Are Business Cycles Gender Neutral?

Transcription

1 gareth.jones Department of Economics Section name Are Business Cycles Gender Neutral? by Giovanni Razzu and Carl Singleton Department of Economics University of Reading Whiteknights Reading RG6 6AA United Kingdom Henley Business School, University of Reading 2014

2 Are business cycles gender neutral? Giovanni Razzu Carl Singleton Abstract We study the relationship between business cycles and gender employment rate gaps in the UK over the last four decades, on which there is surprisingly limited evidence. An analysis of employment rates as opposed to unemployment accounts for the greater tendency of women to move in and out of economic activity between spells of work. We estimate the relationship using a multivariate GARCH model and show results by using both the Christiano Fitzgerald Bass Pand filter and the Hodrick Prescott filter to extract the cyclical components of GDP. We find that business cycles are not gender neutral, their impact being greater on male than on female employment rates. A one percentage point increase in the deviation from trend GDP determines an increase in the gender employment rate gap of percentage points. Key words: business cycles, gender, employment, multivariate GARCH models JEL Codes: E32, J16, C32

3 Correlation coefficient Introduction Cyclical fluctuations in economic activity are widely acknowledged. Likewise, the cyclical behaviour of employment and unemployment is a dominant feature of labour markets (Lilien and Hall, 1986). Hence, the relationship between output and labour market participation has also been widely studied in recent decades, particularly following the seminal work of (Okun, 1962), which suggested a negative short-run empirical relationship between unemployment and output: the Okun s Law. Figure 1 shows the product moment correlation coefficients between employment rates and lagged GDP growth for the period This simple analysis does suggest that, over this period, for any change in GDP, men s employment outcomes are initially impacted more severely than women s, but that the effects on women s employment rates could be more persistent. Therefore, the way in which changes in GDP are linked to changes in employment over subsequent time periods might differ by gender. Figure 1 about here: Relationship between GDP and Employment rates Lags Male Female Source: Blue Book and Labour force Survey,

4 Moreover, during the recession between 2008Q2 and 2009Q3, the male employment rate decreased by 3.5 percentage points whilst the female employment rate decreased by 1.2 percentage points. The aim of this paper is therefore to study this relationship formally so to reach a robust assessment of the gender neutrality of business cycles. Do periods of economic boom or recessions have a differential impact on the employment rates of men and women as the simple correlations above suggest? The paper is structured as follows: in section 1 we review the literature, in section 2 we present the data used, in section 3 we describe the model and its estimation, and in section 4 present the results of the analysis. 1. Literature Review The literature on business cycles is indeed extensive, starting with the seminal contribution by (Burns et al., 1946) which defined and measured business cycles. However, the empirical literature on whether the relationship between business cycles and labour market participation differs by gender is sparse. Perhaps one of the first analyses is by (Clark and Summers, 1981), who considered demographic differences in cyclical employment variation in the U.S., and found that young workers bear a disproportionate share of cyclical fluctuations; more specifically, the employment of young women was more responsive to cyclical changes than the employment of older women, which in turn was more responsive than the employment of older men. This has been confirmed by more recent analysis of the latest economic downturns (Bell and Blanchflower, 2011). In terms of method, (Clark and Summers, 1981) regress the logarithm of participation rates on aggregate demand and time, with the unemployment rate of middle aged men used as measure of aggregate demand. Lagged

5 unemployment rates are considered to take account of recognition and action lags in response to fluctuations. (Blank, 1989), while looking at the effect of the business cycle on the distribution of income of various social groups, found that the relationship between changes in employment and changes in GDP was stronger for women than for men of the same ethnic background. More recently, (Queneau and Sen, 2008, Queneau and Sen, 2009, Queneau and Sen, 2010), whilst assessing the empirical evidence in eight OECD countries either in support of, or against the three main theories of unemployment over the business cycles namely, the natural rate of unemployment theory; unemployment hysteresis and the structuralist theory - found evidence of gender differences in unemployment dynamics in Canada, Germany and the US, but not in the other countries under analysis, which did not include the UK. In their 2008 paper, two regression equations are used in order to undertake unit root testing to distinguish between the different characterizations of unemployment dynamics: one equation tests for the presence of a unit root against the stationary alternative in which men (or women) employment rates fluctuate around a constant mean; another equation tests for the presence of a unit root against the trend-stationary alternative. In the latter, the gender unemployment rate is regressed not just on its lagged value and lagged differences, but also on a time trend variable. A recent contribution on this question is from (Peiró et al., 2012), who looked at the relationship between unemployment and the business cycle in the UK and the US, finding that cyclical changes extend their effect on unemployment over several quarters, and do so in a more intense way on male than female unemployment. They also found some evidence that the strength of this association has become weaker in the UK over the last few years of their sample up to They use a distributed lag model of changes to the unemployment rate regressed on cyclical GDP deviations: variations in unemployment rates are regressed on a

