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THREE PAPERS IN LABOR ECONOMICS

presented by
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THREE PAPERS IN LABOR ECONOMICS
By

David Larson Wetzell

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirement
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2002

ABSTRACT
THREE PAPERS IN LABOR ECONOMICS
By
David Larson Wetzell

The first paper demonstrates that the time-allocation generalization of
labor supply can generate interesting and surprising predictions regarding labor
supply behavior. These predictions follow fi'om the assumptions made about
input combinations available for final consumption. When goods cannot be
produced strictly from time or money then either input could curtail the
substitution effect.

The second paper shows that Korenman and Blackburn’s (1994) finding of
a ten-percentage point drop in the Male Marriage Earning Differential (MMED)
over the years 1967-1988 is biased upWards. It presents evidence that the bias
may be due to the imputation procedures used before 1976. Then, it uses a
residual-based trimmed estimator to remove the bias and construct a more
consistent MMED series. The new series supports the conclusion that both
changes in selection and married female labor force participation affect the
MMED. The paper concludes that, while the MMED does not appear to have
i changed significantly, as of the late 19805, the composition of the MMED has
become more due to selection.

The third paper surveys investigations into the causality of the MMED.
Gray’s (1997) comparison of the returns to years of marriage with the NLS and

NLSY and Stratton’s (2002) estimation of the return to years of marriage and

cohabitation using the NFHS are reexamined with the assistance of a residual-
based trim and then compared with other longitudinal studies’ findings. Then, a
qualitative comparison is made of recent MMED studies’ findings of the
prevalent direction of causality for the MMED. There appears to be evidence
that being married had an effect on earnings before 1970 and 1970-1979.
However, more recent studies either support the selection hypothesis or fail to
find evidence that the household division of labor enhances the husband’s market
productivity. Finally, a meta-analysis of cross-sectional estimates of the MMED
across time and age groups is made. The meta-analysis finds a four-percentage
point decline in the MMED in recent years, after controlling for how the MMED

rises with age.

Copyright by.
DAVID L WETZELL
2002 A

To My Grand-parents, My Father and Mother and

My Three Sisters: Chris, Cathy and Cassandra.

ACKNOWLEDGEMENTS

To acknowledge and thank everyone that has made it possible for
me to complete my dissertation would take more space than the rest of the
dissertation. I owe much thanks to my major professor Dr. David Neumark.
Thank you for your time, for being a role model as to what it means to be a
professional and much constructive criticism. My dissertation is far better than it
would have been without your guidance. I must thank Dr Jeff Biddle for his time,
feedback and support and for, on some occasions, taking the time to boost my
spirits by treating me like a colleague and arguing with me. .I also must thank Dr
John Strauss for his support and useful, clarifying comments on my papers and for
a thoroughly enjoyable course on applied econometrics. I am thankful for Dr.
Jeffrey Wooldridge for joining my committee and for bringing his expertise in
econometrics to bear on my papers.

I am thankful for my friend, Dr. Warren Samuels, for his encouragement
and sound advice over these past five years. I admire and aspire afier your love of
knowledge. I owe much to the faculty of the Michigan State University
Economics Department. In particularly, I am indebted to: Drs. Jack Meyer, Steve
Matusz, Stephen Woodbury, Rowena Pecchenino, Charles Ballard and many
others. I am also thankful to Dr. Daniel Hamermesh for his suggestion to send
my first paper for publication to Economic Letters.

1 am thankful for the encouragement, advice and feedback from my

friendships with David Smith, Jess Reaser and Cheng-Peng Cheng who got their

vi

PhDs from MSU a year before and a year after my arrival. I am thankful for the
comradeship of my more contemporaneous PhD students: Daiji Kawaguchi, Scott
Adams, Ali Berker, Vinit Jagdish, Chien-Ho Wang, Mao-Sheng Chen, Linda
Bailey, Elda Pema, Paul Corrigan, Iva Petrova, Alina Luca, Jongbyung Jun and
many others. I am also thankful for the encouragement from so many friends
from all over that I met while living at Owen Hall and being a student at MSU. I
am thankfiil for Stacy Vatne, Oktay Unlu, Beyhan Asma, Emilio Ungerfeld and
Paola Pastore and many others with whom I can look forward to staying in touch
for the rest of my life.

