PANEL ESTIMATES OF THE EFFECTS OF CAREER INTERRUPTIONS ON THE EARNINGS OF WOMEN

PANEL ESTIMATES OF THE EFFECTS OF CAREER INTERRUPTIONS ON THE EARNINGS OF WOMEN

DONALD COX’

INTRODUCTION

Most working women leave the labor force at least once during their careers, and the earnings profiles of these intermittent workers are expected to differ from those of continuous workers. Planned limitations on investment in on-the-job training caused by expected future career interruptions and depreciation of skills during time spent out of the labor force could cause both the level and growth rate of earnings to be different for the intermittent worker relative to the continuous worker at certain points in the life-cycle. Despite the large number of empirical studies dealing with the problem of women’s life-cycle earnings, studies to date have not examined the impact of labor force participation patterns on large sections of the life-cycle earnings profile. In this study, female earnings profiles are estimated using a long panel (a maximum of 23 yearly observations) created from Social Security records.

Most existing studies of women’s earnings profiles have used summarized work histories, along with schooling and demographic variables, to explain the variation in the earnings of a cross-section.l The measurement of skill depreciation is often a primary focus in studies of female wages,2 and until recently there was some con- troversy as to whether or not skill depreciation was an empirically significant phenomenon. Mincer and Ofek (1982) depart from the cross-sectional methodology by examining female wages at dropout and re-entry points in the intermittent worker’s life cycle. In contrast to most of the earlier cross-section studies, they find strong evidence that earning power deteriorates during time spent out of the labor force. They also find that post-interruption earnings growth is fairly rapid. Mincer and Ofek attribute this rapid growth to the relative ease with which human capital may be “restored.”

While Mincer and Ofek firmly establish that the skill depreciation and post- interruption earnings growth are important, the existing empirical literature on female earnings leave a number of important questions unanswered. First, without a more complete panel, it is impossible to determine whether the existence of a future interruption will have any impact on current earnings growth. This question is important because it is central to the human capital investment hypothesis; women who expect to be in the labor force for shorter periods of time in the future have less incentives to acquire market-related skills because they have a shorter horizon over which the benefits from investing can accrue. Earnings growth early in the career should be affected by the existence and length of future career interruptions.

‘Washington University in St. Louis. This research was supported in part by research grant no. 91-44- 79-24 from the Department of Labor. I have benefited from discussions with John Kennan, Finis Welch, Solomon Polachek, Sharon Smith, Fred Raines and research assistance from Paul Wilson and from the comments of three referees. Responsibility for any errors rests solely with the author.

1 . See, for example, Mincer and Polachek (1974), Sandell and Shapiro (1978), and Corcoran and Duncan (1979).

2. See, for example, Corcoran (1978).

386 Economic Inquiry Vol. XXII. July 1984

COX: CAREER INTERRUPTIONS AND EARNINGS OF WOMEN 387

In this paper, women’s earnings are available for many years both prior to and following a career interruption, so that the impact of future interruptions on early behavior can be measured. The connection between future career interruptions and pre-interruption earnings growth has been widely discussed in the human capital literature [e .g . , Mincer and Polachek (1974), Sandell and Shapiro (1978), and Mincer and Ofek (1982)], but the impact of future interruptions on early wage growth has never been established b e f ~ r e . ~ Second, the interactive nature of the earning profile is difficult to determine from cross-section data or short panels because of multicollinearity problem^.^ The interactive terms are particularly important for testing human capital investment hypotheses; the human capital investment model predicts that the current earnings growth rate will depend on both past and future labor force participation. Third, the existence of time or vintage effects on earnings may obscure any inferences about the lifetime development of earnings made on the basis of a cross-sectional earnings p r ~ f i l e . ~ This issue is important since segmented earnings profiles for women have been estimated from both cross-sections [ e.g. , Mincer and Polachek (1974)l and short panels (Mincer and Ofek) in the past. The type of data used in empirical work generally will affect the estimated slope parameters of the profile. [Weiss and Lillard (1978)l. In this paper a large number of earnings observations for each individual is used to estimate the parameters of a representative woman’s earnings profile in a pooled cross-section time-series. The use of longitudinal data gives some indication of the potential biases involved in making inferences about a representative individual’s behavior on the basis of the earnings of a cross-section.6 The earnings effects of exogenous, time- related factors and the growth rate of starting salaries may be estimated from the longitudinal data.

The main result of this paper is that life cycle earnings growth at each stage of the life cycle is affected by both past and future career interruptions. Despite its some- what narrow scope, a simple human capital accumulation model with an exogenous pattern of life cycle labor force participation is found to be useful in making qualita- tive predictions about the impact of labor force withdrawals on earnings profiles. Each of the implications of the human capital model is supported by the data with one important exception. While short future career interruptions are found to be associated with Zower pre-interruption earnings growth (as the human capital model predicts), more lengthy future career interruptions tend to be associated with a slightly higher rate of earnings growth early in the life cycle. Though this estimated growth effect is small, it is statistically significant.

Career interruptions influence the estimated earnings profiles of working women in a variety of ways. The growth rate of earnings at different life cycle stages

3. Cormran, Duncan and Ponza (1983) investigate the connection between future labor market withdrawals and current wage growth. In contrast to this paper, they find little relationship between the two.

