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Enrica Croda,

Ekaterini Kyriazidou

and Ioannis Polycarpou

Intertemporal Labor Force

Participation of Married Women

in Germany: A Panel Data

Analysis

ISSN: 1827/3580 No. 17/WP/2011

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W o r k i n g P a p e r s D e p a r t m e n t o f E c o n o m i c s C a ’ F o s c a r i U n i v e r s i t y o f V e n i c e N o . 1 7 / W P / 2 0 1 1

ISSN 1827-3580

The Working Paper Series is available only on line (http://www.unive.it/nqcontent.cfm?a_id=86302)

For editorial correspondence, please contact: wp.dse@unive.it

Department of Economics Ca’ Foscari University of Venice Cannaregio 873, Fondamenta San Giobbe 30121 Venice Italy

Fax: ++39 041 2349210

Intertemporal Labor Force Participation of Married

Women in Germany: A Panel Data Analysis

Enrica Croda

Ca’ Foscari University of Venice

Ekaterini Kyriazidou

Athens University of Economics and Business Ioannis Polycarpou

Athens University of Economics and Business

This Draft: October 2011

Abstract

This paper analyzes the intertemporal labor force participation behavior of married women using an annual longitudinal sample from the German Socio-Economic Panel. A predominant characteristic of annual participation behavior is the high degree of persistence in individual participation decisions. We use several model specifications to distinguish among the alternative explanations of this serial persistence: state dependence, individual unobserved heterogeneity, and serial correlation in the transitory error component. Similar to Hyslop (1999), we employ both dynamic “fixed effects” linear probability models as well as several static and dynamic probit models with “random effects” and serially correlated errors. In addition, we apply the estimators proposed by Honoré and Kyriazidou (2000) for dynamic “fixed effects” discrete choice models. We find strong state dependence, and substantial effects for fertility variables. Transitory and permanent non-labor income have in general small effects.

Keywords

State dependence, serial correlation, heterogeneity, panel data, intertemporal labor force participation, GSOEP.

JEL Codes

C33, C36, J22

Address for correspondence:

Enrica Croda

Department of Economics Ca’ Foscari University of Venice Cannaregio 873, Fondamenta S.Giobbe 30121 Venezia - Italy Phone: (++39) 041 2349165 Fax: (++39) 041 2349176 e-mail: enrica.croda@unive.it

This Working Paper is published under the auspices of the Department of Economics of the Ca’ Foscari University of Venice. Opinions expressed herein are those of the authors and not those of the Department. The Working Paper series is designed to divulge preliminary or incomplete work, circulated to favour discussion and comments. Citation of this paper should consider its provisional character.

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1

INTRODUCTION

Although it has been the focus of research for more than thirty years, female labor supply continues to play an important role in empirical microeconomics, raising issues that are at the frontiers of econometrics and still remains the focus of many policy debates (see for example European Union (2010)).

This paper analyzes the intertemporal labor force participation behavior of married women using an annual longitudinal sample from the German Socio-Economic Panel. A predominant characteristic of annual participation behavior is the high degree of persistence in individual par-ticipation decisions. Several sources of this serial persistence have been identified in the literature (see for example Heckman (1978, 1981a, 1981b)): state dependence, individual unobserved hetero-geneity, and serial correlation in the time-varying error component of the latent regression model. Being able to distinguish among them is important because they have different implications for the evaluation of the effects of labor market policies.

We use several model specifications to distinguish among the alternative explanations of the serial persistence in labor force participation. Similar to Hyslop (1999), we employ both dynamic ”fixed effects” linear probability models as well as several static and dynamic probit models with ”random effects”. In addition, we apply the estimator proposed by Honor´e and Kyriazidou (2000) for dynamic ”fixed effects” discrete choice models.

The linear probability model specification is appealing as it allows inference in a widely-studied GMM framework when unobserved individual heterogeneity, serial correlation in the errors, and dynamic feedback from the lagged dependent variable on the current participation decision are simultaneously present. However, similar to all fixed effects approaches, it does not estimate the coefficients of time-invariant variables nor can it produce predicted probabilities. The probit specifi-cation takes into account the discrete nature of the dependent variable but requires strong assump-tions on the conditional distribution of the individual heterogeneity given the observed covariates and the initial observations of the participation series. The Honor´e and Kyriazidou method, while agnostic about the nature of the individual heterogeneity and the initial conditions, makes strong assumptions on the correlation structure of the transitory error term while it shares the same disadvantages with all ”fixed effects” approaches.

The primary goal of this paper is to study the robustness of results from the different estimation methods (a) in measuring the degree of state dependence in women’s labor force participation decisions; (b) in evaluating the interaction between fertility and labor supply decisions; and (c) in assessing the impact of non-labor income. In addition, we will compare women’s labor force participation and its attributes between Germany and the US. We accomplish this by contrasting our results with Hyslop (1999) who used a subsample of the Panel Study of Income Dynamics (PSID) to study married women’s labor participation, using many but not all of the methodologies employed in the current paper. We should however note that the period we study (1990-2007) is not the same as in Hyslop (1979-1985) and therefore there is a limit to the extent of the comparability of results between the two studies.

Our findings may be summarized as follows: From a methodological point of view, we find that the estimated coefficients for the fertility variables and non-labor income, normalized – for comparability across different specifications – by the estimated state dependence parameter, tend to be larger for the dynamic fixed effects logit specification as estimated by the Honor´e and Kyriazidou

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method, while they tend to be smallest for the dynamic linear probability models. The hypothesis of serial correlation in the idiosyncratic errors in the form of a first-order autoregressive process, although not rejected in the linear probability specifications, is rejected in the probit specifications when both heterogeneity and state dependence are allowed for. The assumption of independence between the unobserved individual effects and the observed covariates is rejected in all random effects specifications. In terms of predictive ability, the linear probability models tend to give unsatisfactory results, as expected. We note, however, that the static probit pooled specification performs much worse in that respect. Surprisingly, the simple random effects nonlinear (probit) specification predicts almost as well as the more complicated models that allow for state dependence and serial correlation in the idiosyncratic errors.

From a substantive point of view, we find strong evidence for state dependence and substantial effects for the fertility variables, as measured by the number of children in different age groups, on the probability of participation of German women in the labor force. The effects are stronger the younger the children in the household are. Transitory and permanent non-labor income, constructed using the husband’s labor earnings, are found to have in general quite small effects. Strict exogeneity of the fertility and income variables is (jointly) rejected in all probit specifications of the model.

Comparing our results to Hyslop’s, we find that, although German and American women ex-hibit comparable persistence in their participation decisions, as measured by the state dependence parameter, the sensitivity of German women to non-labor income and the fertility variables, such as number of young children, is higher than that of American women. This may be explained by the substantial motherhood benefits that women enjoy in Germany. In contrast to Hyslop, we reject strict exogeneity of the fertility and income variables while we do not find any statistically significant evidence of serial correlation in the idiosyncratic errors once we account for both state dependence and unobserved heterogeneity in the probit specifications of the model.