I also must acknowledge my indebtedness to my friends and family who
helped to lay the foundation for who I am and have supported me during my
studies. I am thankful for all of my teachers that encouraged me to think outside
the box and ask insightful questions. I am thankful for the mentorship of what it
means to be both a scholar and a humanitarian that I received while I was in
college. I am thankfiil for the fellowship and acceptance of my home church. It
is only through the unconditional love I received while growing up that I was able
to persevere through personal adversities to be able to complete my dissertation as
I have. In the face of all these debts, I can only hope to be able to go out and do

likewise with whatever route along which my life takes me.

vii

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................................... ix
LIST OF FIGURES ....................................................................................................... x
Paper 1: On Some Unappreciated Implications of Becker's Time Allocation

Model of Labor Supply ................................................................................................. l
I. Introduction ................................................. 1
II. The Model ................................................................................................................ 4
III. A Generalized Proof of the Distinctive Features of the Becker Model ...................... 6
IV. An Investigation of the Properties of Labor Supply Curves with "Nice", or

Constant Elasticity of Substitution, Preferences under the Becker Model ....................... 8
V. An Investigation of the Comparative Statics for Labor Supply ................................ 10
VI. Relevance of the Model ......................................................................................... 11
VII. A Reinterpretation of Classical Models of Labor Supply ...................................... 12
VH1. Additional Predictions of the Model .................................................................... 13
D(. How Would One Test this Theory against the Standard Theory ............................. 14
X. Conclusion ............................................................................................................. 15
XI. Bibliography ......................................................................................................... 16
APPENDIX A ............................................................................................................. 17
APPENDIX B ............................................................................................................. 19
APPENDIX C ............................................................................................................. 22
APPENDIX D ............................................................................................................. 24

viii

Paper 2: On the Measurement and Explanation of Recent Changes In the Male

Marriage Earnings Differential .................................................................................... 30
I. Introduction ............................................................................................................. 30
H. Review and Replication of Korenman and Blackburn’s Findings ............................ 33
III. Explaining the Shift: The Misclassification Problem .............................................. 35
IV. An Empirical Examination of the Impact of Misclassification with
Inconsistent Information .............................................................................................. 37
- The difficulty in directly examining the Impact of Misclassification ........... 37
- Predicted Log-Earnings Levels by Marital Status ....................................... 38
- Predicted Skew of Earnings Distribution Residuals by Marital Status ......... 40
- Probability of Classification as Full-Time/Full-Year by Marital Status ....... 42
- A Simulation of the Impact of Different Imputation Procedures ................. 43
- A Reconciliation of the Different Tests for Misclassification ...................... 46
V. Calibrating the Percentages Misclassified and the EXtent of the Bias ...................... 47
- The Results of the Calibration .................................................................... 52
VI. An Alternative Robust Approach to estimating the MMED ................................... 53
VII. Econometric Analysis of Trimmed MMED Series ................................................ 58
- Comparison of Findings for the Controlled and the Raw MMED Series ..... 60
- An Investigation into the Nature of the Changes In Marital Selection ......... 61
VIII. Conclusion .......................................................................................................... 63
IX. Bibliography ......................................................................................................... 65
APPENDIX A: Description of Replication of Korenman and Blackburn’s MMED
Series .......................................................................................................................... 92
APPENDIX B: Description of Additional Changes made to form the Alternative
MMED Series ............................................................................................................. 94
APPENDIX C: Description of Why the 1975 Trimmed MMED is considered an
outlier .......................................................................................................................... 97
APPENDIX D: Comparison of Accuracy of Prediction between the Median and
Mean MMED 1967-1988 Time Series Regressions ................................................... 100
Paper 3: Has the Male Marriage Earnings Differential’s Causality Changed?
A Historical Over-View of the Literature ................................................................... 101
I. Introduction ........................................................................................................... 101
II. Reinvestigation into Gray (1997) .......................................................................... 103
III. Reinvestigation into Stratton (2002) .................................................................... 105
IV. A Comparison of the Findings of Longitudinal Studies ........................................ 107
V. Earliest Studies ..................................................................................................... 108
VI. Studies based on Data Collected during the Seventies .......................................... 110
VII. Studies based on Data Collected during the Eighties/Nineties ............................. 113
VIII. Summary of Meta-Analysis of Cross-Sectional MMEDs .................................. 117
IX. Conclusion .......................................................................................................... 1 18
X. Bibliography ......................................................................................................... 119