4 . An earnings function which contains alternating “segments” of participation and non- participation is often difficult to estimate becauseof multicollinearity. Thesum of the‘kegments” together with years of schooling plus 6 equals the age of the worker. In most data sets higher order terms are difficult toestimateprecisely. Thedata set is used in this study features a long panel with a large number of individual observations, so that higher order terms may be estimated more precisely.

5. No study of female earnings has addressed this problem. Though Mincer and Ofek use panel data for some of their estimations, they ignore exogenous time or vintage-related wage growth.

6. For a detailed discussion of this topic, see Weiss and Lillard (1978).

388 ECONOMIC INQUIRY

and the decay in earning potential during the period of non-market work all depend upon the configuration of lifetime labor force participation. In addition to the variety of new findings with respect to earnings profiles of women, there are two results in this paper which corroborate recent findings of Mincer and Ofek (1982). First, earning potential tends to decline during periods of nonuse. Secondly, the post interruption earnings growth rate is fairly large. While Mincer and Ofek attribute this rapid growth to differences in the technology of “repairing” versus “producing” new human capital, it is shown below that this finding may be reconciled with a simple human capital model with intermittent labor force participation. Although no spe- cial assumptions about the technology of human capital accumulation are needed to explain rapid post interruption earnings growth, this paper produces a result which may support the Mincer-Ofek conjecture. Additional years of schooling raise post- interruption earnings growth. If “restoration” of human capital takes place after a career interruption, schooling apparently aids this process.

In addition to testing an extensive set of hypotheses generated by the human capital model, this paper reports some empirical results which lie outside the scope of the simple model. First, women who experience a career interruption (either past or future) have earnings which are uniformly lower than those of continuous workers. Secondly, some implications of using longitudinal data to measure the effects of labor market experience on earnings are explored. It is shown that panel estimates of earnings growth and depreciation rates are uniformly higher (in algebraic value) compared to parameter estimates from cross-section data.

Human Capital and Career Interruptions Career interruptions need not necessarily affect the earnings development of the

representative individual. Suppose, for example, that earning potential was related only to increasing maturity which comes about by aging, and exogenous productivity gains which occur over time. In this case, treating individuals with equal amounts of potential labor market experience but varying amounts of actual experience as observationally equivalent is not restrictive. More commonly, however, an individual’s stock of knowledge and skills is postulated to be gained from education and learning from work experience. In addition, since the provision of on-the-job training is generally not costless, workers must choose the optimum accumulation of skills depending on the trade-off between current and future earnings, the rate of discount, and the expected length of worklife.

Polachek (1975) and Mincer and Polachek (1974) have applied the human capital planning model to women facing discontinuous lifetime labor force participation patterns. As an aid in organizing the empirical analysis, a similar model with an explicit pattern of lifetime labor force participation is sketched below. Suppose that the individual’s goal is to maximize the present value of lifetime earnings

where earnings are defined as the fraction of the total value of the human capital stock which is actually rented on the market. That is, observed earnings are given by


where K(t ) is the human capital stock, w, is an exogenously determined rental rate, s( t ) is the fraction of human capital used for learning, and L(t) is labor force participation. The individual's problem is to choose a pattern of human capital accumulation s( t ) , in order to maximize (l), subject to the following constraints:

(3) (a) K = Q(t) - 6 K = b o ( s K ) b ' - 6 K .

1 O I t < t *

0 t * 5 t < t 1 t 5 t < T .

- (b)

(4 s(t) 5 1 whenL(t) = 1

s(t) = 0 when L(t) = 0.

Human capital investment, Q(t), is assumed to be produced by the quantity of human capital allocated for that purpose, sK , according to a Cobb-Douglas technology. Labor-force participation, L(t), follows a pattern in which the individual is in the labor force from the outset of the plan until an exogenously determined dropout date, t *, then drops out until the exogenously determined re-entry date, ;, and then remains in the labor force until the end of the plan. In addition, constraint 3-c implies that no human capital investment takes place during the drop-out phase t - t'.

The specification of the human capital model is meant to reflect commonly observed life-cycle behavior. The three period model easily generalizes to any number of drop-out, drop-in periods and may be solved explicitly for disposable earnings. The model contains potentially restrictive assumptions, however. Most impor- tantly, lifetime labor supply is exogenous to the model and all parameters are known with certainty

For interior solutions of s(t), the optimal human capital investment plan is characterized by the following conditions:

-

(4) -wo K + X b, b, sb'-' Kb' = 0 .

(5)

(6)

~ , ( s K ) ~ ' - 6K = K .

(L-s)w, + X(b,b,sb'Kb'- ' - 6 ) = h r - A .

(7) X(T)K(T) = 0 .

The variable X(t) is the shadow price of human capital. Its terminal value is assumed to be zero. Expressions (4)-(7) can be manipulated so that measured - earnings are expressed in terms of the labor force participation parameters t *, t and T The assumption that the production output elasticities with respect to s and K are each equal to b, implies that the optimal investment plan does not depend on the stock of human capital. The assumption insures a closed form solution for earnings. [See Ben-Porath (1967)l. The investment strategy is founded on the shadow price of


human capital which summarizes future benefits from adding to the stock of human capital. The shadow price in turn depends on planned labor force participation.

