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Estimating quarterly gross state product

Victoria's Economic Bulletin showcases a method to estimate the quarterly gross state product of Victoria, as well as other states, using a novel econometric technique with mixed frequency data.

PUBLISHED: June 2021

Written by Bonnie Li and Grace Gao[1].

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Contents

1. Introduction
2. Background
3. Methodology
4. Results
5. Synchronisation of state economic cycles
6. Conclusion
References
Appendix A: Detailed methodology

Abstract

This paper outlines a methodology to estimate the gross state product of Victoria, as well as other states, on a quarterly basis using a mixed-frequency vector auto-regressive model with stochastic volatility. Using these results, we uncover variation in economic performance across the states over the past 30 years and find a reasonably high degree of concordance.

1. Introduction

Growth in gross domestic product (GDP) is one of the most important indicators of a country’s economic performance. However, the availability of such a measure at a sub-national level is often limited. In Australia, while GDP is available on a quarterly basis, at the state level, gross state product (GSP) is only available annually.[2] The lack of frequent and timely economic data for the states limits the ability of economists and policymakers to understand local economic conditions, which may differ significantly from the national experience.

This problem is not unique to Australia. Many economists have attempted to fill the data gap using various methods, including a bottom-up approach based on a range of surveys and proxies. Recently, Koop et al. (2020) took a top-down approach and estimated gross regional product (GRP) at the sub-national level in the United Kingdom (UK) using a mixed-frequency vector auto-regressive model with stochastic volatility (MF-VAR-SV). The model involves quarterly national GDP growth and other quarterly economic variables as well as unobserved quarterly regional economic growth, which was estimated in a state-space framework.

We adapt the model developed by Koop et al. (2020) to Australia and estimate GSP growth – the equivalent of GDP growth for states in Australia – for the past 30 years. Our estimates are comparable to historical publications by the Australian Bureau of Statistics (ABS) and Queensland Treasury’s Queensland State Accounts. We also identify economic cycles in each state and analyse their synchronisation using these estimates of quarterly GSP growth. Our results suggest several economic cycles at the state level which may have been masked by the annual data.

The remainder of this paper is organised as follows. Section 2 provides some background information on existing data and methodology. Section 3 outlines our adaptation of the recent developments in the literature to Australia. Section 4 presents the results. Section 5 discusses the economic cycles identified in the results and section 6 concludes the paper.

2. Background

GDP measures the value of goods and services that an economy produces in a period. A country’s GDP can be measured using three approaches: production, income and expenditure. GDP measurement is often available at a quarterly frequency at the national level, but the availability of such a measure at a sub-national level is often more limited with respect to the frequency of the measurement and its components. This data limit poses significant constraints on the ability of researchers and policymakers to carry out economic analysis.

In Australia, the ABS publishes the Australian GDP quarterly but GSP is only available annually. While state final demand (SFD) and international trade for each state are available quarterly, both measures are only partial indicators of the economic activity and the remainder, interstate trade and inventories, is unavailable.[3] With GSP being a key economic indicator for states, it is unsurprising that many economists have sought to develop a more frequent indicator than the official annual publication. Researchers have often taken a bottom-up approach, focusing on understanding particular components of the economy for which official data is unavailable. An example is the Queensland Treasury’s Queensland State Accounts, which takes the expenditure approach and estimates interstate trade and inventories using a range of partial indicators and survey results. Others have focused on production by industries, such as developing sub-national industrial production indices as proxies for economic growth. The bottom-up approaches are often based on a wide range of surveys and tend to provide a clear economic narrative, but their maintenance can be costly and time demanding.

Recently, Koop et al. (2020) have taken a different approach by adopting a top-down approach to estimate the gross regional product (GRP) for the 12 regions in the UK. They develop a mixed-frequency vector autoregressive model with stochastic volatility (MF-VAR-SV).[4] This approach exploits the availability of quarterly GDP at the national level and annual gross regional product for each of the sub-national regions. Cross-sectional and temporal restrictions are imposed to ensure that quarterly GRP estimates are consistent with observed quarterly GDP and the annual GRP figures. They further include national and regional explanatory variables in the model to better capture macroeconomic linkages and improve its performance.

