DETERMINANTS OF LABOUR FORCE PARTICIPATION FOR SELECTED GROUPS WITH WEAK LABOUR MARKET ATTACHMENT: A PANEL DATA ANALYSIS FOR DENMARK

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1 VELFÆRDS KOMMISSIONEN DETERMINANTS OF LABOUR FORCE PARTICIPATION FOR SELECTED GROUPS WITH WEAK LABOUR MARKET ATTACHMENT: A PANEL DATA ANALYSIS FOR DENMARK DANIEL LE MAIRE AND CHRISTIAN SCHEUER Arbejdsrapport 2006:1

2 DETERMINANTS OF LABOUR FORCE PARTICIPATION FOR SELECTED GROUPS WITH WEAK LABOUR MARKET ATTACHMENT: A PANEL DATA ANALYSIS FOR DENMARK DANIEL LE MAIRE AND CHRISTIAN SCHEUER * Abstract. In this paper we evaluate the e ects of economic incentives on the labour market participation for selected groups with weak labour market attachment. We argue that the people most likely to be a ected by economic incentives are recipients of social assistance and home-working housewives. Partner income only seems to be exogenous to the participation decision for home-working housewives. We also estimate participation equations with own potential income gab from working, which in the case of recipients of social assistence are found to have signi cant positive e ect. The elasticities from changing own disposable income gab on the participation probability is estimated to be in the range per cent. Transforming the elesticities according to de nition in the CGE-model DREAM these amount to Date: December 7, * We gratefully acknowledge the comments we have received from Karsten Albæk, Mette Ejrnæs, Jan Vognsen Hansen, Hans Christian Kongsted, Tove Birgitte Pedersen, Esben Anton Schultz, Anders Sørensen and seminar participants in the DGPE 2005 workshop. Furthermore but not least, we are indebted to Martin Ulrik Jensen for conducting computations using the Law Model of the Ministry of Finance. Finally, we thank Mikael Kirk for research assistance. All remaining errors are ours. 1

3 2 DANIEL LE MAIRE AND CHRISTIAN SCHEUER 1. Introduction In this paper we examine the e ects of economic incentives on the labour market participation for selected groups with weak labour market attachment. The labour supply decision is usually decomposed into the intensive margin, that is the choice of hours, and the extensive margin, that is the participation decision. Even though it is generally believed (see e.g. Heckman (1993)) that the largest e ects are to be found on the extensive margin, most empirical studies have focused on the intensive margin. Empirical studies for Denmark have typically found numerical small elasticities from wages on the amount of labour supplied, see e.g. Frederiksen et al. (2001) and le Maire and Scheuer (2005). In fact, the studies that have found largest elasticities have used a Tobit framework and, hence, it seems as if the small elasticities at the intensive margin have been polluted by the jointly modelling of the participation decision. Several Danish studies have considered the impact of economic incentives on the participation/ employment decision. A part of the literature compares the di erences in disposable income being employed and unemployed, see e.g. Pedersen and Smith (2002). In the most recent analysis the Danish Welfare Commission (2005) nds that for about 5 per cent of the working age population this di erence is less than 1,000 DKK per month. 1 Furthermore, the popularity of the early retirement program has initiated several contributions, which examine the role of economic incentives in the retirement decision. Pedersen and Smith (1992, 1995) nd signi cant e ects of the economic compensation rate on the decision to retire, but no e ects from the compensation rate on the retirement age. Danø et al. (2005) estimate a structural retirement model in order to evaluate the early retirement reform implemented in 1999 and nd that men and women are willing to reduce their income to respectively 80 and 67 per cent when choosing early retirement. We are only aware of one single study on Danish data, which report participation elasticities with respect to income. The study conducted by Graversen (1996) estimates participation elasticities from a natural experiment study of the 1987 tax reform. Graversen nds participation elasticities in the range of for single women and 0.05 for married women. Unlike this study, however, Graversen focus on persons in the labour market. 1 Di erent ways of calculating these di erences in disposable income exists. We as well as the Danish Welfare Commission (2005) - use the Law Model (cf. the Ministry of Finance (2004)) in the computations.

4 LABOUR FORCE PARTICIPATION IN DENMARK 3 In a survey-based study Graversen and Tinggaard (2005) examines the e ects of the implementation of the social assistance ceiling in Approximately 1,000 social assistance recipients were interviewed just before the implementation and again 9 months after the implementation of the social assistance bene t ceiling. Although the ceiling has reduced the amount of social assistance received and, hence, was expected to provide larger incentives Graversen and Tinggaard conclude that there seems to be no e ect on participation and on whether the recipient search or not. Moreover, Graversen and Tinggaard only nd very modest e ects on the search intensity. Internationally natural experiment have been an increasingly popular way of investigating the participation decision in recent years. (see e.g. Eissa et al. (2004) for an analysis of four American tax reforms), but we will rely on reduced-form panel data estimations similarly to Hyslop (1999) and Croda and Kyriazidou (2003). The earned income tax credit and the social assistance bene t ceiling both having e ect from 2004 may be used in a natural experiment. Unfortunately, register data for 2004 is not yet available, so we will not complement our reduced-form panel data participation equations with results from a natural experiment. In Denmark several types of bene ts exists. Each of them is more or less directed to a distinct group of people. With respect to participation, recipients of sickness bene ts and disablement bene ts are for obvious reasons less interesting. Therefore, we restrict our attention to two groups of persons. The rst group is the recipients of social assistance that is persons that are not eligible to unemployment bene ts either because they are not members of an unemployment insurance fund or since they have not been in work recently. The second group is home-working housewives who do not have a wage income 2 and do not receive any bene ts. In a companion paper Kirk et al. (2005) examine the e ects of economic incentives on the length of maternity leave in a duration model setting. A very small elasticity of 0.02 is found. We have access to a rich panel dataset, and we present results from employing di erent panel data estimators. The rst set of estimations follow Hyslop (1999) and Croda and Kyriazidou (2003) closely in the sense that we use spouse disposable income separated into 2 For the latter group we will only focus on women.the reason to abstract from men is rstly that only very few men are home-working, and secondly that one could suspect that men who do not have any wage income and do not receive any bene ts to a larger extend than women are working in the black labour market. Hence, using data extracted from the administrative registers there are reasons to believe that we cannot model the economic incentives.