The impact of changes in lifetime labor force participation plans on measured earnings is summarized below. E , and El denote the level and rate of change Of earnings in the first segment of labor market experience (from 0 to t * ) and E , and E, denote the level and rate of change in the post interruption experience segment (from t to T).

Effect of an increase in

- t * t T

A postponement of the dropout date t * causes the level of earnings, El , to decline early in the first stage as the individual devotes more resources to investment. Then E l rises later on, so that in general the effect of an increase in t* on the level of earnings in the first segment is ambiguous. The growth of earnings in the first stage, E l , increases when the dropout date is postponed. The percentage rate of growth of earnings in the first stage, kl /El is higher for workers who plan to drop out later. A postponement of the dropout date t * raises the level of earnings during the second earning stage (from t to T ) because the individual re-enters the labor force with a larger human capital stock. The growth in earnings during this time, however, k, is unaffected because human capital investment is assumcd to be independent of past behavior. This implies that the rate of earnings growth, E,/E, , during the later stage of the worklife is higher for women who leave the labor force sooner. Earning potential depreciates at the rate 6 during the dropout phase t * to T. 7 Finally, as in the Ben-Porath (1967) model, it may be shown that the optimal number of years of schooling (the length of time in which the individual specializes fully in the production of human capital, so that s = 1) depends upon the future pattern of labor force participation. Longer periods of expected labor force participation bring about larger investments in schoolinga8

7. The assumption of a constant rate of human capital depreciation greatl simplifies the analysis. There are good reasons to believe, however, that the depreciation rate may vary iepending on the magni- tude and type of human capital (or occupation), There is some evidence that women who expect to be out of the labor force for a longer period of time will acquire skills which depreciate moreslowly [see Polachek (1981)l. In addition, women who expect to be in the labor force for longer periods of time in the future ma try to maintain their skills during their hiatus from the labor force. There is some empirical evidence to tiis effect which is presented below.

8. An extensive treatment of the optimal schooling decision is beyond the m p e of this paper, however. The schooling choice depends not only upon expected labor force participation but also upon the expected present value of alternative income streams generated from different schooling decisions, financial constraints, and ability. [See Willis and Rosen 1979)l. In the empirical analysis below, schooling (and therefore the date of entry into the labor markes is treated as exogenous, though the average rate of return to schooling is allowed to interact with the configuration of lifetime labor force participation patterns.

COX: CAREER INTERRUPTIONS AND EARNINGS OF WOMEN 39 1

The Data The data set used in the empirical implementation is a match between the 1973

Current Population Survey - Administrative Record (CPS-SSA) Exact Match File and the 1937-1973 Social Security Longitudinal Earnings (SSLE) Public Use File. The former file is itself a match between the records of individuals sampled in the March 1973 CPS and Social Security earnings and benefit records. Until recently, only summary longitudinal work experience and reported earnings information was available from the CPS-SSA file. In 1977, the 1937-1973 SSLE file was created to be used in conjunction with the former match file. The SSLE file contains longitudinal earnings information from 1951 to 1973. The file also contains the number of quar- tersof coverage (QCS) earned by an individual in each year from 1951 to 1973. A QC is defined as a quarter of a year in which a person has earned $50 or more in employment covered by Social Security. The SSLE file was exactly matched to the CPS-SSA file by using a unique record identifier associated with each individual in the file.

The principal advantage of the combined file is its longitudinal feature which allows experience and earnings of individuals to be tracked over periods as long as twenty-three years. The file is by far the longest on-going longitudinal earnings file, spanning a substantial portion of the worklife both prior to and following work interruptions. Using the Match file one can view the lifetime earning process as it unfolds; time series observations are available for each year of the worklife under consideration. There are, however, two potential problems with using Social Secu- rity data to estimate earnings profiles. First, observations are restricted to sectors covered by Social Security (about 90 percent of the work force in 1973). Most major coverage changes occurred before 1951, but coverage was extended to professional self-employed in 1954. Secondly, the earnings observations are truncated to the Social Security taxable maximum (about 7 percent of all earnings observations are affected). The match between the CPS and the Social Security data facilitates an assessment of the severity of these limitations, and it appears that the undercoverage and truncation problems are not very restrictive for the purposes of this paper.9

The Sample The group of women aged 29 to 43 in 1973 was chosen from the Match File, and

the sample was limited to women employed to industries covered by Social Security in 1973. The former was done to minimize the undercoverage problem discussed above. Thirdly, the sample was limited to full-year workers working 40 hours or less in the survey week. Each individual in the sample started covered employment sometime between 1951 and 1960, and each woman had begun covered employment sometime between one year before completion of schooling and three years after completion of schooling (assuming that no breaks occur during the school years). The data of labor force entry is measured as the first year in which covered earnings are observed. In addition, because of the large number of interaction and higher order terms explored, the primary sample is limited to women with one or no work interruptions for expositional purposes. A year of non-participation is defined as a year in which no QCS were earned. Yearly observations are limited to those in

9. A detailed analysis of the data is presented in an Appendix which is available upon request from the author, or see Cox (1980).


which four QCS have been earned. lo Selected characteristics of the women in the sample are presented in table 1.