The key advantages of this approach include its incorporation of existing official statistics, its transparency and its low cost. Compared with the low-frequency VAR method developed by Chow and Lin (1971), this approach makes use of an additional cross-sectional restriction and reduces the risk of model misspecification (Ghysels et al., 2011).

3. Methodology

This section provides an overview of our methodology which builds on Koop et al. (2020) and discusses the changes to adapt the model to Australia. The technical specification is detailed in Appendix A.

The model takes a state-space approach to estimate the unobserved quarterly GSP growth. The unobserved quarterly growth for the states is modelled together with observed national GDP growth using a quarterly vector auto-regressive model of up to 7 quarter lags.[5]

To better capture macroeconomic linkages, particularly with the external sector, Koop et al. (2020) include additional quarterly economic variables. At the national level, they include: the Bank of England Bank Rate, the exchange rate, the oil price and the consumer price index. Mirroring these inclusions, this paper includes the Reserve Bank of Australia (RBA) cash rate, the trade weighted exchange rate index, the RBA Commodity Price Index and the Consumer Price Index for Australia.

For the observed quarterly state-level variables, we include SFD for each state in the VAR framework. All variables enter the model in the first difference of logarithm, except for the cash rate which enters in levels. The choice to include other regional variables is significantly limited by data availability, particularly for historical data. Regional employment was also considered but it was found that it does not result in better model performance in Australia.

To ensure quarterly GSP growth is consistent with the official annual GSP growth, we set up a measurement constraint following the linear approximation of annual and quarterly GSP growth in Mitchell et al (2005) and Mariano and Murasawa (2010):      

equation (38)

         (1)


where ytr is the quarterly GSP growth rate for region r in quarter t, and ytr,A  is the annual GSP growth rate for region r in quarter t  that is only observed in quarter 4 of each financial year. This temporal constraint ensures that the interpolated quarterly estimates add up to the observed annual data, and preserves the linear structure of the state-space model.

For the cross-sectional restriction, we set that national GDP growth for a quarter equals the average GSP growth weighted by each state’s share of the national economy in the previous financial year. This setting is different from Koop et al. (2020) which used a simple arithmetic average of regional growth. This change is necessary to appropriately model the divergence in economic growth across states over the study period, which saw Western Australia’s share of the national economy increasing from 10 to 15 per cent.

4. Results

Using the methodology and the data outlined in the previous section, we obtain GSP estimates for each state in Australia using Markov Chain Monte Carlo simulations with 30 000 drawings and 10 000 burn-in (Figure 1). Our quarterly estimates suggest that there was significant variation in economic performance across states over the past 30 years, as seen in Figure 1.[6]

Our estimates of economic growth in Queensland and Western Australia (which both have large resources sectors) were significantly stronger than other states in the late 1980s, as Australian commodity export prices rose by around 45 per cent from the low point in mid-1986. These two states also saw a significant uptick in quarterly GSP growth during the ‘mining boom’ in late 2000s and early 2010s. 

As Australia entered a recession in the September quarter of 1990, economic growth slowed significantly across all states, with many seeing negative growth. Our estimates suggest that Victoria and South Australia had the sharpest and longest contraction during this recession, while the contraction in New South Wales and Tasmania was short and shallow. Queensland and Western Australia recorded low but positive growth during this period, partly due to strong commodity prices.

Following the early 1990s recession, Australia enjoyed a prolonged period of economic growth until the COVID-19 pandemic in 2020. Nonetheless, there were periods where economic growth weakened. Most states recorded low growth for a few quarters in 2009–10 following the global financial crisis. Subsequently, the trajectory among the states varied over this period, with the mining states growing much faster than the other states due to high commodity prices. Among the non-mining states, Victoria had the strongest average annual growth after the mining boom from 2015–2019, followed by New South Wales.

Figure 1: Gross state product, annual growth

Note: Shaded areas are the 16th and 84th percentiles of Bayesian estimates. There is no confidence interval for June quarter estimates as they are restricted to be the annual GSP growth rates published by ABS.  

