Long-term unemployment and labour force participation: a decomposition of unemployment to test for the discouragement and added worker hypotheses

ABSTRACT

We sharpen tests for ‘discouragement’ and ‘added worker’ effects by splitting the explanatory variable – the unemployment rate – into a short-term component and a long-term component. While short-term unemployment (STU) might not result in additional workers on a large scale, long-term unemployment (LTU) reduces household income more, increasing the need for additional income. On the other hand, it may discourage older workers for psychological and sociological reasons. Applying our model to the German labour market, these hypotheses could be confirmed. Even for men, about whom only a few empirical studies on this issue are available, distinguishing between STU and LTU reveals added worker as well as discouragement effects.

KEYWORDS:

• Added worker effect
• discouraged worker
• labour force participation
• long-term unemployment

JEL CLASSIFICATION:

• C32
• E24
• J21

I. Introduction

The response of the labour force to fluctuations in unemployment has been discussed for decades. Especially the labour supply of females seems to be affected by the demand side, or by the business cycle. The question of the relationship between cyclical variations in economic activity and labour force participation was typically examined under the dichotomy of the discouragement hypothesis vs. the added worker effect (AWE). According to the discouragement hypothesis, workers withdraw from a deteriorating labour market (e.g. Dernburg and Strand 1966). Following a search-theoretical interpretation, a person who becomes unemployed can be expected to give up looking for work as it does not pay off (e.g. Kollman 1994). On the other hand, additional labour force participants may enter the labour market, especially to ensure their family income (e.g. Prieto-Rodríguez and Rodríguez-Gutiérrez 2000). This AWE is typically discussed in the context of the labour market regime of females as secondary workers.

The literature concerning the AWE provides evidence of a small but significant influence in most but not all cases (e.g. Lundberg 1985; Maloney 1991; Tano 1993). One possible reason for this is that, especially in macro investigations, typically only the net effect of the influence that unemployment has on labour force participation is estimated (e.g. Agbola 2005; Filatriau and Reynès 2012): a positive effect represents the AWE, a negative effect shows discouragement. When applying a modelling that makes it possible to distinguish between the AWE and the discouragement effect, the results show that both ‘are not mutually exclusive’ (Tano 1993, 116). Which effect dominates depends on the relative strength of discouragement and AWE and is thus an empirical question.

Furthermore, studies from different countries indicate the importance of the institutional background (such as the social security system) and some cultural and socio-economic factors. Therefore the results are country-specific. The European Commission shows for the EU that discouragement increases in countries with high shares of long-term unemployment (LTU) (EU <European Commission> 2013, 13). But only a few studies refer to this aspect and only in passing (e.g. Blundell, Ham, and Meghir 1998).

To close this gap in the empirical literature, our article provides an analysis that splits the unemployment rate into a short-term component and a long-term component. Both are subsequently used to explain cyclical variations in the labour force participation rate. The research was conducted for Germany, which serves as a model for a Central European welfare state with a high female participation rate and a long tradition of early retirement.

For most groups, our results support the assumption that LTU has a substantial influence on labour participation. Even for men, about whom only a few empirical studies on this issue are available, the distinctions between LTU and short-term unemployment (STU) reveal significant AWE and discouragement effects. In contrast, German women respond more quickly, i.e. STU leads to discouragement, whereas LTU has weaker discouragement effects.

This article is structured as follows. Section II summarizes the relevant literature and outlines the model. In Section III, we describe the data used in the empirical analysis. The results of our estimations are discussed in Section IV. The following Section V deals with several statistical issues. Section VI concludes.

II. The background theory and the econometric model

Unemployment and labour force participation

The discouragement effect and the AWE are understood as relationships between unemployment and labour force participation. In this context, international comparisons show the importance of the level of labour force participation (Bredtmann, Otten, and Rulff 2014; Prieto-Rodríguez and Rodríguez-Gutiérrez 2003) and the type of welfare regime, i.e. the social security system, the availability of unemployment compensation, the tax and pensions systems (Bredtmann, Otten, and Rulff 2014). Furthermore, results for a broad range of countries suggest that cultural and socio-economic differences also play a role (e.g. Agbola 2005 for Australia; Baᶊlevent and Onaran 2003 for Turkey; Holst and Spiess 2002 for EU countries; Kohare 2010 for Japan; Lee and Cho 2005 for Argentina and the Republic of Korea; Prieto-Rodríguez and Rodríguez-Gutiérrez 2000 for Spain).