Selectivity problems could conceivably bias the earnings profile estimates because the sample is restricted to working women. No attempt is made to correct for selectivity bias in the empirical implementation below. l1

TABLE 1

Selected Characteristics of Women Aged 29-43 in 1973 With At Most One Work Interruption

Standard Mean Deviation

Number of consecutive years in which one or more QC was earned since entering covered employment. 11.1 (7.3)

Number of years in which no QCS were earned 2.6 (3.8)

Number of years in which one or more QCS have been earned following a work interruption. 4.9 (5.6)

Schooling 12.1 (2.1)

Black 13.4%

Married 69.0%

Total Number of Women in the sample. 583

Number of Yearly Earnings Observations. 9,266

Number of observations in which the taxable maximum is reached. 64 1

Number of observations in which the person worked less than full year (QC = 1 ,2 ,3 ) 2,367

Empirical Implementation The human capital model above predicts that the growth rate of earnings will

vary over alternating segments of labor market participation and non- participation. The growth rate of earnings in each segment depends upon past and future labor force participation. As a first step, it is useful to define a few terms. The

10. An earnings function for a sample containing women who have had more than one work interruption is presented in an Appendix available upon request from the author.

11. In order to correct for selection bias it would be necessary to estimate labor force participation probabilities for each woman in every year in the panel. A simultaneous model of lifetime labor supply and human capital investment is be ond the scope of this pa er. The key to the selectivit problem here is the possible impact of omitted varialle bias stemming from t i e omission of the inverse MiEs ratio terms. In cross-section estimates from Match File data indicate that the selectivity problem has a minor impact on the coefficient estimates, but the importance of selection bias for the panel estimates is unknown.

COX: CAREER INTERRUPTIONS AND EARNINGS OF WOMEN

variable PRE is a dummy variable which takes on a value of one for all earnings observations prior to a work interruption. Similarly, the term POST is a dummy variable which takes on a value of one for all earnings observations following a career interruption. Using the notation of the theoretical model above, let t * denote the date at which the woman drops out of the labor force, and let t denote the date of re-entry, so that the variable t - t * measures the length of the interruption. In addition, let istand for the date at which the individual begins work in the first segment of labor market experience. According to the human capital model the growth rate of earnings in the first segment of experience is given by

(8)

393

E,IE, = a, + a, (PRE) + a , ( t - ; ) + a , ( P R E ) ( f - t * )

+ aS(1973-t)(PRE) + z 6 X , t̂ I t I t * ,

and the sign hypotheses are the following: a , > 0, a, < 0, a3 < 0, a, < 0 and a, > 0. The earnings growth rates in each segment may also vary according to a vector of schooling and demographic variables denoted by X. l2 The earnings growth rate early in the life cycle is expected to be lower if there exists a future work interruption (PRE = 1) and the dampening of the earnings growth rate should be more severe the larger is the future interruption (t - t *) and the shorter is the future post interruption work experience (1973 - T ) , The sign hypothesis for a3 is negative because the log earnings profile is expected to be concave. Note that for continuous workers PRE = 0 andE,/E, = a, + a3 ( t - i) + z 0 X . Also note that the simple theoretical model deals with the entire work history up until the date of retirement, but the panel only chronicles the work history until the year 1973. The future work history beyond this year is unknown. l3

The rate of depreciation of earnings during time spent out of the labor force is expressed as:

(9) 4

6 = b, + b 2 ( t - t * ) + b 3 ( t * - i ) + b4(1973-t) + b,X, t * I t < t.

For simplicity, 6 is treated as a constant in the theoretical model, but a more complex treatment of the depreciation of earning potential is used in the empirical implementation. The sign hypothesis for the estimated depreciation rate is negative, but the sign hypotheses for the individual coefficients are conjectural, rather than derived from the theoretical model above. It may be expected that b, < 0 if larger stocks of human capital depreciate at a faster rate.14 Second, it may be expected that b, will be positive if women who anticipate longer spells of post-interruption work experience take measures to prevent their skills from deteriorating during their hiatus from

12. The vector X includes years of schooling and dummy variables for race and marital status. 13. Estimation problems caused by this data limitation are discussed in an Appendix, which is availa-

ble upon request. Post sample career interruptions do not bias estimated preinterruption earnings growth. Post sample interruptions do bias estimates of post interruption earnings growth but the estimates are biased downward, which stacks the cards against the human capital hypothesis.

osits a theoretical model which distinguishes between different t pes of human capital. One aspect o/ tKe differences in human capital is the rate of atrophy. The rate of atrophy may differ, for example, across occupations. Polachek finds that women with shorter career interruptions tend to self-select into occupations with larger atrophy rates.

14. Polachek (1981


the labor force. Finally, the coefficient b, may be either positive or negative, depending upon whether the decline in earning potential decelerates or accelerates with increases in the length of the interruption.

The growth rate of earnings in the second segment of labor market experience is given by

(10) Ez/Ez = C , + c , ( t - t ) + c , ( t * - t * ) + c 4 ( t - t * ) + Z 5 X .

The human capital model predicts that increased preinterruption experience ( t * - t*) will cause the earnings growth rate to be lower in the second segment of experience so that c, is expected to be negative. Similarly, the model predicts that shorter spells out of the labor force [lower values of (i - t *)] should cause the earnings growth rate to be lower in the second segment of experience. Since the log earnings profile is expected to be concave the term cz is expected to be negative. Note that since equations (9) and (10) each apply only to those workers who have experienced a career interruption, these two equations are each multiplied by the variable POST.