5 4 DANIEL LE MAIRE AND CHRISTIAN SCHEUER permanent and temporary income. However, our goal is not to provide a comprehensive comparison of di erent estimators as Hyslop (1999) and Croda and Kyriazidou (2003) and, therefore, we have only selected the most promising. Focusing solely on married women Hyslop (1999) and Croda and Kyriazidou (2003) argue that spouse income is exogenous. Hyslop (1999) nds elasticities of respectively permanent and transitory spouse income of -0.2 and for the US, while Croda and Kyriazidou (2003) for Germany nd small e ects from both permanent and transitory spouse income on the participation decision. However, in the case of Denmark the difference in participation between men and women is less pronounced (see e.g. Dex et al. (1995) for a cross-national comparison). Hence, we may only be able to interpret the results from the participation equation for home-working housewives. If this is the case a similar picture should emerge for men and women among recipients of social assistance and, consequently, we also perform the estimations for men. Instead of solely restricting our attention to the e ect of spouse income on the participation of married women, we also make panel data selectivity predictions of the own wage income for each person. Next, we calculate disposable incomes with the use of the Danish Ministry of Finance s Law Model which has a precise modelling of the Danish tax and bene t system. The paper is organized as follows. In section 2, we present the data used inthe analysis. In section 3 the econometric methodology. In section 4 and section 5, we examine the results when using respectively disposable spouse income and own predicted disposable income gaps. Section 6 concludes. 2. Data We have access to an unbalanced panel dataset for The dataset is a representative 10 per cent sample of the Danish population. The variables originate from three databases. The rst dataset the Income Registry and the second the IDA database are both maintained by Statistics Denmark. The third is the DREAM database of the Danish Ministry of Employment. Furthermore, we use the Law Model of the Danish Ministry of Finance to compute own disposable income from working and from receiving social transfers. We compute permanent and transitory spouse income similarly to Hyslop (1999) and Croda and Kyriazidou (2003): The permanent income is just the average of the spouse s income in the period under consideration, while the transitory income is yearly deviation from this mean. The samples used in the actual estimations only include

6 LABOUR FORCE PARTICIPATION IN DENMARK 5 persons that in at least one of the years covered, , have primarily respectively been receiving social assistance or been a home-working housewife. 3 Hence, persons who have been employed in all years are not included. This trimming of the dataset is done, since persons being in the labour force for the whole period of are most likely to stay in the labour force and, therefore, in several aspects di er from our samples of either recipients of social assistance or people choosing to be home-working housewives. People employed the whole period do not leave the labour force since the main part of those changing jobs are either not unemployed or are insured and only stay temporary unemployed. Furthermore, we have chosen not to include persons observed only once, since they can not be used in the majority of our estimation procedures. In Table I-III we present some characteristics of the three samples. The rst two groups under consideration are persons who at least during one year primarily have received social assistance. These persons are not eligible to unemployment bene ts either since they are not insured in an unemployment insurance fund or since they have not recently been in work for a su cient long period of time. The social assistance is lower than unemployment bene ts and are also means-tested in households. The latter implies that the individual may face a poverty trap if his spouse is also receiving social assistance. The main determinant of the amount of social assistance are whether the individual is older than 25, living with his parents, and whether he has children. 3 We de ne a recipient of social assistance as a person who has received social assistance bene ts in at least 42 weeks in a given calendar year according to the DREAM Registry. A home-working housewife is de ned as a woman receiving no social transfer payment and having a labour income below 5,000 DKK in a given year. Moreover, we exclude self-employed and assisting wives from the sample.