The paper is organized as follows: Section 2 describes the data. Section 3 contains our estimation results. Section 4 concludes. The construction of variables used in the analysis is described in the Appendix.

2

DATA

The data analyzed in this study are drawn from the German Socio-Economic Panel (GSOEP), a continuing annual longitudinal survey of individuals in private households in Germany.1 We use

only the West German and East German subsamples of the GSOEP. Individuals are allocated into two groups, East and West, according to where they resided when they were first surveyed.2 In this paper we focus on the 18 years covering the period 1990-2007. We restrict attention to women aged between 18 and 60 in the beginning of the sample who were married continuously for

1

The survey began in 1984 in the former West Germany. The first wave in the East was administered in June 1990, the month before the monetary, economic and social union came into effect. In 2007, the last year for which we have data, there were more than 11,000 households and more than 19,700 people sampled, consisting of Germans living in the Old and New German States, foreigners and recent immigrants. When appropriately weighted, the GSOEP is representative of the non-institutionalized population residing in Germany.

2

Hence, both East and West German groups may include people who since entering the survey (and in particular since 1990) have migrated from East to West or from West to East, as well as persons who commute to their jobs in either direction.

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the entire sample period and whose husbands were participating in the labor force in each of the sample years.3After discarding records with missing observations on any of the variables used in the analysis, we obtain a sample of 451 women.

TABLE I

employedt= 1 employedt= 0

employedt−1 = 1 91.87% 8.13%

employedt−1 = 0 16.57% 83.43%

Table I clearly illustrates the persistence of labor force participation decision: the 91% of time periods women employed at some given time period will be employed next period as well, whereas roughly 84% percent of women not employed at some given time period will be also not be employed the next period. Table II presents summary statistics for the variables of interest for the full sample as well as for several subsamples with different participation patterns.4 Column 1 describes the

characteristics for the full sample. Women in our sample are on average 33 years old, have a little less than 12 years of education and their husbands earn on average 30,184 EUR per year.5 One third of the women reside in the East. Column 2 pertains to women who are continuously working during the entire sample period. Summary statistics for women who never work are contained in column 3. The next two columns refer to women who had a single transition from employment to unemployment (column 4) and from unemployment to employment (column 5). Finally, the last column summarizes the data for women who experienced multiple transitions from and to work. The lower part of the table reports the observed frequency distributions of number of years worked across the different subsamples.

3Women are defined as labor force participants if they report positive annual hours worked and positive earnings

(see the Appendix for additional information about the construction of this variable). They are defined as married if they are legally married or live with a partner.

4By participation pattern we mean the sequence of zeros and ones, where zero stands for no participation and the

one for participation.

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TABLE II6 Sample Characteristics

Full Employed Employed SingleTransition Single Transition Multiple

Sample 17 years 0 years from Work to Work Transitions

(1) (2) (3) (4) (5) (6) Age(1990) 33.14 35 33.70 35.53 31.9 31.83 (6.41) (5.37) (7.65) (7.43) (4.62) (6.565) Education 11.98 12.38 11.17 11.66 12.30 11.88 (2.57) (2.93) (2.50) (2.20) (2.247) (2.44) East 0.29 0.31 0.025 0.205 0.61 0.265 (0.46) (0.46) (0.15) (0.404) (0.487) (0.441) No. Children 0.75 0.022 0.112 0.094 0.065 0.098 aged 0-2 years (0.28) (0.157) (0.344) (0.306) (0.262) (0.313) No. Children 0.14 0.052 0.197 0.142 0.154 0.176 aged 3-5 years (0.39) (0.25) (0.44) (0.384) (0.396) (0.423) No. Children 0.79 0.56 0.97 0.566 0.980 0.874 aged 6+ years (0.91) (0.80) (1.01) (0.810) (0.923) (0.931) Husband Earnings 3.184 3.015 3.56 3.65 3.04 3.15 (in 10,000 EUR) (2.59) (1.903) (2.38) (2.856) (2.06) (3.034)

Birth Next Year 0.021 0.004 0.032 0.042 0.006 0.030

(0.14) (0.06) (0.17) (0.201) (0.083) (0.17)

Participation No. Years Worked

0 9.09 100 1 3.10 15.38 1.69 3.57 2 2.88 10.26 0 4.59 3 1.33 7.69 0 1.53 4 2.44 7.69 0 4.08 5 2.44 2.56 0 5.10 6 4.66 2.56 0 10.20 7 3.99 5.13 3.69 7.14 8 3.33 10.26 0 5.61 9 2.22 2.56 1.69 4.08 10 2.44 2.56 3.39 4.08 11 2.88 0 0 6.63 12 3.10 5.13 0 4.08 13 5.32 10.26 8.47 7.65 14 5.99 7.69 6.78 10.20 15 8.87 5.13 18.64 13.78 16 10.20 5.13 49.15 7.65 17 25.72 100 0 0 0 Sample Size 451 116 41 39 59 196

Comparison among the various subsamples of Table II provides another illustration of the relationship connecting female labor force participation with demographic characteristics, especially fertility decisions and non-labor income. Compared to the respondents in the full sample, women

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who are continuously working (column 2) and who constitute almost 25% of our sample, tend to be older, are better educated, have fewer dependent children (especially of younger age category 0-2 years old) and their husbands’ labor earnings tend to be lower. On the other end, women who never work during the sample period (column 3) and who constitute almost 15% of our sample, tend to have more children in small age groups (0-2 and 3-5 yers old), are less educated and their husbands earnings are higher than the full sample average. Women with one transition from work (column 4) are older, have a larger on average number of younger kids and are also more likely to give birth next year. Women with one transition to work are younger, and tend to have more older children. Women who experience multiple transitions tend to be younger and to have more kids in small age categories.

It is of interest to compare our German sample with the American sample of 1812 women that Hyslop used in his study and which was extracted from the PSID for the years 1979-1985. First, our overall sample is smaller (approximately 25% of Hyslop’s). Second, women in the German sample tend to have lower participation rates, be older and less educated, have fewer children in each age category, and their husbands tend to have lower labor earnings than in the American sample. Third, the relative sizes of the various subsamples are quite different: The proportion of women who participate continuously in the labor market in the German sample is smaller than in the American one (25% vs. 48%, respectively). The proportion of women who never participate and also of women with one transition from employment in the German sample are larger than in the American sample (9% and 8.6% vs. 11% and 8%, respectively). The proportion of women with a single transition to work in the German sample is smaller than in the American sample (13% vs. 10%, respectively). Finally, a striking 43% of the women in the German sample experience multiple labor transitions compared to a 23% in the American sample.

Overall, we have the same patterns in our GSOEP sample as in the Hyslop’s PSID sample in terms of the relationship between labor force participation and the different demographic charac-teristics. Higher husband labor income tends to lower the likelihood of the woman’s participation. The presence of children (especially younger children) is associated with lower participation rates. Women tend to leave the labor market when intending to have a child, or have younger children. Most importantly they tend to go back to the labor force when their children reach school age. Finally, multiple transitions tend to be associated with a larger number of children especially of younger age.

