enrica croda, ekaterini kyriazidou and ioannis polycarpou
TRANSCRIPT
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
W o rk in g P a pe rs D e pa r t me n t o f Ec o no mic s
C a ’ Fos c a r i U n i ve rs i t y o f V e n i c e N o . 1 7 / W P/ 20 11
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:
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: [email protected]
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.
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 Honore 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 Honore 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 Honore and Kyriazidou
1
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
1The 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.2Hence, 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.
2
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.5Income is expressed in 2001 Euros using the CPI. We apply a different deflator for East and West.
3
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
6NOTES: Standard deviations are in parentheses.
4
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:
yit = γyit−1 +Xitβ + αi + εit (1)
5
where yit is individual’s i participation 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 variables Xit consists
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 year t+ 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 parameter γ 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 of αi with the lagged dependent
variable yit−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 of γ 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 of γ 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
7Here strict exogeneity refers to the assumption that E (εit|Xi0, ..., XiT , αi) = 0 (see Chamberlain (1984)).8It 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)).
6
term, the first-differenced lagged participation decision, ∆yit−1, is also a valid instrument for the
endogenous yit−1 provided that E (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
9For a discussion of this and other assumptions used in estimating linear dynamic panel data models, see Arellano
and Honore (2001).10NOTES: Estimates of the autoregressive parameter γ and the error autocorrelation coefficient ρ (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-stage F -statistic for testing the explanatory power of the instruments, averaged over the period equations,
with (5, 445) degrees of freedom.12First-stage F -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. P− value below.14Second-stage test of over-identifying restrictions with 5 degress of freedom. P− value below.15First-stage F -statistic for testing the explanatory power of the instruments, averaged over the period equations,
with (5, 445) degrees of freedom.16First-stage F -statistic for testing the explanatory power of the instruments, averaged over the period equations,
with (6, 444) degrees of freedom.17Test of over-identifying restrictions with 418 degrees of freedom. P− value below.18Second-stage test of over-identifying restrictions with 5 degress of freedom. P− value below.
7
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 parameter γ from OLS estimation of the first-differenced equation
∆yit = γ∆yit−1 + ∆Xitβ + ∆εit
The estimate of γ 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 the F−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 of γ 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 in εit 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
8
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−1and ∆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) while ρ 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 of yit 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.
9
TABLE IV19
Linear Probability Models of Married Women’s Participation
First Difference Specification Levels Specification
(1) (2) (3) (4) (5) (6)
INCmp - - -0.005 -0.003 -0.004
(0.003) (0.001) (0.003)
INCmt -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 for αi
αi = x′iλ+ ηi (4)
where xi is the average of KIDS0−2it , KIDS3−5=it , KIDS6−2it , INCmt t = 1...T. Now ηi is
independent of Xit and εit for all t and normally distributed with mean zero and variance equal to
σ2η. This approach is usually referred to as the correlated random effects approach (CRE).
19NOTES: 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 that εit = ρεit−1 + uit. In all specifications,
standard errors (in parentheses) account for arbitrary cross-equation correlation and cross-sectional heteroskedasticity.
10
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 sets αi = 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)
INCmp -0.069 -0.063 -0.131 -0.031
(0.042) (0.039) (0.052) (0.008)
INCmt -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) or V 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 (URE) p-value: 0.020
Wald Statistics p-values
mINCmt = 0 0.027
m#Kids0− 2t = 0 0.845
m#Kids3− 5t = 0 0.164
m#Kids6t = 0 0.698
20NOTES: 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) expresses αi 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.
11
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 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 parameter γ 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 between αi 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
12
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 term ui0 follows a N (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 Participation 21
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)
INCmp -0.0546 -0.0955 -0.039 -0.091 -0.0440 -0.0846
(0.0322) (0.0280) (0.027) (0.027) (0.0276) (0.033)
INCmt 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)coeff ρ 0.7684 0.7895 - - -0.0927 -0.065
(0.0255) (0.016) (0.0434) (0.048)
V ar(ai) or V 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 (URE) p-val (0.000) p-val (0.000) p-val (0.0029)
Wald Statistics p-values p-values p-values
mINCmt (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
21NOTES: 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% of H0, though rejection was marginal.
13
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 between αi 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 correlated εit’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 in εit is allowed for. The introduction of state dependence
on top of serial correlation due to the error term causes the estimated AR(1) coefficient ρ to 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).
14
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 Honore and Kyriazidou (2000)
which is described in the next Section.
3.4 Dynamic Fixed Effects Models: The Honore-Kyriazidou Approach
Honore 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 yi0is 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. Honore 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 Honore and Kyriazidou’s identification strategy for T = 3. Consider the events
A = {yi0, yi1 = 0, yi2 = 1, yi3} and B = {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 on αi, 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
15
γ. The resulting estimator will have all the usual properties (consistency and root-n asymptotic
normality).
