RDP 2015-14: Okun's Law and Potential Output 2. Comparisons with Previous Research
December 2015 – ISSN 1448-5109 (Online)
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2.1 Measures of Potential Output
A simple measure of potential output growth is the average rate of GDP growth. A linear trend of the logarithm of GDP is very similar. One difficulty with these measures is that average rates of GDP growth vary across time, and hence these estimates will be sensitive to the sample period. For example, real GDP growth averaged 5 per cent in the 1960s, around 3.2 per cent in the 1970s, 1980s and 1990s, but only 2.9 per cent since 2000. Assuming that more recent observations are more relevant, this instability could be accommodated by using a shorter moving average or a statistical filter, such as Hodrick-Prescott (henceforth HP). However, these approaches have two important problems. First, they involve an arbitrary judgement about either the length of the moving average or the degree of smoothness in the HP trend. Second, as more weight is placed on recent outcomes, the more will estimates of potential reflect temporary changes, such as the business cycle and noise.
A common motivation across most definitions of potential output is to remove temporary variations. In our assessment, the most important temporary factor associated with Australian GDP growth in recent decades has been changes in the unemployment rate. Cyclical variations in unemployment are well known but longer-term variations are also important. Unemployment averaged 8.8 per cent in the 1990s and 5.4 per cent over the past 10 years. On the assumption that this downward trend will not continue, the GDP growth that accompanied it is an overestimate of growth going forward. Accordingly, it is desirable to remove this effect from an estimate of potential output growth.
A popular method for removing the effect of variations in unemployment is to construct ‘production function’ estimates of potential output. The non-accelerating inflation rate of unemployment (NAIRU) is typically estimated from a Phillips curve regression. Then the NAIRU-consistent level of employment is combined with separate contributions from capital and technology in a production function. Examples of this approach include OECD (2015), which draws on Johansson et al (2013); International Monetary Fund (2015), which draws on De Masi (1997) and references therein; and de Brouwer (1998, Section 2.5).
In principle, the Phillips curve/production function approach makes it possible to allow for other influences on potential GDP growth, such as expected demographic changes. In practice, typical production function estimates model many components as univariate processes, such as HP trends. So little extra information is gained and information on other variables and covariances between the components is lost. This approach makes potential GDP vary with the cycle, particularly near end points. Furthermore, this approach incurs costs of complexity and loss of transparency. We are not aware that these complications have been shown to provide a useful benefit. Indeed, forecasts that employ this approach have not performed well, as we discuss in Section 5.
Structural macroeconomic models provide several measures of potential output. Perhaps the most prominent measure, typically associated with dynamic stochastic general equilibrium models, is defined as GDP that is consistent with flexible wages and prices (e.g. Basu and Fernald 2009; Vetlov et al 2011). One limitation of such measures is that they are highly model-dependent. Changes to the specification of the economy's underlying structure can yield quite different estimates. Another limitation is that it is not clear that these measures satisfy other purposes of potential output.
The Kalman filter is commonly used to distinguish between trends, cycles, noise and other influences. Accordingly, it is an increasingly popular tool for estimating the growth rate of potential output. See, for example, Fleischman and Roberts (2011) and references therein. However, this research has typically involved large systems that draw signals from many variables. We also use the Kalman filter, but only draw signals from the unemployment rate, which makes our approach simpler to estimate, interpret and evaluate.
To be clear, our measure is not designed to serve every purpose of estimates of potential output. For example, we do not claim that it directly helps forecast inflation or short-term movements in GDP. Nor do we see our measure as a substitute for measures designed for these purposes. Different measures for different purposes can coexist. It would be nice to have one measure that did everything well, but that has yet to be found.
As noted above, potential output has been defined in many different ways. Those accustomed to other measures may find our usage confusing. This difficulty is regretted, but seems unavoidable if one is to be clear about what the term potential output means. We view our definition as reasonable and informative: it is simple, useful, standard in the literature on Okun's law, consistent with Okun's original usage and consistent with the main way that central banks use the concept. That said, little of substance depends on definitions. Were other measures to be in active use, more precise terminology would probably be necessary.
2.2 Okun's Law
Arthur Okun (1962) pointed out a negative relationship between unemployment and output, which became known as ‘Okun's law’. The ‘levels’ form of the relationship can be written as:
where U is the unemployment rate and Y is the logarithm of the level of real GDP. Okun called U* ‘full employment’ and Y* ‘potential output’. There are many estimates of relationships like this using Australian data, including Kalisch (1982), Nguyen and Siriwardana (1988), Peters and Petridis (1988) and Ball, Leigh and Loungani (2013). However, as we discuss in Section 6.2, we have not found estimates of U* and Y* to have predictive power either within sample or out of sample. Moreover, although measures of U* and Y* can be constructed so that Equation (1) fits the data, ‘explanations’ that rely on unobservable variables constructed after the event are not compelling.
Okun also pointed out that a similar relationship can be written in differences.
where ΔU is the change in the unemployment rate, ΔY is growth in log GDP (typically represented in terms of annualised percentage changes) and μ is the rate of GDP growth consistent with stable unemployment. Using quarterly US data from 1947 to 1960, Okun estimated μ = 4 and β = −0.3.^{[2]} Under some assumptions Equation (2) can be derived from Equation (1). However, we prefer to think of Equation (2) as a separate and simpler way of modelling the data that avoids some of the problems with Equation (1) noted above.
Variations on Equation (2) have been estimated for many different countries, at different frequencies and for different sample periods. Borland (2011) estimates μ = 3.2 and β = −0.41 based on four-quarter changes from 1979 to 2011 in Australia. Earlier, similar Australian estimates include Watts and Mitchell (1991), INDECS Economics (1995) and Dixon and Thomson (2000). These estimates are broadly similar to those from Okun's law in changes for other countries, such as those in Ball, Jalles and Loungani (2015).^{[3]} Ball et al also report that an equation like (2) describes the relationship between output and unemployment in professional forecasts in many countries.
One of the main objectives of our paper is to re-examine Equation (2). We estimate over a long sample period (1960–2015) and pay close attention to its stability and specification. We corroborate previous researchers' finding that simple ordinary least squares (OLS) models of Okun's law are not stable. Watts and Mitchell (1991) attribute instability in the Okun's law relationship in Australia to a decline in trend GDP growth over time. Fortunately, we can model this instability, as we show in the next section.
More importantly, our paper differs from previous estimates of Okun's law in drawing out its implications. In particular, Okun's law provides (a) time-varying estimates of potential output and (b) forecasts of the unemployment rate that compare favourably with alternative forecasts.
Footnotes
We have rearranged coefficients from his ‘first differences’ specification to be in comparable units to those elsewhere in our paper. Okun's preferred estimates, which are similar, averaged estimates from a range of specifications. [2]
Ball et al's estimates for −β are, in ascending order, Germany (0.08), Japan (0.11), Italy (0.16), New Zealand (0.24), France (0.27), Canada (0.43), the United States (0.5) and Australia (0.5). [3]