Australia’s economy entered into a technical recession in the June quarter 2020 as the COVID-19 pandemic triggered two consecutive quarters of negative growth, with a record 7.0 per cent fall in the GDP for the June quarter. The recession was over in the September quarter with the economy expanding by 3.4 per cent. Since the model is based on annual GSP growth figures, this paper presents quarterly GSP estimates up to the June quarter 2020.[7]

We compare our results to other published estimates. The ABS did previously publish quarterly GSP data between 1993 and 1997, with historical data provided from 1984–85.[8] Our estimates of GSP growth in the early 1990s are broadly in line with the historical ABS estimates (Figure 2). There are a few exceptions where our estimates are quite different from ABS estimates, although these differences primarily reflect subsequent revisions to ABS annual GSP data. The ABS estimates are from the 1995 vintage publication of quarterly GSP, while our estimates are based on the most recent ABS annual GSP figures, which covers all data revisions over time.[9]

The Queensland Treasury also publishes quarterly GSP estimates for that state in its Queensland State Accounts. Our estimates of Queensland quarterly GSP growth are also aligned to the Queensland Treasury’s (Figure 3). Our estimates are generally less volatile, and the annual estimates derived from the quarterly results are consistent with ABS annual GSP estimates due to restrictions imposed in the model.

Figure 2: Comparison of results with historical ABS State Accounts and Queensland State Accounts, Dec 1988 – June 1997

Figure 3: Comparison of results with Queensland State Accounts, September 1989 – June 2020

5. Synchronisation of state economic cycles

Seeing the divergence in our estimates between states, we use our quarterly GSP estimates to identify business cycles for each state which may have been masked by annual state or quarterly national statistics. To do so, we use the non-parametric algorithm of Harding and Pagan (2002).[10] Figure 4 illustrates the economic cycles of each state since the late 1980s.[11]

The results suggest that Australia was in a recession from the September quarter of 1990 to the June quarter of 1991. Over these four quarters, all states experienced some contraction, though with some variation in timing and duration. Victoria, Queensland and South Australia entered the recession in the June quarter, a quarter earlier than the other states. Our data suggests that Victoria and South Australia remained in contraction the longest, for 7 and 8 quarters respectively. A number of financial institutions failed during 1990–1992, including the State Bank of Victoria, the State Bank of South Australia, the Victorian-based Pyramid Building Society and several merchant banks [12] (RBA 2000). Dixon and Mahmood (2008) also concluded that the tariff cuts in the textiles, clothing and footwear sector in 1989–90 resulted in a massive reduction in employment in firms mainly located in Victoria. The large increase in unemployment led to a significant and accelerated outflow of population along with a decline in overseas immigration.

Figure 4: Economic cycles of Australian states, September 1978 – Jun 2019

Notes: An elevated line indicates an expansion and a dent in the line represents a contraction. Expansions and contractions are at least two quarters long. The grey shading indicates the national recession in early 1990s.

Australia then experienced a very good growth performance after the early 1990s recession. The output of the mining, financial services and professional services industries grew at a much faster rate than average during 1991–92 to 2008–09, while the output of the manufacturing sector increased by less than average (RBA 2010). Two resource-rich states, Queensland and Western Australia, outperformed the nation as a result of improving commodity prices and world economic recovery after the 1990s recession.

There were a couple of periods when economic growth slowed noticeably after the 1990s, but at no time did quarterly growth turn negative in two consecutive quarters. One slowdown was in 2000–01 following the collapse of the ‘dot-com bubble’; and one in 2008 following the collapse of the US sub-prime housing bubble. Due to its sound financial system and substantial macroeconomic stimulus, the Australian economy performed much better than most other advanced economies during the global financial crisis. The temporary but sharp fall in the exchange rate during the crisis also helped cushion the economy on the downside, as did Australia’s economic exposure to China’s economy.

After commodity prices peaked in July 2011, the decline in mining investment in Australia from 2012 led to lower growth in overall mining activity. Economic conditions in Western Australia, which has a high reliance on the mining sector, weakened and our model suggests negative quarterly growth over the four quarters of 2016–17. The high exchange rate over 2010 to 2014 had put pressure on many industrial sectors and hence state economies that were not benefitting directly from high commodity prices. South Australia recorded state final demand fall in two consecutive quarters during 2013–14 and our model also identified a short period of contraction in the State’s GSP growth. The progressive reduction in official interest rates from November 2011 and the depreciation of the exchange rate underpinned a rise in growth of non-mining activity, which led to an improvement in economic conditions in states like New South Wales and Victoria over 2015–2018. Our model also identified a short contraction in Queensland by the end of 2018, compared to Queensland Treasury’s estimates which suggested negative quarterly GSP growth in September 2018 and March 2019 separately. 

