Okun coefficients and participation coefficients by age and gender

Evans, Andrew Article Okun coefficients and participation coefficients by age and gender IZA Journal of Labor Economics Provided in Cooperation with: IZA – Institute of Labor Economics Suggested Citation: Evans, Andrew (2018) : Okun coefficients and participation coefficients by age and gender, IZA Journal of Labor Economics, ISSN 2193-8997, Springer, Heidelberg, Vol. 7, Iss. 5, pp. 1-22, https://doi.org/10.1186/s40172-018-0065-8 This Version is available at: https://hdl.handle.net/10419/195027 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ IZA Journal of Labor Economics Evans IZA Journal of Labor Economics (2018) 7:5 https://doi.org/10.1186/s40172-018-0065-8 ORIGINAL ARTICLE Open Access Okun coefficients and participation coefficients by age and gender Andrew Evans Correspondence: [email protected] Macquarie University, Sydney, NSW 2109, Australia Abstract Estimates of the Okun coefficient are made for Australian workers grouped by age and gender using an unobserved components model. By analogy we define and estimate a participation coefficient which measures the cyclical response of the labour force participation rate to cyclical output shocks. The trend and cycle decomposition methodology used here leads to higher absolute estimates of the Okun coefficient than those typically found in the literature, although we find a pattern of variation in the coefficient by age and gender which is typical. We also find that, in aggregate, participating males in the middle age groups tend to stay in the labour force throughout the business cycle whereas females of the same age tend to participate procyclically. This has policy implications for attempts to increase the rate of participation of particular groups by age and gender following a cyclical downturn. JEL Classification: C32, E32, J21 Keywords: Okun’s Law, Labour force participation, Trend and cycle decomposition 1 Introduction One of the most robust historical relationships in macroeconomics has been the negative relationship between unemployment and output growth as described by Okun (1962). This knowledge alone is not useful for guiding policy prescriptions without differentiating between the permanent and transitory components of unemployment and output. Structural or institutional change is necessary to influence the permanent trend whereas short-run policy initiatives are likely to affect only the transitory cycle. The response of cyclical unemployment to cyclical output shocks is of particular interest to policymakers. In this research, a trend and cycle decomposition is performed on the unemployment rate and the log of real GDP, and the cyclical components are interpreted as measures of the unemployment gap and output gap respectively. The estimated gaps are used to generate estimates of the Okun coefficient for workers grouped by age and gender. The behaviour of the labour force participation rate1during the business cycle also needs to be considered because, without it, the unemployment rate is an incomplete indicator of the level of unutilised labour. Discouraged workers who transition from unemployment to non-participation during a recession may mask the true number of people who want more work. Participation was identified as a key driver of economic © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Evans IZA Journal of Labor Economics (2018) 7:5 Page 2 of 22 growth, improvement in living standards and community prosperity in the Intergenerational Report (Commonwealth of Australia 2015). Usually, the long-run trends affecting participation are of most interest to policymakers, such as the changing age structure of the population, migration effects and the participation of females and the elderly in the workforce, but cyclical effects also need to be understood. Policy initiatives which are intended to increase participation in a given context need to be designed either to influence the trend or the cyclical component. In this research, the focus is the business cycle behaviour of participation. We define a participation coefficient by analogy to the Okun coefficient which measures the cyclical response of the participation rate to output. In the literature, the decomposition of macroeconomic time series is often performed using a Hodrick-Prescott filter (hereafter HP). Shortcomings of the approach are well known, arising from the requirement to choose a value for the smoothness parameter which controls the relative variance of trend and cycle components. The apparent behaviour of the HP cycle may be to some degree an artefact of the filtering process rather than a reflection of characteristics of the true data-generating process (Harvey and Jaeger 1993). For a recent criticism of the HP filter, see Hamilton (2017). As an alternative, we use the structural time series model developed by Harvey (1985)tomakemaximumlikelihood estimates of unobserved trend and cycle components. The key advantage of the unobserved components (UC) model is that the components are estimated using a statistical model rather than being imposed by the structure and parameters of the HP filter. A multivariate model of output, unemployment, participation and total hours worked which incorporates a common business cycle is jointly estimated