The log earnings profile will be estimated in level form. The initial level of earnings is given by

(11) In E ( i ) = Bo + B,(INTERRUPT) + BE, (SCHOOL) + B,(BLACK)

+ B,(SZNGLE) = Bo + B,(INTERRUPT) + kX,

where INTERRUPT is a dummy variable which takes on a value of 1 for intermittent workers. The variable SCHOOL denotes years of schooling, and the latter two variables are dummy variables indicating race and marital status. These variables comprise the vector X which is included in equations (8-10).

The random component of log earnings is assumed to consist of both a time- related element, YA(t), and a completely stochastic element ~ ( i , t). The variable YR(t) denotes random influences on earnings common to all women in year t , and ~ ( i , t ) denotes random influences across individuals and time.15 The yearly error component is estimated as a series of dummy variables.

Integrating equations (8-lo), adding equation (1 1) and the random components, and allowing the post-interruption earnings profile to shift by adding the variable POST, obtain:

(12a) l n ~ , ( i , t ) = B, + B , ~ N T E R R U P T ) + i 2 x + a , ( t - i ) + a 2 ( t - i ) ( p ~ ~ )

+ a,(t - ; ) ' I2 + a l ( t - i)(t - t*)(PRE) + a5(t - i)(1973 - t ) (PR E )

+ Z , X ( t - i) + YR(t) + e(i , t ) , i 5 t 5 t * .

15. The error structure could be extended to include an individual as well as a time specific error component. The equation is estimated by OLS rather than by variance components methods. In large samples there is virtually no differences between the coefficient estimates, which is the focus of this paper. On this matter, see Lillard and Weiss (1979). Measured standard errors in the OLS specification will be lower compared to a variance component specification however. Note also that earnings, rather than wage, profiles are being measured here. The Match File contains no information about hours worked. Earnings observations are restricted to four quarter years.

COX: CAREER INTERRUPTIONS AND EARNINGS OF WOMEN

(12b) I n E , ( i , t ) = B, + B,( INTERRUPT) + g 2 X + B,(POST) + a , ( t * - t ^ )

+ ~ , ( t * - i ) ~ 1 2 + 7 i , X ( t * - i ) + b , ( t - t * ) + b , ( t - t* ) ' 12

+ b , ( t - t* ) ( t * - i) + b, (t - t*)(1973 - t) + z , X ( t - t* )

+ c , ( t - t) + c2(1 - t ) * / 2 + C ? ( t - i ) ( t * - F )

395

+ c , ( t - t ) ( t - t * ) + & X ( t - t ) + YR( t ) + c ( i , t ) ,

- t I t I 1973.

The regression estimates are more easily presented by adopting the following mnemonics:

EXPl = min ( t - i, t * - i)

EXP2 = m a x ( t - t , O )

HOME = t - t * for t 2 t * , Ootherwise.

In addition, future segments of the work history are denoted by (*) and past segments by ('). These future and past values of the work history do not vary with time, so that E X P l ' = ( t * - i), for example, and H O M E * = (t - t *).

The equations (12a-b) may be rewritten as

(12a') In E , ( i , t ) = B, + B , (INTERRUPT') + g 2 X + a , (EXPl )

+ a,(EXPl)(PRE*) + U , ( E X P ~ ) ~ I ~ + a, (EXPl) (HOME*)(PRE*)

+ aS(EXPl)(EXP2*)(PRE*) + ;,X(EXPl) + YR(t ) + E(i, t ) ,

t I t I t* .

(12b') In E2( i , t ) = B, + B , ( INTERRUPT') + 2 , X + B,(POST')

+ a , (EXPl ' ) + a,(EXP1')2/2 + a"X(EXP1') + b , ( H O M E ' )

+ b2(HOME')Z12 + b, (HOME') (EXPl ' ) + b, (HOME' j (EXP2)

+ z , X ( H O M E ' ) + c,(EXP2) + C , ( E X P ~ ) ~ / ~ + c3(EXP2)(EXP1')

+ c,(EXP2)(HOME') + 2,X(EXP2) + YR( t ) + c(i , t ) , - t I t I 1973.


The form of equation (12a-b) allows for a test of all of the earnings profile related human capital hypotheses outlined above. The estimating equation differs from most other specifications of segmented earnings functions because, consistent with the model above, the level and growth rates of earnings at various points in the life- cycle are expressed as a function of both past and future labor market experience patterns. Note, however, that the potential endogeneity of schooling or market experience is neglected in this formulation.

Equation (12a-b) is estimated for a sample of 583 women for whom earnings observations are available from the date of entry into covered employment until 1973. The total number of observations is 6,899. An average of 2.6 years were spent out of covered employment in this sample. Forty-nine percent of the women in the sample worked continuously from the date of entry into covered employment until 1973. The remainder experienced one work interruption. The average number of years in which one or more QC's were earned is 11 in the first segment of experience and 5 in the second segment of experience. Over two-thirds of the women in the sample were married in the CPS survey year and 13 percent were black.