7 6 DANIEL LE MAIRE AND CHRISTIAN SCHEUER Experience Union membership Table I 4 : Mean values: Social Assistance - Males Received sickness benefit Unskilled Vocational training Short cycle higher education Medium cycle higher education Long cycle higher education Immigrant Second generation immigrant Married Age Copenhagen Large city Rural area Vacancies Children aged 0 6 years Children aged 7 17 years Owner Unemployment on municipality and gender Unemployment on education and age Unemployment on age and gender Partner's disposable income Two adults in the familly Received social assistance Working Hourly gross wage Years with social assistance Number of changes Total number of years in the sample Full Sample Social Assistance All Years Single Transition from Social Assistance Single Transition from Work Multiple Transitions (5.87) (4.67) (5.78) (6.92) (6.19) (0.41) (0.18) (0.49) (0.48) (0.46) (0.34) (0.12) (0.40) (0.43) (0.44) (0.47) (0.46) (0.48) (0.47) (0.47) (0.42) (0.39) (0.43) (0.44) (0.44) (0.17) (0.19) (0.16) (0.14) (0.14) (0.19) (0.19) (0.21) (0.15) (0.15) (0.16) (0.17) (0.18) (0.15) (0.13) (0.48) (0.49) (0.50) (0.37) (0.38) (0.08) (0.08) (0.07) (0.09) (0.08) (0.47) (0.48) (0.49) (0.40) (0.41) (9.79) (9.93) (9.63) (9.54) (9.38) (0.42) (0.43) (0.41) (0.39) (0.41) (0.39) (0.42) (0.38) (0.38) (0.35) (0.50) (0.50) (0.50) (0.50) (0.50) (0.02) (0.01) (0.02) (0.02) (0.02) (0.72) (0.78) (0.72) (0.60) (0.60) (0.82) (0.94) (0.81) (0.59) (0.68) (0.32) (0.26) (0.34) (0.37) (0.34) (1.76) (1.73) (1.77) (1.77) (1.78) (2.11) (2.10) (2.14) (2.06) (2.10) (0.85) (0.85) (0.85) (0.83) (0.84) 77,801 75,787 79,177 79,420 80,438 (25,982) (21,186) (30,042) (29,983) (27,745) (0.49) (0.49) (0.50) (0.46) (0.48) (0.46) (0.00) (0.49) (0.50) (0.50) (0.46) (0.00) (0.49) (0.50) (0.50) (38.62) (0.00) (35.85) (41.87) (39.13) (1.79) (1.45) (1.19) (1.35) (1.35) (0.81) (0.00) (0.00) (0.00) (1.35) (1.34) (1.45) (1.22) (1.24) (0.51) No. Years of Social Assistance Sample size 34,588 16,000 7,447 5,895 5,246 Focusing on the column for the full sample in table I we see that the number of males who primarily received social assistance in at least one year in the period is 34,588. Looking at the number of years the individuals received social assistance; about 22 per cent received social assistance in precisely one year during the period while about 17 per cent received social assistance in the full period. 4 Standard deviations are in parantheses.

8 LABOUR FORCE PARTICIPATION IN DENMARK 7 From the sample means a few things are worth noticing. Firstly, even though the mean age is above 36 years the mean value of experience (in years) is only 4.4. This might suggest a high degree of persistence in the labour market status, since males receiving social assistance are clearly less likely to become employed compared to the average male, who by the age of 36 would on average be better educated and still have more than 4.4 years of experience. Secondly, as the average experience indicates our sample is quite di erent from the average population suggesting that the group under consideration is marginalized in the labour market. The most prominent di erences are that 35 per cent are immigrants (whereas immigrants only constitute 6 per cent of the Danish population), that 68 per cent are unskilled (in the whole population between the corresponding gure is 33 per cent) and that only 11 per cent are homeowners (out of all homes 53 per cent is inhabited by the owner). Finally, the average wage is 109 DKK per hour while the mean wage for private employed males was 230 DKK in We proceed by splitting the full sample into 4 subgroups; those receiving social assistance all years (16,000 persons), those who have one single transition from social assistance to work (7,447 persons), those having one single transition from work to social assistance (5,895 persons) and those who have more than one transition between work and social assistance (5,246 persons). When breaking the sample down by transition patterns we notice that even though the labour market experience is quite di erent between the three groups of people who at some point have been on the labour market ( years) the average wage for the people working is much alike ( DKK) suggesting that the minimum wage restriction is binding for the majority of persons belonging to the group. Further, immigrants are much overrepresented among those receiving social assistance in all years and among those having only one single transition from social assistance (43 per cent vs. 17 per cent). This may explain why a larger fraction of these groups is married and why the groups on average have more children. Finally, it is worth noticing that for people receiving social assistance in all years, the partner income is a little lower.

9 8 DANIEL LE MAIRE AND CHRISTIAN SCHEUER Experience Table II 5 : Mean values: Social Assistance - Females Union membership Received sickness benefit Unskilled Vocational training Short cycle higher education Medium cycle higher education Long cycle higher education Immigrant Second generation immigrant Married Age Copenhagen Large city Rural area Vacancies Children aged 0 6 years Children aged 7 17 years Owner Unemployment on municipality and gender Unemployment on education and age Unemployment on age and gender Partner's disposable income Two adults in the familly Received social assistance Working Hourly gross wage Years with social assistance Number of changes Total number of years in the sample Full Sample Social Assistance All Years Single Transition from Social Assistance Single Transition from Work Multiple Transitions (4.33) (3.57) (4.38) (5.59) (5.19) (0.36) (0.16) (0.48) (0.48) (0.46) (0.28) (0.09) (0.39) (0.42) (0.41) (0.41) (0.38) (0.43) (0.45) (0.45) (0.36) (0.32) (0.38) (0.42) (0.42) (0.13) (0.13) (0.15) (0.12) (0.10) (0.18) (0.18) (0.20) (0.18) (0.15) (0.11) (0.10) (0.11) (0.08) (0.13) (0.49) (0.50) (0.48) (0.36) (0.34) (0.08) (0.07) (0.09) (0.10) (0.10) (0.49) (0.50) (0.49) (0.41) (0.41) (9.49) (9.63) (9.30) (9.39) (8.83) (0.39) (0.39) (0.37) (0.37) (0.38) (0.39) (0.41) (0.36) (0.35) (0.34) (0.50) (0.50) (0.50) (0.50) (0.50) (0.02) (0.02) (0.02) (0.02) (0.02) (0.88) (0.95) (0.77) (0.70) (0.75) (1.06) (1.14) (0.96) (0.84) (0.92) (0.33) (0.28) (0.39) (0.39) (0.39) (1.79) (1.77) (1.75) (1.91) (1.84) (2.15) (2.15) (2.15) (2.15) (2.12) (1.64) (1.66) (1.59) (1.66) (1.60) 93,331 85, ,325 98, ,930 (37,960) (33,927) (40,752) (41,534) (40,327) (0.50) (0.50) (0.49) (0.49) (0.50) (0.41) (0.00) (0.49) (0.50) (0.50) (0.41) (0.00) (0.49) (0.50) (0.50) (34.52) (0.00) (32.55) (38.39) (35.01) (1.82) (1.43) (1.27) (1.40) (1.46) (0.69) (0.00) (0.00) (0.00) (1.46) (1.35) (1.43) (1.17) (1.30) (0.42) No. Years of Social Assistance Sample size 35,952 22,096 7,063 3,766 3,027 The second group for whom we present mean values is females primarily receiving social assistance in at least one of the years The pattern of table II does to a large extent replicate the pattern in table I. Therefore, the most important information we retrieve is that also females recipients of social assistance seem to be marginalized in the labour market attachment. The mean age is 5 Standard deviations are in parantheses.