to extract the trends and cycles. Estimates are made separately by age and gender for Australian data. The first contribution of this paper is a new set of estimated Okun coefficients derived from the relative magnitude of the unemployment and output cycles. The second contribution is a set of participation coefficients which reveal the estimated magnitude of the cyclical response of labour force participation by age and gender to shocks to cyclical output. In Section 2literature is reviewed which provides theoretical grounds for and empirical description of the business cycle behaviour of unemployment and participation. Section 3 describes the labour market data used for the empirical analysis and illustrates some of the salient features of particular age and gender groups. A detailed specification of the empirical model is provided in Section 4. Empirical results are given in Section 5 and the estimated trend and cycle components are illustrated graphically. Estimates of the Okun and participation coefficients are given by age and gender and a comparison is made with estimates of the former made in the literature. Section 6concludes the paper. 2 Theoretical background 2.1 Okun’s Law A negative relationship between output and unemployment can be easily motivated by theory, for example, the assumption of a Cobb-Douglas production function with a labour force of fixed size yields an approximately negative linear relationship between log output and the unemployment rate, with sensitivity determined by the output elasticity of labour input. Most studies focus simply on the empirical relationship, such as the relationship between first differences described by Okun (1962): Evans IZA Journal of Labor Economics (2018) 7:5 Page 3 of 22 ut=α−βyt+εt,(1) where utis the change in the unemployment rate, ytis percentage change (or log change) in a measure of real output such as GDP and εtis an error term. βis interpreted as the Okun coefficient2. A shortcoming of this representation is that it implies that the relationship between utand ytis purely contemporaneous. The model can be improved easily by adding lagged terms in both variables: ut=α+ p  i=1 γiut−i+ q  j=0 βjyt−j+εt.(2) The Okun coefficient can also be interpreted as the long-run impact of yton ut (also ‘long-run multiplier’ or ‘dynamic beta’) which can be derived from the coefficient estimates as (Harvey 1993, 159) β=q j=0βj 1−p i=1γi.(3) A difficulty which remains using this approach is that there is no explicit distinction made between temporary and permanent shocks acting through yt. Another expression for the relationship between unemployment and output (similar to the ‘gap version’ described by Okun (1962)) is ut−u∗ t=−βyt−y∗ t+εt.(4) Different interpretations of y∗ tmay apply depending on the context of the research. In Okun’s original paper, it represented potential output, the amount the economy could produce under conditions of full employment, and the econometric model was used to generate estimates of potential output. In this paper, we interpret y∗ tas the (log) natural level of output when the economy is operating at sustainable full capacity. This level will vary though time depending on many factors we have not explicitly modelled, such as the level of demand and institutional constraints. It follows that u∗ tcan be interpreted as the equilibrium rate of unemployment which should prevail when output is being produced at its natural rate. It must be emphasised that there would be a conceptual difference between what is being measured by the parameter βin each of Eqs. 1,3 and 4, but each of them are sometimes described as ‘the Okun coefficient’ in the relevant context. A trend and cycle decomposition of both ytand utwill be made in which the estimated trend will be interpreted as the time-varying equilibrium (y∗ tor u∗ t)andthecycleasa measure of the gap represented in Eq. 4. By construction, the gaps will be stationary with zero mean. The sensitivity of the unemployment gap to the output gap will be interpreted as a measure of the Okun coefficient. Separate estimates of the coefficient will be made by gender and by age bracket. There is ample evidence that estimates of the Okun coefficient vary across countries which is likely to reflect different institutions, policy settings and cultural differences between them. There are mixed results regarding the stability of estimates through time within country but, on balance, there is evidence that the relationship between output and unemployment may vary due to structural changes which occur over time. Ball et al. (2013) considered whether Okun’s Law was still robust some 50 years after Okun’s original paper and found it to be strong and stable Evans IZA Journal of Labor Economics (2018) 7:5 Page 4 of 22 in most countries, but with significant variation between countries. They rejected the idea that the relationship has broken down after the most recent recessions leading to claims of so-called jobless recoveries in the USA. Lee (2000)findsstatistically significant Okun coefficients across a range of OECD countries but with great variation in magnitude. Some of the variation is attributed to higher rigidity in some of the European labour markets and Japan compared to the USA (see also Nickell (1997)).Leealsofindsstrongevidenceofstructuralbreaksmostlyin