i.\'

LIST OF TABLES

Paper 2: ON THE MEASUREMENT AND EXPLANATION OF RECENT
CHANGES IN THE MALE MARRIAGE EARNINGS DIFFERENTIAL.
Table 1A: Descriptive Statistics for Replication of Korenman and

Blackbum.Years 1967-1996 ........................................................................................ 84
Table 1B: Summary of Comparison of Replication with Korenman and
Blackburn’s Reported Time Series Results .................................................................. 84

Table 1C: Results from the Regression of Korenman and Blackburn’s
Marriage Earnings Differential Series on the Replication Marriage Earnings

Differential Series ....................................................................................................... 84
Table 2A: Summary of Sample Statistics For Simulation of Early

Imputation Procedures using Data from 19888 March CPS ......................................... 85
Table ZB: Summary of Alternate Hot-Decking Procedure’s Impact on the

MMED using Data from 19888 March CPS ................................................................ 85
Table 3: Statistics Used for Calibration of Misclassification of Work-

History ........................................................................................................................ 86
Table 4: Summary of Alternative MMED Series Descriptive Statistics ............ 87
Table 5: Descriptive Regressions ..................................................................... 88
Table 6: Summary of Time Series Regressions of 2. 58 Cut- Off, Trimmed

MMEDs on Descriptive Statistics ................................................................................ 89
Table 7: Summary of Time Series Regressions of Trimmed Raw (Age

Controls Only) MMEDs on Descriptive Statistics ........................................................ 90
Table 8A: Summary of Importance of Earnings for Probability of Being

Married or Divorced/Separated For the Years 1967 and 1988 ...................................... 91
Table SB: A Table Summary of Changes In Means and Dispersion of

Probabilities of Being Married or Divorced/Separated for 1967 and 1988 .................... 91
Table D-l: Summary of Median Regression Assessments of Accuracy of

Predicted Trimmed 2.58 Controlled MMEDs for the years 1989-1994 ....................... 100

Paper 3: HAS THE MALE MARRIAGE EARNINGS DIFFERENTIAL’S
CAUSALITY CHANGED? A HISTORICAL OVERVIEW OF THE LITERATURE.

Table 1: Summary of Trimmed Versions of Gray (1997) ............................... 121
Table 2A: Comparison of Descriptive Statistics Stratton (2002) ..................... 122
Table ZB: Summary of Reexamination of Stratton (2002) .............................. 122
Table 3: Summary of the Impact of Cohabitation ........................................... 123
Table 4: Summary of Returns to Years Married from Longitudinal MMED
Studies With Controls for Years Married .................................................................... 124

Table 5: Summary of Earliest studies based on data collected before 1970 ..... 125
Table 6: Summary of MMED Studies based on Data Collected 1970-1980 126
Table 7: Summary of MMED Studies based on Data Collected 1980-1990 127
Table 8: Summary of MMED Studies based on Data Collected 1984-1998128
Table 9A: List of Values Used for Meta-Analysis of Cross-Sectional

MMED across Age Groups and Over Time ............................................................................ 130
Table 93: Summary of Meta-Analysis of Changes in Cross-Sectional
MMED ...................................................................................................................... 130

LIST OF FIGURES

Paper 1: ON SOME UNAPPRECIATED IMPLICATIONS OF BECKERS
TIME-ALLOCATION MODEL OF LABOR SUPPLY.