6 constant and changes in the cyclical component of GDP. They de-trend the data series using the standard Hodrick-Prescott (HP) filter for quarterly data (Hodrick and Prescott, 1997). The model is chosen to mitigate problems of high collinearity among the cyclical components in successive quarters resulting from the de-trending procedure. (Belloc and Tilli, 2013) study the persistence of the gender unemployment gap in the Italian regions between 1992 and 2009, showing how the process of catching up in the gender unemployment rate gap, although common, is not homogeneous but it is taking place to a different extent in the regions of the country. They adopt the same approach used by (Queneau and Sen, 2008) to assess persistence of gender unemployment rate gaps in Italian regions, and whether random shocks have permanent effects. They therefore test whether the series follow a unit root process. In summary, although cyclical fluctuations in economic activity affect the labour market experience of all demographic groups, the available evidence surveyed above suggests that these effects vary: young individuals are impacted differently from old individuals; women differently from men. Whilst unemployment rates of different demographic groups move together, the levels about which they fluctuate and the amplitude of cyclical fluctuations are different. From a methodological perspective, the evidence cited above adopts various approaches, possibly a result of the differing research questions under analysis. In fact, for most of them, the gender element is not central to the research hypothesis but either additional or indirect. This indirect interest on gender has possibly meant that the focus of the analyses has been on the relationship between unemployment rates and GDP fluctuations. Instead, there is a strong rationale, when looking at gender inequality in the labour market, and in particular its dynamics, to focus on employment as opposed to unemployment. Employment rates offer a truer reflection of the relative labour market performance of men and women for various reasons (Johnson, 1983), including the fact that unemployment rates

7 are affected by the greater tendency of women to leave and re-enter economic activity between spells of employment. This is not to say that gender unemployment rates are not important. They indeed are if the research aim was to assess the relative probability of men and women becoming unemployed once they decide to be active in the labour market (Azmat et al., 2006). Our analysis therefore makes three important contributions to the literature. First, it adds empirical evidence on whether business cycles are gender neutral in the UK, for which there is, as seen above, very limited evidence and understanding. Second, the paper improves on the existing evidence because we assess the relationship between employment rates and changes in GDP, rather than unemployment rates, as done in the studies cited above. Third, we extend the methodological approaches described above in two ways, which will be fully detailed in Section 2 and 3. One extension is from the use of GARCH models, which allow us to control for autoregressive conditional heteroscedasticity (ARCH) effects as well as any simultaneous correlation between the error terms. Secondly, we highlight the sensitivity of the results to the method used to de-trend the time series. For comparison, we analyse and present the results from models that are estimated using GDP data that has been de-trended using either the Christiano-Fitzgerald Band-Pass (CF-BP) filter (Christiano and Fitzgerald, 2003), or the HP filter with a less restrictive smoothing parameter than the one generally adopted in the literature. The simple correlation and the sparse literature, therefore, do suggest that business cycles are not gender neutral but affect men and women s employment rates different. This represents our research hypothesis. 2. Data