While inference based only on observations for which Xi2 = Xi3 may be reasonable in some cases
(in particular, experimental cases where the distribution of Xi is in the control of the researcher), it
is not useful in many economic applications. However, if the continuous variables in Xi2−Xi3 have
positive density at 0, we may think of constructing estimators that use observations for which Xi2
is close to Xi3. In particular, assuming (for ease of exposition) that all of the k variables in Xit are
continuously distributed, and that sampling across individuals is random, Honore and Kyriazidou
propose estimating β and γ by maximizing
n∑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 observation i, while hn is a bandwidth which shrinks to zero as n increases. The
asymptotic theory will require that K(·) be chosen so that a number of regularity conditions, such
as K(ν)→ 0 as |ν| → ∞, are satisfied. The effect of the term K(Xi2−Xi3
hn
)is to give more weight
to observations for which Xi2 is close to Xi3. The estimator θn ≡(βn, γn
)of θ0 ≡ (β, γ) is shown
to be consistent and to converge to a normal distribution at rate√nhkn, which, although slower
than the standard√n rate, can be made close to
√n under 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 middle T −1 periods. In the case of general T, the objective function takes
the form:
n∑i=1
∑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})
)Honore 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 Honore
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.
16
The results applying Honore 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 function K (·). We specify hn = c×n−1/5 where c is 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
INCmt 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 Honore 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.
17
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.
REFERENCES
Amemiya, T. (1985): Advanced Econometrics. Harvard University Press.
Angrist, J.D.,Evans,W.N.,1998.Children and their parents’ labor supply: evidence from exogenous
variation in family size. American Economic Review 88 (3), 450–477.
Arellano, M. and S. Bond (1991): “Some Tests of the Specification fro Panel Data: Monte Carlo
Evidence and an Application to Employment Equation,” Review of Economic Studiess, 58,
277-297.
Arellano, M. and B. Honore (2001): “Panel Data Models: Some Recent Developments”, in Hand-
book of Econometrics, Vol. 5, edited by J. Heckman and E. Leamer, Elsevier.
Bonin, H. and R. Euwals (2001): “Participation Behavior of East German Women after German
Unification”, Discussion Paper No. 413, IZA.
Bowsher, Clive G. (2003), ıOn Testing Overidentifying Restrictions in Dynamic Panel Data Mod-
els, Economics Letters, 77(2), 211-220
Browning, Martin (1992): ”Children and Household Economic Behavior,” Journal of Economic
Literature, 30, 1434-1475.
Carrasco, R.,2001.Binary choice with binary endogenous regressors in panel data: Estimating the
effect of fertility on female labor participation. Journal of Business &Economic Statistics
19(4),385–394.
Chamberlain, G. (1993): “Feedback in Panel Data Models,” unpublished manuscript, Department
of Economics, Harvard University. (April 1993)
Eckstein, ZvI, AND Kenneth I. Wolpin (1989a):” Dynamic Labor Force Participation of Married
Women and Endogenous Work Experience,” Review of Economic Studies, 56, 375-390.
18
European Commission (2010): Employment in Europe 2010. Luxembourg: Publications Office of
the European Union.
Heckman, J. J. (1978): “Simple Statistical Models for Discrete Panel Data Developed and Applied
to Test the Hypothesis of True State Dependence against the Hypothesis of Spurious State
Dependence,” Annales de l’ INSEE, 30-31, 227-269.
Heckman, J. J. (1981a): “Statistical Models for Discrete Panel Data,” Chapter 3 in Structural
Analysis of Discrete Data, ed. by C. Manski and D. McFadden, Cambridge, MIT Press.
Heckman, J. J. (1981b): “Heterogeneity and State Dependence,” in Studies of Labor Markets,
edited by S. Rosen. The National Bureau of Economic Research. Chicago: The University of
Chicago Press.
Haisken-DeNew, J. and J. Frick (2003): Desktop Companion to the German Socio-Economic Panel
Study. DIW Berlin.
Honore, B. E. and E. Kyriazidou (2000): “Panel Data Discrete Choice Models with Lagged De-
pendent Variables,” Econometrica, 68, 839-874.
Hotz, V Joseph & Kydland, Finn E & Sedlacek, Guilherme L, 1988. ”Intertemporal Preferences
and Labor Supply,” Econometrica, Econometric Society, vol. 56(2), pages 335-60, March
Hyslop, D. R. (1999): “State Dependence, Serial Correlation and Heterogeneity in Intertemporal
Labor Force Participation of Married Women,” Econometrica 67, 1255-1294.
Jakubson, George (1988): ”The Sensitivity of Labor-Supply Parameter Estimates to Unobserved
Individual Effects: Fixed- and Random-Effects Estimates in a Nonlinear Model Using Panel
Data,” Journal of Labor Economics, 6, 302-329.
Keane and Sauer R. (2009): ”Classification error in Dynamic Discrete Choice Models: Implications
for Female Labor Supply Behavior”, Econometrica 77, 975-991
Mroz, Thomas A, 1987. ”The Sensitivity of an Empirical Model of Married Women’s Hours of
Work to Economic and Statistical Assumptions,” Econometrica, Econometric Society, vol.
55(4), pages 765-99, July.
Sevestre, P. and A. Trognon (1985): “A Note on Autoregressive Error Components Models,”
Journal of Econometrics, 28, 231-245.
Whitney Newey & Frank Windmeijer, 2005. ”GMM with many weak moment conditions,”
CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Insti-
tute for Fiscal Studies.
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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 time and in 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).24For 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.
20
- 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.
25The procedure adopted is fairly standard and is documented in Haisken-DeNew and Frick (2003).26This is the reason why, in constrast to Hyslop (1999), we do not consider children who are 17 years old.
21