The fact that earnings, rather than hourly or weekly wage rates, is the dependent variable in equation (12a-b) should be borne in mind. Longitudinal data for hours worked are not available from the Match File. Therefore some of the variation in earnings will stem from variations in hours worked. Earnings observations are limited to four-quarter workers, but earnings development over the life cycle could stem from both changes in hours worked and wage rate increases.

Estimation The OLS estimate of equation (12a-b) is presented in table 2. In order to examine

the human capital hypotheses it is useful to write the empirical versions of the earnings growth equations and compare the estimated coefficients with their sign hypotheses. The growth rate of earnings in the first segment of labor market experience is given by the expression

(8' ) E J E , = a, + a, (PRE*) + a, ( E x p i ) + a, ( P R E * ) ( H O M E * ) ( + I (-1 (4 (-1

( + I + 6, (PRE*) (EXP2*) + a',X.

= 0.056-0.0ll(PRE*)-0.003(EXPL) + 0 .0055(PRE*) (HOME*)

+ 0.0042(PRE*)(EXP2*) + a',X.

The major empirical findings in equation (8') are that (1) the earnings growth rate is 1.1 percentage points lower if a future work interruption exists; (2) larger future interruptions are associated with higher earnings growth rates; and (3) longer segments of post interruption labor market experience are associated with higher earnings growth rates. Findings (1) and (3) are consistent with the human capital model but the second finding is not, A postponement of the re-entry date 7 by one year, for example, adds .55-.42 = -13 percentage points to the annual pre-


TABLE 2

OLS Regression Results - Equation (12a-b) - Women Aged 29-43 in 1973 - One or No Work Interruptions

Dependent Variable - Log of Yearly Earnings in 1967 Dollars

Variable Coefficient t-stat. Variable Coefficient t-stat.

INTERRUPT SCHOOL BLACK SINGLE EXPl HOME EXPB (EXP1) (HOME) * (EXP2)2 (EXP1) (SCHOOL) (HOME) (SCHOOL) (EXP2) (SCHOOL) (EXP1) (BLACK) (HOME) (BLACK) (EXP2) (BLACK) (EXP1) (SINGLE) (HOME) (SINGLE) (EXPZ) (SINGLE) (EXP1) (PRE ') (EXP1) (HOME') (PRE) (EXPl)(EXP2*) (PRE) (HOME) (EXP1') (HOME) (EXP2*) (EXP2) (EXPl') (EXPB) (HOME') POST

YR 54 YR 55' YR 56 YR 57 YR 58 YR 59' YR 60 YR 61 YR 62 YR 63 YR 64 YR 65 YR 66' YR 67 YR 68'

YR 58

-0.319 0,040

-0.227 -0,011 0.056

-0.023 0.080

-0.00 15 0.0011

-0,0039 0,00005

-0.0008 0.0020 0,011 0.035

-0.010 0.011 0.002 0.012

-0.011 0.0055 0.0042

-0.0075 0.0026

0.0026 0.014 0.0006 0.090 0.111 0.108 0.101 0.070 0.131 0.126 0.156 0.132 0.121 0.173 0.191 0.210 0.230 0,257

-0.0027

-7.40 6.36

-6.03 -0.44

5.78 -0.85 4.84

1.13 -6.65 0.10

-0.67 2.77 3.17 4.12

-2.10 4.97 0.32 3.40

4.84 3.85

-5.94 2.16

-3.57 1.80 0.66 0.00 0.96 0.95 0.94 0.87 0.62 1.14 1.11 1.36 1.15 1.05 1.50 1.64 1.80 1.96 2.20

-5.80

-1.57

YR 69 YR 70 YR 71 YR 72' YR 73' CONST

R2

F

N

OBS

0.241 2.05 0.236 2.00 0.257 2.20 0,288 2.43 0.277 2.33 5.7444

0.31

63.79

583

6899


interruption earnings growth rate. The estimated effect is small but statistically significant. Women who drop out of the labor force in the future generally experience lower preinterruption earnings growth, but the estimated earnings growth effect is larger for women who experience Shorter career interruptions. The average growth rate of earnings in the first segment of experience, evaluated at sample means (including means of the vector X ) is 3.8 percent.

The estimated depreciation rate is

(9') 8 = i, + b2(HOME) + b,(EXPl ' ) + i , (EXP2*) + c 5 X

= -0.023 + O,OO22(HOME) - O.O075(EXPl') + O.O026(EXP2*) + c s X .

The sign hypotheses are not based on the human capital model (which for simplicity was characterized by an exogenous rate of human capital depreciation) but instead are based on some conjectures about the atrophy of skills for women with differing past and future labor market experience. Larger preinterruption work experience is associated with larger human capital depreciation rates (measured in absolute value). This finding indicates that higher stocks of human capital depreciate at faster rates, which is consistent with the findings of Polachek (1981). An additional year of preinterruption labqr market experience adds .75 percentage points to the estimated depreciation rate (b, = -0.0075). In addition, women who expect to remain in the labor force for longer periods of time in the future experience lower rates of human capital depreciation. An additional year of post-interruption experi- eFce lowers the depreciation rate in absolute value by -26 percentage points (b, = 0.0026).