3

RESULTS

In this section we present estimation results for a variety of empirical specifications of women’s labor force participation.

3.1 Linear Probability Models

In this section we consider linear probability models of the form:

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whereyit is individual’siparticipation decision for period t,Xit is a vector of strictly exogenous7 individual- and period-specific characteristics,αi is an unobservable individual effect and εit is an unobservable time and individual-varying error term. The vector of exogenous variablesXitconsists of both time-varying and time-invariant observable individual characteristics. In particular, it contains the respondent’s age and its square; the number of children in each age category (#KIDS0-2t, #KIDS3-5t, #KIDS6+t); the dummy variable BIRTHt+1 that indicates whether the woman

gives birth in the yeart+ 1; the years of education; an indicator for whether she is from the East; and non-labor income measured as her husband’s labor earnings. The latter is decomposed into permanent income (INCmp), calculated as the average labor earnings over the sample period, and transitory income (INCmt), calculated as the deviation of current labor earnings from their time average.

Model (1) is estimated both in levels, ignoring the correlation between the lagged dependent variable and the individual effect as well as the possible correlation between the exogenous covariates and the individual effect, and in first differences, which takes into account these correlations. The results are presented in Tables III and IV. Table III presents the results for the state dependence parameter γ while Table IV also presents results of other parameters of interest. In both tables, the right panels contain estimates for different levels specifications while the left panels contain estimates for several first-difference specifications.

The results for the state dependence parameterγ from various levels specifications are presented in the right panel of Table III. We start by assuming no serial correlation in εit. In the absence of the individual effect αi, the model may be consistently estimated by OLS. If such an effect is present however, OLS becomes inconsistent due to the correlation ofαi with the lagged dependent variableyit−1. The same is true in general,8 in either the presence or absence of individual effects,

for the GLS (alias random effects) estimator which naively corrects for the two-error component structure of the model’s unobservables but ignores the endogeneity problem due to the correlation between αi and yit−1. The results from OLS and GLS are presented in rows (0) and (1) of the

right panel of Table III. The point estimates ofγ are 0.708 and 0.901, respectively, and they can be both shown to be biased upwards if individual effects are in fact present. In order to account for the presence of unobserved heterogeneity, in row (2) we use out-of-period realizations of the assumed exogenous covariates as instruments for the lagged dependent variable also assuming that they are uncorrelated with the individual effects. At this point we must note that although every lag and lead of the exogenous covariates, under strict exogeneity and uncorrelatedness with the individual effect, would be valid to use as instrument for the lagged dependent variable, doing so would increase the number of moment conditions above a ”healthy” level. Specifically, using too many instruments produces severely biased 2-step efficient GMM estimates and too small standard errors (Windmeijer (2005)). For this reason we use only one period ahead lead of the exogenous covariates as instruments. The estimate ofγ drops to 0.505. The high value of the F−statistics when we test the explanatory power of the instruments in the first stage regressions suggests that our instruments have significant explanatory power. The average value of these F− statistics is presented in the last column of the table. In the absence of serial correlation in the transitory error

7

Here strict exogeneity refers to the assumption thatE(εit|Xi0, ..., XiT, αi) = 0 (see Chamberlain (1984)).

8

It is known that GLS is consistent in linear autoregressive models with individual effects only if the initial conditions are fixed (see Sevestre and Trognon (1985)).

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term, the first-differenced lagged participation decision, ∆yit−1, is also a valid instrument for the

endogenousyit−1provided thatE(αiyit) is constant over time, which is a sort of mean-stationarity assumption.9

TABLE III

Linear Probability Models of Married Women’s Participation10

First Differences Specification

Instruments γ ρ Test Stat.

(0) OLS -0.283 -(0.016) (1) GLS - -(2) ∆Xi,t+1 -0.265 5.6111 (0.116) (0.000) (3) ∆Xi,t+1 0.363 14.5212 yit−2 (0.039) (0.000) (4) yit−s, 0.402 101.2513 6≥s≥2 (0.020) (0.002) (5) yit−2 0.391 -(0.033) (6)yit−2 0.0106 0.133 15814 (0.037) (0.041) (0.00) Levels Specification

Instruments γ ρ Test Stat.

OLS 0.708 (.015) GLS 0.901 (0.011) Xi,t+1, 0.505 25.6215 (0.015) (0.000) Xi,t+1 0.506 51.9916 ∆yit−1 (0.010) (0.000) ∆yi,t−s, 0.559 33617 6> s >2 (0.007) (0.99) ∆yit−1 0.515 -(0.014) ∆yit−1 0.402 0.086 3418 ∆yit−2 (0.049) (0.052) (0.00)

The optimal GMM estimate of γ using these additional instruments, presented in row (3), is 0.506, virtually unchanged. The explanatory power of the augmented instrument set is substantial as the, now larger, F−statistics from the first stage regressions show. When only ∆yit−1 is used

9

For a discussion of this and other assumptions used in estimating linear dynamic panel data models, see Arellano and Honor´e (2001).

10

NOTES:Estimates of the autoregressive parameterγ and the error autocorrelation coefficientρ(where

appli-cable). All specifications include unrestricted time effects, a quadratic in age, a dummy for East, years of education, permanent and transitory non-labor income, and the number of children aged 0-2, 3-5, and 6+. Specifications in rows (0)-(5) assume that the transitory error is serially uncorrelated, while the specification in row (6) assumes that εit =ρεit−1+uit.Row (0) is estimated by OLS, while row (1) by GLS. Rows (2)-(5) are estimated by two-stage

Optimal GMM. Row (6) estimates are obtained in two steps: In the first stage equations (2) and (3) of the text, for the Levels and First Difference specifications, respectively, are estimated by Optimal GMM. In the second stage the “structural” parameters are estiamted by Optimal Minimum Distance. In all specifications, standard errors (in parentheses) account for arbitrary cross-equation correlation and cross-sectional heteroskedasticity.

11First-stageF-statistic for testing the explanatory power of the instruments, averaged over the period equations,

with (5,445) degrees of freedom.

12First-stageF-statistic for testing the explanatory power of the instruments, averaged over the period equations,

with (6,444) degrees of freedom.

13Test of over-identifying restrictions with 128 degrees of freedom. Pvalue below. 14

Second-stage test of over-identifying restrictions with 5 degress of freedom. P−value below.

15

First-stageF-statistic for testing the explanatory power of the instruments, averaged over the period equations, with (5,445) degrees of freedom.

16

First-stageF-statistic for testing the explanatory power of the instruments, averaged over the period equations, with (6,444) degrees of freedom.

17

Test of over-identifying restrictions with 418 degrees of freedom. P−value below.

