The effect interruptions in work experience have on wages.

Stratton, Leslie S.

I. Introduction

Individuals who interrupt their employment are generally expected to pay a price in the workplace [15]. Most researchers acknowledge that wages rise more rapidly with time spent in paid employment than with time spent in other noneducational activities. Thus, the wages received by individuals reentering employment are expected to be below those obtained by similar individuals with continuous work records. How far below, is still a matter of debate.(1) One important line of research has focused upon the difference between pre-interruption and post-interruption wages. Specifically, do real wages rise, fall, or remain unchanged during periods of nonemployment?

Two findings stand out from past research. First, a wide variety of studies employing a wide variety of data sets have found that wages fall during periods of nonemployment. The estimated decline ranges from 0.6% to over 5% annually, but averages around 2%. Second, this estimated depreciation rate is higher when the sample under investigation contains a greater proportion of recent reentrants. Thus, there is a pattern to the estimates.

The purpose of this study is to investigate the observed sensitivity to sample composition. In the past such sample sensitivity has been attributed to a rapid depreciation followed by a rebound in wages that over time partially offsets the initial decline. If true, the depreciation rate will be underestimated, especially if the data include few recent reentrants. Two alternative hypotheses are tested in this study.

The first relies upon certain assumptions regarding part-time employment patterns and wages. If part-time workers are paid less than full-time workers, and if part-time employment is more common following reentry because it is used as a bridge to full-time employment, then estimates of the depreciation rate will be biased upward particularly when obtained from samples of recent reentrants, if information on hours worked is ignored. There may, in fact, be no depreciation at all. Results indicate that while part-time workers are paid less than full-time workers, estimates of the depreciation rate remain substantially unchanged when wages in full-time and part-time jobs are allowed to differ.

Alternatively, the sensitivity of the estimated depreciation rate to the sample composition may represent a specific sort of sample selection bias. If individuals who receive lower post-reentry wages are more likely to exit again than those who receive higher post-reentry wages, then samples containing fewer recent reentrants will naturally contain fewer individuals whose post-reentry wages were relatively low and vice versa. This hypothesis is tested by allowing the depreciation rate to be a simple function of post-reentry experience. The results confirm that the longer the spell of post-reentry experience, the lower the estimated depreciation rate.

This paper is organized as follows. A brief review of the literature is presented in section II. In section III the data are introduced. The empirical specification and the sampling technique are discussed and applied in section IV. The alternative hypotheses for the sensitivity of the estimated depreciation rate to the sample composition are developed in section V and tested in section VI. Section VII concludes.

II. Literature Review

Numerous studies have attempted to identify the impact interruptions in work experience have upon wages. One of the first was a study of married women age 30 to 44 by Mincer and Polachek [11]. Using the 1966 cross-section from the National Longitudinal Survey (NLS) of Mature Women, they estimated wage equations including both years of employment and years of non-employment as explanatory variables. Their results indicate that a period of nonemployment not only carries a penalty of forgone experience, but also a significant negative return of about 1.5% per year.

Corcoran [2] attempted to replicate these results using a cross-section of women from the Panel Study of Income Dynamics (PSID). She found a significant 1.2% net depreciation rate when restricting the sample to a comparable group of 30 to 44 year olds, but a much lower 0.6% rate when women of all ages were included. She attributes this differential to sample composition: those in the 30 to 44 year old age group are more likely to be observed shortly after reentry than are those in the more inclusive sample. Thus, the 1.2% depreciation rate is portrayed as the short run effect and the 0.6% depreciation rate is portrayed as the long run effect of a withdrawal upon wages. Mincer and Ofek [10] obtained similar results using data from the NLS of Mature Women, and became the first to suggest that wages may initially decline following an interruption but then rebound and make up in part for the initial decline.

Such a wage-experience profile can be justified in several ways. For example, if job skills or job market information deteriorates during periods of nonemployment, reentry wages will be lower than wages received just prior to the interruption. If these skills or this information is regained more rapidly than it was first learned, then reentry wages will rise more rapidly than the wages of others with similar experience.(2) These explanations are based upon human capital theory. Other explanations relying upon signaling theory, fixed training costs, or differential quit rates could be constructed.

Since 1982, many additional studies have provided evidence of a significant net depreciation rate for time spent not employed. These studies have employed a wide variety of different data sets as well as several alternative specifications. The data sets employed include the 1973 Current Population Survey/Social Security Match File [4], the Canadian Survey of Social Change [13], MBA graduates from the University of Pittsburgh [12], the NLS of Young Women and Men [9], home economics majors from the University of Illinois [8], and SIPP data [7]. The finding of a significant depreciation rate appears robust to such variation, as does the finding of different long run and short run effects, when permitted by the specification. While point estimates range from 0.6% to over 5% per year, most are around 2%.(3) This is true even when an individual specific fixed effects model is used in order to eliminate any bias caused by unobservables such as ability or motivation, or by imperfectly recalled prior work experience [10; 3].