The estimated depreciation rate at sample means (including means of the vector X ) is 4.1 percent. This estimate is a bit lower than the estimates obtained by Mincer and Ofek (1982) (5.6-8.9 percent) when they compare dropout and re-entry wage rates in the NLS data. The estimates are reasonably close, however, considering differences in methodology, samples and data sets. l6 The estimates reinforce Mincer and Ofek's findings that earnings depreciation is an empirically significant phenomenon. Further, the estimates indicate that depreciation rates vary with both past and future patterns of labor force participation. Ceteris paribus, the earnings of women who drop out of the labor force at a later date depreciate more both in percentage and absolute terms. Postponing both the dropout date t * and the re-entry date ? by one year raises the estimated depreciation rate by a percentage point.

The estimated rate of growth of earnings during the post interruption segment of labor market experience, along with the sign hypotheses implied by the human capital model are presented below.

16. Mincer and Ofek estimate depreciation rates from panel data in two ways. One method they use is to regress the difference between re-entry and dropout wages on the length of time spent out of the labor force. The second method they use is to regress re-entry wages or dropout wages and time spent out of the labor force. In the estimations they include schooling and other variables, including a constant term. Unless there exist second-order wa e effects of withdrawals (beyond depreciation) the constant term should be omitted from the model.%heir depreciation estimates are difficult to compare with the estimates presented here because they include a constant term.


(10’) E,/E, = 2, + 2, (EXP2) + e3 ( E X P l ‘ ) + 2, (HOME’) + A X ( + ) (-) (-) ( + )

= 0.080 - 0.0078(EXP2)

- O.O027(EXPl‘) + 0.0026(HOME) + c‘,X.

The estimates of the interaction term coefficients t3 and 2, support the predictions of the model outlined above. The model predicts that shorter prior labor market experience and a longer hiatus from the labor force will result in afaster post interruption earnings growth rate. If the representative worker drops out of the labor force a year earlier but re-enters at the same date as before, for example, the estimated post interruption earnings growth rate rises by .53 percentage points (.27 + .26).

Evaluated at sample means, the post interruption earnings growth rate is 8.6 percent. This estimated growth rate is remarkably high, but the finding is not unprecedented. Mincer and Ofek estimate first year wage growth rates of between 5.8 and 6.4 percent from a cross-section. While Mincer and Ofek attribute rapid post-interruption wage growth to differences in the nature of human capital investment during re-entry into the labor force (the “repair” of human capital), the finding is predicted from the human capital model presented above. In the model, the marginal benefits of human capital investment depend only on future values of labor force participation, but the current stock of human capital depends on past patterns of labor force participation. If two workers face the same planning horizon, but one has a lower stock of human capital, the rate of growth of earnings for this worker will be higher because the same increases in earning potential will be calculated from a lower base.17

This reasoning, however, implies that years of schooling should be related inversely to earnings growth rates. The interaction between years of schooling and EXPl, however, is not statistically significant and the interaction between years of schooling and EXP2 is positive (table 2). These findings suggest that schooling may play a role in human capital investment which differs from that of on-the-job training. Schooling appears to complement experience-related human capital in the production of skills, but this effect occurs only during the re-entry period.

Other Effects of Career Interruptions A dummy variable adjusting the level of log earnings for individuals who at any

time experience a work interruption (INTERRUPT) was entered into the estimating equation. The variable INTERRUPT takes on a value of 1 for all time series earnings observations of workers who experience an interruption. This variable was found to

17. Rapid postinterruption earnings growth provides some insights into the nature of the functional form of the human capital production function. ’ h o functional forms are popular in the human capital literature. The first is the additively neutral form, Q = f ( sK) which originated with Ben-Porath (1967) and is used in this paper. The second is the multiplicatively neutral form Q = Kg(1-s) which is due to Blinder and Weiss (1976). The second form implies that the rate o f r w t h earnings (slope of the log profile) is independent of K . That hypothesis is rejected here. The qu itative predictions for post interruption earnings growth rates derived from the additive form are not rejected by the data.


be negative and statistically significant. The profile of log earnings shifts downward by 32 percent for individuals who have at any time experienced a career interruption. This finding indicates that women who experience a work interruption have some permanent, unmeasured characteristic which lowers the earnings profile even prior to a work interruption. One possible explanation for this finding is that women who anticipate a career interruption will acquire less human capital prior to entering the labor force (during school, for example). Furthermore, these women may have additional family responsibilities early in life which affect work effort in the market place. l8

In addition, a dummy variable which takes on a value of 1 for all earnings observations following a career interruption (POST) was entered into the estimating equation, but its coefficient was found to be negligible. The depreciation terms discussed earlier account for all of the erosion in earning potential which takes place.

Demographic Difjerences in Earnings Profiles Dummy variables indicating 1973 marital status and race were entered into

equation (14a-b) in level form and interacted with segments of labor market experience and time spent out of the labor force. Though 1973 marital status is an ex post realization, it may proxy expectations about future work experience. Women who were not married by 1973 experienced earnings growth rates which were on average about a percentage point higher compared to married women, but there were no estimated differences between depreciation rates for the two groups.