18

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as an instrument for yit−1, the estimate for γ increases marginally to 0.515 (row (5)). Under the

same assumptions as in row(3), any lagged first differences of the dependent variable can be used as instruments. Again taking into account the length of our panel (T=18) and the need to keep a moderate number of instruments in view of the above considerations on the bias of 2-step GMM, we have restricted the lags up to 5 periods back. We note at this point that Bowsher (2003) has shown in Monte-Carlo simulations that even with a moderate T-dimension, the Arellano-Bond strategy of using all lags as instruments leads to an extremely undersized Hansen test of overidentifying restrictions with extremely poor power properties. Essentially, the Hansen test never rejects the null when the number of instruments is too large. In row (4) we estimate γ using lagged first differences of the dependent variable as instruments for yit−1, which under the assumption of no

serial correlation in εit are also valid instruments for yit−1. The estimate increases to 0.558. The

value of the statistic for testing the overidentifying restrictions (reported in the last column of the table) suggests overwhelming acceptance of this instrument set.

The problem with the specifications estimated in levels, even when the endogeneity of the lagged dependent variable is accounted for, is that the possible correlation between the observed individual characteristics and the unobserved heterogeneity is ignored. To account for the latter, we estimate model (1) in first differences, thereby eliminating any time-invariant unobserved individual effects. The left panels of Tables II and III present the results. Row (0) of Table III reports the results for the state dependence parameterγ from OLS estimation of the first-differenced equation

∆yit=γ∆yit−1+ ∆Xitβ+ ∆εit

The estimate ofγ is now negative and equal to -0.283. The estimate is obviously inconsistent and in fact downward biased due to the correlation between ∆yit−1 and ∆εit.Using one period ahead only (the same concerns on instruments proliferation apply here as well) first differenced X’s as instruments for the endogenous ∆yit−1 yields an even more negative estimate of γ at -0.295 (row

2) which is very different from the estimate in the respective levels specification. However theF−

statistics of the first stage regressions are quite low, as their average value of 5.59 demonstrates. Assuming no serial correlation in εit,the participation decision lagged twice is also a valid instru-ment for ∆yit−1.Adding this instrument on top of the ∆X’s yields a positive estimate ofγ equal to

0.363 (row (3)) which is still lower than the one obtained in the corresponding levels specification - but the two estimates are now closer in value and agree in sign. The explanatory power of the instruments however improves considerably as demonstrated by the average F−statistic of 14.52 from the first stage regressions. Dropping the differenced exogenous variables from the instrument list we obtain an estimate of 0.391 for γ (row (5)). Adding the rest of the lags of the participation decision to the instrument set, we obtain a higher estimate for γ, equal to 0.402 (row (4)). The Hansen test rejects the null showing a problem with the specification in first differences.

The results of rows (0)-(5) refer to the case of serially uncorrelated transitory errors. There is evidence however in the levels specification that the model dynamics may be misspecified. Following Hyslop (1999) we proceed to allow for serial correlation inεit in the form of an AR(1):

εit=ρεit−1+vit, −1< ρ <1, vit∼iid 0, σ2v

The results are presented in row (6) of Table II. Note that in the presence of serial correlation, estimation of the model either in levels or first differences using lag(s) of the dependent variable or

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linear transformations thereof, as in rows (3)-(5) above, will in general yield inconsistent estimates since the instruments are correlated with the errors. In particular, ∆yit−s (s≥1) is correlated with εit in the levels specifications and yit−s (s≥2) is correlated with ∆εit in the first difference specifications. It is possible however to transform the model to eliminate the serial correlation if the latter is of known form, as in the AR(1) case assumed above. In particular, we may quasi-difference equation (1) to obtain

yit = (ρ+γ)yit−1−ργyit−2+Xitβ−Xit−1ρβ+ (1−ρ)αi+vit (2) Note that the new transitory error term vit is no longer serially correlated and therefore ∆yit−1

and ∆yit−2 are valid instruments for yit−1 and yit−2 in the levels specification under a similar

stationarity assumption as before. Alternatively, we may first difference the individual effect in (2) to obtain

∆yit= (ρ+γ) ∆yit−1−ργ∆yit−2+ ∆Xitβ−∆Xit−1ρβ+ ∆vit (3) where ∆yit−1 is correlated with ∆vit. However, yit−2 is now a valid instruments for ∆yit−1. The

unknown reduced form coefficients in (2) and (3),(ρ+γ, ργ, ρβ) may be estimated by GMM, while the primitive parameters of interest, (β, ρ, γ) can then be obtained by minimum distance.

As reported in row (6), the estimates of γ in the levels and first-difference specifications are 0.402 and 0.010, respectively, significantly different from zero only in levels, while ρ is estimated positive at 0.086 and 0.133, respectively, statistically significant only in the first-differences case. The goodness-of-fit second stage test statistics, reported in columns (3) and (6) of row (6) of Table III reject this specification, though notably the rejection is stronger in first differences.

Overall, the magnitude of the estimates for γ as well as the pattern across the different specifi-cations are very close to those obtained by Hyslop except in the case where we allow for an AR(1) process in the errors. In his sample and for this specification (corresponding to row (6) of Table II),

γ was found to be very large in both the levels and first-difference specifications (0.563 and 0.647, respectively) whileρ was estimated to be significantly negative around -0.2 in both specifications. In all specifications however, our estimates of the exogenous covariate coefficients β are quite different than Hyslop’s counterparts. We present a subsample of our results in Table IV. In partic-ular, we report the estimates for the specifications of rows (4)-(6) of Table III which use only one or more lags ofyit and ∆yit, either in levels or in first differences, as instruments for the endoge-nous right hand side variable. The estimated coefficients have the expected signs. In particular, transitory non-labor income has a (weak) negative effect on participation which however is statis-tically significant only for the levels specification. The range of the estimates for that coefficient is between -0.0004 and 0.0001 in the latter case. In the first difference specifications, the estimates are lower and statistically insignificant. Compared to Hyslop we obtain a much lower transitory income effect. The permanent income effects estimated in the levels specifications are in the same range (-0.003) and is statistically significant. The children variables have strong negative effects on women’s labor force participation, especially those that refer to pre-school children. Moreover, the estimated coefficients are invariably much higher than Hyslop. The estimated coefficients of the 0-2 year old children variable range from -0.266 to -0.089 while Hyslop’s are in the range of -0.028 to -0.050. For the other two age categories, our coefficients are also several times higher. The effect of the future birth is similar to Hyslop in the first difference specifications (positive), but negative in the levels specification.

