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

Figures & data

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.

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.

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.

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.