Forecasting the Australian economy with DSGE and BVAR models

ABSTRACT

Reflecting the importance of commodities for the Australian economy, we construct a dynamic stochastic general equilibrium (DSGE) model of the Australian economy with a commodity sector. We assess whether its forecasts can be improved by using it as a prior for an empirical Bayesian vector autoregression (BVAR). We find that the forecasts from the BVAR tend to be more accurate than those from the DSGE model. Nevertheless, for output growth these forecasts do not outperform benchmark models, such as a small open economy BVAR estimated using the standard priors for forecasting. A Bayesian factor augmented vector autoregression produces the most accurate near-term inflation forecasts.

KEYWORDS:

• Australian economy
• commodities
• DSGE
• BVAR
• forecasting

JEL CLASSIFICATION:

• E17
• F47
• E37

Acknowledgements

We thank two anonymous referees for comments which improved this article.

Disclosure statement

The views are those of the authors and do not necessarily reflect those of the Reserve Bank of Australia.

Supplementary Material

Supplemental data for this article can be accessed here.

Notes

¹ For an overview of forecasting with DSGE models, see Del Negro and Schorfheide (2013).

² Brischetto and Voss (1999) adapt the Kim and Roubini (2000) model to Australia to study the impact of monetary policy shocks.

³ An early contribution is Trevor and Thorp (1988).

⁴ An expression for the evolution of nominal net foreign assets as a share of GDP, $h$, can be obtained using the budget constraint.

⁵ We allow for rule-of-thumb pricing, following Galí and Gertler (1999), and include a mark-up shock.

⁶ Value added is defined as $V{A}_t\equiv Y_{1,t}+\frac{{\bar{P}}_2}{{\bar{P}}_1}{Y}_{2,t}$

⁷ The data are not real time. The detrending was done with a Hodrick-Prescott filter with $\lambda =1 600$.

⁸ For an overview of BVAR models see Wozniak (2016).

⁹ Drawing on the estimates of Iacoviello and Neri (2010) for the United States.

¹⁰ The average acceptance rate was 37.75 per cent. A second chain was run to check for convergence.

¹¹ There is little change in the remaining parameters if these indexation parameters instead are calibrated.

¹² This could reflect that we have allowed technology to be non-stationary, whereas they linearly detrend observed output.

¹³ We experimented with allowing a separate adjustment cost parameter for the export sector, but this appeared to be difficult to identify.

¹⁴ For simplicity, we set $p=q$.

¹⁵ As we are drawing from the posterior of the DSGE this is an empirical Bayesian approach. For an overview of empirical Bayes analysis, see Casella (1985).

¹⁶ This places a multivariate normal prior over the (vectorized) parameters of the VAR, and a Wishart prior over the inverse of the variance-covariance matrix of the reduced-form shocks. We set the degrees of freedom parameter in the latter to be $n+2$.

¹⁷ As the number of parameters in the BVECMX is greater than that in the DSGE, to ensure that the prior for the variance-covariance matrix of the parameters is non-singular, we add a small amount (0.01) to the standard deviation for all parameters after any scaling by $\lambda$.

¹⁸ We simulate 31 000 observations, dropping the first 1 000. The stability condition is implemented by dropping all unstable draws.

¹⁹ For investment, the sample was 1986:Q1 onwards due to data availability.

²⁰ We use the Minnesota prior to save computational time, and exclude business investment due to data availability.

²¹ As before, we set the degrees of freedom parameter in the Wishart distribution to be $n+2.$

²² For simplicity, we use the posterior mean of the VAR parameters, rather than taking into account parameter uncertainty. Kadiyala and Karlsson (1997) describe this as the ‘customary’ approach.

²³ The mean of the data over the estimation period is added back into the forecasts.

²⁴ A common approach is to assess whether the performance of the forecasts are statistically significant using the Diebold and Mariano (1995) statistic. Unfortunately the Diebold-Mariano statistic is not applicable as, for example, it does not accommodate nested models. The recursive estimation sample also means that the Giacomini and White (2006) test is not applicable. As the Australian inflation-targeting sample is short, it seemed preferable to maintain the recursive, rather than rolling, sample.

²⁵ In contrast, Kolasa, Rubaszek, and Skrzypczyski (2012) found that a modified version of Smets and Wouters (2007) generally outperformed a BVAR-DSGE model using it as a prior.

²⁶ Abbas et al. (2016) also are critical of the New Keynesian Phillips curve as a model of inflation for Australia, although they focus on evaluating variants of the curve in Galí and Monacelli (2005), rather than the approach in this model which allows for incomplete short-run pass through in import prices, which is a common specification in empirical small-open economy DSGE models.

²⁷ This is not an uncommon result; for example, it was also found by Beechey and Österholm (2008) and Jiang et al. (2017).

²⁸ Ghent (2009) examines forecast combination, but of BVAR-DSGE models with different DSGEs (real business cycle and sticky price) used to generate the prior. Little improvement is found from combining these models.

²⁹ For one discussion of trends in Australian productivity over the 2000s, see Eslake (2011).

³⁰ To do this, we regress all variables against a constant and a dummy for the inflation-targeting period, rather than demeaning the data, which is akin to allowing the intercept to shift for all equations in the VAR in 1993:Q1. Given that other countries, such as the United Kingdom and Canada, also deflated at around this time and are included in the aggregates we use for the foreign variables, we also allow for breaks in these series. The DSGE parameters obtained are similar to the short sample estimates, and are given in the on-line appendix.

³¹ Pagan and Robinson (2012) examine whether a similar extension of Smets and Wouters (2007), due to Gilchrist, Ortiz, and Zakrajšek (2009), can forecast recessions (that is, they focus on turning points). They find that ‘…at best it would seem that the GOZ model would have predicted two of the seven recessions’. A key reason demonstrated for this is that the business cycle characteristics of the model are heavily influenced by the contemporaneous innovations to the structural shocks, which cannot, by definition, be forecast. It should be noted that many models find it difficult to forecast recessions (see Harding and Pagan (2016)).

³² For the Iacoviello and Neri (2010) model of the U.S., however, Pagan and Robinson (2012) found a similarly large role for the innovations to the contemporaneous shocks in influencing the characteristics of the business cycle as for the financial accelerator approach, suggesting that the power of models containing collateral constraints for forecasting recessions may also be limited.

³³ Brzoza-Brzezina and Kolasa (2013) compare the estimated models including either type of financial friction using marginal likelihoods and other methods and conclude that the financial accelerator approach is preferred, although ‘…even this model does not make a clear improvement of the New Keynesian benchmark…’.

³⁴ Kolasa and Rubaszek (2015) also consider density forecasts, and find that ‘…during normal, non-crisis times, … the average quality of the density forecasts actually deteriorates.’ (p.2).

Additional information

Funding

This work was supported by to Australian Research Council [DP160102654];