Regarding the AWE, it is assumed that women’s labour market attachment is much weaker than of married men. This is often described as the male breadwinner model. Some doubt rises whether this behavioural model still works in the case of northern European countries like Germany, Sweden, the UK and others (see Holst and Spiess 2002). A high level of female labour participation indicates that females’ role as secondary workers has changed. In fact, for these countries, empirical macro analyses for the AWE and discouragement effect are conducted without differentiating by the marital status (e.g. Briscoe and Wilson 1992, Fuchs and Weber 2013; Österholm 2010).

Discouragement is often explained within a search-theoretical approach. With increasing unemployment, the costs of job search rise, making efforts to find a job less worthwhile (e.g. Blundell, Ham, and Meghir 1998; Kollman 1994). Nevertheless, some psychological aspects should also be considered, as the level of the reported unemployment seems to signalize to unemployed persons what chances they have of finding a job again (Gong 2011). This might be especially relevant if the unemployed person belongs to a group with particularly poor prospects (see Benati 2001; Van Ham, Mulder, and Hooimeijer 2001). In the case of older workers, this effect could be reinforced by the possibility of retirement (see O´Brien 2000).¹ The job-search prospects and the option of alternative roles might be reasons why the empirical results for the discouragement/AWE depend on age and sex.

Explaining his nonsignificant results for older workers, Benati (2001) argues that these groups can stay outside the labour market permanently, i.e. the influence of unemployment might be outperformed in some cases when alternative roles are available, such as taking retirement. As this represents rather permanent decisions, short-term labour market developments would less likely affect participation. The question arises of whether this also is true of LTU. O´Brien (2000) found a highly significant influence of LTU, but he did not use a direct measure for the long-term unemployed. Instead, he assumed that individuals receiving an unemployment allowance for older unemployed persons were ‘actually long-term unemployed’ (O´Brien 2000: 217).

As unemployment duration might be relevant for labour participation, this article adds an analysis that splits the unemployment rate into a short-term component and a long-term component. Both are subsequently used to explain cyclical variations in the labour force participation rate.

Our research was conducted for Germany, which serves as a model for a Central European welfare state. Important aspects for our analyses are that (i) older unemployed persons are entitled to unemployment compensation for a longer period and (ii) early retirement, although being reduced for a number of years, is still a possible option.

All in all, reviewing the empirical literature above, STU should not, in the German case, activate many additional female workers, because female participation rates are high, even if most women only work part-time. Therefore, our impression is that the role of women as secondary workers has become less important in Germany (see Holst and Wieber 2014).

The discouragement effect should thus be stronger. In contrast, as unemployment compensation is paid for a limited duration, LTU might reduce household income, thereby increasing the need for additional income. The opposing conflictive hypothesis would be that long-term unemployed individuals may become discouraged for some psychological/sociological reasons and leave the labour force on these grounds (see Mayer 2014).

The model

At the current stage in our analysis, we formulate a model that is typical in this field of macroeconomic research (e.g. Agbola 2006; Briscoe and Wilson 1992; Österholm 2010). The general model is formulated for a yearly frequency, because only annual data are available.

We denote the observed participation rates by $p_t$ (see Equation 1). Following the literature and to improve the matching with the data, the dependent participation rate $p_t$ was transformed into its logistic value $ln(\frac{p_t}{1-p_t})$ (e.g. Briscoe and Wilson 1992). The logit-transformation ensures that the estimated participation rates remains within the range of 0–1.

The unemployment rate $u_t$ is decomposed into the LTU rate $lt{u}_t$ and the STU rate $st{u}_t$. (To be precise, $lt{u}_t$ and $st{u}_t$ add up to the overall unemployment rate $u_t$.) As most studies have shown the influence of age and sex for the analysis, the models are estimated for different age groups, with the population aged 25–64 split into five-year age groups.² So, $p_{it}$, $lt{u}_{it}$ and $st{u}_{it}$ are differentiated by age and sex and 16 equations are estimated.

There are numerous factors determining labour supply. In a time series framework, with a limited number of observations, including to many explanatory variables means that only few degrees of freedom would be left. As our primary objective is to analyse the influence of STU and LTU, we decided to specify a parsimonious model which only incorporates age and sex-specific wages and several deterministic variables. The deterministic variables only serve to control for seminal developments in the data.

The model takes into account the possibility of shifts in levels and trends occurring at the time of the German reunification in 1990, a substantial modification in the unemployment insurance in the year 2000, and the Hartz labour market reforms³ in 2005. In addition, the German labour force survey, one of our data sources, was redesigned in 2005. Up to 2004, the survey was conducted once a year in April/May; since 2005, it has been conducted monthly, so yearly averages are available. In the time series for older workers, a further break might have occurred in the time period 1996–2000, when early retirement schemes were phased out, gender specific and with different age limits and eligibility requirements for different birth cohorts (see OECD 2005).