Figure 1: Possible Labor Supply Curve Shapes With Time Costs of
Consumption and Pecuniary Costs of Leisure ................................................................ 9

Paper 2: ON THE MEASUREMENT AND EXPLANATION OF RECENT

CHANGES IN THE MALE MARRIAGE EARNINGS DIFFERENTIAL.
Figure 1: Comparison of Smoothed and Non-Smoothed Original and

Replication of Korenman and Blackburn's Male Marriage Earnings Differential

Series ........................................................................................................................ 66
Figure 2: Alternative Series for White Male Marriage Earnings

Differential .................................................................................................................. 67
Figure 3: Trends in Education Coefficients Over the Years 1969-1981 ............ 68
Figure 4: Trend in White-Collar Coefficient over Time .................................... 69
Figure 5: Comparison of Predicted Mean Earnings in 1987 Dollars for

Full-Time/Full-Year Workers by Marital Status .......................................................... 70
Figure 6: Probability Density Functions for Normal and Mixed Normal

Distributions with parameters ...................................................................................... 71
Figure 7: Comparison of Average Skew of Residuals from Median

Regression by Marital Status ....................................................................................... 72
Figure 8: Comparison of Probability Employed Full-Time/Full-Year by

Marital Status for Employed Males ............................................................................. 73
Figure 9: Comparison of Proportions of Sample Trimmed because

Residual was too High or too Low by Marital Status ................................................... 74
Figure 10: Comparison of Trimmed with Non-Trimmed OLS Male

Marriage Earnings Differential Series ................................................... . ...................... 75
Figure 11: Comparison of Trimmed OLS Male Marriage Earnings

Differential Series ....................................................................................................... 76
Figure 12: Independent Regressors Used in the MMED Time Series ............. '...77
Figure 13: Comparison of Observed and Predicted Male Marriage

Earnings Differentials .................................................................................................. 78
Figure 14: Comparison of Observed and Predicted Male Marriage

Earnings Differentials (Age Only Controls) ................................................................. 79
Figure 15: Predicted Probabilities of Being Married by Age and Log-

Earnings Year 1967 ..................................................................................................... 80
Figure 16: Predicted Probabilities of Being Married by Age and Log-

Earnings Year 1988 ..................................................................................................... 81
Figure 17: Probability of Being Divorced/Separated Conditional On

Having Been Married Year 1967 ................................................................................. 82
Figure 18: Probability of Being Divorced/Separated Conditional On

Having Been Married Year 1988 ................................................................................. 83
Figure C-l: Comparison of Average Heteroskedastic Standard Deviations

by Marital Status ......................................................................................................... 98

xi

LIST OF FIGURES CONTINUED

Figure C-2: Trends in the Proportion of Observations by Marital Status
with Imputed Earnings Last Year ................................................................................ 99

Paper 3: HAS THE MALE MARRIAGE EARNINGS DIFFERENTIAL’S
CAUSALITY CHANGED? A HISTORICAL OVERVIEW OF THE
LITERATURE. ‘
Figure 1: Comparison of Predicted and Observed Trimmed MMED .............. 131
Figure 2: Comparison of the Observed MMED and DSED series For
Years of Survey 1991-96 ........................................................................................... 132

xii

PAPER 1
On Some Unappreciated Implications of Becker's Time Allocation Model of
Labor Supply
Introduction.

Economists have largely overlooked some of the implications of Gary
Becker’s generalization of labor supply theory. Becker's (1965) paper considers
time allocation across many goods and primarily analyzes the comparative statics
of changes in efficiency of work-place production and household consumption or
production. In his paper, Becker does suggest that an additional implication of his
theory would be that an increase in the wage could induce a negative substitution
effect. However, Atkinson and Stern (1979) show the impossibility of a negative
substitution effect. Following this proof, the consensus in economics, as
articulated in Mark Killingsworth (1983), has been that the time-allocation
model's inclusion of time costs of consumption and a pecuniary price of leisure is
useful as a household production model where the comparative statics of changes
in household production technology on market and non-market work can be
examined. However, the model was not perceived as adding anything
fundamentally new to our understanding of labor supply.

