RDP 2014-12: A State-space Approach to Australian GDP Measurement 1. Introduction

The level and growth of real economic activity is of great interest to economic policymakers as well as the general public. Increases in activity are typically associated with rising living standards. And economic activity influences other economic outcomes, such as inflation and unemployment.

But measuring economic activity is difficult. In Australia, a key measure of activity, gross domestic product (GDP), is measured using three different approaches, based on expenditure (GDP(E)), income (GDP(I)) and production (GDP(P)).^[1] Conceptually, the three measures should be equal, but in practice the measures differ because they are constructed from different data sources and have varying degrees of measurement error.^[2] It is important to emphasise that the term measurement error does not imply any failure on the part of statistical agencies. It is a statistical term that refers to the inherent errors that occur when one infers aggregate quantities from a sample of observations.

In this paper, we use state-space methods to combine the three Australian Bureau of Statistics (ABS) measures of GDP into an estimate of aggregate economic growth. In contrast to existing approaches, our method allows us to capture three salient features of GDP measurement. First, GDP(E), GDP(I) and GDP(P) should be equal. Second, all three of these quantities are measured with some degree of error. Third, because of overlap between the data sources that feed into the three published estimates of GDP, these measurement errors are likely to be correlated. Once we account for these features of the data, we generate an estimate of economic activity which is smoother than suggested by conventional measures of GDP. This suggests that many large quarterly fluctuations in the rate of economic growth reflect errors in measurement rather than fundamental shifts in the pace of economic activity.

In Australia, the most common alternative to our approach is to take a simple average of the three measures, known as GDP(A).^[3] The ABS considers this to be the most reliable estimate of final output, in part because independent errors in the underlying measures are often offsetting (Aspden 1990; ABS 2011). More broadly, the literature on model averaging suggests that if one possesses a set of estimates for some quantity being measured, then a combination of the estimates tends to perform better than any individual estimate.^[4]

While using a simple average of the three GDP measures as an estimate for actual GDP is simple and transparent, it does not fully exploit all available information. For example, if one measure of GDP is particularly noisy, so that any given observation is likely to be quite different from actual GDP, then it may make sense to place less weight on that measure and more weight on the remaining two. The technique we explore in this paper provides one way of achieving this: it uses the time series properties of the three GDP measures to construct a composite GDP measure that more fully exploits the available information.

Our paper builds on the existing literature on GDP measurement. Most directly, it represents an application to Australian data of the techniques derived by Aruoba et al (2013), who construct a state-space measure of US GDP.^[5] The Australian dimension of our study is of interest for two reasons, aside from our natural curiosity as Australian researchers. First, whereas the US statistical authorities only construct income and expenditure measures of GDP at a quarterly frequency, the ABS also publishes a production measure. We show that the methods of Aruoba et al (2013) extend to this environment. Second, the Australian economy differs in several respects from that of the United States in ways that may make GDP measurement more challenging. In particular, Australia is a smaller, more trade-exposed economy with a large resource sector. Our results support the idea that these variations in economic structure translate into a different pattern of GDP measurement errors in Australia.

Our work is also related to research evaluating the relative merits of expenditure, income and production as measures of economic activity. The primary focus of the research to date has been on the US economy, for which the most widely reported measure of output is derived from the expenditure side of the accounts. Despite this, a common finding is that expenditure-side estimates of output in the United States suffer from more severe measurement issues than income-side estimates. For example, Nalewaik (2010) cites the imprecise source data for personal consumption expenditure on services as a likely source of noise in the US GDP(E) estimates. In contrast, movements in many US GDP(I) components can be estimated reliably using tax data. Estimates of US GDP(I) tend to be less variable than GDP(E), while also being more highly correlated with other indicators of economic conditions (Fixler and Grimm 2006; Nalewaik 2010, 2011). Further, in the United States, GDP(E) tends to be revised towards GDP(I) over time.

Research using Australian national accounts data favours the use of the production-side rather than expenditure- or income-side estimates (Aspden 1990; ABS 2012; Bishop et al 2013). The relatively large share of resources in Australian GDP makes measures of output particularly responsive to trade data. Timing differences in imports and exports and variability in trade prices can introduce noise into estimates of expenditure and income (ABS 2012). In addition, GDP(I) and GDP(E) are reliant on the ABS register of businesses, which is typically updated with a delay. Bishop et al (2013) found that GDP(P) tends to be revised less than the other two measures and is as reliable in real time as GDP(A). These factors provide a case for applying a larger weight on GDP(P) in model averaging.

While it is useful to know the relative merits of expenditure, income and production measures of economic activity, using just one measure is unlikely to be optimal. The techniques that we use in this paper allow information from all three measures of GDP to be combined, and allow more weight to be placed on the more reliable measures.

Footnotes

GDP(E) is calculated as the sum of all expenditure by resident households, businesses and governments on final production, plus exports and the change in inventories, less imports; it is available at a quarterly frequency in both nominal and real terms. GDP(I) measures the income received for providing labour and capital services as inputs to production, adjusted for indirect taxes and subsidies, and is available in nominal terms; an estimate of real GDP(I) is obtained by dividing nominal GDP(I) by the GDP(E) deflator. GDP(P) measures the value of production in the economy as the difference between the value of outputs and the value of intermediate inputs consumed in production, and is available at a quarterly frequency in real terms and annually in nominal terms. For more detail on the data construction methods, see ABS (2007, 2011, 2012). The Australian Bureau of Statistics is one of only a few statistical agencies in the world to compile and publish all three measures of GDP. [1]

See, for example, Bishop, Gill and Lancaster (2013) for a recent discussion of measurement error associated with the various GDP estimates. [2]

In many other countries a single measure of GDP is typically used. [3]

See, for example, Timmermann (2006) for an overview of the literature, or Laplace (1818) for an early application of model averaging. [4]

In unpublished work using Australian national accounts data, Scutella (1996) also explored the possibility of extracting underlying economic growth from the noisy expenditure, income and production measures. [5]