To understand the similarities in business cycles across the states, Table 1 presents the degree of concordance. The concept was proposed by Harding and Pagan (2002) to measure co-movements between individual cycles. The degree of concordance is defined as the fraction of time both series are simultaneously in the same state of expansion or contraction. If two economies always record growth peaks and troughs at the same time over the whole period, the degree of concordance of these two economies is 100 per cent. A concordance of 80 per cent means both economies are in expansion/contraction in four out of five quarters.

While each state may experience different conditions, state economic growth appears to be in a similar phase (expansion/contraction) to national growth the vast majority of the time, consistent with previous studies such as Norman and Walker (2004). Nonetheless, as Figure 1 and the earlier discussion demonstrated, during expansion phases the economic conditions among states can vary considerably.

Table 1: Concordance between states and the nation

 

AUS

NSW

VIC

QLD

SA

WA

TAS

AUS

100%

96.1%

97.7%

96.9%

96.1%

94.6%

83.7%

NSW

 

100%

95.3%

94.6%

93.8%

92.2%

82.9%

VIC

 

 

100%

96.1%

98.4%

92.2%

82.9%

QLD

 

 

 

100%

94.6%

91.5%

82.2%

SA

 

 

 

 

100%

90.7%

81.4%

WA

 

 

 

 

 

100%

79.8%

TAS

 

 

 

 

 

 

100%

Note: The degree of concordance is the fraction of time both series are simultaneously in the same state of expansion (St=1) or contraction (St=0).
That is, #{Sit=Sjt=1}+#{Sit=Sjt=0}/n, where i and j represent regions, n is the total number of quarters (n=129), and # represents the total number of quarters that the condition is satisfied. If two GSP series move together with the same cyclical component, the degree of concordance would be unity. 

6. Conclusion

This paper proposes a methodology to estimate quarterly gross state product in Australia. We closely follow the approach maintained by Koop et al. (2020) where we made modifications to adapt the model to Australia.

We also use these estimates to identify economic cycles in each state since 1987. Our results confirm that there is variation in economic growth among states and suggest there may have been several short periods of contractions in some states which were masked by the annual GSP data. Analysing the state and national economic cycles from these new estimates, we find a reasonably high degree of concordance in expansions and contractions between the states’ and national economy despite variations in economic performance.

We hope these estimates help economists and policymakers overcome current data limitations in their research and policy decisions in the absence of official quarterly GSP data.

References

Australian Bureau of Statistics (ABS). Australia National Accounts: State Accounts, Catalogue Number 5220.0. Available on the ABS website

Australian Bureau of Statistics (ABS). Australian National Accounts: State Accounts, Catalogue Number 5242.0. Available on the ABS website

Australian Bureau of Statistics (ABS). Australian National Accounts: National Income, Expenditure and Product, Catalogue Number 5206.0. Available on the ABS website.

Bhattacharya, A., Pati, D., Pillai, N.S. and Dunson, D.B. (2015). “Dirichlet–Laplace Priors for Optimal Shrinkage.” Journal of the American Statistical Association 110(512): 1479-1490.

Chan, J.C. and Eisenstat, E. (2018). Bayesian Model Comparison for Time‐Varying Parameter VARS with Stochastic Volatility. Journal of Applied Econometrics, 33(4): 509-532.

Chow, G.C. and Lin, A.L. (1971). “Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series.” The Review of Economics and Statistics 53(4): 372-375.

Dixon, R. and Mahmood, M. (2008). “The Victorian Economy in the 1989/90-1992/93 Recession.” Australasian Journal of Regional Studies, 14(2): 155-166.

Ghysels, E., Andreou, E. and Kourtellos, A. (2011). “Forecasting with Mixed-Frequency Data.” In The Oxford handbook of economic forecasting.

Harding, D. and Pagan, A. (2002). “Dissecting the Cycle: a Methodological Investigation.” Journal of Monetary Economics 49(2): 365-381.

Norman, D. and Walker, T. (2004).  “Co-movement of Australian State Business Cycles.” Reserve Bank of Australia Research Discussion Paper, 2004-09.