III. The Data

The data used for this study are drawn from the National Longitudinal Survey of Young Women (NLSYW). This survey follows 5159 women from 1968, when they were between the ages of 14 and 24, until either they are lost through attrition or until 1982, the last year of data employed here. As none of the women had reached age 40 by the conclusion of this period, the results reported below may not be applicable to women who have longer interruptions and return to the work force after age 39. This sample is also restricted to include only white women in recognition of apparent racial differences in labor supply patterns [2], and the results should be interpreted accordingly.

For each woman, a time path of employment activity is recorded, beginning with her last date of full-time school enrollment and ending with her last interview date. This activity log is constructed using information obtained at every interview regarding when the current job (if applicable) began, when the last job ended, when the last job began, . . . etc. When this information is unavailable or incomplete for some period of time, it is so noted in the activity log. Such recording gaps are treated as missing data.

For each period of employment, information on both actual hours worked and the hourly wage (in constant 1982 dollars(4)) is gathered. In those rare cases (1.5% of all reported wages) in which real wages fall below $1.50 per hour - approximately the minimum wage for employees who receive tips - or above $27.50 per hour, wages are recoded as missing. Since the estimation technique entails wage differencing to control for unobserved, individual-specific fixed effects, only individuals who report wages at two or more points in time and for whom no intervening activity data are missing are included in the final sample. Women who exit employment to return to full-time school are also excluded from the analysis as their wage patterns are expected to be quite different. These criteria are satisfied by 2612 individuals.(5)

While the data sets used in earlier studies were constructed in much the same way, there are important differences in these data that could affect the estimates. These data contain far more precise measures of employment and hours worked than do most of the earlier studies. Earlier studies [2] were often restricted by data availability to code employment spells one year at a time using information on hours worked during the year to classify that year as one of full-time, part-time, or no employment. While full-time, full-year work can certainly be identified using such information, part-time employment is indistinguishable from part-year or intermittent employment. Much more precise definitions are applied here. Part-time employment, for example, is defined as work involving thirty or fewer hours per week and non-employment means no paid employment. Interruptions of virtually any length are observable. Since job skills are not expected to become obsolete overnight, however, and unemployment or job search is not exactly a non-market activity, spells of non-employment lasting less than three months are ignored. These data differences should generate more accurate estimates of the return to part-time and full-time employment. They may also result in different estimates of the depreciation rate, particularly if the duration of nonemployment is an important factor influencing depreciation.

IV. The Empirical Specification and Sampling Technique

In order to test for such data driven differences, a fairly standard empirical specification and sampling technique were applied first in an effort to replicate earlier findings. The equation estimated is perhaps the most commonly used specification in the literature [3]. A similar specification is used in the final analysis.

The dependent variable consists of the difference between two log wage observations for a single individual, hence any fixed or individual specific effects are differenced out. The explanatory variables consist of experience measures derived from the intervening period. Specifically, the period between wage observations is divided into three parts: 1) the time preceding the most recent interruption but following the initial wage observation, 2) the time of the most recent interruption, and 3) the time following the most recent interruption and preceding the second wage observation. All time spent employed is further subdivided into time spent in full-time and time spent in part-time employment. The length of time spent in full-time (part-time) employment prior to the most recent withdrawal is designated PREFT (PREPT). The time spent not employed during this period is designated PRENT. In the case of post-interruption experience, the length of time spent employed full-time (part-time) is denoted FT (PT). The square of such experience is denoted by appending a 2 to the name (FT2 = FT x FT, PT2 = PT x PT). Finally, the length of the most recent interruption in work experience is denoted NT. The precise specification used is:

ln [W.sub.t+s] - ln [W.sub.t] = [[Tau].sub.1]PREFT + [[Tau].sub.2]PREPT + [[Tau].sub.3]PRENT + [Delta]NT + [[Beta].sub.1]FT + [[Beta].sub.2]FT2 + [[Beta].sub.3]PT + [[Beta].sub.4]PT2 + [[Epsilon].sub.1]. (1)

If skill or knowledge is lost during interruptions in work experience, then the coefficient to NT, [Delta], should be negative and significant. This is the depreciation rate. If post reentry experience has a positive and declining impact upon reentry wages, then [[Beta].sub.1] and [[Beta].sub.3] should be positive and [Beta].sub.2] and [[Beta].sub.4] negative. If full-time experience is more valuable than part-time experience, then [[Beta].sub.1] will probably be greater than [[Beta].sub.3].