the early 1970s but which also vary by country. Dixon et al. (2017)estimatedan Okun coefficient using a panel of 20 OECD countries (including Australia) for the period 1985–2013, having controlled for the influence of labour market institutions such as union coverage, unemployment insurance and employment protection legislation. They rejected the hypothesis that the Okun coefficient had remained the same over time in their base model but were able to explain most of the increase using the share of temporary workers in the workforce, amongst other changes to institutional variables. Further cross-country studies of the Okun coefficient can be found in International Monetary Fund (2010)andMoosa(1997)). There have also been many studies which consider a potential non-linear relationship between output and unemployment. Cuaresma (2003)specifiesamodelwitharegimedependent Okun coefficient which allows an asymmetric response of unemployment to output depending on whether the economy is in either of two regimes which correspond approximately with expansion or recession. The absolute sensitivity measured by the Okun coefficient is found to be approximately twice as large when the economy is in recession. Holmes and Silverstone (2006) estimate a model with two forms of asymmetry whereby, in the first case, the Okun coefficient depends on two regimes defined by positive and negative cyclical output and, in the second case, the absolute value of the coefficient depends on the sign of the shock. The authors find evidence of both forms of asymmetry. Lee (2000) finds mixed evidence of asymmetry depending on the specific country. Dixon et al. (2017) are unable to reject the hypothesis of symmetry. Bodman (1998, 410) finds evidence of non-linear behaviour in unemployment in Australia, in particular he finds that shocks are more persistent in recessions than expansions, which is broadly suggestive of hysteresis in the labour market. There are sound reasons to expect different responses to the business cycle amongst different age and gender groups. For example, younger workers are likely to have less experience than older workers and have less employment protection (such as may occur under a temporary contract) and so be more likely to suffer involuntary job loss in a recession. Equally, recent school-leavers are likely to take into account the state of the business cycle when they choose between higher education and joining the labour force (Dellas and Sakellaris 2003). Both of these factors would contribute to greater cyclicality of youth unemployment. Unemployment for males may be more cyclical than for females because they have higher representation in cyclical activities like building construction (Zanin 2014). Some females with young children may elect to leave the labour force during an economic downturn, thereby not affecting the official unemployment measure. Lastly, older workers may have a difficult choice to make in a downturn between unemployment and participation given the difficulty they may face re-joining the workforce at a later date, so there may be a more complex interaction between cyclical unemployment and participation for older workers. Evans IZA Journal of Labor Economics (2018) 7:5 Page 5 of 22 In this research the focus will be on the differences in coefficients for age and gender groups rather than on possible asymmetry and stability of the coefficients through time. The model will have an inherently linear relationship between output and unemployment shocks. However, the basic framework for estimating the Okun coefficient will be extended to allow joint estimation of the sensitivity of unemployment and labour force participation to the business cycle, to capture any interaction between them during the cycle. 2.2 Cyclical participation Mincer (1966) put forward theories to explain cyclical movement of workers in and out of the labour force. The added-worker effect was used to explain the type of worker who is more likely to join the labour force in an economic downturn to compensate for the potential loss of income by another household member who may become unemployed. Historically, this concept was applied mainly to married women who sought to add to household income to mitigate loss of income by their spouse. The addedworker effect would generate counter-cyclical participation. Mincer also described the discouraged-worker effect which posited that some unemployed workers stop looking for work in an economic downturn (and therefore become non-participants) because they perceive that the probability of finding work is so low it is not worth searching. This same group are likely to re-join the labour force when the economy improves, generating procyclical participation. The added-worker and discouraged-worker effects can coexist and aggregate labour market data tends to reveal only the net contribution of the two effects. It has been argued by Dixon et al. (2004) that in relation to the Australian economy it is not credible to try and explain the variation in the participation rate with a sole focus on the movement of discouraged workers between the states of unemployment and non-participation. In the first place, gross flow data3reveals that the largest average flows are between non-participation and employment. The magnitude