8 Log GDP ( ) For GDP, we use seasonally adjusted quarterly data from the ABMI series of the HMT Blue Book, covering the period from 1971Q1 to 2012 Q3. For employment rates, we use the seasonally adjusted quarterly data from the Labour Force Survey, covering the period from 1971 Q2 to 2012 Q4, for working age males and females (aged 16-64). Figure 2 shows the trends in log GDP (left axis) and gender employment rate gap (right axis) over the period. UK recessions, as defined by UK Office for National Statistics as two consecutive periods of negative quarterly real GDP growth, are indicated by the vertical shaded segments. Over the last four decades, the employment rate gap between working age men and women has narrowed by almost 30 percentage points with roughly half of this narrowing attributed to a rise in the female employment rate and the other half to a fall in the male employment rate. Figure 2 about here: Output and gender employment gap, UK, Log Real GDP (UK, SA, CVM) Gender Employment Rate Gap (%) % q2 2009q2 2007q2 2005q2 2003q2 2001q2 1999q2 1997q2 1995q2 1993q2 1991q2 1989q2 1987q2 1985q2 1983q2 1981q2 1979q2 1977q2 1975q2 1973q2 1971q2

9 Sources: ABMI series of the Blue Book and Labour Force Survey. Note: Gender employment rate gap calculated as (ER m -ER f )/ER m. Economic recessions are: 1973q3-1974q1, 1975q2-1975q3, 1980q1-1981q1, 1990q3-1991q3, 2008q2-2009q2, 2011q4-2012q2. GDP is a typical exponential series and so we consider its natural logarithm. We further obtain the cyclical components of the GDP series by dynamically de-trending using the HP (Hodrick and Prescott, 1997) and the BP-CF filters (Christiano and Fitzgerald, 2003). The HP is possibly the most commonly used filter in macroeconomic time series analysis. Most studies using the HP filter settle for the value of the smoothing parameter of λ=1600 for quarterly data suggested by (Hodrick and Prescott, 1997), whilst recognising that results are likely to be sensitive to this assumption. However, (Perron and Wada, 2009) demonstrate, using US GDP data that λ=1600 is perhaps too small, and attributes too much variation to the trend and not enough to the cycle. They suggest exploring the use of a very large parameter value to counteract this effect, such as λ=800,000. We also apply the BP-CF filter, which provides a better estimate of the cyclical component for business cycle analysis, where series tend to follow near random walk processes, compared to the more general band pass filter of (Baxter and King, 1999). We use a bandwidth of 6-32 quarters as a reasonable range for capturing business cycle fluctuations. Here the BP-CF filter is appropriate as we make no distinction between major and minor cyclical components of the series. Figure 3 shows a comparison of the cyclical component of logarithmic GDP (or % deviation) using the three dynamic decomposition filters introduced above: HP1600, HP and BP- CF filters. Figure 3 about here: Cyclical components of GDP, UK,

10 Deviation from trend GDP (%) HP1600 HP BP-CF q1 2009q1 2007q1 2005q1 2003q1 2001q1 1999q1 1997q1 1995q1 1993q1 1991q1 1989q1 1987q1 1985q1 1983q1 1981q1 1979q1 1977q1 1975q1 1973q1 1971q1 Source: ABMI series of the Blue Book The HP1600 and BP-CF cyclical deviations appear to be relatively similar. However, as expected, when we reduce the role of the trend in determining variation, the HP series shows a much clearer cycle. In particular, we note that the cyclical representation of UK GDP performance appears to be much more similar to what one might expect, particularly in recent times. With the standard smoothing parameter, for the recent Great Recession, the downturn has been so long-lasting that with finite data, the algorithm calculates that low growth in 2012 has become the norm, rather than representing a protracted slump. Since the BP-CF and HP1600 series are similar, in what follows we will only use the former. We also use the HP8000 series, in order to show comparisons with a more volatile and more cyclical representation of GDP variation.