This function has typically been estimated [3] using the first and last observed wage for each individual. Consider the hypothetical example shown in Table I. This individual's work history stretches from time [t.sub.1] to time [t.sub.6], a period of 4.5 years. The individual is employed continuously [TABULAR DATA FOR TABLE I OMITTED] [TABULAR DATA FOR TABLE II OMITTED] from time [t.sub.1] to time [t.sub.3] (a period of 2 years) and from time [t.sub.4] to time [t.sub.6] (a period of 1.25 years). The conventional sampling technique would involve differencing the log wages from the first and sixth periods (ln [W.sub.6] - in [W.sub.1]) and explaining the difference as a function of preinterruption experience ([t.sub.3] - [t.sub.1] = 2 = PREFT + PREPT), the interruption ([t.sub.4] - [t.sub.3] = 1.25 = NT), and postinterruption experience ([t.sub.6] - [t.sub.4] = 1.25 = FT + PT). Individuals who did not interrupt (NT = 0) were not excluded in the conventional analysis, rather their experience was encoded as if it were post interruption experience. Individuals for whom there is insufficient wage information were either excluded from the sample or were accommodated using a simple sample selection correction.

This sampling technique and empirical specification were employed with the data set discussed above in an effort to replicate the results of earlier studies and to demonstrate that these data are not unusual. These results are reported in Table II. Column 1 contains sample means, measured in years.(6) Columns 2 and 3 of Table II report results for specification (1) with and without maximum likelihood estimation of sample selection corrections. Such corrections are of concern because only individuals reporting two or more wages with no missing activity data are included in the sample. Some of those not included were lost to attrition, some changed jobs so much they were difficult to follow, and some held too few paying jobs. The wage differencing specification employed should itself control for individual specific wage effects, but changes in unobservable factors over time may also influence wage differences. Unfortunately because some individuals are only interviewed in 1968, only data from that year are consistently available for use in the sample selection equation.(7) Especially for those individuals still in school in 1968, these data are not very informative.(8) The variables used include age, school enrollment status, marital status, number of household members, health, region of residence, and years of school completed. Dummy variables for the respondent's major activity at the time of the 1968 interview(9) were also incorporated. Limited sensitivity testing indicates that the results are robust to alternative specifications of the selection equation. Estimates of the sample selection equations are not of central importance to this paper and are reported in Appendix B.

The estimated depreciation rate using simple OLS on the difference between the first and last observed wage ranges from 1.4% without sample selection corrections to 2.1% with such a correction. These estimates are well within the range obtained in previous studies. Nor are the results particularly sensitive to alternative definitions of NT, in which only periods of nonemployment greater than six, nine, or even twelve months are recognized. The duration of nonemployment does not appear to be a factor in the depreciation rate.

There are, however, several reasons why this conventional sampling approach may provide a less than accurate measure of the depreciation rate. Three such reasons are discussed below. In each case, a modification to the specification and/or sampling approach is suggested to address the point of concern.

First, the conventional approach fails to distinguish between the return to uninterrupted experience and the return to reentry experience. PT and FT reflect either post reentry experience or the experience of those not observed interrupting. Forcing these potentially very different experience patterns to generate the same wage impact may bias the estimated depreciation rate. Such a bias can be eliminated by restricting the sample to only those individuals who experience an interruption. While the number of individuals in the wage sample falls from 2612 to 1311 as a result of this sampling change, the change does return attention to interruptions, the subject of this analysis.

Second, the conventional sampling technique, which takes the last minus the first observed wage for any individual, often unnecessarily wastes resources estimating pre-interruption wages. In specification (1), pre-interruption wages are estimated as: in [W.sub.t] + [[Tau].sub.1]PREFT + [[Tau].sub.2]PREPT + [[Tau].sub.3]PRENT. In the hypothetical example presented earlier, this estimate is Ln [W.sub.1] + [[Tau].sub.1] x 2, assuming the individual worked only full-time. Since the [Tau] terms are estimated with error, the longer the pre-interruption work experience, the less accurate will be the estimate of the pre-interruption wage. The greater the inaccuracy associated with the pre-interruption wage, the more difficult it will be to estimate the impact an interruption has upon wages.