We use the following basic model for the logit of the LFPR:

(1) $logit{p}_{i,t}\hspace{0.17em}=a_{i,1}+a_{i,2}t+a_{i,3}st{u}_{i,t-k}+a_{i,4}lt{u}_{i,t-l}+a_{i,5}{w}_{i,\mathrm{t}}+\hspace{0.17em}shift{s}_i+{\epsilon }_{i,t}$(1)

where

$logit{p}_{i,t}=ln\left(\frac{p_{i,t}}{1-pi{,}_t}\right)$

index i represents groups by age and sex

stu_i,t = STU by group i in the year t,

ltu_i,t = LTU by group i in the year t,

w_i,t = wage by group i (the squared value variable w² was also included) and

shifts_i = represents possible breaks in the trend and dummies.

Concerning the unemployment variables, the equation allows for different lags $k,l$ in different groups $i$. Several specifications were tested and discriminated based on statistical significance. Following the literature (for overall unemployment), a specification without any lag or with lag 1 should generally perform well. For the LTU, variable specifications with longer lags were additionally tested. In the case of older workers, where early retirement and the different compensation regulations play a role, longer lags could be visible.

Discouragement effects would be implied by $a_3<0$ or $a_4<0$ for STU and LTU, respectively. AWE would follow from $a_3>0$ or $a_4>0$.

III. Data

Labour force participation rates are obtained from the German labour force survey (LFS). Until 2004, they were observed every 12 months, since then an annual average has been available (see discussion earlier). As the German LFS is a 1% sample of the overall population (ca. 80m), age- and gender-specific labour force participation rates are based on large samples. The participation rate of each group under consideration has at least 18 000 respondents in the denominator. We use western German data, for which the time series cover a period from 1984 to 2011.

Our unemployment data are defined according to the Federal Employment Agency (FEA), that is, we use the national unemployment register, which covers all unemployed persons in Germany in a given year. As a consequence, information about the duration of unemployment was not obtained from individuals’ answers in a survey (like the LFS), but was drawn from the register of the FEA. The data about the duration are recorded once a year in September. Long-term unemployed persons are those who have been unemployed for one year or longer, which follows the definition of the International Labour Organization (ILO).⁴

The rates for LTU and STU were constructed as follows: the numerator contains the number of long-term or short-term unemployed respectively. For the denominator we added the number of employed persons and all unemployed persons. Our rates therefore correspond to the usual definition of the unemployment rate, but are differentiated by duration. The two rates add up to the overall unemployment rate.⁵

The wage variable are also obtained from the FEA. Median daily wages of full-time employees are provided by age groups and sex. We deflated the wage data with the consumer price index, published by the Federal Statistical Office of Germany.

The labour force participation rate in western Germany has risen steadily since the 1970s. The main driving factor was the labour participation of prime aged women, which increased strongly in the past. In addition, the participation of the older workforce has improved considerably, particularly in the last decade. In contrast, the participation rate of the young, especially of females, peaked in the early 1990s and declined afterwards. This picture of labour force participation is quite similar to many other EU countries and the US.

Unemployment in western Germany in general shows several upward steps, some swings and a major downward step over the course of the strong labour market development in recent years. This development was mainly driven by STU. LTU did not develop entirely differently, but the series is slightly less volatile. In addition, the movements seem to be shifted to the right compared to the STU rate, i.e. LTU is lagged behind STU.

As far as age- and gender-specific relationships are concerned, Figure 1 shows two typical examples for the link between labour force participation and unemployment among prime-age women and men.

Figure 1. Labour participation rate vs. total, short-term and long-term unemployment rate by gender, measured in per cent of the 45- to 49-years-olds. Source: Authors’ calculations based on annual data from the Federal Statistical Office and the Federal Employment Agency.

The upper panel of Figure 1 contains the data for females, aged 45–49, the lower panel the data for males of the same age. Both panels plot time series of the labour participation rate (right axis), the total unemployment rate, the STU and the LTU rates (unemployment on the left axis). There appears to be no striking difference in the change in the gender-specific unemployment rates. The trends in the participation rates, however, differ strongly with respect to the direction. Whereas female labour force participation has increased considerably, men’s participation has fallen slightly since 1983.