However, this does not take into consideration the possibility that Becker's
assumption that all final goods require inputs of time and intermediary inputs

purchased with money may permit one of the input constraints to dominate the

maximization problem. This can only take place if time and money (or
intermediary inputs) are not completely substitutable for each other in the
production of goods for final consumption. Otherwise, Killingsworth is accurate
in his assessment that the inclusion of time costs for consumption and pecuniary
prices to leisure does not affect the basic predictions for labor supply. Money and
time are completely substitutable for each other in production when, at any
feasible ratio of time and money used, it is possible to substitute more of one
input for the other, as is assumed in household production models with Cobb-
Douglas household production functions.

The assumption of complete substitutability of inputs in the household
production function may be a nontrivial assumption for labor supply, particularly
in situations of poverty. It assumes there are no limitations in how time and
money can be combined to produce utility. This assumption about technology is
not easily amenable to direct testing since we only observe a subset of possible
feasible inputs at any point in time and what is observed is subject to what is
rational. Conversely, excluding the theoretical possibilities of pure consumption
and leisure does not assist in ascertaining what is the case empirically, specially
since what is feasible is subject to change over time. However, the difficulty in
pinpointing what is possible at any point in time does not affect the qualitative
implications for labor supply of theoretical restrictions as to what is possible.

It should be acknowledged that the observation of individuals willing to
supply a significant positive number of hours of labor to the market at lower

wages is also consistent with the implications of fixed-costs of work models.

Fixed-costs of work are costs that must be born if and only if one decides to
supply a positive number of hours to the labor force. A good overview of fixed-
costs of work models is given in Killingsworth (1983) on pages 23-28. Both
models set out situations where cost-constraints make working lower levels of
hours infeasible, or undesirable. The major difference is that, while a fixed cost
of work model leaves the option to choose not to work1 as a theoretical
possibility, the time allocation model potentially removes it from the locus of
rational labor supply responses to wage offers.

The only other paper that appears to have dealt with the implications of
Gary Becker's time allocation model for labor supply is Stern (1986). In his
comprehensive review of properties of different functional forms for labor supply,
Stern graphically illustrates that, with a CBS (Constant Elasticity of Substitution)
utility function and a negative unearned income, leisure can "become a normal
good for individuals with high hours of work (pp.162-163)." Stern also proves for
LES (Linear Expenditure System) utility with positive time costs of consumption
that the hours worked will go to zero as the wage goes to infinity. There also may
be no positive wage where the hours worked is zero if the time to money
endowment ratio is too high, (pp.186-187). This is consistent with the results
found here. However, Stern does not explore this possibility any further. He does
not point out how this property coincides with his earlier finding in Atkinson et al
(1981) where a direct incorporation of Becker's theory led to the finding of a
similar nonlinearity in labor supply. Atkinson et a] (1981) find that, while the

estimated labor supply curve was largely negatively-sloped for British workers, it

 

lWork is defined, here, as all activities engaged in primarily for pecuniary gain.

3

becomes positively sloped for higher wages. Stern also does not prove his results
under a generalized set of assumptions about utility and the production process.
The Model

This paper distinguishes its model from existing versions of Becker's
theory of time allocation by expanding the set of sets of feasible time-money
ratios for the production of goods for final consumption to include any subset of
the positive real numbers. Attention is given to the cases where the extreme
values of the set of feasible input ratios are not positive infinity and zero since, in
these cases, any additional consumption will always require additional inputs of
both time and money. To simplify the presentation of the potential complexity
introduced by expanding the production functions considered and to emphasize
that this is a labor supply model, the household production (or individual time-
allocation) problem is rewritten as,

maximize U(L, C) subject to
tL(w) L+tc(w) C+H=l
pL(w) L+pc(w) C=w H+A
with the usual non-negativity constraints for L, C and H.