of these flows is almost twice as large as those between non-participation and unemployment (Dixon et al. 2015, 2530) which suggests that they are an important part of the overall dynamics of the labour market. Similar observations have been made in other markets including the USA (Blanchard and Diamond 1990, 91-92). Dixon et al. (2004) find that the main influence on the growth rate of the labour force is the size of the net flow between non-participation and employment. Dixon et al. (2015)arguethatitisessential to treat flows to and from non-participation as endogenous within a system also including employment and unemployment flows. Other studies which treat participation as endogenous to examine its behaviour during the business cycle can be found in Darby et al. (2001), Elsby et al. (2015) and an Australian study by Ponomareva and Sheen (2013). The Intergenerational Report (Commonwealth of Australia 2015)projectsthatparticipation in Australia will decline over the next 40 years due to a changing age demographic which will see a relative decline in age cohorts of people where participation tends to be highest. This is despite an anticipated increase in participation within each cohort. On the other hand, the health of older Australians is improving so that a greater number of them are capable of continuing to work beyond traditional retirement age if circumstances permit. The importance of increasing participation Evans IZA Journal of Labor Economics (2018) 7:5 Page 6 of 22 to the Government is reflected in policy measures to support the participation not only of mature-age job seekers but also youth, women and parents (Commonwealth of Australia 2015, 96). Even though the report focusses on long-term trends, we observe that temporary output shocks can have a long-term effect on participation and unemployment if there is hysteresis. Duval et al. (2010) find that severe recessions have a significant and persistent impact on the level of participation in a panel of 30 OECD countries including Australia. They find that aggregate participation may be 1.5–2.5% lower 5 to 8 years after the previous cyclical peak before the commencement of the recession. Persistent or permanent impact on older workers may be explained by irreversible retirement decisions made in response to a recession, which can be influenced by early retirement incentives arising from policy initiatives or those embedded in pension schemes (Duval et al. 2010). Persistent impact on the participation of younger workers may be explained by choices to enrol in longer programmes of higher education and training during a downturn. These findings show that it is important for policymakers to consider cyclical shocks to participation as well supporting long-term trend growth. There has been much less empirical analysis of the cyclicality of participation than unemployment in the literature in most countries, including Australia. In macroeconomic studies of the USA, the size of the labour force has often been assumed to be acyclical as discussed in Erceg and Levin (2014), with participation sometimes modelled as a fixed percentage of the civilian population. Benati (2001) found evidence of procyclical participation at a business cycle frequency (a net discouraged-worker effect) in the USA at an aggregate level and for a number of age-sex groups. In many developed countries, participation rates declined following the Great Recession and attempts have been made to determine how much of the decline was cyclical and how much reflected a permanent change in labour supply, without universal agreement as to the conclusion. Erceg and Levin (2014) found evidence that cyclical factors accounted for most of the decline since 2007. Van Zandweghe (2012)foundthatparticipation was very weakly procyclical from 1948 to 2011 but that since 2007 the participation rate had become more sensitive to the state of the economy and that about half of the decline in participation from 2007 to 2011 could be attributed to cyclical factors. The empirical relationship between participation and output cycles can be measured using an equation conceptually similar to Eq. 4with the unemployment gap replaced by the participation gap. The estimated trend from a decomposition of the participation rate will incorporate all of the permanent influences on the level of participation such as changing demographics and attitudes towards gender and age in the workforce. The cycle component will be interpreted as the participation gap, a transient deviation of the current level from the permanent trend. The sensitivity of the participation gap to the output gap will be estimated by gender and age bracket. 