IV. Empirical results

Men

First, we analyse the results for males. The models were estimated using weighted least squares with the empirical weights $p_t\left(1-p_t\right)$.⁶ Table 1 shows the condensed results. Our results for both STU and LTU indicate that men can become discouraged, but the effects differ according to age. Our results hold for different specifications in respect to the lags structure as well as the wage variable.

Table 1. Basic results for the labour force participation rate of males.

Age	25–29	30–34	35–39	40–44	45–49	50–54 ^1)	55–59 ^2)	60–64
STU	−0.024426	0.052676	−0.052399	0.044341	0.074153	0.025768	−0.050526	−0.041224
	(−5.635)***	(2.732)**	(−1.211)	(1.594)	(1.435)	(1.462)	(−3.095)***	(−3.821)***
LTU	−0.02703	0.115004	0.178595	0.12167	0.148866	0.069762	−0.030413	−0.033403
	(−1.424)	(3.312)***	(2.987)***	(3.978)***	(4.665)***	(2.927)***	(−2.366)**	(−2.649)**
Wage (WM)	0.38527	0.365526	−0.087612	0.145079	0.119524	0.092286	0.246455	−0.114764
	(6.874)***	(1.050)	(−0.241)	(0.444)	(0.728)	(1.136)	(1.320)	(−1.623)
WM × WM	−0.002472	−0.002104	0.000295	−0.000644	−0.000548	−0.000334	−0.001228	0.000615
	(−7.288)***	(−1.075)	(0.159)	(−0.403)	(−0.681)	(−0.814)	(−1.350)	(1.753)*
Trend				−0.050477	−0.039638	−0.060633
				(−6.574)***	(−4.054)***	(−5.696)***
TB1996							0.024814
							(9.7687)***
TB2000		−0.035776		0.052182		0.091683
		(−6.618)***		(4.092)***		(5.578)***
TB2005	−0.0176		−0.091998		0.063500			0.134900
	(−4.772)***		(−7.898)***		(2.248)**			(29.072)***
Adj. R^2	0.695	0.665	0.632	0.861	0.672	0.857	0.96	0.986
Akaike	−3.825	−2.23	−1.283	−2.279	−1.952	−3.380	−3.104	−3.57
BG–LM test	10.19***	0	9.135***	0.997	6.434**	2.29	.99	7.335**
RESET	1.506	0.524	1.047	2.32	0.652	1.674	.277	1.122
J-statistic	.669	6.188(*)	4.297	5.029	2.768	2.809	4.045	1.557

Notes: Dependent variable is the logit of the labour force participation rate ln (p/(1 − p)), with participation rate p.

STU, LTU: short-term and long-term unemployment rate, respectively; STU without lag, LTU with lag 1.

Wage (by age and sex): median wage of full-time employees; W × W is the squared value of the wage variable, W and W × W without lag.

TB1996: break in the trend; 0 before 1996, from 1996 onwards plus 1 year on year.

TB2000: break in the trend; 0 before 2000, from 2000 onwards plus 1 year on year.

TB2005: break in the trend; 0 before 2005, from 2000 onwards plus 1 year on year.

Logit coefficients in the cells, < 0 indicating discouragement, >0 indicating AWE.

t-Statistic in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1; (*) p very close to 0.1, otherwise not significant.

BG–LM test: Breusch-Godfrey LM test for serial correlation (with Lag 2 for the residuals).

RESET: F-test, df(number of fitted terms equals 2; number of observations (after adjustment for lags) – number of regressors – number of fitted terms).

J-statistic: Durbin–Wu–Hausman test, df 3; alle instruments were included with lag 1.

1) Long-term unemployment with Lag 2.

2) Long-term unemployment with Lag 3.

Source: Own calculations.

The age-specific STU rate is significant for the younger and the older age groups, whereas for the middle age groups insignificant coefficients are found. The LTU rates take, in essence, the same sign as the STU, with the exception of the 35- to 39-year-olds.

Our findings show that the youngest as well as older men can become discouraged (even though the coefficient of the LTU of the 25- to 29-year-olds, with a t-value of −1424, is only ‘almost’ significant). This can be seen in view of existing alternatives. In the short run, for example, the young can opt for staying in or returning to education (see Clark 2011).

The two oldest groups seem to be especially susceptible to discouragement. This is in line with studies that highlight the unemployment problem of older workers in Germany. The statistic shows that older workers have very low prospects of re-employment (see Dietz and Walwei 2011). Our results for older workers should also be seen within the relevant institutional framework in Germany.⁷ In spite of several changes during our investigation period, older unemployed workers continued to have longer entitlement to unemployment compensation, special disability pensions due to labour market problems were available, and early retirement schemes were still feasible for those aged 60 years and over. The latter option could provide an incentive to retire after entitlement to unemployment compensation has expired.