Here, an individual's time and income for a period are decomposed into
the amounts used for Leisure (L), Consumption (C) and Work (H). Rationality in
production makes the amount of time and money spent producing a unit of
Consumption and Leisure, or tc(w), tL(w), pc(w) and pL(w), functions of the wage

offer. The requirement of time and money inputs for all final goods guarantees

that the above time and money costs are positivez. The positive time and money
costs for both Consumption and Leisure permit one constraint to dominate if the
agent is unable to substitute between the inputs in the production of any good.
Hence, in the proofs below, the distinctive prediction that technology will
dominate preferences in determining the slope of labor supply curves can only be

made when the wage offer approaches zero or infinity.

 

2 It is shown under general assumptions in appendix A that when pure leisure and pure
consumption are excluded as possibilities for time allocation that time inputs and money inputs for
consumption and leisure will always be positive. Or, in other words, the limits as w-—>oo or as

w—)0 of tc(w), tL(w), pc(w) and pL(w)will be positive.

A Generalized Proof of the Distinctive Features of the Becker Model.
Backward Bend: A proof that labor supply curves will be negatively-sloped for
higher wage levels consists of making the simple observation that, as the wage
gets large, the budget constraint becomes no longer binding. The maximization
problem becomes subject only to the time constraint. Thus, if

limw_,,,tc (w), tL (w) > 0 then the hours of work supplied to the labor force will be

zero asymptotically. This guarantees that the labor supply curve will bend
backwards at some point if, at any wage level, it was upward sloping.

If limwg, tC (w) = O , as is the case when the inputs into the household
production are assumed to be completely substitutable, then, as in the standard
case, we can no longer sign the slope of the labor supply curve when the wage
offer gets large. It depends upon preferences.

Forward Bend: A generalized proof can also be made for when the labor supply
curve will be negatively-sloped as the wage gets small. It requires that U(L, C), is
concave with both L and C normal while U1, (0, C)=oo and Uc(L, 0): 00 so as to

ensure that the first order conditions will hold. To simplify the algebra, the above

average cost equations can be replaced with constants representing their limits:
limwo pL(w)= p2, limwotdw): t2, limwo pc(w)= p; , & limwo tc(w)= 1;.
As the wage rate approaches zero, either the budget or time constraint will

dominate the maximization problem. So utility is maximized with respect to
p; L + p; C=A or I; L +1; C+H=1. Here we assume that A>O. Since workers

are indifferent to hours worked, ceteris paribus, when the budget constraint

dominates the maximization problem the hours worked will become a slack
variable in the time constraint. This guarantees that t; L +t2C+H=1 as the wage

approaches zero.

If the reservation wage is equal to zero, as is the case when unearned
income is insufficient to consume the entirety of the time endowment in the most
time-intensive activity, ( p; >A), then it follows that a positive level of hours will
be supplied as the wage approaches zero. This indicates that the budget constraint
will dominate as the wage approaches zero. Hence, an increase in the wage, by
increasing income, will increase both Consumption and Leisure since they are

normal goods. However, since the time constraint is necessarily binding, it also

follows that lim 9!: <0. Otherwise, if the reservation wage, wR, is positive

then limwgwR H=0 and the labor supply curve must necessarily be upward sloping

as it approaches the reservation wage.
If A<0 then the proof is similar to the above proof that the labor supply

curve is negatively-sloped for higher wages.

An Investigation of the Properties of Labor Supply Curves with "Nice", or
Constant Elasticity of Substitution, Preferences under the Becker Model

It is well established that under homothetic preferences, labor supply
curves in the standard model can be monotonically upward-sloping or backward-
bending. The set of possible labor supply curve shapes, maintaining the
assumption of nice preferences, changes when all consumption requires positive
time and money costs. In this framework, the utility maximization problem

becomes...