The approach taken here to address this contingency is to subtract from post-interruption wages, not the first wage observed for an individual, but the last wage observed just prior to their interruption. In the case of the example, this wage is Ln [W.sub.2] and the new estimate of the pre-interruption wage is Ln [W.sub.2] + [[Tau].sub.1] x 1/2. As individuals are asked to report their wages upon termination of employment, the effect of this specification change is even more dramatic within the data set itself. The fraction of individuals whose pre-interruption wage is known with certainty (i.e., for whom PREFT + PREPT + PRENT = 0) increases from 33% to 93%. For the remaining individuals, the mean length of pre-interruption experience drops from 2.37 to 0.68 years. While estimates of the [Tau] are likely to be less precise when based off of less data, the increased confidence in pre-interruption wages generated by this approach is of greater importance and, as discussed later, the results are not sensitive to alternative assumptions regarding [Tau].

Finally, the conventional technique fails to use all the available wage information and hence is inefficient. In the hypothetical example presented above, the wages reported at [t.sub.2], [t.sub.4], and [t.sub.5] are ignored. Even after wage information at [t.sub.1] is set aside in favor of the wage information available in [t.sub.2], as discussed above, fully fifty percent of the available wage information is wasted. This inefficiency is addressed here by permitting multiple observations per individual. Instead of using only the [t.sub.6] - [t.sub.2] wage difference, three wage difference observations would be employed for this one individual: ln [W.sub.4] - ln [W.sub.2], ln [W.sub.5] - ln [W.sub.2], and ln [W.sub.6] - ln [W.sub.2]. In general, the dependent variable is created by subtracting the log of the most nearly pre-interruption wage from the log of each successive wage until/unless another period of non-employment is encountered, at which point the differenced wage is reset (say from In [W.sub.2] to ln [W.sub.6], if the individual interrupts again in 1979) and the differencing begun again (ln [W.sub.7] - ln [W.sub.6], ln [W.sub.8] - ln [W.sub.6],...). Multiple completed interruptions per individual are relatively rare, but the use of multiple post reentry wage observations per individual increases the number of observations to 3896.

The chief problem introduced by this sampling procedure is the unusual error structure created by the differencing pattern. In the example above, the error terms are shown to illustrate the correlation problem. While errors will be uncorrelated across individuals, even if the error terms generated by distinct observations on a single individual are independent, the differencing scheme will yield a correlation matrix ([Sigma]) with off-diagonal [+ or -]0.5 terms. This will not bias the ordinary least squares (OLS) results, but OLS will produce inefficient estimates and inconsistent standard errors. Since the [Sigma] matrix is of known form, weighted least squares can be performed to generate efficient estimates. See Appendix A for details concerning the appropriate generalized least squares (GLS) transformations.

The results obtained using this estimation procedure and this specification are presented in Table III. Sample means for the explanatory variables are presented in column 1. The coefficient estimates are reported in columns 2 and 3 for analysis with and without a gross sample selection correction. The approach taken to sample selection correction is identical to that discussed earlier and the sample selection equations are again reported in Appendix B. The primary difference [TABULAR DATA FOR TABLE III OMITTED] between this selection correction and that implemented earlier is that the former sample consisted of all those reporting at least two wages while this sample consists only of the further subset of individuals reporting an interruption in work experience.

Despite the dramatically different sampling technique employed here, the estimated coefficient to NT or the depreciation rate, remains significant at between 1.6 and 2.4% annually, well within previously observed limits. These results are robust to alternative specifications (not shown here) in which PREPT and PREFT are excluded from the specification and in which the sample is restricted to individuals whose initial wage is that received immediately prior to an interruption (i.e., to those for whom PREPT + PREFT + PRENT = 0). Thus, the results reported here are not sensitive to the poorer estimates of [Tau] obtained using this technique. The other coefficient estimates indicate that the returns to full-time experience are positive but decline over time and that the returns to part-time experience are similar, but substantially smaller and not as statistically significant. Overall, the results obtained here confirm those reported in earlier studies.

V. The Depreciation Rate and Sample Sensitivity: Theory

These past results have, however, been shown to vary substantially depending upon the fraction of recent reentrants in the sample. The more recent the reentrants, the greater the estimated depreciation rate. This sensitivity has been attributed to the existence of a rebound effect in post-reentry wages which makes reentrants' wages rise relatively more rapidly than those of individuals with comparable experience or wages. This rebound compensates in part for the depreciation incurred during the interruption; individuals who interrupted many years ago will therefore appear to have experienced little depreciation. Estimates of the depreciation rate under these circumstances will be biased toward zero, and thus provide a lower bound for the true value.

Several other explanations for this sample sensitivity call into question this conclusion, and suggest that estimates of the depreciation rate may have been over- rather than under-estimated. Two such misspecifications are explored in this paper: failure to adequately distinguish between part-time and full-time employment and failure to control for relatively subtle sample selection induced biases.