10 LABOUR FORCE PARTICIPATION IN DENMARK 9 34 years and the experience only 2.5 years, 39 per cent are immigrants and 79 per cent unskilled. Again breaking down on di erent transition patterns we see that di erences in experience are not re ected in the wage rate of those employed from the di erent groups, again suggesting the minimum wage restriction to be binding. Furthermore, the partner income is now somewhat lower for the group receiving social assistance all years. This may suggest that to some extent persons cohabiting are likely to have a similar attitude towards participating in the labour market.

11 10 DANIEL LE MAIRE AND CHRISTIAN SCHEUER Table III 6 : Mean values: Home-Working Housewife - Females Experience Union membership Received sickness benefit Unskilled Vocational training Short cycle higher education Medium cycle higher education Long cycle higher education Immigrant Second generation immigrant Married Age Copenhagen Large city Rural area Vacancies Children aged 0 6 years Children aged 7 17 years Owner Unemployment on municipality and gender Unemployment on education and age Unemployment on age and gender Partner's disposable income Two adults in the familly Being home working housewife Working Hourly gross wage Years with social assistance Number of changes Total number of years in the sample Home Working Housewife All Years Single Transition from Home Working Housewife Full Sample Single Transition Multiple from Work Transitions (6.65) (5.15) (5.56) (8.41) (8.43) (0.37) (0.18) (0.48) (0.49) (0.50) (0.19) (0.03) (0.33) (0.30) (0.27) (0.50) (0.49) (0.50) (0.48) (0.47) (0.45) (0.44) (0.44) (0.49) (0.49) (0.21) (0.20) (0.21) (0.23) (0.18) (0.29) (0.26) (0.31) (0.34) (0.40) (0.20) (0.19) (0.23) (0.23) (0.24) (0.46) (0.46) (0.50) (0.36) (0.39) (0.06) (0.04) (0.11) (0.04) (0.12) (0.24) (0.16) (0.29) (0.36) (0.40) (10.91) (10.50) (10.57) (9.70) (9.50) (0.34) (0.32) (0.38) (0.36) (0.35) (0.31) (0.31) (0.28) (0.32) (0.32) (0.49) (0.48) (0.49) (0.50) (0.49) (0.02) (0.02) (0.02) (0.02) (0.02) (0.68) (0.64) (0.73) (0.73) (0.70) (0.86) (0.78) (1.01) (0.94) (0.91) (0.49) (0.48) (0.50) (0.47) (0.47) (2.01) (2.05) (1.81) (2.02) (1.92) (1.98) (1.89) (2.09) (1.95) (2.01) (1.98) (2.08) (1.67) (1.77) (1.64) 150, , , , ,615 (210,323) (181,905) (240,365) (313,281) (135,480) (0.14) (0.00) (0.25) (0.21) (0.26) (0.40) (0.00) (0.49) (0.50) (0.46) (0.40) (0.00) (0.49) (0.50) (0.46) (54.22) (0.00) (41.75) (64.18) (56.77) (1.93) (1.49) (1.13) (1.32) (0.93) (0.61) (0.00) (0.00) (0.00) (0.93) (1.42) (1.49) (1.33) (1.27) (0.32) No. Years as Home Working Housewife Sample size 12,813 8,460 1,950 1, The nal group analyzed is home-working housewives. As one might suspect there are fairly large di erences between this group and the two groups receiving social assistance. The sample consists of 12,813 females of which 33 per cent have been housewives in all 6 years. Furthermore, 8,460 (66 per cent) have been housewives in all years they appear in the sample. Hence, even though the mean age is 45 years the mean experience is 6 Standard deviations are in parantheses.

12 LABOUR FORCE PARTICIPATION IN DENMARK 11 only 5 years. Nevertheless in the groups either starting out on the labour market (1,679 persons) or having multiple transitions (724 persons) the mean experience is years. In contrast to what we saw for the other groups this leads to higher wages (124 and 130 DKK compared to 108 DKK). This seems to indicate that the proportion of marginalized housewives is smaller than in the case of recipients of social assistance. In other words, staying outside the labour market is probably less involuntary. Another feature indicating a voluntary choice is that partner income for the group being home-working housewives the whole period is clearly larger than for the other groups. Thereby, it seems as we have a positive income e ect exerted by husband s earnings on home-working housewives non-market time as also found generally for married women in Hyslop (1999) and Croda and Kyriazidou (2003). Compared to recipients of social assistance we also notice that the average amount of partner income is more than 50 per cent higher for home-working housewives. In other words, only for home-working housewives the partner income seems to be exogenous in the labour market participation choice. 3. The econometric framework The estimations dealt with in this paper are reduced-form participation equations. There are di erent possible sources of the high degree of persistence in individual labour market participation decision. Here we examine the e ects of unobserved heterogeneity and state-dependence, while we do not consider serial correlation in the time-varying error component. The latter extension does not seem to matter as Croda and Kyriazidou (2003) nd an insigni cant correlation coe cient when letting the error term be generated from a rst order autoregressive process. We will only shortly consider the econometric speci cations, and we refer to references mentioned below as well as textbooks such as Greene (2003) and Wooldridge (2002) for a more detailed treatment. The rst estimation is the pooled probit estimation (3.1) Pr (y it = 1jX it ) = 1 (X it + " it 0) = (X it ) where y it is the binary variable for the participation decision of individual i at time t, X it contains the explanatory variables, and the error term " it is assumed to be independent of the explanatory variables and distributed in (0; 1).