11 As expected, both selected GDP deviations series ( ) appear to demonstrate a random walk. Therefore we difference, and use the percentage point change in deviation from trend GDP as an explanatory variable ( ). Turning to employment, both the male and female employment rate series in the UK, in their level form, are clearly not stationary for the period in question. We find that regressing the employment rates on a polynomial time trend, up to and including the third power, performs well, and so we use the residuals from this as our de-trended series. We then take the first difference such that our dependent variable is the percentage point change in the employment rate (, ). Table A.1 in the Appendix shows descriptive statistics for the variables described above: GDP growth, percentage point change in deviation from trend GDP using BP and HP filters, and percentage point change in employment rates for men and women. The resultant regression equation is therefore balanced (i.e. variables on both sides are integrated of order 1). To confirm that our variables are weakly stationary, we carry out the standard DF-GLS unit root tests (Elliott et al., 1996) and KPSS stationarity tests (Kwiatkowski et al., 1992). The results for both variables suggest that the de-trended and differenced GDP and employment rate series are stationary (See tables A.2 and A.3 in Appendix). However, we should be cautious that in the presence of significant GARCH effects, Dickey- Fuller type tests can have a severe over-rejection problem, which could remain significant even if using heteroskedastic robust standard errors (Kim and Schmidt, 1993, Cook, 2006). Also, as suggested by (Barassi, 2005), in finite samples, the KPSS test has size and power distortions. Using an ad hoc approach, we confirm the unit root and stationarity testing results by accounting for low order GARCH effects in the de-trended and differenced series

12 and performing the same tests on the derived standardised residuals (see Table A.4). The results confirm that we can treat and as weakly stationary, and also confirm that both maintain significant GARCH effects which ought to be accounted for in our estimation of the relationship between them i. 3. Model estimation First, we consider whether the change in the employment rate has any auto-regressive properties. Correlogram and regression analyses using Schwarz Information Criterion as measure of fit, which has been suggested as more accurate than other criteria in the case of quarterly data (Ivanov and Kilian, 2001) - indicate that an AR(2) process offers the best representation of both the male and female employment rate series. Second, the time series properties of the integrated BP-CF and HP series are well represented as white noise. This also indicates that any multicollinearity between lagged changes in the cyclical component of GDP in a distributed lag model should be small. We estimate the following models for each combination of j and i, where is a constant and the error term: (1) We found that the models estimated using OLS are not appropriate: significant serial correlation in the error term (Durbin-Watson and Breusch-Godfrey test) and autoregressive conditional heteroscedasticity (ARCH) effects for multiple lag values (Lagrange Multiplier test) were all detected. Therefore, we consider GARCH(p,q) models, with the mean equation as per (1).

13 Assuming Gaussian errors, a GARCH(1,1), using maximum likelihood estimation with robust standard errors, is the best fit compared to alternative values of (p,q), and is also sufficient to remove the observed ARCH effects for each combination of the data series. Hence, the conditional variance ( ), is given by: (2) From equation (1), the relative responsiveness of the male and female employment rate to the business cycle is given by: (3) The total impact of a cyclical change in GDP on the change in employment rates is: (4) We can use these to consider the impact of the macroeconomic business cycle on the gender employment rate gap, here defined as percentage point difference, ( ): (5) We could estimate equations (1) and (2) for both male and female separately (see tables A5.1 and A5.2), however, in order to control for any contemporaneous correlation between error terms, we estimate the relationship using a multivariate GARCH approach, thus improving the efficiency of the parameter estimates and the estimated relationship between the economic business cycle and the gender employment rate gap. To ensure that the maximisation converges, we use a form of the constant conditional correlation model popularised by (Bollerslev, 1990).

14 Given the lag length selected using standard information criteria and specification tests, the relationship, for each combination of male and female and HP and BP-CF de-trended data, is expressed by: ( ) (6a) ( ) (7a) ( ) (6b) ( ) (7b) If, are the conditional variances for the male and female equations respectively, is the conditional covariance, and is a parameter to be estimated such that the covariance is always proportional to ( ), the corresponding GARCH equations are: for j=male (8) for j=female (9) ( ) for covariance between the two (10) 4. Results We limit the degrees of freedom by using the IGARCH representation, whereby and. Table 1 shows the results from estimating the multivariate GARCH model described above. Table 1 about here: Multivariate GARCH estimation results BP-CF (I) HP (II)