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TABLE IV19

Linear Probability Models of Married Women’s Participation

First Difference Specification Levels Specification

(1) (2) (3) (4) (5) (6) IN Cmp - - -0.005 -0.003 -0.004 (0.003) (0.001) (0.003) IN Cmt -0.0006 -0.0005 0.0001 -0.002 -0.0004 -0.0007 (0.001) (0.001) (0.0001) (0.001) (0.0006) (0.001) #Kids0−2t -0.141 -0.129 -0.089 -0.225 -0.205 -0.266 (0.033) (0.027) (0.007) (0.013) (0.008) (0.026) #Kids3−5t -0.051 -0.077 -0.041 -0.087 -0.086 -0.102 (0.024) (0.020) (0.005) (0.009) (0.006) (0.019) #Kids6+t -0.033 -0.032 -0.0094 -0.046 -0.045 -0.067 (0.014) (0.012) (0.004) (0.004) (0.004) (0.009) Birtht+1 0.053 0.014 0.005 -0.092 -0.002 -0.050 (0.037) (0.031) (0.0017) (0.009) (0.010) (0.038) yit−1 0.391 0.402 0.0106 0.515 0.558 0.402 (0.033) (0.020) (0.0372) (0.014) (0.074) (0.049) ρ - - 0.133 - - 0.086 (0.041) (0.052) Instruments yit−2 yit−s yit−2 ∆yit−1 ∆yit−s, ∆yit−1 2< s <6 2< s <6 ∆yit−2

3.2 Static Random Effects Probit Models

We next present results for various nonlinear specifications that account for the discrete nature of the dependent variable. In this subsection we focus on static probit models with random effects of the form:

yit= 1{Xitβ+αi+εit≥0}

where the transitory error term εit is assumed to be independent of the exogenous covariates

Xit for all t, independent over time, and normally distributed with mean zero and unit variance. We will make two different assumptions on the permanent error component αi. First, we follow the traditional (uncorrelated) random effects (URE) approach and assume that αi is independent of Xit and εit and normally distributed with mean zero and variance equal to σ2α. Second, to capture possible correlation between the permanent unobserved heterogeneity and the fertility and transitory income variables, we postulate the following functional form forαi

αi =x

0

iλ+ηi (4)

where xi is the average of KIDS0−2it, KIDS3−5=it, KIDS6−2it, IN Cmt t = 1...T. Now ηi is independent ofXit and εit for alltand normally distributed with mean zero and variance equal to

σ2η.This approach is usually referred to as the correlated random effects approach (CRE). 19

NOTES:All specifications include unrestricted time effects, a quadratic in age, a dummy for East, and years

of education. Specifications in columns (1) and (4) (corresponding to row (4) of Table II) and columns (2) and (5) (corresponding to row (5) of Table II) assume that the transitory error is serially uncorrelated. Specifications in columns (3) and (6) (corresponding to row (6) of Table II) assumes thatεit =ρεit−1+uit.In all specifications,

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The estimated coefficients of the various static specifications of the model are presented in Table V. In the last column we report results for the simple (pooled) probit model that setsαi = 0 for all i. The other 3 columns present the estimates for the static probit model with random effects. Columns (1) and (2) contain the results for the (same) uncorrelated random effects probit model. The columns differ in that they use a different approximation of the (single) integral in the likelihood function. In particular, column (1) displays the estimates using a Gauss-Hermite quadrature approximation with 20 quadrature points. In column (2) the model is estimated via Maximum Simulated Likelihood (MSL) with 20 simulation replications. Column (3) reports the results of the correlated random effects approach which assumes that αi is given by equation (4). It uses the Gauss-Hermite quadrature approximation also used in column (1).

TABLE V20

Static Probit Models Of Married Women’s Labor Force Participation

Random Random CRE Simple

Effects(Quad) Effects(MSL) (Means) Probit

(1) (2) (3) (4) IN Cmp -0.069 -0.063 -0.131 -0.031 (0.042) (0.039) (0.052) (0.008) IN Cmt -0.0004 -0.001 -0.001 0.0003 (0.013) (0.0128) (0.013) (0.010) #Kids0−2t -1.718 -1.709 -1.660 -1.183 (0.095) (0.094) (0.096) (0.076) #Kids3−5t -0.892 -0.878 -0.843 -0.699 (0.067) (0.066) (0.068) (0.046) #Kids6gt -0.408 -0.402 -0.378 -0.331 (0.036) (0.0353) (0.037) (0.019) V ar(ai) orV ar(ηi) 1.597 (71%) 1.513 (71%) 1.57 (71%) (0.080) (0.2160) (0.080) Log - Likelihood -2817.63 -2827.19 -2808.98 -4270.43 H0 :λ= 0 (U RE) p-value: 0.020

Wald Statistics p-values

mIN Cmt= 0 0.027

m#Kids0−2t= 0 0.845

m#Kids3−5t= 0 0.164

m#Kids6t= 0 0.698

20

NOTES: All specifications include unrestricted time effects, a quadratic in age, a dummy for East and years

of education. Standard errors are in parentheses. All specifications assume that the transitory error is serially

uncorrelated. The variance of the composite error term is normalized to unity. The model in column (1) is estimated by MLE using a Gauss-Hermite quadrature with 20 quadrature points, while in column (2) the model is estimated

via Maximum Simulated Likelihood with 20 simulation replications. The CRE model in column (3) expressesαi as

a linear function of the means of transitory income and all children’s variables (see equation (4) in the text). The Wald statistics test the null hypotheses that the coefficients of the corresponding variables are all zero. P−values are in parentheses.

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Table V shows that the effects of the fertility variables in the static random effects specifications are qualitatively similar to those obtained in the linear probability models and they show a strong negative effect of having an additional child on women’s labor force participation decisions in par-ticular when unobserved heterogeneity is allowed for. The permanent income effects are estimated in all three models to be larger than the transitory income effects. The variance of the individual effect in the random effects specifications is estimated to account for three quarters of the total error variance. Allowing for unobserved heterogeneity improves greatly the fit of the model as measured by the value of the log-likelihood. The effect of having a child in any age category is now much larger; in particular it increases by 45, 28 and 23 percent for the 0-2, 3-5, and 6+ year old children categories, respectively. Similarly the effect of both income variables is now much stronger, with the estimated permanent income coefficients doubling when individual effects are included in the model.

Comparing the quadrature approximation (column 1) of the likelihood function with the MSL approach (column 2), we find that the two give very similar results, indicating that even with 20 simulation draws MSL in this case seems to be reasonably accurate. The hypothesis of uncorrelated random effects is strongly rejected by the Wald tests of joint statistical significance of the coefficients corresponding to each variable in (4).

Turning to the CRE specification, which allows the means of the fertility variables and non-labor income to affect the non-labor force participation decision, we see that the estimated coefficients of the fertility variables decrease for the 0-2, 3-5, and 6+ year-old children’s age categories and transitory income.

3.3 Dynamic Random Effects Probit Models

We next focus on the dynamic aspects of female labor force participation. Table V contains our MSL estimates for several dynamic random effects probit specifications of the model

yit= 1{γyit−1+Xitβ+αi+εit ≥0}

In columns (1) and (2), labelled RE+AR(1) and CRE+AR(1), the state dependence parameterγ is set equal to zero while the transitory error is specified to follow a first order autoregressive process of the form εit = ρεit−1+vit so that all temporal persistence in labor force participation comes through the unobserved composite error term. In column (1) the random effect is assumed to be independent of Xit, while in column (2) we allow for correlation between αi and Xit in the form of equation (4) above. In columns (3) and (4), labelled RE+SD(1) and CRE+SD(1),we allow for structural state dependence but we restrict the transitory error term to be serially uncorrelated. The two columns differ in the assumption about the relationship between αi and Xit as before. In columns (5) and (6), labelled RE+SD(1) +AR(1) and CRE+SD(1) +AR(1), we present results that account for structural state dependence, unobserved heterogeneity and serial correlation in the time-varying error component. Again, the two columns differ in the assumption about the relationship betweenαi and Xit.