Among the 30- to 54-year-olds, the AWE predominates, especially in a labour market that remains structurally weak, i.e. we observe an AWE for the LTU rates. Early returns from further training or shorter periods of sickness (or a few longer periods) should be considered as possible pathways back to the labour force. The influence of the STU is less clear-cut, but on the whole an AWE prevails over discouragement, although the coefficients of the STU rates are mostly insignificant.

Compared to an earlier study by Briscoe and Wilson (1992), who used the overall unemployment rate and 10-year age brackets, our modelling reveals important differences by the distinction between STU and LTU. Briscoe and Wilson got an insignificant negative sign for each unemployment variable of middle aged men. In addition, they reported a significant discouragement effect for 60- to 64-year-olds caused by LTU, without, however, taking STU into consideration. We think this supports our approach to disentangle unemployment in respect to duration.

Women

Again, we concentrate our discussion on the effects of STU and LTU (Table 2). For the young and the middle aged, the coefficient of the STU rate is significant and, due to its negative sign, indicates discouragement. A significant AWE was detected for women aged 50 and older. The LTU rate proves to be influential for most women aged 35 and above and signalizes discouragement. For the younger, neither discouragement nor AWE was detected for the LTU variable.

Table 2. Basic results for the labour force participation rate of females.

Age	25–29	30–34	35–39	40–44	45–49	50–54	55–59 ^1)	60–64 ^1)
STU	−0.039896	−0.028324	−0.057017	−0.027531	−0.032112	0.026194	0.015724	0.046224
	(−4.381)***	(−2.152)**	(−5.889)***	(−3.654)***	(−3.352)***	(2.147)**	(1.701)*	(4.204)***
LTU	−0.022387	0.016429	−0.024244	−0.046529	−0.030626	−0.001661	−0.01294	−0.017587
	(−0.738)	(0.907)	(−2.016)*	(−4.871)***	(−3.336)***	(−0.254)	(−5.787)***	(−2.513)**
Wage (WF)	−0.16651	−0.219442	−0.097914	−0.006231	0.061160	0.03635	0.061196	0.404662
	(−1.049)	(−2.429)**	(−2.27)**	(−0.219)	(2.821)**	(1.141)	(0.519)	(1.451)
WF × WF	0.001117	0.000598	0.000612	2.23E-05	−0.000478	−0.000299	−0.000401	−0.002615
	(1.037)	(2.393)**	(2.099)**	(0.118)	(−3.258)***	(−1.375)	(−0.548)	(−1.458)
Trend	0.014092	0.037376	0.051667	0.06268	0.076257	0.063389	0.032421
	(10.05)***	(6.867)***	(18.57)***	(33.83)***	(37.829)***	(39.64)***	(3.495)***
TB1996							0.030379	0.075172
							(3.166)***	(18.812)***
DU2005		−0.194771
		(−2.941)***
TB2005			−0.058955	−0.048386	−0.054868
			(−10.24)***	(−11.87)***	(−12.61)***
Adj. R2	0.918	0.974	0.994	0.997	0.997	0.997	0.996	0.988
Akaike	−1.733	−1.667	−4.419	−4.437	−4.106	−4.288	−4.309	−2.812
BG–LM test	0.0	0.0	0.0	0.893	5.978 **	0.777	2.843	5.015 *
RESET	0.924	1.805	0.318	0.206	0.964	1.726	0.482	1.418
J-statistic	2.945	3.969	1.921	2.712	4.293	5.194	5.194	3.027

Notes: see also Table 1.

DU2005: Dummy, 0 until 2004, 1 from 2005 onwards.

1) Long-term unemployment with lag 3.

Source: Own calculations.

Altogether, discouragement plays a role for women comparable with the findings in the literature. A different reaction can be seen for older women, where STU causes an AWE and LTU leads to discouragement. There seem to be some short-term pressure or incentive to enter the labour market, but in the long run older women tend to withdraw, as there are still some early retirement options available.

In addition to the above-mentioned interpretations for men, the aspect of starting a family may be important as young women can take the alternative role of motherhood.⁸ In general, women have still better social accepted alternative roles as men, so they can withdraw more easily. The situation may change when getting older. In the short run, taking up a job could become necessary, e.g. due to retirement, unemployment or long-term sickness of the partner or after a separation from the spouse. After a while, and we observe rather long lags for the older age groups, the pensions system makes it possible for older women to retire.