3 Australian labour market data We use seasonally adjusted monthly time series of the unemployment rate (ut)andlabour force participation rate (pt) for 13 groups of workers: all persons, males, females and each gender separated into five 10-year age brackets. The youngest age bracket is 15-24 Evans IZA Journal of Labor Economics (2018) 7:5 Page 7 of 22 years old, followed by 25-34 years old and so on up to 55-64 years old. The characteristic behaviour of unemployment and participation for each age bracket is illustrated in Fig. 1from February 1978 to June 2017. For output we use the log of seasonally adjusted real quarterly GDP (gt) multiplied by 100. We also make use of a seasonally adjusted series of total monthly hours worked in all jobs by all persons, from July 1978. Growth in hours worked over several decades mostly reflects population growth so we use the log of hours worked multiplied by 100 which we denote by ht. Seasonally adjusted series are used in each case so that any seasonal pattern in the raw series which may appear to a c e g b d f h Fig. 1 Historic unemployment and participation rates by age bracket. aMale unemployment rate (age 15–44 years). bFemale unemployment rate (age 15–44 years). cMale unemployment rate (age 45–64 years). dFemale unemployment rate (age 45–64 years). eMale participation rate (age 15–44 years). fFemale participation rate (age 15–44 years). gMale participation rate (age 45–64 years). hFemale participation rate (age 45–64 years) Evans IZA Journal of Labor Economics (2018) 7:5 Page 8 of 22 be some form of annual cycle does not interfere with the estimation of the cycle component at a business cycle frequency. The relationships between output, unemployment and participation are the main interest in this research, whereas the monthly hours worked series is used primarily to assist in identifying a common cyclical component across the series. The estimation period used for our empirical results will be September 1980 to June 2017. 4 Empirical model A trend and cycle decomposition methodology is required to generate estimates of gaps foroutputandthelabourmarketseriessothatitispossibletomeasuretheresponsiveness of cyclical unemployment and participation to cyclical output shocks in a relationship analogous to the empirical relationships described by Eq. 4. Studies of Okun’s Law in the literature have frequently made use of the HP filter to extract an estimate of the output gap and sometimes also the unemployment gap. A problem with the HP filter for this application is that the chosen smoothness parameter can have a dramatic effect on the relative variance of the trend and cycle components. In this research, an alternative decomposition methodology is used to generate maximum likelihood estimates of the components without prior restrictions on the relative magnitude of the trend and cycle variances. 4.1 Multivariate unobserved components model with common cycle The following is a typical specification of an unobserved components model with stochastic trend and cycle components, mostly following the notation of Harvey (1985). The model has been represented in so-called state space form so that it can be estimated using the Kalman filter. The state space form requires a measurement equation in which an observable series is linearly related to a set of unobservable state variables. We will make a joint estimation of a system including output, unemployment, participation and hours worked, but first we present only the parts of the system relating to output in Eq. 5. gt=τgt +ct+εgt,εgt ∼iid 0, σ2 εg, τgt =τgt−1+βgt−1+ηgt,ηgt ∼iid 0, σ2 ηg, βgt =βgt−1+ζgt,ζgt ∼iid 0, σ2 ζg,(5) ct c∗ t=ρcos(λ) sin(λ) −sin(λ) cos(λ) ct−1 c∗ t−1+κt κ∗ t,κt,κ∗ t∼iid 0, σ2 κ. The trend in log output is represented by τgt,withslopeβgt,andthecyclebyct.The irregular component εgt can be interpreted as random noise or as a measurement error. The specification of the trend is very flexible in terms of the types of data-generating processes that it can be used to fit. In the most general form, both of the variances σ2 ηg and σ2 ζgare freely estimated and, if both variances are non zero, the trend would be an integrated process of second order (in the literature this is usually referred to as a local linear trend (LLT) model). If the slope variance σ2 ζgis restricted to zero, then the trend will be a random walk with drift (also known as the local level (LOCL) model). If the level variance σ2 ηg=0 whilst σ2 ζg>0 then the trend will be ‘smooth’ (known as the integrated random walk (IRW) model). Evans IZA Journal of Labor Economics (2018) 7:5 Page 15 of 22 Table 2 Estimated Okun and participation coefficients by age and gender Okun Particip. Group coeffic. s.e. 95% Conf. coeffic. s.e. 95% Conf. Persons (all age) −0.67*** 0.097 [−0.86, −0.48] 0.22*** 0.049 [0.12, 0.31] Male (all age) −0.77*** 0.106 [−0.98, −0.56] 0.18*** 0.044 [0.09, 0.26] Female (all age) −0.52*** 0.082 [−0.69, −0.36] 0.34*** 0.069 [0.21, 0.48] Male 15–24 years −1.44*** 0.177 [−1.78, −1.09] 0.41*** 0.105 [0.20, 0.61] Male 25–34 years −0.81*** 0.122 [−1.05, −0.57] 0.08 0.059 [−0.03, 0.20] Male 35–44 years −0.52*** 0.081 [−0.68, −0.36] 0.00 0.048 [−0.09, 0.09] Male 45–54 years −0.50*** 0.073 [−0.65, −0.36] 0.12 0.072 [−0.02, 0.26] Male 55–64 years −0.57*** 0.105 [−0.78, −0.37] 0.46*** 0.142 [0.18, 0.73] Female 15–24 years −0.87*** 0.138 [−1.14, −0.60] 0.52*** 0.126 [0.27, 0.77] Female 25–34 years −0.56*** 0.086 [−0.73, −0.39] 0.30*** 0.102 [0.10, 0.50] Female 35–44 years −0.39*** 0.078 [−0.54, −0.24] 0.34*** 0.097 [0.16, 0.53] Female 45–54 years −0.31*** 0.070 [−0.45, −0.18] 0.46*** 0.125 [0.22, 0.71] Female 55–64 years −0.16** 0.071 [−0.30, −0.02] 0.20 0.131 [−0.06, 0.45] Significance at 1%, 5% and 10% indicated by ***,**,*respectively coefficients for the youngest age group (15–24 years) are typical of the pattern found in the literature (for example, 1.14 for males 15–24 years, 0.76 for females 15–24 years by Dixon