The estimated differences between earnings profiles for black and white women indicate a substantial narrowing of estimated black-white earnings differentials for women. l9 Initial earnings for black women are estimated to be 22.7 percent lower than for whites. During the sample period, however, the earnings of the average black woman grew more quickly and depreciated less, though post interruption earnings grew less rapidly for blacks compared to whites. Applying these differential growth and depreciation rates to the average work history in the sample implies that the black-white earnings differential narrowed markedly from 22.7 percent in 1955 to 5.4 percent in 1973. The coefficient estimates should not be interpreted as differences in “representative” profiles, because time-related effects are confounded with experience effects, The estimated race-experience interaction terms will be sensitive to the sample period.

Yearly Dummy Variables Dummy variables indicating the year of observation were entered for years 1953

through 1973. The year 1952 is used as a reference category. The large value of the 1954 dummy may be attributed to Social Security coverage legislation which occurred in that year. Coverage was extended to professional self-employed workers. Even though the sampling procedure was designed to minimize coverage bias, a large number of professional workers with high earnings may have been drawn into the sample in that year.

18. Alternatively, women with lower earning potential will be more likely to withdraw from the labor force. ceterispartbus, so that the coefficient for INTERRUPT would in part be picking up the relationship between earning potential and lifetime labor supply.

19. For a detailed analysis of this phenomenon, see Smith (1979).


The taxable maximum was increased by $600 between 1954 and 1955 and between 1958 and 1959. The maximum was increased by $1,800 between the years 1965-66 and 1972-73 and was increased by $1,200 between the years 1967-68 and 1971-72. Years following changes in the taxable maximum are marked with an aster- isk. The effects of the legislative increases are reflected in the yearly dummies.

A rough estimate of the growth rate of initial earnings for women in the sample may be obtained by dividing the 1973 time dummy by 22. This calculation yields an average rate of increase of 1.3 percent. The yearly dummies could reflect gains in earnings due to a variety of factors, such as time-related productivity increases or increases in the quality of schooling. This estimate is likely to be biased downward however. About 6 percent of the women in the sample earned the taxable maximum in 1973, while no individuals in the sample earned the taxable maximum in 1952.

A Comparison of Cross Section and Longitudinal Estimates of Experience and Depreciation Effects

The majority of existing estimates of female wage or earnings profiles are derived using cross-sectional retrospective data. Mincer and Ofek alternate between using cross-section and panel data in order to estimate human capital depreciation. Cross- section estimates of earnings profiles may be expected to differ from longitudinal estimates for two reasons, however. First, time related productivity gains may influence earnings growth and depreciation over the life cycle. Second, women who have more potential work experience will have have entered the later market at an earlier date. Each of these effects would tend to cause the estimated coefficients in the cross- section to be lower compared to the panel.

A simplified version of equation (14a-b) was estimated in order to compare growth and depreciation estimates with those obtained in the 1973 CPS cross- section. Experience segments were entered linearly in each equation.20 The coefficient estimates for experience segments are contrasted below.

1973 Cross-section Longitudinal Data

E XPl .019 ,032

HOME - ,046 - ..026

EXP2 .035 .036

The panel estimates are systematically higher than the cross-section estimates. There are two reasons for these differences.21 First, in the cross-section regressions, a higher level of experience in the labor market tends to be associated with an earlier

20. The form of the estimating equation for the panel is

In E ( i , t ) = B,, + i 1 X + a , ( E X P l ) + b , ( H O M E ) + c , (EXP2) + YR(t) + c ( i , t ) .

The form of the estimating equation for the cross-section is

In E ( i , 1973) = B, + g , X + a , ( E X P l ) + b , ( H O M E ) + c ( E X P 2 ) + e ( i ) .

Each coefficient estimate issignificant at the .01 level. 21. For a detailed treatment of this problem, see Weiss and Lillard (1978), pp. 428-30.


starting date. For continuous workers, there is a negative linear relationship between the two. Secondly, in the pooled regressions, a higher level of experience tends to be associated with a later point in time. For continuous workers, of the same vintage, the accumulation of t years of experience is observationally equivalent to the passage of the same t years. The pooled estimates are expected to be higher because of the existence of these two effects, as long as vintage and time effects are positive.

Note that the measured depreciation rate is much higher in the cross-section regression (4.6%) than in the pooled regression (2.6%). If exogenous, time-related productivity gains accrue to individuals even during their hiatus from the labor force, this result is to be expected, If these mitigating factors are purely time related, the cross-section estimate is unbiased, since it controls for such factors. However, the estimate would only apply for one point in time, because the true parameter value would vary over time.

CONCLUSIONS

The results from the Match File data clearly indicate that work interruptions have a significant impact on the earnings profiles of women. These interruptions affect the lifetime earnings development in a variety of ways. The growth rate of earnings in each life cycle stage and the depreciation rate of human capital all depend upon prior and future labor market experience. The empirical findings are in most cases consistent with the human capital model but postponement of the re- entry date is associated with a slightly higher pre-interruption earnings growth rate.

Finally, comparisons of cross-section and longitudinal earnings profiles indicate that estimates of earnings growth rates and human capital depreciation rates are sensitive to the type of data being used in the estimations. Panel estimates of the earnings effects of experience or time spent out of the labor force are uniformly higher than cross-sectional estimates.


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PANEL ESTIMATES OF THE EFFECTS OF CAREER INTERRUPTIONS ON THE EARNINGS OF WOMEN

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