13 12 DANIEL LE MAIRE AND CHRISTIAN SCHEUER The pooled probit estimator does not exploit the fact that we observe the persons again and again, and since it is very likely that the errors are correlated because the same persons are observed several times, we also estimate a random-e ects probit (3.2) Pr (y it = 1jX i ; i ) = 1 (X it + i + " it 0) = (X it + i ) where the compound error-term i + " it is assumed to be independent of the explanatory variables and both terms are normally distributed. Failing to allow for state-dependence will bias the parameter estimates in presence of (true) state dependence. In addition to that, it is of interest in itself whether employment is truly state-dependent, since this implies becoming a recipient of social assistance signi cantly deteriorates the future labour market prospect of the individual. In order to address this issue, we estimate a dynamic random-e ects probit (3.3) Pr (y it = 1jX i ; i ; y it 1 ) = 1 (y it 1 + X it + i + " it 0) = (y it 1 + X it + i ) Estimating a dynamic probit raises the question of how to treat the initial observations of the dependent variable y i0. Heckman (1981) suggests approximating the conditional density of the initial dependent variable by estimating a probit using observations from the rst year only and simultaneously specifying the unobserved heterogeneity conditional on the explanatory variables. We use the simpler estimation procedure for the dynamic correlated random-e ects probit outlined in Wooldridge (2005) where the approximation of the density of the initial dependent variable is left out. Instead the unobserved heterogeneity is allowed to be arbitrarily correlated with the initial dependent variable by inclusion of the values of the explanatory variables from all years. However, since the dataset is unbalanced we cannot include the values of the explanatory variables from all years and instead we include the means. The two nal estimators use the logit speci cation and, hence, instead of assuming that the error-term " it is normally distributed we assume that it is logistically distributed. With the logit speci cation we can let the explanatory variables X it and the unobserved e ect i be arbitrarily correlated. We need to observe a person in two periods when estimating the conditional maximum likelihood xed-e ects logit. The idea is that only a person that changes state, that is y i1 + y i2 = 1, contributes to the likelihood function.

14 LABOUR FORCE PARTICIPATION IN DENMARK 13 Therefore, the trimming of the dataset by excluding persons that are employed in all years does not a ect the likelihood function in the xed-e ects logit case, since these observations would not contribute anyway. In the same manner, also persons that are respectively receiving social assistance or are home-working housewives in the entire period do not contribute to the likelihood function. For y i1 + y i2 = 1 we have (3.4) Pr (y i1 = 1jX i ; i ; y i1 + y i2 = 1) = exp ((X i2 X i1 ) ) 1 + exp ((X i2 X i1 ) ) As with the random-e ects probit model, naturally, we want to allow for state-dependence. Chamberlain (1993) has shown that if individuals are only observed in three periods, the parameters of the dynamic xed-e ects logit model are not identi ed. Subject to some regularity conditions Honoré and Kyriazidou (2000) have shown that the parameters are identi ed when we have four or more consecutive observations per individual. The basic idea follows that of the conditional likelihood approach. Consider the following events A = fy i0 ; y i1 = 0; y i2 = 1; y i3 g and B = fy i0 ; y i1 = 1; y i2 = 0; y i3 g where y i0 and y i3 are either 0 or 1. In this case we have Pr (AjX i ; i ) = p 0 (X i ; i ) y i0 (1 p 0 (X i ; i )) 1 y i0 Pr (y i1 = 0jX i ; i ; y i0 ) Pr (y i2 = 1jX i ; i ; y i0 ; y i1 ) Pr (y i3 = 1jX i ; i ; y i0 ; y i1 ; y i2 ) y i3 (3.5) (1 Pr (y i3 = 1jX i ; i ; y i0 ; y i1 ; y i2 )) 1 y i3 = p 0 (X i ; i ) y i0 (1 p 0 (X i ; i )) 1 y i exp (X i1 + y i0 + i ) exp (X i2 + i ) 1 + exp (X i2 + i ) exp (y i3x i3 + y i3 + y i3 i ) 1 + exp (X i3 + + i ) while (3.6) Pr (BjX i ; i ) = p 0 (X i ; i ) y i0 (1 p 0 (X i ; i )) 1 y i0 exp (X i1 + y i0 + i ) 1 + exp (X i1 + y i0 + i ) exp (X i2 + + i ) exp (y i3x i3 + y i3 i ) 1 + exp (X i3 + i ) Noticing that if X i2 = X i3 we can get rid of the i s so that we end up with Pr (AjX i ; i ; A [ B; X i2 = X i3 ) = (3.7) = Pr (AjX i ; i ; X i2 = X i3 ) Pr (AjX i ; i ; X i2 = X i3 ) + Pr (BjX i ; i ; X i2 = X i3 ) exp ((X i1 X i2 ) + (y i0 y i3 ))