15 Male Female Male Female.710 *** (.0611).664 *** (.0605).684 *** (.0597).646 *** (.0595).0443 *** (.0137).0560 *** (.0134).0163 * (.00901).0382 *** (.0146).0266 ** (.0103).0538 *** (.0144).0358 *** (.00953).0356 ** (.0139).0226 ** (.00931) Constant ( ) 4.79e-7 * (2.49e-7) 1.44e-7 * (8.64e-8) 3.76e-7 * (2.23e-7) 1.64e-7 * (8.94e-8).387 *** (.0928).311 *** (.0755).322 *** (.0979).349 *** (.0812).613 *** (.0928).689 *** (.0755).678 *** (.0979).651 *** (.0812).508 *** (.0584).472 *** (.062) Estimation Period 71q4 12q3 ( ) 71q4 12q3 ( ) Log-likelihood BIC Standard errors in parentheses estimated using observed information matrix *, **, *** indicate significance at 10%, 5%, and 1% levels respectively 1 Schwarz-Bayesian Information Criterion used for model selection, alongside Akaike criterion We can interpret as the speed of adjustment parameter, with higher values implying that employment rates take longer to return to their trend levels following a change in the business cycle component of GDP. Model (I) is estimated using the BP-CF de-trended data; Model (II) is estimated using the HP de-trended data. In both models, male employment rates adjust

16 more slowly than female. However, the difference is not significant from zero at standard levels. We find that the IGARCH approach is sufficient to remove any surviving ARCH effects from the standardised residuals. We also note that the implied magnitude of shocks to the conditional volatility of the estimated relationship ( ), and their persistence ) have similar magnitudes and balance of effects for both male and female equations. Shocks to volatility are correlated, although not perfectly. Results are also sensitive to the choice of GDP series. Model (I) implies a less sensitive relationship between male and female employment rates and the business cycle than model (II). This is unsurprising since the dynamic smoothing implied by the HP is very slight, and allows much greater variation in the implied GDP series, and perhaps a more realistic picture of the UK business cycle. To interpret these results more fully we calculate the impact multipliers on changes to the employment rates and gap resulting from a one percentage point change in deviation of GDP from its trend, using equations (3)-(5) above. The results are in Tables 2 and Figure 4. Table 3 shows approximated 95% confidence intervals using the delta method (Oehlert, 1992). Table 2 about here: Estimated Impact Multipliers BP-CF HP s (forward lags) Male Female Gap Male Female Gap

17 Total Table 3 about here: 95% Confidence Intervals for Impact Multipliers Total BP-CF HP Lower Upper Lower Upper Male Female Gap Figure 4 about here: Impact Multipliers for Multivariate GARCH models

18 Percentage point change in employment rate BP Male BP Female HP Male HP Female s (quarters following initial impact) As already discussed, the sensitivity of the results to the de-trending method of GDP is pronounced. A one per cent change in the cyclical component of GDP determines a more pronounced response in the male employment rate that in the female one in both models, but this response is larger in the case of the model estimated with the HP filter. In addition, in this model, the response to a one percentage increase in the cyclical component of GDP for both male and female employment rates is more sustained than in Model (I). However, the estimated magnitude of the total impact of the business cycle on the employment rate gap is similar in both models. A one percentage point increase in deviation from trend GDP increases the gender employment rate gap by percentage points. We check the sensitivity of these results to the estimation period chosen. Tables A.6 and A.7 in the Appendix shows the results of the multivariate GARCH models when we exclude the most recent economic downturn and the oil price shock years of the 1970s in turn. With the smaller sample size for the BP-CF de-trended GDP data, the rejection of the gender neutrality of business cycles becomes less clear. Moreover, when we exclude the recent economic

19 downturn, results suggest a slightly stronger relationship between gender and the business cycle. Likewise, excluding the 1970s suggest a weaker relationship, leading us to possibly conclude that although the business cycle appears to not be gender neutral over the whole estimation period, it may have become more neutral over time. We can also estimate the implied impact of the business cycle on the employment rates of men and women individually. The implied Okun s law style relationship for male employment is far more significant than for women. If the economy was at its long-run trend level of employment and GDP, then an increase in male employment rates of one percentage point above trend corresponds to a required one-off increase in GDP of approximately 2-3%, whereas correspondingly for female employment rates, an increase in GDP of 5-12% is required. Finally, we can apply these results to a contemporary UK context. In June 2010, the Office for Budget Responsibility estimated a UK output gap of around 6% in the first quarter of 2010, compared with a more or less zero output gap 36 quarters earlier in the first quarter of 2007, and in the preceding few years. The model estimates suggest that moving to an output gap of this magnitude might have resulted in a reduction in the gender employment rate gap of as much as percentage points below trend (and the trend for this period was roughly flat) by the end of 2012 (conditional on the output gap not changing any further). In fact, the UK gender employment rate gap was 12.1 percentage points in 2007q1, and decreased by 1.7 percentage points to 10.4 by 2012q4. And whilst the magnitude of this change may appear small, it actually relates to differences of 100,000s of men and women being in or out of employment over the course of the business cycle. 5. Conclusion