For the estimation of the models that account for state dependence (columns (3)-(6)), we need to specify not only the relationship between the unobserved heterogeneity and the exogenous

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covariates, but also the initial conditions and their relationship to αi. For the latter, we follow the flexible reduced form approach of Heckman (1981b), also adopted by Hyslop (1999), which uses a reduced form probit specification for the first period outcome in terms of the initial period covariates:

yi0= 1{Xi0β0+ui0 ≥0}

where the unobserved error termui0follows aN(0,1) and is possibly correlated with the composite

error term uit(≡αi+εit) of the model for periods 1 through T with (a possibly time varying) covariance, say φt≡Cov(ui0, uit).

TABLE VI

Dynamic Probit Models of Married Women’s Participation21

RE+ CRE+ RE+SD CRE+SD RE,AR(1) CRE,AR(1)

AR(1) AR(1) +SD(1) +SD(1) (1) (2) (3) (4) (5) (6) IN Cmp -0.0546 -0.0955 -0.039 -0.091 -0.0440 -0.0846 (0.0322) (0.0280) (0.027) (0.027) (0.0276) (0.033) IN Cmt 0.0053 0.0013 -0.0015 -0.0023 -0.0014 -0.0030 (0.0153) (0.0122) (0.0144) (0.015) (0.0157) (0.0149) #Kids0−2t -1.0142 -0.8909 -1.137 -1.055 -1.1347 -1.0352 (0.0988) (0.0705) (0.104) (0.083) (0.1044) (0.110) #Kids3−5t -0.4344 -0.3692 -0.389 -0.3085 -0.3572 -0.286 (0.0710) (0.0579) (0.0748) (0.0655) (0.0754) (0.082) #Kids6gt -0.2380 -0.1844 -0.203 -0.1537 -0.1900 -0.142 (0.0417) (0.0382) (0.038) (0.036) (0.0379) (0.043) yit−1 - - 1.5655 1.561 1.682 1.643 (0.060) (0.049) (0.0722) (0.083) Covariance Par. AR(1)coeffρ 0.7684 0.7895 - - -0.0927 -0.065 (0.0255) (0.016) (0.0434) (0.048) V ar(ai) orV ar(ηi) 1.1245 - 53% 0.8813 - 47% 0.9531 - 49% 0.9089 - 47% 0.884 - 46% 0.894 - 46% (0.1982) (0.1372) (0.124) (0.148) (0.127) (0.148)

H0:λ= 0 (U RE) p-val (0.000) p-val (0.000) p-val (0.0029)

Wald Statistics p-values p-values p-values

mIN Cmt (0.000) (0.000) (0.026)

m#Kids0−2t (0.2462) (0.2656) (0.043)

m#Kids3−5t (0.000) (0.000) (0.052)

m#Kids6t (0.4944) (0.1282) (0.363)

Comparing column (1) of Table VI to columns (1) or (2) of Table V, we note that the intro-duction of correlation in the time-varying error term decreases the effect of all variables, excluding

21

NOTES:All specifications include unrestricted time effects, a quadratic in age, a dummy for East and years of

education. Standard errors are in parentheses. The variance of the composite error term is normalized to unity. All models are estimated via Maximum Simulated Likelihood using 20 simulation replications. Specifications (1),(2),(4) and (6) assume constant correlation between the period 0 error,u0, and the subsequent periods’ errors,ut≡α+εt.

Specification (3) allowed time varying correlation between the initila period error and the subsequent periods’ errors. When we tested for equicorrelation, we got strong rejection at 5% ofH0,though rejection was marginal.

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transitory income. The autoregressive parameter is estimated at 0.768 and is highly significant. The variance of the random effect is reduced to roughly a half of the total error variance. Allowing for correlation betweenαi and Xi (column (2) of Table VI) reduces the estimated coefficients even further, similarly to the static case. The introduction of state dependence (columns (3) and (4)) has a similar effect on the estimates as the introduction of serial correlation in the idiosyncratic error term. The estimated state dependence parameter γ is strongly positive and highly statistically significant. Comparing columns (3) and (4), we see as before that the introduction of correlation between the observed covariates and unobserved heterogeneity reduces the estimated coefficients of the children variables. As expected, the introduction of state dependence decreases the magnitude of the estimated variance of the unobserved permanent error component, and its contribution to the total variance is reduced.

The next two columns ((columns (5)-(6)) present results when both state dependence and serial correlation in the errors are allowed for, and they correspond to the uncorrelated and correlated random effects specifications, respectively. In column (3) we allow the correlation between the initial period error term and the subsequent periods’ errors to differ over time, although the restriction that these correlations are in fact equal is not rejected at 10%.

Overall, the results for the models with state dependence (columns (3)-(6)) show a large state dependence effect, similar in magnitude in all specifications with or without serially correlatedεit’s. Allowing for state dependence leads to a slight increase in the magnitude of the effect of younger children variable and a significant decrease in the effect of the other two fertility variables compared to the case when only serial correlation inεit is allowed for. The introduction of state dependence on top of serial correlation due to the error term causes the estimated AR(1) coefficientρto become small and statistically insignificant. This is in sharp contrast to the linear probability specifications (see last row of Table III).

Comparing the URE with their respective CRE specifications, we see that the exogeneity of the fertility and income variables with respect to the permanent unobserved component αi is rejected for the 3-5 year old children category and transitory income, as the individual Wald tests of statistical significance show. It is not rejected though individually for children 0-2 years old and permanent income. However, the joint Wald significance tests strongly (at 1% and 5% significance levels) the exogeneity assumption in the most general specification of columns (5) and (6), in disagreement with Hyslop’s PSID finding. Furthermore, the effect of allowing for correlated random effects changes the magnitude of the estimated effects of most fertility variables. This finding is in accordance with the literature that treats the fertility decision as endogenously and jointly determined with the participation decision. Hyslop’s finding has already been shown not to be robust in the case of classification error (Keane and Sauer (2009)), and actually even a small amount of classification error is enough to overturn the exogeneity result of Hyslop. We find here that exogeneity is strongly rejected for European data for a significant time span even when no classification error considerations are taken in.

Finally, we find similar patterns as in Hyslop (1999) in all coefficients. Noticeable differences between our and Hyslop’s results are the following. We find much smaller income effects and larger effects for the fertility variables. The magnitude of γ, σ2α and ρ are similar except that in our case the error autoregressive parameter ρ is much smaller and insignificant in the most general specification (column (6) in Table VI).

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The possibility of misspecification of this relationship as well as of the initial conditions in the CRE specifications leads us to consider the method developed by Honor´e and Kyriazidou (2000) which is described in the next Section.