et al. (2017) for a panel of 20 OECD countries, and 1.10 for males 15–24 years, 0.61 for females 15–24 years by Zanin (2014) for Australia). The different patterns of cyclicality of participation for males and females are visible in the table. For the middle age brackets 25–54 years, the participation coefficients for males are small and not significant, whereas they are positive and significant at 1% for females, which supports our earlier graphical interpretation of the prominence of participation cyclicality for females in the middle age groups. The participation coefficients for the oldest and youngest age groups are also positive and significant except for the oldest female group6. This research is useful for policymakers because it highlights the cyclicality of unemployment and participation for specific age and gender groups, and in particular, it provides higher estimates of the cyclicality than typically reported in the literature. In addition to their stated focus on the long-term trend, the cyclicality of participation maybeofconcerntotheGovernmentbecauseoftheriskthatapersonwholeaves the labour force in a cyclical downturn may become a permanent non-participant. The importance of the persistence of participation is explicitly recognised in the Intergenerational Report which stresses the need to ‘encourage those currently not in the workforce, especially older Australians and women, to enter, re-enter and stay in work’ (Commonwealth of Australia 2015, iii). The analysis in this research uses aggregate historic data which naturally includes the impact of any existing policy initiatives, and is not designed to identify the effectiveness of any specific policy. However, if the Government is concerned about the potential decline in participation in a downturn, particularly amongst certain groups such as females in the middle age brackets, then the results indicate that there is cyclical behaviour which could be the target of further policy support. The types of support suggested in the Intergenerational Report (Commonwealth of Australia 2015, 96) include the provision of flexible and affordable child care and Evans IZA Journal of Labor Economics (2018) 7:5 Page 16 of 22 early learning facilities, including fee assistance rebates for parents and prospective parents7, and the Restart Programme8which provides incentives to employers to hire and retain older workers. Policy measures to support participation need to be viewed in conjunction with support for movement of participants into employment rather than unemployment. 5.4 Robustness The point estimates of the Okun coefficients made here for Australia and shown in Table 2are somewhat higher (absolute) than other estimates in the literature (for example 0.67 for all persons vs. 0.54 by Ball et al. (2013), 0.40 by Borland (2011) and 0.35 by Lancaster and Tulip (2015)), noting that estimates for Australia are already at the high end of international estimates (for example, most countries in a group of 20 advanced countries had an estimate in the range 0.23–0.54 (Ball et al. 2013)andDixonetal. (2017) made an estimate of 0.48 for a panel of 20 OECD countries). This could reflect the particular sample period, the decomposition methodology or conceptual differences between what the coefficient measures in different forms of analysis. In this paper, the coefficient has a specific meaning which can be interpreted as the ratio of the amplitude of a common business cycle component which is shared by unemployment and output. To perform a reasonableness test for the particular sample period, we derived another, simpler estimate of the Okun coefficient for all persons by calculating the long-run multiplier as defined by Eq. 3. Using quarterly data from the same sample period of September 1980 to June 2017 and a regression of uton ytwith one lag of uand three lags of yt as explanatory variables generated an estimated long run multiplier of −0.48 (see Table 3), which is comparable with typical estimates of the average Okun coefficient for an OECD country. Many authors have used a HP filter to extract the cyclical components of one or more elements used in the estimation of the Okun coefficient (for example, Dixon et al. (2017)andBalletal.(2013)) so we also consider the impact of the chosen model against the HP filter. The empirical model framework in this research can be used to generate an alternative set of estimates of the Okun and participation coefficients consistent with the use of the HP filter for the trend and cycle decomposition. It is well known that the HP filter can be represented Table 3 Estimation of the long-run multiplier Dep. variable uCoeff. Std. Error pvalue Constant 0.2725 0.0477 0 u(−1)0.2560 0.0810 0.0019 g−0.1144 0.0269 0 g(−1)−0.1409 0.0279 0 g(−2)−0.0455 0.0298 0.1291 g(−3)−0.0577 0.0272 0.0356 Long-run multiplier −0.4820 LM(4) 5.0408 0.2831 LM(12) 13.8881 0.3079 Breusch-Godfrey serial LM(n) test. No serial correl. up to nlags Evans IZA Journal of Labor Economics (2018) 7:5 Page 17 of 22 in state space form with an underlying process which is the sum of an integrated walk and an irregular component (which is interpreted as the cycle) with a restriction applied to the ratio of the slope and irregular variances which imposes a level of smoothness on the trend (Harvey and Trimbur 