20 Although the literature on the relationship between business cycles and labour market outcomes is extensive, this has tended to look specifically at the impact of changes in GDP on unemployment rates, and has devoted very occasional attention to the differential impact business cycles might have on men and women s labour market outcomes. In this paper we have aimed to fill these gaps. Therefore, we considered the relationship between gender employment rate gaps and business cycles and assessed whether business cycles have a differential impact on men and women s employment rates. The focus is on employment rather than unemployment rates, the former being more appropriate when looking at gender inequality due to the tendency of women having a higher tendency to leave and re-enter economic activity between spells in work. In the paper we also adopt several methodological improvements on the existing evidence. First, we use a multivariate GARCH model, and secondly, we present results for time series data de-trended using two types of filters: the HP with a parameter value of , which appears to present a more realistic picture of the UK business cycle, and the BP-CF filter. Our results do suggest that business cycles in the UK are not gender neutral. Short term fluctuations in GDP are typically associated with greater changes in male than female employment, therefore impacting on the gender employment rate gap. More specifically, a one percentage point increase in deviation from trend GDP has historically determined an increase in the UK gender employment rate gap of percentage points. Moreover, male employment rates take longer than female employment rates to return to their trend levels following a change in the cyclical component of GDP. It is also interesting to note that these results are sensitive to the choice of de-trended GDP series. The relationship between gender employment rates and the business cycle is less pronounced when a typical quarterly BP-CF filter is used, compared with using HP filter which reduces the variation accounted for

21 by a variable trend, and which perhaps offers a more realistic representation of the UK business cycle. References AZMAT, G., GUELL, M. & MANNING, A Gender gaps in unemployment rates in OECD countries. Journal of Labor Economics, 24, BARASSI, M On KPSS with GARCH Errors. Economics Bulletin, 3, BAXTER, M. & KING, R. G Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics, 81, BELL, D. N. F. & BLANCHFLOWER, D. G Young people and the Great Recession. Oxford Review of Economic Policy, 27, BELLOC, M. & TILLI, R Unemployment by gender and gender catching-up: Empirical evidence from the Italian regions. Papers in Regional Science, forthcoming. BLANK, R. M Disaggregating the Effect of the Business-Cycle on the Distribution of Income. Economica, 56, BOLLERSLEV, T Modeling the Coherence in Short-Run Nominal Exchange-Rates - a Multivariate Generalized Arch Model. Review of Economics and Statistics, 72, BURNS, A. F., MITCHELL, W. C. & NATIONAL BUREAU OF ECONOMIC RESEARCH Measuring business cycles, New York, National Bureau of Economic Research. CHRISTIANO, L. J. & FITZGERALD, T. J The band pass filter. International Economic Review, 44, CLARK, K. B. & SUMMERS, L. H Demographic Differences in Cyclical Employment Variation. Journal of Human Resources, 16, COOK, S The robustness of modified unit root tests in the presence of GARCH. Quantitative Finance, 6, ELLIOTT, G., ROTHENBERG, T. J. & STOCK, J. H Efficient tests for an autoregressive unit root. Econometrica, 64, HODRICK, R. J. & PRESCOTT, E. C Postwar US business cycles: An empirical investigation. Journal of Money Credit and Banking, 29, IVANOV, V. & KILIAN, L A Practitioner's Guide to Lag-Order Selection for Vector Autoregressions. CEPR Discussion Paper JOHNSON, J. L Sex Differentials in Unemployment Rates - a Case for No Concern. Journal of Political Economy, 91, KIM, K. W. & SCHMIDT, P Unit-Root Tests with Conditional Heteroskedasticity. Journal of Econometrics, 59, KWIATKOWSKI, D., PHILLIPS, P. C. B., SCHMIDT, P. & SHIN, Y. C Testing the Null Hypothesis of Stationarity against the Alternative of a Unit-Root - How Sure Are We That Economic Time-Series Have a Unit-Root. Journal of Econometrics, 54, LILIEN, D. M. & HALL, R. E Cyclical fluctuations in the labour market. In: O., L. R. A. A. (ed.) HAndbook of Labour Economics. Elsevier Science. OEHLERT, G. W A Note on the Delta Method. American Statistician, 46, OKUN, A. M Potential GNP: Its Measurement and Significance. PEIRÓ, A., BELAIRE-FRANCH, J. & GONZALO, M. T Unemployment, cycle and gender. Journal of Macroeconomics, 34, PERRON, P. & WADA, T Let's take a break: Trends and cycles in US real GDP. Journal of Monetary Economics, 56, QUENEAU, H. & SEN, A Evidence on the dynamics of unemployment by gender. Applied Economics, 40,