8
Maximize [(fl - L8_1)€_1 + ((1 — fl) . C8-1)5_l ]£—l
S.t. L+tc C+H=1

pL L+ C: w H+A

H(,B.A. w, pL .tc )=

(l—flXW‘i' PL): +fl(PL "AXH‘W'ICY
(l-fl)(w+pL)‘(l+w-tc)+fl(w+ pL)(l+w-tc)‘

 

The parameters tc , pL represent the average time cost of consumption and
the average money cost, or pecuniary price, of leisure, respectively. In the
standard labor supply model, these parameters are set equal to zero.

The features that determine possible shapes when there are positive time
costs to all consumption are the degree of substitutability between Consumption
and Leisure, 3, and whether unearned income, A, is sufficient to provide for
consumption of leisure for the entirety of the time endowment, p1,. The impact of

the two factors on the possible shapes of the labor supply curves is examined

below. The thinner curves reflect the case when 8 =7, the thicker curves, 8 =5.
The smooth and discontinuous curves illustrate the respective cases where

A=.6>p1, and A=.2<pL. The other parameters are assigned the values ,6 =5,

pL=.3, Ic=..3

Figure 1
Possible Labor Supply Curve Shapes
With Time Costs of Consumption and Pecuniary Costs of Leisure

 

-0.2 0.2 0.4 0.6

 

 

This graphically demonstrates that, given CBS preferences and positive
time and money costs for all utility-producing activities, labor supply curves can
be backward-bending, monotonically downward-sloping, or both backward and
forward-bending. It is proved in appendix B that this exhausts the possibilities.
It should be noted that while it has been proven that labor supply curves will be
negatively-sloped for lower wages when unearned income is lower than the cost

of consuming Leisure for the entirety of their time endowment, this does not

imply its converse. This still depends upon the relative strengths of the
substitution and income effects’.
An Investigation of the Comparative Statics for Labor Supply

The economic significance of the predictions depend on both the
implications for economic activity of the existence of negatively-sloped labor
supply curves, and on the proportion of all individuals who are operating on a
negatively-sloped portion of their labor supply curve. This opens up the question
as to how the domain of wage offers corresponding to the upward-sloping portion
of the labor-supply curve is affected by changes in unearned income and other
parameters of the problem.

It is easier to look at how the exogenous parameters affect the bends in the
labor supply curve since, as shown in the last section, a CBS preferences and
constant time and money costs of consumption" limit the number of bends in
labor supply curve to at most two. It can be shown that an increase (decrease) in
unearned income will augment (diminish) the range of wages for which the labor
supply curve is upward sloping by both lowering (raising) the wage level at which
the labor supply curve bends forward and raising (lowering) the level at which it
bends backwards. It is also proven that a decrease (increase) in the pecuniary
price of leisure will have the exact same qualitative effect as an increase

(decrease) in unearned income on the bends in the labor supply curve.

 

3 However, appendix C proves that the labor supply curve will become positively

sloped for lower wages as unearned income rises.

‘ The constant costs of consumption simplification, relative to the more general framework
presented earlier, is necessary since the algebraic proofs given in appendix D are quite
complicated.

10

Additional effects proven are that if leisure and consumption are
substitutable that a decrease in the time cost of consumption, or a change in
preferences toward money-intensive consumption for individuals with a
preference for leisure, will act to lower the wage level at which the labor supply
curve bends forward. No additional discernible effects on the shape of the labor
supply curve are noticeable for these parameters.

Relevance of the Model

It may be argued that this model is not relevant to developed countries. It
may not be relevant to situations where the majority of the population has some
access to a safety net as a source of unearned income or relatively few worker's
potential income exceeds the amount needed to purchase the optimal bundle of
goods given their time endowment. In which case, the model's implications are
not different from standard theory. To say that an individual's labor supply curve
will bends backwards or forwards at some point does not imply that it will do so at
observed wage levels. Hence, the above theory's empirical relevance depends
upon the breadth and depth of potential resources available to workers; whether or
not workers are able to make viable exit threats.