The specification employed here and in most past research allows the slope of the age-earnings profile to vary with part-time and full-time experience, but does not accommodate differences in wage levels due to part-time and full-time employment status.(10) If wages received by part-time employees are below those received by full-time employees (as most studies suggest [1]) and if those reentering employment are more likely to accept part-time employment initially and move on to full-time work later, then both a depreciation effect and a rebound effect would appear to exist even when they were, in fact, spurious. Since tabulations from these data reveal that movement from full-time to part-time employment is indeed almost twice as common (19.9%) as movement from part-time to full-time employment (11.2%) when an interruption has occurred, such speculation is quite relevant.

This possibility is explored using a specification which permits the level of wages to vary between full-time and part-time employment. Specifically:

ln [W.sub.t+s] - ln [W.sub.t] = [[Tau].sub.1]PREFT + [[Tau].sub.2]PREPT + [Delta]NT + [[Beta].sub.1]PT

+ [[Beta].sub.2]PT2 + [[Beta].sub.3]FT + [[Beta].sub.4]FT2 + [Alpha]PTDUM + [[Epsilon].sub.2] (2)

where PTDUM is a dummy variable having a value of 1 if the individual moved from full-time to part-time employment, a value of - 1 if the individual moved from part-time to full-time employment, else zero. At issue is what effect this modification will have upon estimates of [Delta] or the depreciation rate.

The role of sample selection in determining the estimated depreciation rate is more difficult to describe and test. Wage studies are necessarily restricted to those individuals for whom wages are observed. This sort of gross sample selection problem is addressed here, as in much of the literature on wage depreciation, by modeling sample selection with a separate equation. Unfortunately, studies of the impact an interruption has upon wages involve far more than a simple yes/no labor supply decision. In order to examine wages following reentry to employment, an individual must be observed first employed, then not employed, and finally reemployed. This requires a complex sequence of events. Bias may be introduced in any number of different ways.

Of particular concern here is how the behavior of individuals upon reentry might be affected by reentry wages.(11) Clearly an individual observed at a job must be receiving a wage in excess of her reservation wage. If, however, there is a stochastic component to the reservation wage (or to the value of time spent not employed), then the degree to which the observed wage exceeds the reservation wage becomes an important predictor of the duration of the employment spell. The wage preceding an interruption is presumably fairly close to the reservation wage for that period, ceteris paribus. A wage upon reentry that is below this level is likely to be closer to the reservation wage than a wage upon reentry that is at or above this level. Thus, another interruption is more likely when the reentry wage is low relative to the pre-interruption wage. In general, the duration of reemployment is likely to be positively correlated with the wage change.

This would explain why the choice of sample has been an important determinant of the estimated depreciation rate. A sample containing fewer recent reentrants will contain fewer individuals whose reentry wages were relatively low. Hence, the estimated depreciation rate obtained from such a sample will be relatively small. Conversely, a sample containing more recent reentrants will contain more individuals whose reentry wages were low and so will yield a higher estimated depreciation rate. When ordinary least squares is forced to estimate a single depreciation rate for all reentrants, the return to post-interruption experience will be biased upward as a counterbalance. The depreciation rate will be estimated based upon the experience of those who have only recently reentered and the return to post-interruption experience will increase to compensate those who reentered long ago without necessarily experiencing any depreciation. Thus, a spurious rebound effect will be observed. While this study does not pretend to introduce a complete model of the simultaneous labor supply/wage relationship, it does include a simple test for this sort of sample selection bias.

The hypothesis that the estimated depreciation rate is sensitive to the length of post reentry experience is tested by interacting post-reentry experience and the length of the interruption.(12) Truncation problems necessitate further restricting the sample to include only those who interrupt, reenter, and are observed post-reentry for a minimum of three years. A dummy variable FUT is then constructed based upon the post-reentry employment record. It takes on a value of 1 if the individual remains employed for the full three years following reentry, else 0. FUT is then interacted with NT. If individuals who reenter at relatively higher wages (as measured by their pre-interruption wage), are more likely to remain employed, then the coefficient to NT x FUT ([[Delta].sub.1]) should be positive and significant.

ln [W.sub.t+s] - ln [W.sub.t] = [[Tau].sub.1]PREFT + [[Tau].sub.2]PREPT + [[Delta].sub.0]NT + [[Delta].sub.1]NT x FUT + [[Beta].sub.1]PT

+ [[Beta].sub.2]PT2 + [[Beta].sub.3]FT + [[Beta].sub.4]FT2 + [Alpha]PTDUM + [[Epsilon].sub.3] (3)