In the light of the secondary worker hypothesis, we checked for cross-effects of male unemployment on female participation with regard to household (or spouse) influences. The females’ LTU were replaced by the corresponding LTU of males. Although both age-specific rates correlate high, the correlation between females’ and males’ LTU is more than 0.7 across all age groups, the quality of the results fall somewhat behind those of Tables 1 and 2. Only the coefficients of the lagged males’ LTU rate for the age groups 35–49 were significant.

To sum up, discouragement arises from STU with a magnitude comparable to results found in the existing literature for the overall unemployment rate. Our analysis indicates, however, an AWE for women aged 50 and above. The influence of the LTU rate slightly varies with age, which was revealed by the decomposition of unemployment in our approach. There is no evidence for an AWE caused by LTU. This can be explained in the light of empirical findings in the literature often referring to the labour market situation of married women as secondary workers. The very high labour force participation rates of German women, compared to other European countries, suggest that this labour market regime has become less important in Germany.

V. Modelling issues

Specification

Every estimated equation was checked in respect of its specification using Ramsey’s RESET test (see Wooldridge 2013). Following Wooldridge, squared and cubed terms were added to the equations. The results are reported in Tables 1 and 2, respectively. As the F-test is not significant in any case, our estimations are well specified.

Different other specifications were tested. The equations on which the results of Table 1 and Table 2 are based proofed to be the best, although there is no distinct difference to a specification without a lag for the LTU rate or a modelling that does not include the squared value of the wage variable. This evaluation rest on the Akaike information criteria, the statistical significance of the coefficients and the statistical properties of the estimated equations (see discussion later).

Our results are slightly less significant when the total STU or LTU rates are used instead of the age-specific rates. Although we could not analyse the reason for this in more depth, it might be concluded that personal experience of unemployment is more influential than the signalling effect of a high (low) unemployment rate, which was mentioned earlier.

Stationarity

We checked the correlogram of all variables in order to get an impression of persistence. Autocorrelations show a rather quick decay, which makes nonstationarity unlikely.

Moreover, ADF tests were carried out to check whether the time series are stationary. In case of a break in the time series, the unit root test of JMulti 4 (Lütkepohl 2007) was applied. Due to the well-known low power of unit root tests in small samples, we limited ourselves to the 10% significance level.

The results are given in the Appendix (see Tables A1 and A2). In nearly all cases, our impression is confirmed that nonstationarity is unlikely. If the ADF test slightly exceeded the 10% level, e.g. for males aged 25–29, the significance level for the ULT rate was 10.6%, the KPSS test was applied additionally. For all time series concerned, KPSS was not significant at the 5% level, i.e. the stationarity hypothesis was not rejected.

Only for males aged 60–64 nonstationarity of the logit of the LFPR cannot be ruled out. Table A1 in the Appendix show the result for a unit root test with a break in the year 2000, which can almost reject the null hypothesis of a unit root at the 10% level. As the correlogram has shown no critical persistence in the autocorrelation function, we rely on the stationarity hypothesis. Finally, we can rule out the risk of a spurious regression since the estimation result proved to be robust against considering the lagged endogenous variable on the right hand side.

Autocorrelation

Tables 1 and 2 show the Breusch–Godfrey test statistic for serial correlation (with Lag 2; all results are identical for Lag 1). The test indicates autocorrelation at the 5% level for males aged 25–29, 35–39, 45–49 and 60–64, and for females aged 45–49 and 60–64 at the 5% respective 10% level. In these cases, we applied a heteroskedasticity and autocorrelation consistent (HAC)  method to get robust SEs.

In sum, this shows that the equations are dynamically well specified. The major effects should be captured and no risks of spurious regressions are evident.

Endogeneity

On both sides of each equation, the number of unemployed persons is included in the generated rate, as the labour force participation rate, on the right hand side, is defined as the number of employed plus the unemployed divided by the population.⁹ An obvious case of endogeneity would occur if lower participation reduced unemployment to a disproportionate extent and vice versa (i.e. if there were a positive effect between the rates). We therefore applied an instrumental variable method to address a possible bias due to simultaneity. The lagged values of the explanatory variables, i.e. STU, wages and squared wages, were used as instruments (with lag 1).¹⁰ The Durbin–Wu–Hausman test for endogeneity was not significant in any case (see J-statistic in Tables 1 and 2).

VI. Conclusion

We analysed the influence of LTU and STU on labour force participation in Germany. Following the literature, we expected STU not to result in additional workers in general. In this respect, the discouragement effect should be stronger. LTU, however, might reduce household income more strongly, thereby increasing the need for additional income. On the other hand, it may discourage especially older workers for psychological and sociological reasons.

