Integration refers to the presence of unit roots in the data (i.e. the data are difference stationary). Stochastic trends is a broader concept which includes most trends other than purely deterministic ones (such as time trends). Common trends and co-integration refer to the fact that some variables (e.g. income and consumption) are likely to “trend” together. That is, the same factor gives rise to non-stationary in both series. [2]

A random walk model is: X_t = X_t−1 + ε_t. [3]