Koop, G., McIntyre, S., Mitchell, J. and Poon, A. (2018). Regional Output Growth in the United Kingdom: More Timely and Higher Frequency Estimates, 1970-2017. EScoE Discussion Paper 2018-14.

Koop, G., McIntyre, S., Mitchell, J. and Poon, A. (2020). "Regional Output Growth in the United Kingdom: More Timely and Higher Frequency Estimates from 1970." Journal of Applied Econometrics 35(2): 176-197.

Mitchell, J., Smith, R.J., Weale, M.R., Wright, S. and Salazar, E.L. (2005). “An Indicator of Monthly GDP and an Early Estimate of Quarterly GDP Growth.” The Economic Journal 115(501): 108-129.

Mariano, R.S. and Murasawa, Y. (2010). “A Coincident Index, Common Factors, and Monthly Real GDP.” Oxford Bulletin of Economics and Statistics 72(1): 27-46.

Queensland Treasury. Queensland State Accounts. Available on the Queensland Government Statistician's Office website.

Reserve Bank of Australia. (2000). “The Australian Economy in the 1990s.” Available on the RBA website.

Reserve Bank of Australia. (2010). “Twenty Years of Economic Growth.” Available on the RBA website.

Appendix

Footnotes

[1] The authors are grateful for the generous assistance from James Mitchell and Aubrey Poon. This paper also benefited from comments from Anthony Rossiter. The views expressed are those of the authors and do not necessarily reflect the views of DTF.

[2] Australian Bureau of Statistics (ABS) published quarterly GSP estimates for the first time in the December quarter of 1993 and the release was discontinued after the June quarter of 1997.

[3] GSP as measured by a single approach also includes a statistical discrepancy to account for the difference from the headline GSP measure, which is the average of three measures based on the income approach, expenditure approach and production approach.

[4] Stochastic volatility is allowed to capture the change in volatility of residuals over time.  

[5] The selection of lags is supported by maximum likelihoods and is consistent with the number of lags in the intertemporal restriction in equation (1). 

[6] While the model also produces estimates for the Northern Territory and the Australian Capital Territory, these estimates are not included due to high volatility and uncertainty, likely reflecting their small shares of Australia’s economic activity. These territories account for 1 and 2 per cent of GDP respectively – and hence GDP is not representative of their conditions.

[7] The pandemic has led to considerably large uncertainties in the quarterly GSP estimates for 2020. Econometric models struggle to accommodate the exceptionally severe downturn that the economy experienced in the June quarter of 2020, given the complete absence of any comparable episode in the historical data. Therefore, the estimates for the 2019–20 financial year should be treated with caution. For a similar reason, estimating GSP for the September quarter 2020 is not included in this paper as it requires assumptions on the 2020–21 GSP growth and the contribution from September quarter. 

[8] Our estimates start from 1988 as the VAR model includes 7 lags and the annual GSP data (in a consistent chain volume measure) starts from 1986–87.   

[9] For example, 1995 vintage ABS estimates suggest Tasmania’s economic growth was negative during 1993–94. However, the most recent ABS State Accounts release shows that Tasmania recorded positive economic growth in every year since 1992–93 to 1999–2000. Similarly, according to the latest ABS annual GSP release, Victoria’s GSP grew by 3.4 per cent in 1993–94 and 3.0 per cent in 1994–95, which are closer to our quarterly estimates than the 1995 vintage ABS estimates.

[10] The program is widely used for dating business cycles in recent literature, available on the National Cente for Econometric Research website. We used the parameters for quarterly data suggested by Harding and Pagan (2002): MinimumPhase=2 quarters, MinimumCycle=5 quarters, SymmetricWindow=2 quarters and Threshold=25%. That is, contractions/expansions are at least two quarters of negative/positive growth and cycles (peak-to-peak and trough-to-trough) are at least five quarters long.

[11] The results for the 2019–20 financial year is not included in the figure due to high uncertainty in the quarterly GSP estimates for the June quarter 2020 and the incomplete phase of contraction in some states and territories.

[12] Large losses were recorded by Westpac, ANZ, the Bank of Melbourne and Metway Bank, which was merged with Suncorp in 1996.

Reviewed 22/06/2021
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