The estimations were conducted according to age and sex. The coefficients for both the STU and the LTU variables are significant for most groups, or, in some cases, the t-statistic is close to the 10% significance level. Even for men, about whom only a few empirical studies on this issue are available, distinguishing between STU and LTU reveals AWE and discouragement effects.

In conclusion, STU seems to discourage women, younger workers and older men. We suspect that these patterns should be seen within the possibility of ‘alternative’ roles (housewife, sickness, disability, student).

Older women and middle-aged men, in contrast, enter the labour market due to STU, i.e. we found a significant AWE. The surprising result for men can be explained, for example, with the participation in training programmes. Middle-aged men should typically re-enter the labour market afterwards. A similar effect might have shorter long-term sickness periods (or few longer sickness periods).

According to our estimations, older workers become discouraged by LTU after some time. This can be explained by the institutional framework. In Germany, older unemployed individuals were permitted to retire earlier during the period under investigation. When entitlement to unemployment compensation expires, early retirement schemes provide an incentive to exit from the labour market.¹¹

LTU increases the labour force participation of men aged 30–54 and women aged 30–34. Possible explanations has been already given above associated with STU.

For women aged 30–34, this AWE could be expected under the ‘secondary worker hypothesis.’ In general, the AWE seems to be less relevant for females in Germany. Given the background of a high female labour participation being married is not, by now, that important for the labour market attachment of women. It should be noted, however, that in Germany more than half of all female workers only work part-time. Holst and Wieber call this the ‘modernized breadwinner model (father in full-time/mother part-time)’ (Holst and Wieber 2014, 33). The AWE could insofar be more important on the level of working hours, i.e. married women can increase (or reduce) the number of hours works as a reaction on her husbands (threat of) unemployment. This open question might be of interest for future research.

Many OECD countries are expected to suffer from population ageing and, as a consequence, from a shrinking labour force in the future (OECD 2015). As a consequence, the development of labour force participation rates has received considerable attention. The influence of LTU on the appearance of discouraged and added workers might therefore be of particular importance when considering our results in conjunction with high LTU rates in many OECD countries. Especially older workers are seen as a tremendous resource to compensate for a possible lack of skilled workers (for Germany, see Fuchs 2015; OECD 2005). But also the entry of women and younger workers into the labour market offers considerable potential. Against the background of our results, combating unemployment, especially LTU, would integrate not only the officially unemployed but also the so-called hidden unemployed into the labour market. Therefore, reducing unemployment would increase the labour force beyond the number indicated by official statistics (see Weber 2017).

Acknowledgements

The authors benefited from valuable comments by two anonymous referees. Thanks also to the participants of the UR-seminar of the University of Regensburg for their helpful comments on an earlier version of this paper. The usual disclaimer applies.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

There was no funding of the study.

Notes

¹ Long-term sickness or invalidity can also be regarded as options for unemployed workers with poor chances of reemployment . At least in Germany this might be the case for older individuals.

² We did not analyse the situation for young workers, aged 15–24, because long-term unemployment (LTU) should be quite irrelevant for them. This is due to age (with a tendency towards left censoring) and the German education and training system (with great importance attached to vocational training).

³ There were various labour market reforms in Germany in the early years of this millennium (see Klinger and Rothe 2012). For our research question, the last reform in 2005 should be the most important, as the system of unemployment compensation was subjected to fundamental reforms.

⁴ As the ILO unemployment is based on a questionnaire, the self-reported duration of unemployment in ILO/OECD statistics does not correspond entirely to the duration obtained from the national register. The latter, for example, excludes spells of long-term sickness. Respondents’ answers in the labour force survey can differ for different reasons (for instance, due to recall errors).

⁵ In order to calculate age-specific rates, the employment figures were taken from the labour force survey (LFS). There are small differences to the official unemployment rate, which is calculated using several statistical sources for the employment data in addition to the LFS.

⁶ Due to the large number of cases, the empirical participation rates p_t should be a good representation of the true rates. Therefore, no attempt was made to estimate the weights with a two-step approach. In cases where tests exhibited autocorrelation, the Newey–West procedure (HAC) was applied, but not weighted least squares. All these estimations were conducted using EViews 8.

⁷ For some background information, see OECD (2005): Box 3.1, 70f.

⁸ The average age of women giving birth in Germany has risen steadily in the last few decades. Currently, mothers are over the age of 30 on average when giving birth; the average age was 27.6 years in 1990.

⁹ Due to differences in definition and data collection, the total number of unemployed persons in the ILO survey and the Federal Employment Agency register only overlap for about 60 %.