15 14 DANIEL LE MAIRE AND CHRISTIAN SCHEUER Honoré and Kyriazidou (2000) propose to estimate and by maximizing (3.8) nx 1 fy i1 + y i2 = 1g K i=1 Xi2 h n X i3 ln! exp ((X i1 X i2 ) b + g (y i0 y i3 )) yi1 1 + exp ((X i1 X i2 ) b + g (y i0 y i3 )) over some compact set. K () denotes a kernel density function which is a standard normal density function. The great advantage of the Honoré and Kyriazidou estimator is that it is completely agnostic about the nature of individual heterogeneity. The estimator, however, makes use of the assumption of independent errors, but this does not distinguish the Honoré and Kyriazidou estimator from most other maximum likelihood estimators. On the other hand, it is problematic that the Kyriazidou and Honoré estimator does not allow year dummies, since the real disposable income has increased from Identi cation as described above naturally extends to the case with more than 4 observations for each individual, see Honoré and Kyriazidou (2000). Identi cation in this case comes from all individuals changing state between two of the middle periods (that is any period but the rst and last): (3.9) 2 nx X 4 i=1 1t<sT 1 ln 1 fy it + y is = 1g K Xit+1 X is+1 h n exp((xit X is )b+g(y it 1 y is+1 )+g(y it+1 y is 1 )1fs t>1g) yit 1+exp((X it X is )b+g(y it 1 y is+1 )+g(y it+1 y is 1 )1fs t>1g) Does Partner Income Create Work (dis-)incentives In this section and the following we report our results. We begin by focusing on whether the partner income a ects the decision of belonging to the group either receiving social assistance or being home-working housewives. Table IV-IX give the results for the three groups using the econometric speci cations considered in the previous section. For each group ve di erent estimators are used and the elasticities from the pooled and randome ects probit estimations are calculated. Following Hyslop (1999) and Croda and Kyriazidou (2003) we have split partner income into a permanent and a temporary part. Implicitly we need to assume that partner income is exogenous to own income that is, we observe the level of partner income before deciding our own labour supply. It is most likely that women decide whether to participate after observing their husband s participation choice than the other way around. In fact, in the literature this has not been a seldom assumption. Furthermore, it is most obvious that this sequential

16 LABOUR FORCE PARTICIPATION IN DENMARK 15 decision structure is relevant for home-working housewives, since among this group we nd that the husbands earnings are highest. In addition to that, women receiving social assistance are more likely to belong to a marginalized group being involuntary out of the labour market. If this sequential decision structure is not present for women in social assistance, we would expect that a similar picture should emerge for men and women among recipients of social assistance and, consequently, we also perform the estimations for men. As described in Hyslop (1999) there are two alternative ways of interpreting the reactions to permanent vs. transitory income. In the classical labour supply model, people choose their labour supply subject to the budget constraint. Therefore, a change in permanent partner income changes the budget constraint and, hence, directly a ects the labour supply decision. Changes in transitory income, on the other hand, are only important if the agents are credit constrained. Instead Hyslop models the labour supply as a dynamic programming problem arguing that the direct e ect on labour supply is found from transitory non-labour income. The argument is that since permanent income is the income that individuals expect to have in all future periods this is already incorporated from the beginning of the process, such that unexpected changes in income - that is changing temporary income - is the important determinant of people s behaviour. Permanent income only varies between individuals and, hence, the coe cient cannot be identi ed in the xed-e ects speci cations. Temporary income, on the other hand, varies both between and within individuals. 7 Our a priory expectation is that an increase in partner income should lead to weaker work incentives and, therefore, to a lower participation probability. It should be noted that in the absence of major policy changes the within change in partner income the transitory part - is limited. If it takes a certain amount of change in partner income to a ect the labour market status, we could fear that we actually see too little variation in our data to properly identify our parameters. 7 Note that estmating using xed-e ects the coe cient will only be signi cant if the labour market participation adjustments happen in the same period as the change in partner income.

17 16 DANIEL LE MAIRE AND CHRISTIAN SCHEUER Table IV: Participation Probability, Partner Income, Social Assistance, Males d0 (social assistance in 1998) Lagged participation Partner's temporary disposable income / 10,000 Partner's permanent disposable income / 10,000 Age Age Squared Experience Experience Squared Vocational training Short cycle higher education Medium cycle higher education Long cycle higher education Married Immigrant Second generation immigrant Copenhagen Large city Rural area Children aged 0 6 years Children aged 7 17 years Union membership Unemployment on education and age Unemployment on municipality and gender Vacancies Mean (Partner's temporary disposable income) Mean (Age) Mean (Age Squared) Pooled probit Random effects probit Dynamic randomeffects probit Fixed effcets logit Dynamic fixedeffects logit (0.072) (0.056) (0.203) (0.014) (0.018) (0.019) (0.033) (0.063) (0.008) (0.015) (0.012) (0.018) (0.035) (0.099) (0.000) (0.000) (0.001) (0.009) (0.019) (0.068) (0.129) (0.138) (0.000) (0.001) (0.003) (0.005) (0.069) (0.123) (0.105) (0.104) (0.216) (0.177) (0.094) (0.192) (0.157) (0.099) (0.204) (0.167) (0.047) (0.088) (0.178) (0.055) (0.110) (0.094) (0.355) (0.671) (0.560) (0.067) (0.134) (0.394) (0.780) (0.070) (0.140) (0.478) (0.794) (0.057) (0.115) (0.415) (0.716) (0.021) (0.039) (0.070) (0.123) (0.211) (0.018) (0.035) (0.074) (0.132) (0.040) (0.074) (0.092) (0.069) (0.019) (0.031) (0.027) (0.076) (0.013) (0.024) (0.021) (9.130) (1.301) (2.433) (2.057) (0.000) (0.103) (0.001) Mean (Experience) Mean (Experience Squared) Mean (Married) Mean (Copenhagen) Mean (Large city) Mean (Rural area) Mean (Children aged 0 6 years) Mean (Children aged 7 17 years) Mean (Union membership) Year dummy 2000 Year dummy 2001 Year dummy 2002 Year dummy 2003 Intercept (0.070) (0.003) (0.196) (0.406) (0.490) (0.426) (0.080) (0.080) (0.122) (0.053) (0.069) (0.075) (0.133) (0.055) (0.073) (0.096) (0.158) (0.057) (0.077) (0.123) (0.188) (0.061) (0.084) (0.157) (0.245) (0.343) (0.656) (0.585) Likelihood Value 3,405 3,023 2, R No. Persons 2,339 2,339 No. Observations 7,501 7,501 7, ,633 1,092