2008). Table 4illustrates the estimated Okun and participation coefficients with a version of our model modified to match the HP specification of the trend and cycle components using a typical value for the smoothness parameter9. The Okun and participation coefficients are calculated as the ratio of the standard deviation of the relevant cycle to that of the output cycle. Full results for the model estimation are not shown10. This procedure has generated estimates of the Okun coefficients which are comfortably within the range of the estimates of the other cited authors (notwithstanding other significant differences in methodology to those studies cited). This suggests that the particular UC decomposition methodology used in this research, with freely estimated variances for trend and cycle components rather than those imposed by the restrictions embedded in a HP specification, is responsible for the higher absolute estimates of the Okun coefficients. 6Conclusions We have used a multivariate unobserved components model to decompose output and three labour markets time series in Australia into trend and cycle components. A key assumption used for identification was that the series share a common business cycle component. The model framework provided a direct estimate of the sensitivity of the labour market series to cyclical output shocks. The results were used to generate estimates of the Okun coefficient and a participation coefficient by age and gender. The estimates of the Okun coefficient are higher (absolute) than those generally reported in the literature which was attributed to the decomposition methodology. The unobserved components model finds maximum likelihood estimates of the components in contrast to more typical cycle extraction using the HP filter. The variation in the absolute values of our Okun coefficients by age and gender tends to follow the pattern found in the literature, with higher values for males than for females, notably higher values for the youngest age group and which tend to decline with age thereafter. Participation is less cyclical than unemployment but the coefficients are positive (it is procyclical) and mostly significant apart from males in the middle age groups. Participation is more cyclical for females than males, particularly in the middle age groups. Taken together these results show that, in aggregate, males in the middle age groups tend to stay in the labour force throughout the business cycle, perhaps moving between employment Table 4 Okun and participation coefficients derived using HP filter specification Cycle innovation std. dev. Okun Partic. Group utptgtCoeff. Coeff. Persons (all age) 0.568 0.277 1.162 0.49 0.24 Male (all age) 0.669 0.251 1.162 0.58 0.22 Female (all age) 0.466 0.357 1.162 0.40 0.31 Evans IZA Journal of Labor Economics (2018) 7:5 Page 18 of 22 and unemployment, whereas females of the same age have a higher tendency to move in and out of the labour force procyclically. This has policy implications for attempts to increase the rate of participation of particular groups by gender and age following a cyclical downturn. Endnotes 1The participation rate is the percentage of the civilian population who are in the labour force, which comprises employed and unemployed persons. People who are not working and not actively looking for work are not in the labour force. 2If the empirical relationship between output and unemployment is negative as anticipated then the estimate of βin Eq. 1would be a positive number. In the literature the Okun coefficient may be reported as a positive number, and at other times as the negative value −β. 3The Australian Bureau of Statistics report monthly gross flow data for the labour market in Catalogue 6202, data cube GM1. The data measures the gross flow of workers in both directions between each of the labour market states of employment, unemployment and non-participation, by comparing the status of matched respondents in a monthly survey which make it possible to determine whether a transition of a worker between states has occurred within the period. 4Variance parameters were estimated as the argument of an exponential function to ensure that estimated variance was greater than or equal to zero. 5Some parameters such as correlation coefficients were estimated as the argument of a logistic function so that the parameter would be constrained to lie between a specified lower and upper bound. 6The higher standard errors of coefficient estimates for the oldest female group is thought to reflect noisier data from the generally small number of participants in this group. The point estimate of the participation coefficient is positive (0.20) but it is not significant. 7Analysis of the cost effectiveness of subsidised child care is complex, since there is likely to be interaction between tax and welfare policies which may encourage shorter working hours for second income earners within a family unit. Further, subsidised childcare without an activity test may in fact discourage participation (Productivity Commission 2014,2). 8Details of the Restart Programme of employment assistance can be found on the website of the Australian Government Department of Jobs and Small Business website at https://www.jobs.gov.au/restart-help-employ-mature-workers-0. 