VI. The Depreciation Rate and Sample Sensitivity: Practice

Estimates of equations (2) and (3) are presented in Table IV for specifications both with and without gross sample selection corrections. The estimates from equation (2) clearly indicate that [TABULAR DATA FOR TABLE IV OMITTED] part-time jobs pay less than full-time jobs, approximately three percent less. This specification assumes that wage movements between full-time and part-time jobs are symmetric, i.e., that the wage decline observed in moving from a full-time to a part-time job is equal in size to the wage increase observed in moving from a part-time to a full-time job. Estimation of a more general specification which incorporates three dummy variables for hours changes - one for movement from part-time to full-time employment, another for movement from full-time to part-time employment, and a third for movement between part-time jobs - yields insignificantly different results. Tests fail to reject the hypothesis that a single dummy variable, PTDUM, suffices$at even the 90% significance level in both the simple GLS and sample selection corrected GLS cases.(13)

Of more import, the impact including PTDUM has on the estimated depreciation rate is minimal. The depreciation rate remains robust at between 1.5 and 2.3% annually. Differences in the level of pay for part-time and full-time workers exist, but accounting for them does not affect estimates of the depreciation rate.

The depreciation rate does, however, appear to be related to the duration of reemployment. Estimation of equation (3) requires a further reduction in sample size to those whose post-reentry activities are observed for three or more years. While the sample size drops by twenty-five percent, estimates of equation (2) on the reduced sample (not reported here) are substantially unchanged. Results from equation (3), however, reveal that those individuals who remained employed for at least three years following reentry did not experience as great a depreciation in wages upon withdrawal as those who reexited. Temporary reentrants experience a 1.7% (2.9%) annual depreciation rate whereas more permanent reentrants experience only a 0.7% (1.2%) annual depreciation rate (the numbers in parentheses are from the gross sample selection corrected formulations). The difference is statistically significant only when controlling for gross sample selection, but in neither case can the hypothesis that there is no depreciation for those who remain employed for three or more years be rejected at the 95% confidence level.(14) Whereas previous researchers attributed the finding of different apparent depreciation rates across different samples to post-reentry wage rebounding, the evidence presented here strongly suggests that the depreciation rates themselves were different.

Sensitivity testing about the reemployment spell length provides further support for this conclusion. When the required reemployment spell length is reduced from three years to two, the coefficient to NT x FUT remains positive, but becomes smaller and insignificant in both specifications. When the required reemployment spell length is increased to four years, the coefficient to NT x FUT rises to approximately the same size (but opposite sign) as that of NT and attains statistical significance in both specifications. There is clearly a relationship between post-reentry spell length and the wage change observed about an interruption.

VII. Conclusions

The findings reported here attest to the robust nature of earlier work on the rate of wage depreciation during interruptions in work experience, but more importantly demonstrate a major shortcoming of this work. Estimated depreciation rates remain on the order of two percent even as a new data set is employed, part-time and full-time jobs are better distinguished, more accurate and shorter measures of non-employment are introduced, and a new sampling technique which focuses more directly upon withdrawals and which makes greater use of the available data is tested. Even a specification which permits the level of full-time and part-time wages to vary does not significantly change estimates of the depreciation rate. These stable estimates lend considerable credence to the earlier results.

Unfortunately this specification appears to be sensitive to sample selection bias of a sort not previously noted. While researchers have introduced controls for very gross sample selection criteria such as the existence of two reported wage values, they have not typically considered the decisions which might lead to an interruption in and subsequent reentry to employment. Yet theory clearly tells us there is a link between wages and labor force behavior. There is likely to be a positive correlation between reentry spell length and the apparent depreciation rate. A test of this hypothesis reveals that women who remained employed for three or more years following reentry did not experience any significant wage 'depreciation' during their interruption; women who reexited employment more rapidly, did. Estimates of a depreciation rate are, therefore, very sensitive to the manner in which the labor supply decision is handled. A much more complex model which incorporates a period by period or continuous time labor supply decision is needed to truly measure the effect interruptions in work experience have on subsequent earnings.

Appendix A. GLS Data Transformations

This analysis assumes that wages are best modeled by an equation similar to (A1):

Ln [Wage.sub.it] = [[Alpha].sub.0] + [X.sub.i][[Alpha].sub.1] + [Z.sub.it][[Alpha].sub.2] + [[Theta].sub.it]. (A1)

Log wages in this example are a linear function of a constant term [[Alpha].sub.0]; a vector, X, of individual specific characteristics (like education); and a vector, Z, of cumulative labor market experience. The error term [[Theta].sub.it] can be split into two independent parts, an individual specific component, [[Mu].sub.i], and a random component, [[Epsilon].sub.it]. Each of these is distributed with mean zero and variance [Mathematical Expression Omitted] and [Mathematical Expression Omitted] respectively. Both error terms are assumed to be independently distributed across individuals and [[Epsilon].sub.it] is assumed to be independently distributed across time, as well. Perhaps the chief weakness of this specification is its failure to allow for serial correlation of the errors terms for a given individual. The independence assumptions are summarized in (A2).