22 QUENEAU, H. & SEN, A Further evidence on the dynamics of unemployment by gender. Economics Bullettin, 29, QUENEAU, H. & SEN, A On the persistence of the gender unemployment gap: evidence from eight OECD countries. Applied Economic Letters, 17. Appendix Table A.1: UK Sample Descriptive Statistics Mean Standard Dev. Min Max Quarterly GDP Growth (1971q1-2012q3) (1971q1-2012q3) (1971q1-2012q3) (1971q2-2012q3) (1971q2-2012q3) (1971q3-2012q4) (1971q3-2012q4) Although, GDP series is de-trended from Employment series are residuals, so mean values are zero.

23 Table A.2: Stationarity Test - Deviations from GDP trend Unit Root Test Stationarity Test DF-GLS 1 KPSS 2 BP-CF HP *, **, *** indicate significance at 10%, 5%, and 1% levels respectively 1 Generalised Least Squares Dickey Fuller (DF-GLS) statistic with no linear trend of Ellitot, Rothenberg and Stock (1996); null hypothesis that unit root exists. Lag length selection using Schwarz information criterion: BP = 10, HP = 9. Although here we cannot reject null for automatic lag selection, we can reject null for lower lags and when using Augmented Dickey-Fuller. 2 Kwiatkowski, Philips, Schmidt and Shin (1992; KPSS) stationarity test with no trend using Quadratic Spectral kernal; null hypothesis that series is stationary. Critical values: 10% , 5% , 1% KPSS statistic uses automatic bandwidth (maximum lag order 3 for both series) routine to avoid multiple statistics. Table A.3: Stationarity Test -Changes in Employment rates Unit Root Test Stationarity Test DF-GLS 1 KPSS *** ***.0838 *, **, *** indicate significance at 10%, 5%, and 1% levels respectively. 1 Generalised Least Squares Dickey Fuller (DF-GLS) statistic with no linear trend of Ellitot, Rothenberg and Stock (1996); null hypothesis that unit root exists. Lag length selection using modified Akaike information criterion: Male = 1, Female = 2 2 Kwiatkowski, Philips, Schmidt and Shin (1992; KPSS) stationarity test with no trend using Quadratic Spectral kernal; null hypothesis that series is stationary. Critical values: 10% , 5% , 1% KPSS statistic uses automatic bandwidth selection (maximum lag order 3 for both male and female) routine to avoid multiple statistics.

24 Table A.4: Further Stationarity Tests Unit Root Test Stationarity Test / DF-GLS 1 KPSS 2 GARCH(p,q) 3 BP-CF ***.0331 I 4 HP *.186 I ***.272 (2, ) ***.12 (1, ) *, **, *** indicate significance at 10%, 5%, and 1% levels respectively. 1 Generalised Least Squares Dickey Fuller (DF-GLS) statistic with no linear trend of Ellitot, Rothenberg and Stock (1996); null hypothesis that unit root exists. Lag length selection using modified Akaike information criterion: BP = 2, HP = 14, Male = 2, Female = 6. Although here we can only reject null for automatic lag selection for HP at 10% level, we can reject null for lower lags and when using Augmented Dickey-Fuller. 2 Kwiatkowski, Philips, Schmidt and Shin (1992; KPSS) stationarity test with no trend using Quadratic Spectral kernal; null hypothesis that series is stationary. Critical values: 10% , 5% , 1% KPSS statistic uses automatic bandwidth (maximum lag order) 3 Tests performed using standardised residuals from GARCH estimation of series, with no explanatory variables other than constant term. 4 Uses IGARCH