9For monthly data a smoothing parameter of 14400 is sometimes suggested for the HP filter, although there is no general agreement as to the best value for this parameter. The parameter setting will generate a relatively smooth trend and allocate deviations from this trend to the cyclical component. 10 The log likelihood at the solution was materially lower than that obtained for the original model, indicating that the smooth trend plus cycle model was a poor fit to the data. A substantial improvement in the log likelihood was seen when the ratio of the variances was freely estimated, but the fit was still materially worse than that for the original model. Evans IZA Journal of Labor Economics (2018) 7:5 Page 19 of 22 Appendix Table 5 Estimation results of LOCL plus common cycle model Male Female std. Natural 95% Confid. std. Natural 95% Confid. Param. Coef. err. pval coef. Low High Coef. err. pval coef. Low High λ−1.086 0.195 0.000 0.077 0.068 0.087 −1.983 0.420 0.000 0.059 0.051 0.075 period 81.950 72.087 92.393 105.646 83.437 123.269 ρ3.005 0.475 0.000 0.989 0.976 0.994 3.140 0.660 0.000 0.990 0.970 0.996 σ2 κ−3.677 0.264 0.000 0.025 0.015 0.041 −3.604 0.301 0.000 0.026 0.015 0.047 σ2 εu−5.005 0.280 0.000 0.007 0.004 0.012 −3.785 0.115 0.000 0.023 0.018 0.029 σ2 τu−4.232 0.228 0.000 0.015 0.009 0.023 −4.246 0.204 0.000 0.014 0.010 0.022 ωu−0.770 0.106 0.000 −0.770 −0.982 −0.557 −0.525 0.082 0.000 −0.525 −0.689 −0.360 σ2 εp−4.074 0.099 0.000 0.017 0.014 0.021 −3.997 0.146 0.000 0.018 0.014 0.025 σ2 τp−4.643 0.178 0.000 0.010 0.007 0.014 −4.067 0.171 0.000 0.017 0.012 0.024 ωp0.176 0.044 0.000 0.176 0.088 0.265 0.344 0.069 0.000 0.344 0.206 0.482 σ2 εg σ2 τg−2.070 0.123 0.000 0.126 0.099 0.161 −1.968 0.111 0.000 0.140 0.112 0.174 ωg1.000 1.000 σ2 εh−1.891 0.093 0.000 0.151 0.125 0.182 −1.951 0.097 0.000 0.142 0.117 0.172 σ2 τh−2.993 0.273 0.000 0.050 0.029 0.087 −4.718 1.260 0.000 0.009 0.001 0.111 ωh1.428 0.193 0.000 1.428 1.042 1.813 1.939 0.270 0.000 1.939 1.400 2.479 γu12 −0.103 0.034 0.002 −0.103 −0.171 −0.035 −0.068 0.034 0.048 −0.068 −0.137 0.001 γu24 −0.051 0.033 0.123 −0.051 −0.116 0.015 −0.052 0.032 0.106 −0.052 −0.116 0.012 γp12 −0.035 0.032 0.279 −0.035 −0.100 0.030 −0.009 0.032 0.790 −0.009 −0.073 0.056 γp24 −0.091 0.028 0.001 −0.091 −0.148 −0.035 −0.038 0.033 0.250 −0.038 −0.105 0.028 γh12 −0.093 0.040 0.021 −0.093 −0.173 −0.013 −0.099 0.039 0.011 −0.099 −0.177 −0.021 γh24 −0.208 0.040 0.000 −0.208 −0.288 −0.128 −0.186 0.040 0.000 −0.186 −0.267 −0.106 Evans IZA Journal of Labor Economics (2018) 7:5 Page 20 of 22 Table 5 Estimation results of LOCL plus common cycle model (Continued) Male Female std. Natural 95% Confid. std. Natural 95% Confid. Param. Coef. err. pval coef. Low High Coef. err. pval coef. Low High γh30.068 0.033 0.038 0.068 0.003 0.133 0.079 0.031 0.011 0.079 0.017 0.142 γh50.078 0.032 0.015 0.078 0.014 0.143 0.078 0.034 0.021 0.078 0.010 0.145 γh13 −0.090 0.039 0.020 −0.090 −0.168 −0.013 −0.093 0.037 0.012 −0.093 −0.167 −0.019 γh25 −0.168 0.039 0.000 −0.168 −0.246 −0.091 −0.150 0.038 0.000 −0.150 −0.227 −0.073 rεup 1.901 0.523 0.000 0.740 0.404 0.900 2.114 0.305 0.000 0.785 0.637 0.877 log lik. −412.44 −525.33 obs./partial 442 294 442 294 Convg. status Convg. achieved Convg. achieved no. iterations 74 86 upgh upgh Q(12) pval 0.017 0.266 0.976 0.056 0.841 0.269 0.807 0.053 Q(24) pval 0.136 0.736 1.000 0.113 0.857 0.124 0.997 0.158 Q(36) pval 0.322 0.850 1.000 0.191 0.895 0.191 1.000 0.323 Notes: The notation γu12 represents the coefficient of the seasonal adjustment factor created using the first difference of utlagged 12 months, with corresponding notation for other components and lag lengths. The confidence intervals for parameter estimates shown in natural terms are approximate only Evans IZA Journal of Labor Economics (2018) 7:5 Page 21 of 22 Table 6 Data sources Series Group Source Notes Unemp. rate, Particip. rate. Persons, males, females. ABS Catalogue 6202 Table 1 Seas. adj. monthly series. When required, quarterly series created using average of 3 months. Unemp. rate, Particip. rate. Males and females in 10-year age groups. ABS Cat.6291.0.55.001 Data cube LM1. Original terms. Seas. adj. series were generated using X12-ARIMA. Gross Domestic Product – ABS Catalogue 5206 Table 2 Real, seasonally adjusted. gt= 100ln(GDP) Mthly. hours worked in all jobs. Persons ABS Catalogue 6202 Table 19 Seas. adj. A dummy variable was used to remove outliers in June 1979 and June 1980. ht= 100ln(MHW) Acknowledgements The author would like to thank Lance Fisher, Ben Wang, Jonas Mansson and seminar participants at the Western Economic Association International 14th International Conference at the University of Newcastle, Australia, for helpful discussions on the earlier drafts. The author would also like to thank two anonymous referees and the editor for helpful suggestions to improve the paper. Responsible editor: Pierre Cahuc Availability of data and materials All of the data used in this report is available from the website of the Australian Bureau of Statistics at www.abs.gov.au. For more details refer to Table 6 in the Appendix. Competing interests The IZA Journal of Labor Economics is committed to the IZA Guiding Principles of Research Integrity. The author declares that he observed these principles. 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