E([[Mu].sub.i][[Mu].sub.j]) = 0 i [not equal to] j

E([[Epsilon].sub.it][[Epsilon].sub.js]) = 0 i [not equal to] j or t [not equal to] s

E([[Mu].sub.i][[Epsilon].sub.jt]) = 0 for all i, j, t (A2)

When two such log wage observations are differenced, the intercept [[Alpha].sub.0], the individual specific characteristics [X.sub.i], and the labor market experience accumulated prior to the first wage observation, [Z.sub.i,t-1], fall out of the equation. The individual specific component of the error term, [[Mu].sub.i], is also eliminated. Thus the model becomes:

Ln [Wage.sub.i,t] - Ln [Wage.sub.i,t-1] = ([Z.sub.i,t] - [Z.sub.i,t-1])[[Alpha].sub.2] + [[Epsilon].sub.i,t] - [[Epsilon].sub.i,t-1]. (A3)

This error term has a variance of 2[[Sigma].sup.2]. The assumption that wages for a given individual are not serially correlated eliminates the correlation term that would otherwise enter these calculations.

A single observation of this type per individual would not require GLS estimation. It is the unusual sampling technique employed that results in heteroskedasticity. Employing the simple example from the text (see Table I) of an individual who is observed working for two periods, withdrawing once, then reentering for three periods, the heteroskedasticity problem and the solution can be examined in detail. The correlation matrix generated by this individual's employment history is:

[Mathematical Expression Omitted].

The goal is to discover a linear transformation of the data that will yield a post-transformation correlation matrix equal to the identity matrix. Since [Sigma] is symmetric and positive definite, so is its inverse and thus there exists a nonsingular square matrix P, further restricted to be a lower triangular matrix, such that P[prime]P = [[Sigma].sup.-1]. P will be an appropriate transformation matrix.

The chief difficulty encountered in applying this method to this particular problem is the diversity of the data. First, each individual has a unique pattern of work experience and hence a unique P. Likewise, if the sample is restricted in any way, a completely different transformation matrix is usually required for each individual. Thus, a program was written that is able to a) determine each individual's labor market pattern and b) transform the data by applying the appropriate weights. The general form of P, and therefore the formula for the weights is:

[Mathematical Expression Omitted].

This general formula must be altered each time a withdrawal from the labor force is encountered, i.e., each time a new wage is employed as the reference wage, the wage to be differenced. Recall that the wage which will be differenced is fixed at that wage which is observed just prior to an interruption. Its log is then subtracted from each subsequent log wage until another withdrawal (or experience gap) is encountered. Thus, [W.sub.2] is the initial reference wage.

The formula change involves multiplying a particular column of the above P matrix by a constant. The column whose number (D) corresponds to the last observation which makes use of the "old" reference wage is multiplied by (-D). In the example above, there is no second interruption so no such switch occurs. N is set equal to 3 and the transformation is performed. All the data observations are handled in a similar manner.

Appendix B. Gross Sample Selection Corrections

A simple maximum likelihood procedure is used to control for the sample selection process. This process is modeled as follows:

S = Z[Pi] + [Mu]

where S is an indicator variable for inclusion in the sample, Z is a matrix of individual specific characteristics believed to influence S, [Pi] is an unknown parameter vector, and [Mu] is a vector of unobservable error terms. S is itself never observed. Instead, [S.sup.*] is observed.

[S.sup.*] = 1 if the individual is included in the sample

= 0 else

The variables, Z, used to explain inclusion in the wage sample come from the 1968 interview which was completed by all individuals. These variables include the respondent's age, school enrollment status, marital status, number of household members, health, region of residence, years of school completed, and major activity at the time of the 1968 interview.

Normally, researchers control for possible sample selection bias by employing a two-step approach or Heckman correction. Maximum likelihood procedures are employed here instead, because of the heteroscedasticity of known form introduced by the sampling technique. The likelihood function used closely resembles that discussed in Dhrymes [5]. The primary distinction is that the variables in the wage regression are weighted to correct for heteroscedasticity before estimation. The resulting coefficient estimates will be consistent. The standard errors in the sample selection equation will, however, be incorrect in those specifications employing the new sampling technique since multiple wage differences are allowed per individual. The number of distinct individuals upon which these estimates are based is actually only 3637 and the standard errors reported here have been scaled up to reflect this.