18 LABOUR FORCE PARTICIPATION IN DENMARK 17 We begin by examining how partner income a ects the participation decision, and whether there is state dependence among males having received social assistance in the period In the rst four speci cations we see that the in uence from partner temporary income is signi cantly negative, that is, higher temporary income leads to lower participation probability, whereas the in uence from partner permanent income is insigni cant in all three speci cations. Using any of our rst four speci cations our hypothesis about positive change in income leading to a lower probability of participating in the labour market is con rmed. Turning to the nal speci cation, the dynamic xed e ect, the parameter is still negative but now insigni cant. So when controlling for unobserved heterogeneity and state dependence the e ect from changing partner income vanishes. The two dynamic speci cations allow us to control for state dependence. Both lead to the conclusion that the lagged dependent variable is positive and very signi cant and, hence, we nd state-dependence in the participation choice. Table V: Elasticities, Partner Income, Social Assistance, Males Lagged dependent variable Partner's temporary disposable income Partner's permanent disposable income Pooled probit Random effects probit Dynamic randomeffects probit (0.022) (0.019) (0.016) (0.021) (0.078) (0.099) (0.106) Change in Partner's temporary disposable income, 10,000 DK Change in Partner's permanent disposable income, 10,000 DK Table V presents the elasticities for males receiving social assistance. The elasticities from changing temporary income are low. This is the consequence of the small parameter estimates and the small mean value of temporary partner income. To anyway help interpret the elasticities we, therefore, focus on how much increasing respectively the permanent and transitory income by 10,000 DKK on average will a ect the probability of participation. From table V it can be seen that increasing the temporary partner income by 10,000 DKK will decrease the probability of participation in the labour market by 3-4 per cent, but that the elasiticity is insigni cant despite the fact that it is estimated from

19 18 DANIEL LE MAIRE AND CHRISTIAN SCHEUER a signi cant parameter estimate. Furthermore, from the dynamic random-e ects probit model it can be seen that participation in itself increases the probability of also being in the labour market next year by 19 per cent.

20 LABOUR FORCE PARTICIPATION IN DENMARK 19 Table VI: Participation Probability, Partner Income, Social Assistance, Females d0 (social assistance in 1998) Lagged participation Partner's temporary disposable income / Partner's permanent disposable income / Age Age Squared Experience Experience Squared Vocational training Short cycle higher education Medium cycle higher education Long cycle higher education Married Immigrant Second generation immigrant Copenhagen Large city Rural area Children aged 0 6 years Children aged 7 17 years Union membership Unemployment on education and age Unemployment on municipality and gender Vacancies Mean (Partner's temporary disposable income) Mean (Age) Mean (Age Squared) Pooled probit Random effects probit Dynamic randomeffects probit Fixed effcets logit Dynamic fixedeffects logit (0.091) (0.062) (0.211) (0.009) (0.013) (0.014) (0.024) (0.040) (0.006) (0.012) (0.010) (0.019) (0.040) (0.101) (0.000) (0.001) (0.001) (0.013) (0.029) (0.079) (0.156) (0.152) (0.001) (0.002) (0.005) (0.010) (0.066) (0.137) (0.113) (0.124) (0.311) (0.237) (0.106) (0.251) (0.202) (0.171) (0.377) (0.329) (0.047) (0.097) (0.183) (0.054) (0.120) (0.102) (0.244) (0.540) (0.457) (0.068) (0.153) (0.418) (0.783) (0.071) (0.159) (0.562) (1.003) (0.060) (0.136) (0.387) (0.689) (0.024) (0.048) (0.082) (0.147) (0.208) (0.018) (0.039) (0.081) (0.154) (0.042) (0.095) (0.106) (0.058) (0.015) (0.027) (0.024) (0.092) (0.012) (0.026) (0.022) (9.343) (1.272) (2.641) (2.231) (0.000) (0.105) (0.001) Mean (Experience) Mean (Experience Squared) Mean (Married) Mean (Copenhagen) Mean (Large city) Mean (Rural area) Mean (Children aged 0 6 years) Mean (Children aged 7 17 years) Mean (Union membership) Year dummy 2000 Year dummy 2001 Year dummy 2002 Year dummy 2003 Intercept (0.083) (0.005) (0.201) (0.436) (0.576) (0.401) (0.093) (0.088) (0.142) (0.053) (0.073) (0.079) (0.134) (0.054) (0.079) (0.101) (0.164) (0.056) (0.085) (0.131) (0.201) (0.059) (0.091) (0.167) (0.240) (0.343) (0.720) (0.642) Likelihood Value 3,352 2,869 2, R No. Persons 3,292 3,292 No. Observations 10,508 10,508 10, ,552 1,737