25 Table A 5.1: GARCH(1,1) models BP-CF HP Male Female Male Female.799 *** (.0556).730 *** (.0626).750 *** (.0539).689 *** (.0595).0547 *** (.0138).0412 ** (.0204).0308 *** (.00835).0576 *** (.0141).0384 *** (.0019).0323 ** (.0127).0234 *** (.00751) Constant ( ) 5.66e-7 (3.58e-7) 1.53e-7 (1.44e-7) 3.18e-7 (2.05e-7) 1.34e-7 (1.15e-7).243 ** (.107).267 * (.106).210 ** (.0903).280 ** (.134).689 *** (.0989).715 *** (.101).755 *** (.0821).711 *** (.117) Estimation Period 71q4 12q4 ( ) 71q4 12q4 ( ) 71q4 12q3 ( ) 71q4 12q4 ( ) Log-likelihood BIC Standard errors in parentheses estimated using robust full Huber/White sandwich formation *, **, *** indicate significance at 10%, 5%, and 1% levels respectively 1 Schwarz-Bayesian Information Criterion used for model selection, alongside Akaike criterion

26 Table A 5.1: GARCH(1,1) models, Estimated Impact Multipliers BP-CF HP s Male Female Gap Male Female Gap Total (

27 Table A.6: Multivariable GARCH Estimation Results, BP-CF (I) HP (II) Male Female Male Female.774 *** (.0622).710 *** (.0556).720 *** (.0481).678 *** (.0525).0374 *** (.0132).0652 *** (.0155).0201 ** (.00953).0351 ** (.0163).0260 ** (.0103).0592 *** (.0136).0384 *** (.00976).0346 *** (.0131).0256 *** (.00927) Constant ( ) 1.68e-6 *** (6.31e-7) 1.34e-7 (8.29e-8) 1.92e-6 *** (5.25e-7) 1.67e-7 * (8.78e-8).822 *** (.180).291 *** (.0845).930 *** (.124).358 *** (.0873).178 (.180).709 *** (.0845).070 (.124).642 *** (.0873).502 *** (.064).484 *** (.065) Estimation Period 71q4 07q4 ( ) 71q4 07q4 ( ) Log-likelihood BIC Standard errors in parentheses estimated using observed information matrix *, **, *** indicate significance at 10%, 5%, and 1% levels respectively 1 Schwarz-Bayesian Information Criterion used for model selection, alongside Akaike criterion

28 Table A.7: Multivariable GARCH Estimation Results, BP-CF (I) HP (II) Male Female Male Female.722 *** (.0759).627 *** (.0854).617 *** (.0742).551 *** (.0798).0751 ** (.039).0535 ** (.0233).0967 *** (.0294).0624 *** (.0193).0734 ** (.0314).0412 * (.0221) Constant ( ) 9.78e-7 (6.63e-7) 4.01e-7 (2.65e-8) 5.90e-7 (4.71e-7) 3.43e-7 (2.22e-7).442 ** (.180).388 *** (.122).312 ** (.158).397 *** (.125).558 *** (.180).612 *** (.122).688 *** (.158).603 *** (.125).469 *** (.076).439 *** (.0783) Estimation Period 80q2 12q4 ( ) 80q2 12q4 ( ) Log-likelihood BIC Standard errors in parentheses estimated using observed information matrix *, **, *** indicate significance at 10%, 5%, and 1% levels respectively 1 Schwarz-Bayesian Information Criterion used for model selection, alongside Akaike criterion

29 i We are also confident that although both series are integrated of order one, there is no evidence using the standard Engle-Granger method of analysis that they are co-integrated, and therefore there is no need to use the Error Correction Method to analyse any possible relationship (i.e. the standardised residuals of the long-run relationship between the de-trended employment rates and GDP, accounting for GARCH effects and autocorrelation, are non-stationary).