3.4 Dynamic Fixed Effects Models: The Honor´e-Kyriazidou Approach

Honor´e and Kyriazidou (2000) use the idea underlying the conditional likelihood approach to iden-tify and estimate the following panel data logit model, which contains unobservable individual– specific effects, exogenous explanatory variables, as well as the dependent variable lagged once:

P(yi0 = 1|Xi, αi) =p0(Xi, αi)

P(yit = 1|Xi, αi, yi0, . . . , yi,t−1) =

exp(Xitβ+γyi,t−1+αi) 1 + exp(Xitβ+γyi,t−1+αi)

t= 1, ...T (5) where T ≥ 3. Xi denotes the union of all periods’ exogenous covariates: (Xi1, Xi2, ..., XiT). The model is left unspecified in the initial period 0 of the sample. It is assumed, however, that yi0

is observed, so that there are at least four observations per individual. Note however that the approach described below does not require that the X’s for the initial period of the sample be observed.

For the model (5), Chamberlain (1993) has shown that, if individuals are observed in three time periods, i.e. if T = 2, then the parameters of the model are not identified. Honor´e and Kyriazidou (2000) show that β and γ are both identified (subject to regularity conditions) in the case where the econometrician has access to four or more observations per individual, i.e. T ≥3.

We will describe Honor´e and Kyriazidou’s identification strategy forT = 3. Consider the events

A={yi0, yi1= 0, yi2= 1, yi3} andB ={yi0, yi1 = 1, yi2 = 0, yi3}, where yi0 and yi3 are either 0 or

1. Then, by a sequential decomposition of the joint probability we obtain

P(A|Xi, αi) = p0(Xi, αi)yi0(1−p0(Xi, αi))1−yi0 × 1 1 + exp(Xi1β+γyi0+αi) × exp(Xi2β+αi) 1 + exp(Xi2β+αi) ×exp(yi3Xi3β+yi3γ+yi3αi) 1 + exp(Xi3β+γ+αi) and P(B|Xi, αi) = p0(Xi, αi)yi0(1−p0(Xi, αi))1−yi0 × exp(Xi1β+γyi0+αi) 1 + exp(Xi1β+γyi0+αi) × 1 1 + exp(Xi2β+αi+γ) × exp(yi3Xi3β+yi3αi) 1 + exp(Xi3β+αi)

In general,P(A|Xi, αi, A∪B) will depend onαi, which is the reason why a conditional likelihood approach will not eliminate the fixed effect. However,if Xi2 =Xi3, then

P(A|Xi, αi, A∪B, Xi2 =Xi3) = 1 1 +exp((Xi1−Xi2)β+γ(yi0−yi3)) (6) P(B|Xi, αi, A∪B, Xi2 =Xi3) = exp((Xi1−Xi2)β+γ(yi0−yi3)) 1 +exp((Xi1−Xi2)β+γ(yi0−yi3))

which do not depend on αi. In the special case where all the explanatory variables are discrete and the Xit process satisfies P(Xi2 = Xi3) > 0, one can use (6) to make inference about β and

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γ. The resulting estimator will have all the usual properties (consistency and root-n asymptotic normality).

While inference based only on observations for whichXi2=Xi3 may be reasonable in some cases

(in particular, experimental cases where the distribution ofXi is in the control of the researcher), it is not useful in many economic applications. However, if the continuous variables inXi2−Xi3 have

positive density at 0,we may think of constructing estimators that use observations for whichXi2

is close toXi3. In particular, assuming (for ease of exposition) that all of thekvariables inXit are continuously distributed, and that sampling across individuals is random, Honor´e and Kyriazidou propose estimating β and γ by maximizing

n X i=1 1{yi1+yi2= 1}K Xi2−Xi3 hn ln exp((Xi1−Xi2)b+g(yi0−yi3))yi1 1 + exp((Xi1−Xi2)b+g(yi0−yi3))

over b and g in some compact set. Here K(·) is a kernel density function which gives the appro-priate weight to observationi, while hn is a bandwidth which shrinks to zero as n increases. The asymptotic theory will require thatK(·) be chosen so that a number of regularity conditions, such asK(ν)→0 as |ν| → ∞, are satisfied. The effect of the term KXi2−Xi3

hn

is to give more weight to observations for whichXi2 is close to Xi3. The estimator ˆθn≡

ˆ

βn,γˆnofθ0≡(β, γ) is shown

to be consistent and to converge to a normal distribution at rate pnhk

n, which, although slower than the standard √n rate, can be made close to√nunder appropriate smoothness assumptions. The identification idea described above extends in a natural manner to the case of more than four observations per individual. It is based on sequences where an individual switches between states in any two of the middleT−1 periods. In the case of generalT, the objective function takes the form: n X i=1 X 1≤t<s≤T−1 1{yit+yis = 1}K Xit+1−Xis+1 hn × ln exp ((Xit−Xis)b+g(yit−1−yis+1) +g(yit+1−yis−1) 1{s−t >1})yit 1 + exp ((Xit−Xis)b+g(yit−1−yis+1) +g(yit+1−yis−1) 1{s−t >1})

Honor´e and Kyriazidou (2000) also show that the model is identified even in the case where the logit assumption is relaxed and the distribution of the unobservable time-varying errors is left unspecified. In either the logistic or the semiparametric case, their approach suffers from several limitations: (i) The assumption that the errors in the underlying threshold–crossing model are independent over time. This assumption however underlies many fixed and random effects approaches for estimating nonlinear panel data models. (ii) The assumption that Xit−Xis has support in a neighborhood of 0 for any t 6= s, which rules out time–dummies as well as other variables that grow deterministically over time (such as age) as explanatory variables. (iii) The fact that neither the individual unobservable effects nor the coefficients of time-invariant variables cannot be estimated, and hence it is not possible to carry out predictions or compute elasticities for individual agents or at specified values (e.g. means) of the explanatory variables, a drawback to all fixed effects approaches. But in contrast to other likelihood-based approaches, the Honor´e and Kyriazidou approach does not make any assumptions about the statistical relationship of the individual effects with the observed covariates or with the initial conditions.

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The results applying Honor´e and Kyriazidou approach are presented in Table VII. For the reasons explained above, the specification does not include time-dummies and age variables. Fur-thermore, the coefficients on the time invariant variables (such as Education and the East dummy) are not identified. The method requires choosing the bandwidth,hn,and a functional form for the kernel functionK(·). We specifyhn=c×n−1/5 wherecis a positive constant, set equal to 7, 5, 3, 1, 0.5, 0.3, and 0.1. The kernel function is taken to be the standard normal density function. Note that in this case the objective function is globally concave so that we do not have to worry about local maxima.

All estimated coefficients have the expected sign. Furthermore, we estimate large effects for the fertility variables which is consistent with our findings from all the previous specifications. The state dependence parameter γ is large and very precisely estimated. Given the large standard errors, the results do not seem to be very sensitive to the choice of the bandwidth constant.