21 20 DANIEL LE MAIRE AND CHRISTIAN SCHEUER For females receiving social assistance we nd that the e ect from temporary income is insigni cant, but that the e ect from permanent income is signi cantly positive. This result is somehow surprising since one should expect economic incentives to pull in the opposite direction but what we see is a positive correlation between the incomes of the spouses - that is, high income women tend to marry high income men. Furthermore, it should be noted that also for females receiving social assistance the parameter to the lagged dependent variable is positive and very signi cant in both speci cations. Table VII: Elasticities, Partner Income, Social Assistance, Females Lagged dependent variable Partner's temporary disposable income Partner's permanent disposable income Pooled probit Random effects probit Dynamic randomeffects probit (0.022) (0.062) (0.046) (0.065) (0.103) (0.125) (0.136) Change in Partner's temporary disposable income, 10,000 DKK Change in Partner's permanent disposable income, 10,000 DKK Looking at the elasticities we see that for females receiving social assistance participating in the labour market in itself increases the possibility of participation in next period by 15 per cent. By calculating the elasticities as above, we nd that increasing the partner s permanent income by 10,000 DKK gives us an increased probability of receiving social assistance by per cent. However, since the partner income here probably is endogenous, one shall not put to much emphasis on these results.

22 LABOUR FORCE PARTICIPATION IN DENMARK 21 Table VIII: Participation Probability, Partner Income, Home-Working housewives d0 (social assistance in 1998) Lagged participation Partner's temporary disposable income / 10,000 Partner's permanent disposable income / 10,000 Age Age Squared Experience Experience Squared Vocational training Short cycle higher education Medium cycle higher education Long cycle higher education Married Immigrant Second generation immigrant Copenhagen Large city Rural area Children aged 0 6 years Children aged 7 17 years Union membership Unemployment on education and age Unemployment on municipality and gender Vacancies Mean (Partner's temporary disposable income) Mean (Age) Mean (Age Squared) Pooled probit Random effects probit Dynamic randomeffects probit Fixed effcets logit Dynamic fixedeffects logit (0.132) (0.088) (0.391) (0.001) (0.002) (0.002) (0.002) (0.006) (0.001) (0.004) (0.003) (0.022) (0.055) (0.152) (0.000) (0.001) (0.001) (0.010) (0.026) (0.106) (0.173) (0.122) (0.000) (0.001) (0.003) (0.005) (0.088) (0.203) (0.166) (0.098) (0.287) (0.215) (0.098) (0.226) (0.194) (0.112) (0.330) (0.243) (0.097) (0.203) (0.376) (0.064) (0.172) (0.144) (0.392) (0.830) (0.785) (0.081) (0.207) (0.540) (1.308) (0.094) (0.264) (0.883) (1.707) (0.065) (0.169) (0.571) (1.192) (0.038) (0.077) (0.146) (0.239) (0.328) (0.025) (0.061) (0.134) (0.221) (0.051) (0.138) (0.167) (0.104) (0.029) (0.056) (0.050) (0.114) (0.015) (0.036) (0.031) (12.826) (1.583) (3.769) (3.217) (0.000) (0.155) (0.001) Mean (Experience) Mean (Experience Squared) Mean (Married) Mean (Copenhagen) Mean (Large city) Mean (Rural area) Mean (Children aged 0 6 years) Mean (Children aged 7 17 years) Mean (Union membership) Year dummy 2000 Year dummy 2001 Year dummy 2002 Year dummy 2003 Intercept (0.108) (0.003) (0.431) (0.568) (0.907) (0.588) (0.171) (0.146) (0.202) (0.061) (0.089) (0.116) (0.164) (0.065) (0.098) (0.166) (0.199) (0.067) (0.104) (0.229) (0.234) (0.073) (0.116) (0.302) (0.290) (0.475) (1.172) (1.009) Likelihood Value R 2 No. Persons No. Observations 2,221 1,746 1, ,000 1, ,324 7,324 7,323 1,647 1,394

23 22 DANIEL LE MAIRE AND CHRISTIAN SCHEUER Looking at the home-working housewives we again nd signi cant parameters to the lagged dependent variable and therefore evidence for state dependence. In all speci cations the partner temporary income has only insigni cant in uence on the decision of being home-working housewife. The permanent income, on the other hand, is found to have a signi cant negative e ect people with partners earning more have lower probability of participating. Hence, the unconditional positive income e ect from the husband s earnings from table III is con rmed. Table IX: Elasticities, Partner Income, Home-Working housewives Lagged dependent variable Partner's temporary disposable income Partner's permanent disposable income Pooled probit Random effects probit Dynamic randomeffects probit (0.023) (0.025) (0.017) (0.021) (0.055) (0.092) (0.099) Change in Partner's temporary disposable income, 10,000 DKK Change in Partner's permanent disposable income, 10,000 DKK The two things to notice from table IX are that for home-working housewives participating increases the probability of also participating next period by 11 per cent, and that increasing the partner s permanent income by 10,000 DKK decreases the probability of participating by per cent, but note that the last results are only borderline signi cant. The preliminary conclusion to draw from the results is that there is a substantial difference between the groups of social assistance recipients and home-working housewives. Home-working housewives appear to have voluntarily chosen to stand outside the labour force since the household can a ord her to do so. In contrast to that, social assistance recipients seem to be marginalized into involuntary unemployment. 5. Does Own Income Create Work Incentives In the absence of an exogenous policy change in the considered period we used partner income to examine the e ects of economic incentives on the participation decision. The obvious weaknesses are that partner income may be endogenous and that it is likely that