Table BI presents the sample means for these explanatory variables and the sample selection equation results for the regressions presented in Tables II and III, in columns 1 through 3. The average age of these [TABULAR DATA FOR APPENDIX B, TABLE I OMITTED] women is 19 in 1968, almost half of them are still enrolled in school in that year, about six percent report being in poor health, one-third are married, and almost one-third live in the south. They have an average of 11 years of education and four family members. Approximately half report being at home, one-quarter being in school, and one percent unemployed. The remainder are employed. Results indicate that older individuals and those still enrolled or otherwise involved in school are significantly less likely to be in the wage sample. This reflects the fact that the employment record of many older women is difficult to follow and the fact that ten percent of the respondents are lost through attrition before they even complete school. Controlling for this, those who have more education are more likely to be in the sample - presumably because they are more likely to be in the labor force. Poor health has the expected negative effect on sample selectivity but it is in no case significant. Unemployment status appears to have a significant negative impact when all individuals reporting two or more wages are included in the sample but not when the sample is restricted to only those experiencing an interruption (i.e., when the new sampling technique is employed). Finally, there is a statistically significant positive correlation between the probability of being in the wage sample and the observed wage difference. This implies that the more likely one is to be in the sample, the more likely one is to experience an unexplained positive wage change. This result is consistent with labor supply theory.

Table BI, columns 4 and 5 present the sample selection equation results associated with Table IV, specifications (2) and (3). The effect of all the school variables is unchanged in sign and significance. The same is true of the correlation term. Age has the same effect but it is not significant in specification (3). Marital status becomes a significant positive factor in specification (2). Basically these gross sample selection results are quite similar across all the specifications.

1. So, too, is the reason. The most common explanation for lower wages is that job skills depreciate when not practiced and hence so will wages. Mincer and Polachek [11] discuss several other reasons such a differential might exist.

2. Mincer and Ofek [10] present an argument based upon job skills. Corcoran [2] presents an argument based upon job market information. The latter is at least theoretically testable as it implies that job turnover rates for reentrants are greater than those for continuously employed individuals.

3. Light and Ureta [9] employ a different specification and estimate a 32% decline in first year wages for reentrants. This effect declines to 8% in the second year and disappears entirely within four years.

4. Results are robust to adjustments based on the CPI or on the aggregate wage index. Those reported in the paper are adjusted by the CPI.

5. See author for further details and a copy of the computer programs used to generate these data.

6. The average period for which an individual is observed is just over five years. Although the survey stretches over fourteen years, many individuals were in school for the initial years. Others were lost to attrition prior to 1982, had unexplained gaps in their employment history records, or remained out of the labor force for several years following graduation. In each case, the result is to shorten the longest continuous spell of complete information and hence the period of observation.

7. One individual is excluded from the sample selection corrected specification due to missing data.

8. Information reflecting an individual's status upon completing school and perhaps entering the labor force would be preferable, but such data are not available for much of the sample.

9. The relevant activities correspond to those employed by the Bureau of Labor Statistics to determine employment status: employed, unemployed, in school, at home, and other. Most individuals reporting their chief activity to be school are also enrolled in school. However, only about half of those enrolled report that school is their chief activity. Employment and unemployment take precedence, much as they do in the Current Population Surveys.

10. Corcoran, Duncan, and Ponza [3] did perform this but found it changed their results very little. Only movement from part-time to full-time employment had an effect that was significant and then only at the 10 percent level. This information was obtained via correspondence with Grog Duncan in June 1987. Since part-time and full-time employment are identified in their data set by examining hours worked per year rather than per week, this ambiguous finding may be the result of insufficiently detailed data.

11. The actual direction of casuality between wages and employment behavior is uncertain. Gronau [6] reports evidence that wages influence employment more than employment influences wages, hence the discussion presented here will tend to err in this direction. However, individuals who plan to reexit will have a lower reservation wage upon reentry causing post-reentry employment plans to influence post-reentry wages. Basically, it is the correlation itself and the effect this correlation has upon the empirical calculation of the depreciation effect with which this paper is concerned.

12. A weak version of this test was implemented by Corcoran, Duncan, and Ponza [3]. They introduce a dummy variable which takes on a value of one if the respondent was employed in the final year of their panel data series. The estimated coefficient to this variable was of the hypothesized sign but, perhaps because of its low power, not statistically significant.

13. Wald test statistics were 0.60 for the GLS specification and 1.04 for the sample selection corrected GLS specification. These statistics are distributed chi-squared with two degrees of freedom. The critical value is 4.605 at the 90% significance level.

14. The test statistic is 1.0425 for the simple GLS equation and 3.4795 for the sample selection corrected GLS equation. This statistic is distributed chi-squared with one degree of freedom. The critical value for the 95% confidence level is 3.841, for the 90% confidence level it is 2.706.

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