# RDP 2005-07: The Australian Business Cycle: A Coincident Indicator Approach 2. Coincident Indices and Factor Models

Consider a world in which the growth rate of each macroeconomic variable can be regarded as the sum of a common cyclical component and an idiosyncratic term (which might include any sector-specific shocks). For example, residential construction should broadly follow the overall economic cycle but might also be affected by tax changes or immigration flows. By taking an average of a large number of variables from a wide range of sectors, the shocks to specific series or groups of series – the idiosyncratic components – should tend to average out to zero, leaving just the common component. This common component would capture the business cycle – that is, the overall state of economic activity, which we would expect to be fairly persistent or slow moving and not noisy like individual series.

This is the essence of what coincident indices attempt to achieve – averaging a range of variables to capture the common economic cycle. In practice, there are complexities in the data that alternative methods of constructing coincident indices address in different ways. To account for the fact that some variables are more cyclical than others, coincident indices are often constructed using normalised growth rates, or binary variables to indicate whether a series increased or fell. Some coincident indices place greater weights on series that are considered to be more reliable indicators of the business cycle, while others take a simple average of all of the series. Finally, not all economic series are going to be perfectly aligned; some, such as finance approvals, may be leading while others, such as the unemployment rate, may be lagging. Some techniques restrict the index to series that are coincident, while other methodologies attempt to align the series according to their typical leading or lagging relationships.

The more recent factor methodologies that we use in this paper use advanced statistical techniques to address these issues. They use a broad panel of series with the idea that using more series means that the influence of idiosyncratic shocks of any one series will be smaller, thereby making the estimate of the economic cycle more precise. In addition, they weight particular series according to the information they contain about the common cycle. Series that typically experience larger idiosyncratic shocks will receive a smaller weight. They also use normalised growth rates, rather than censoring the data as binary variables, so as to extract the greatest amount of information from each series. One of the techniques used (FHLR) explicitly takes account of leading and lagging relationships among the variables, while the other (SW) can potentially also deal with this issue. Finally, these methodologies allow for the possibility of several common ‘cycles’ or factors (rather than just one), some of which may be affecting some economic series more than others.

These new methodologies that extract multiple common factors from large panels of data have not been used to study the Australian business cycle. However, this paper can be seen as the latest iteration in a long literature that has constructed simpler coincident indices to study the Australian economy. Beck, Bush and Hayes (1973) and Bush and Cohen (1968) use large panels of data to construct historical coincident indices by first defining peaks and troughs for each series and then calculating the index as the proportion of series that were in an expansion phase in each month. Haywood (1973) constructs several coincident indices using unweighted and judgementally-weighted averages of both normalised monthly changes and binary indicators of the sign of monthly changes. Boehm and Moore (1984) construct a coincident index from an average of six economic series. The Boehm and Moore work has carried forward as the coincident indicators produced by the Melbourne Institute of Applied Economic and Social Research and the Economic Cycle Research Institute.