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© Henley Business School, University of Reading 2014

Are Business Cycles Gender Neutral?

by

Giovanni Razzu

and Carl Singleton

Department of Economics

2013 104 Department of Economics University of Reading Whiteknights Reading RG6 6AA United Kingdom www.reading.ac.uk

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 0.2-0.25 percentage points.

Key words: business cycles, gender, employment, multivariate GARCH models

JEL Codes: E32, J16, C32

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 1971-2012. 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

Source: Blue Book 1971-2012 and Labour force Survey, 1971-2012

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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

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 2008. 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

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

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

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, 1971-2012

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)

Log Real GDP (UK, SA, CVM) Gender Employment Rate Gap (%)

Sources: ABMI series of the Blue Book and Labour Force Survey. Note: Gender employment rate gap

calculated as (ERm

-ERf)/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, HP800000 and BP-

CF filters.

Figure 3 about here: Cyclical components of GDP, UK, 1971-2012

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 HP800000 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.

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HP1600 HP800000 BP-CF

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

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 themi.

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 HP800000 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).

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).

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) HP800000 (II)

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 1592.6 1603.1

BIC

1 -3134.2 -3139.0

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

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 HP800000 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 HP800000

s (forward lags) Male Female Gap Male Female Gap

0 0.044 0.000 0.044 0.056 0.016 0.040

1 0.070 0.027 0.043 0.092 0.046 0.046

2 0.050 0.018 0.033 0.099 0.053 0.046

3 0.036 0.012 0.025 0.067 0.034 0.033

4 0.026 0.008 0.018 0.046 0.022 0.024

5 0.019 0.005 0.014 0.032 0.014 0.017

6 0.014 0.003 0.010 0.022 0.009 0.012

7 0.010 0.002 0.007 0.015 0.006 0.009

8 0.007 0.002 0.006 0.010 0.004 0.006

Total ∑

0.294 0.079 0.215 0.460 0.211 0.249

Table 3 about here: 95% Confidence Intervals for Impact Multipliers

Total ∑

BP-CF HP800000

Lower Upper Lower Upper

Male .096 .492 .281 .639

Female .011 .147 .111 .311

Gap .029 .402 .087 .411

Figure 4 about here: Impact Multipliers for Multivariate GARCH models

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 HP800000 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 0.2-0.25 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

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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 1-1.5 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

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 800000, 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 0.2-0.25 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

by a variable trend, and which perhaps offers a more realistic representation of the UK

business cycle.

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Appendix

Table A.1: UK Sample Descriptive Statistics

Mean Standard Dev. Min Max

Quarterly GDP

Growth

(1971q1-2012q3)

.00572 .00977 -.0244 -.0514

(1971q1-2012q3)1

.000 .0144 -.0305 .0504

(1971q1-2012q3) .000 .0388 -.0867 .0873

(1971q2-2012q3) .000 .00904 -.0300 .0453

(1971q2-2012q3) .001 .00971 -.0309 .0449

(1971q3-2012q4) -

2 .00372 -.0115 .00985

(1971q3-2012q4) -

2 .00230 -.00502 .00559

1 Although, GDP series is de-trended from 1955-2012

2 Employment series are residuals, so mean values are

zero.

Table A.2: Stationarity Test - Deviations from GDP trend

Unit Root Test Stationarity Test

DF-GLS

1 KPSS2

BP-CF -.792

.148

HP800000 -1.249

.133 *, **, ***


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% - 0.347 , 5% - 0.463, 1% - 0.739. 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


DF-GLS

1 KPSS

2

-3.463***

.108

-3.708

***

.0838

*, **, *** indicate significance at 10%, 5%, and 1% levels respectively.


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


statistic uses automatic bandwidth selection (maximum lag order 3 for both male and female) routine to avoid

multiple statistics.

Table A.4: Further Stationarity Tests


/

DF-GLS1 KPSS

2 GARCH(p,q)

3

BP-CF -7.852***

.0331

I4

HP800000 -1.877*

.186

I4

-4.117

*** .272 (2, )

-3.117

*** .12 (1, )

*, **, *** indicate significance at 10%, 5%, and 1% levels respectively.


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


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

Table A 5.1: GARCH(1,1) models

BP-CF HP800000


.799

***

(.0556)

.730***

(.0626)

.750***

(.0539)

.689***

(.0595)

.0547

***

(.0138)

.0412

**

(.0204)

.0308***

(.00835)

.0576***

(.0141)

.0384***

(.0019)

.0323

**

(.0127)

.0234***

(.00751)


(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)


( )

71q4 – 12q4

( )

71q4 – 12q3

( )

71q4 – 12q4

( )

Log-likelihood 761.7

814.1

769.0

819.2

BIC

1 -1497.8

-1602.6

-1502.2

-1607.8

Standard errors in parentheses – estimated using robust full Huber/White sandwich formation *, **, ***



Table A 5.1: GARCH(1,1) models, Estimated Impact Multipliers

BP-CF HP800000

s Male Female Gap Male Female Gap

0 0.000 0.000 0.000 0.055 0.000 0.055

1 0.041 0.031 0.010 0.099 0.038 0.060

2 0.033 0.022 0.010 0.106 0.050 0.056

3 0.026 0.016 0.010 0.080 0.034 0.045

4 0.021 0.012 0.009 0.060 0.024 0.036

5 0.017 0.009 0.008 0.045 0.016 0.029

6 0.013 0.006 0.007 0.034 0.011 0.022

7 0.011 0.005 0.006 0.025 0.008 0.017

8 0.009 0.003 0.005 0.019 0.005 0.014

Total (∑

0.205 0.114 0.091 0.579 0.199 0.380

Table A.6: Multivariable GARCH Estimation Results, 1971-2007

BP-CF (I) HP800000 (II)


.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)


***

(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)


( ) 71q4 –07q4

( )


BIC

1 -2802.9 -2813.6




Table A.7: Multivariable GARCH Estimation Results, 1980-2012

BP-CF (I) HP800000 (II)


.722

***

(.0759)

.627***

(.0854)

.617***

(.0742)

.551***

(.0798)

.0751

**

(.039)

.0535**

(.0233)

.0967***

(.0294)

.0624***

(.0193)

.0734

**

(.0314)

.0412*

(.0221)


(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)


( ) 80q2 – 12q4

( )


BIC

1 -2429.6 -2442.8




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 auto-

correlation, are non-stationary).

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