TABLE VII22

Dynamic Fixed Effects Logit Models of Married Women’s Participation Bandwidth Constant c= 7 c= 5 c= 3 c= 1 c= 0.5 c= 0.3 c= 0.1 IN Cmt 0.071 0.067 0.071 0.146 0.176 0.121 -0.019 (0.055) (0.059) (0.066) (0.096) (0.135) (0.165) (0.162) #Kids0−2t -1.370 -1.394 -1.438 -1.428 -1.681 -1.789 -2.610 (0.500) (0.514) (0.535) (0.589) (0.850) (1.102) (1.310) #Kids3−5t -0.248 -0.236 -0.215 -0.288 -0.318 -0.434 -0.569 (0.401) (0.414) (0.437) (0.542) (0.678) (0.786) (1.062) #Kids6−17t 0.008 0.041 0.115 0.180 0.287 0.415 0.854 (0.266) (0.277) (0.299) (0.409) (0.484) (0.540) (0.722) Birtht+1 1.125 1.275 1.713 2.182 3.672 6.449 12.528 (1.589) (1.499) (1.380) (1.441) (1.170) (1.323) (1.424) yt−1 2.162 2.147 2.129 2.220 2.288 2.322 2.411 (0.179) (0.178) (0.178) (0.179) (0.185) (0.194) (0.241)

4

CONCLUSIONS

This paper analyzes married women’s intertemporal labor force participation decisions using a German panel during the period 1990-2007. We consider several empirical specifications that allow for state dependence and unobserved heterogeneity. Some specifications in addition allow for serial correlation in the unobserved transitory error component. In all specifications we find strong state dependence, and substantial effects for fertility variables as measured by the number of children in

22NOTES:All specifications are estimated by the Honor´e and Kyriazidou (2000) method using a standard normal

kernel and bandwidth equal to hn = c×n−1/5. The method uses only 237 observations in effect. To become

comparable with the probit estimates, the estimated coeffecients (and standard errors) need to be multiplied by

3/π i.e. by approximately 0.591. Amemiya (1985) argues that a better approximation emerges if one multiplies

the logit estimates by 0.625. Furthermore, he argues that the OLS slope estimates should be approximately equal to 0.25 times the corresponding logit slope parameter estimates, while the intercept and dummy variable coefficient estimates should be approximately equal 0.25 times the corresponding logit estimates plus 0.5.

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different age groups. Transitory and permanent non-labor income, constructed using the husband’s labor earnings, are found to have small effects except for the dynamic fixed effects specification.

ACKNOWLEDGEMENTS

We thank Jochen Kluve for helpful comments and Dean Hyslop for providing his code for maximum simulated likelihood estimation. Shizu Lee provided excellent research assistance during the initial stage of the project. The paper was presented at the 2011 Annual Congress of the European Society for Population Economics in Hangzhou, China.

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Whitney Newey & Frank Windmeijer, 2005. ”GMM with many weak moment conditions,”

CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice,

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APPENDIX

This appendix provides details not otherwise discussed in the text on the construction of the variables used in the analysis. Further details on the original variables can be found in Haisken-DeNew and Frick(2003).

In each wave, the GSOEP questionnaire asks income and labor supply information at different level of detail both for the current year and for the previous year. The previous year section of the questionnaire asks about employment status and sources of income received in every month, from January through December.23 The structure of this section has changed over time.24 However, basically, it provides the following variables for employment status and type of income received: a variable indicating whether a given employment status could apply to the respondent for at least one month from January through December, a variable indicating whether the respondent received a type of income for at least one month from January through December, a variable counting the number of months in a given employment status or having received a given type of income, and finally, the average monthly amount of income received.

The variables HUSBAND’S EARNINGS and women’s labor force participation (PARTICIPA-TION) in any specific year are constructed using the calendar information from the next year’s survey. In particular, respondents’ earnings are constructed summing yearly bonuses to income from employment and self employment, estimated using the available calendar information. For consistency, labor earnings are calculated only if respondents report having worked full time or part time.

Women’s labor force participation (PARTICIPATION) is measured by an indicator, which denotes whether the female respondent worked either full time or part timeandin addition received positive labor earnings that year, based on the calendar information for the previous year. In contrast, for simplicity, her husband’s participation information, necessary to select the sample for our analysis, is obtained relying on the current year’s information about employment status. A husband is defined as participant if he is currently engaged in paid employment, working either full time or part time.

The variable EDUCATION denotes the maximum number of years of schooling or occupational training completed over the sample period, based on the degree that the individual has obtained or is in the process of obtaining. Respondents are asked about the degrees of schooling they have attained and the additional occupational training they have engaged in. The years of schooling and of occupational training are based on the typical average number of years required to obtain a particular degree (e.g. 13 years for the Abitur). The years of schooling mapping is based on the following rules:

- no degree is associated with 7 years of education

23An exception to the January-December calendar was made for the East German subsample in the first two waves

to account for the special circumstances of the region at the beginning of the post-communist transition. Only for the East German subsample, the calendars ran from July 1989 to June 1990 in the first wave (survey year 1990), and from July 1990 to March 1991 in the second wave (survey year 1991).

24

For instance, in the first waves, the questionnaire asks for each single month of the previous year whether the respondent had received income of a certain type (e.g. income from wages and salary, or income from self-employment) and the monthly income amount for each source. Starting in 1995, the GSOEP started asking for the number of months during which a given type of income was received, and for the average income amount received. See Haisken-DeNew and Frick (2003) for more details.

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- a lower school degree is associated with 9 years of education

- an intermediary school degree is associated with 10 years of education - a degree from a professional college is associated with 12 years of education - an high school degree is associated with 13 years of education

- ”other” is associated with 10 years of education

The years of additional occupational training and universities mapping is based on the following rules:

- apprenticeship is associated with 1.5 additional years of education - technical schools are associated with 2 additional years of education

- civil servants apprenticeship is associated with 1.5 additional years of education - higher technical college is associated with 3 additional years of education - university degree is associated with 5 additional years of education

Years of education is obtained by summing the years of schooling and the years of occupational training. For every wave, we use the highest degree achieved by the respondent. In order to avoid underestimation, we set to missing the years of education for those individuals for whom the schooling attainment information is missing even though occupational training information may be available for them.25 In addition, for the analysis we used the maximum number of years of education completed over the sample period.

Finally, the fertility variables are obtained from information on the number of children in a woman’s household, and their year of birth. This information is provided in a specific GSOEP children file that contains information on children up to the age of 16.26 We aggregate children in three age groups, and derive three indicator variables, KIDS0-2, KIDS3-5 and KIDS6+ to denote the presence of children younger than or at most 2, between 3 and 5 years old, and older than 6 (between 6 and 16 to be precise), respectively. We construct an indicator for whether a woman has given birth in the next year, BIRTH, which is equal to 1 if she has a child born in the year after the current year.

25

The procedure adopted is fairly standard and is documented in Haisken-DeNew and Frick (2003).

26

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References

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