¹⁰ Endogeneity could result from the fact that contemporaneous unemployment may rise in presence of a positive shock on participation. However, this cannot happen to a lagged variable at it is predetermined. As the LTU entered into all final equations of Tables 1 and 2 in a lagged form, endogeneity could not play a role in this case.

¹¹ In fact, unemployment compensation for older unemployed persons is granted in full for a certain period and is then followed by a period at a reduced rate, but in many cases, due to mandatory statutory regulations, an older unemployed person has to retire as early as possible.

Appendix

Table A1. Tests for stationarity, males.

Age group	Logit participation rate	UST	ULT	Wage
25–29	−3.516	−2.665	−3.211	−4.411
	(−2.625, c, 28)	(−2.58, c, 26, 2005)	(−3.243, t, 24)	(−2.58, c, 23, 1997)
30–34	−3.359	−3.018	−3.277	−4.0722
	(−3.255, t, 22)	(2.63, c, 26)	(−3.243, t, 24)	(−2.58, c, 25, 2001)
35–39	−3.621	−2.916	−3.383	−2.732
	(−2.58, c, 25, 2005)	(−2.63, c, 26)	(−3.243, t, 24)	(−2.58, c, 27, 1995)
40–44	−3.737	−2,743	−2.984	−2.767
	(−2.58, c, 25, 2005)	(−2.58, c, 26, 1993)	(−2.58, c, 27, 2003)	(−2.58, c, 27, 2003)
45–49	−3.459	−2.687	−2.69	−2.944
	(−2.58, c, 26, 1991)	(−2.58, c, 26, 2006)	(−2.58, c, 22, 2005)	(−2.633, c, 25)
50–54	−2.647	−3.129	−4.124	−3.398
	(−2.58, c, 25, 2005)	(−2.58, c, 26, 1993)	(−2.76, t, 23, 2003)	(−2.58, c, 26, 2005)
55–59	−3.0	−2.698	−3.894	−2.854
	(−2.76, t, 26, 2000)	(−2.58, c 23, 2005)	(−2.58, c, 26, 2005)	(−2.58, c, 27, 1997)
60–64	−2.482	−3.433	−2.986	−2.678
	(−2.58, c, 2000, 25)	(−2.642, c, 22)	(−2.58, c, 23, 2008)	(−2.58, c, 27, 1995)

Notes: ADF/Unit Root-Test with break (estimated with EViews/JMulti): The cells show the test statistic, and in brackets 10% critical values, model, obs, date, where

●‘model’ indicates the deterministics, namly c constant; t trend (including a constant), no in case of no deterministic variable; model selected by significance (t-value) of the deterministic variable,

●‘obs’ equals observations after adjustments for number of lags and

●‘date’ is the break date in case of a unit root test with break.

Table A2. Tests for stationarity, females.

Age group	Logit participation rate	UST	ULT	Wage
25–29	−3.298	−1.561	−2.793	−2.712
	(−3.225, t, 28)	(−1.61, no, 27)	(−2.63, c, 26)	(−2.63, c, 26)
30–34	−3.540	−3.163	−2.605	−2.821
	(−2.76, t, 27, 2005)	(−3.229, t, 27)	(−2.63, c, 26)	(2.63, c, 26)
35–39	−4.283	−2.529	−3.886	−2.657
	(−2.58, c, 1990)	(−2.627, c, 27)	(−3.243, t, 24)	(−2.625, c, 28)
40–44	−3.818	−3.130	−3.955	−2.655
	(−2.58, c, 27, 1990)	(−2.58, c, 23, 2005)	(−3.243, t, 24)	(−2.625, c, 28)
45–49	−3.948	−2.979	−4.025	−3.288
	(−2.58, c, 27, 1990)	(−2.58, c, 26, 2005)	(−3.243, t, 24)	(−2.58, c, 27, 1987)
50–54	−3.05	−2.714	−3.564	−2.694
	(−3.225, t, 28)	(−2.58, 27, c, 2006)	(−2.58, c, 26, 2005)	(−2.625, c, 28)
55–59	−2.754	−3.7196	−2.597	−3.217
	(−2,58, c, 2005, 27)	(−2.58, c, 23, 1996)	(−2.58, c, 26, 2005)	(−3.255, 6, 22)
60–64	−3.332	−3.484	−3.316	−3,528
	(−2.76, t, 23, 2000)	(−2.646, c, 21)	(−2.58, c, 26, 1996)	(−2.58, c, 27, 1998)

Notes: see Table A1.