Clearly, in developed countries today, workers are more likely to have
viable exit threats. However, in the past, there have been situations that may have
been better characterized by the above theory than by the standard theory. If
Economics aspires to explain economic behavior with generality then it should be

able to explain diverse forms of economic behavior that occur over time, without

ll

resorting to explanations involving differences in tastes. Becker's generalization
of labor supply appears to make this possible.
A Reinterpretation of Classical Models of Labor Supply

A way to verify whether the model helps to explain past behavior is
through the observations of past economists. This assumes that the informal
observations of economists back then were descriptively accurate of the exigent
labor market realities of their day. In England, both Classical and Mercantilist
Economists often described labor supply behavior as having a negatively
correlation between wages and hours of work. Mercantilist used this empirical
regularity to justify the policy of keeping wages low. For Classical Economists,
negatively-sloped labor supply curves may have underlay the Wage Fund model.
The Wage Fund model postulates that a set amount of money is allocated to
laborers at large and that individual wage levels were inversely proportional to the
number of workers. In other words, population was the operative factor in the
variation of aggregate labor supply and there was a very low level of dispersion in
the worker wage distribution.

These‘two stylized facts could be attributed to negatively-sloped labor
supply behavior since it could make a worker/family willing to work as many
hours as physically possible at their given wage offers. Hence, it would take a
reduction in population to restrict aggregate labor supply and increase wages and
an increase in population would cause a reduction in wages. Similarly, a potential

over-supply of labor relative to labor demand could reduce wage dispersion

12

through competition among workers, making the concept of a single “wage” for
labor used in Classical Economics empirically feasible.
Additional Predictions of the Model

However, as was perhaps misunderstood in the past, negatively-sloped
labor supply curves did not characterize a permanent feature of labor market
behavior. The time-allocation model implies that a change in labor supply
behavior over time need not be attributed to changes in tastes. Instead, it may be
that workers became able to "afford" a positive reservation wage. But, the model
also predicts that positively-sloped labor supply behavior is not a permanent trait
of workers. A significant shock to the value of workers’ unearned assets, not
unlike what occurred during the Great Depression, or a decline in the real
earnings of lower skilled workers may induce a reversion to negatively-sloped
labor supply behavior. Although, the institutionalization of governmental
transfers to workers strongly reduces the likelihood that a similar reversion to
negative labor-supply curve behavior will take place. The ways in which labor
supply behavior can change illustrates how the applicability of the model depends
on both the available technology for consumption and the distribution of wealth.

The model makes additional predictions. One prediction is that, even if the
majority of a population's labor-supply curves are locally, upward sloping, there
still may remain a portion of the population with negatively-sloped labor-supply
curve behavior. Another prediction is that5 access to government programs,

social networks and personal equity help to smooth labor market operations by

 

5 This prediction takes as given that everything takes both time and money (or access to
purchasable resources).

l3

ensuring that workers have a positive reservation wage. Finally, the model
predicts that a rise in workers’ wages and access to additional forms of wealth
over time should necessitate an evolution of labor market institutions. In the past,
reductions in competition between workers through labor market institutions, such
as workweek restrictions, minimum wages or unions, may have been socially
justifiable given the negatively-sloped labor-supply curve behavior of workers.
However, as more workers came to exercise a more viable exit threat by virtue of
their ability to afford to search for a better job or to choose not to work for a
period, the model predicts that the need for these institutions would decline.

How Would One Test this Theory against the Standard Theory?

The chief testable implication here for labor supply6 is whether an increase
in an individual's wage may move her/his labor supply behavior from being well
characterized by negatively-sloped to positively sloped labor supply curves.
Hence, an ideal test would measure how a substantial change in the return to work
affects the slope of an individual's labor supply curve in response to a change in
their wage. This could be estimated by measuring the Marginal Rate of
Substitution between Income and Leisure before and after an exogenous change
in tax policy or social program. An independent measurement of the MRS was
introduced byL. F. Dunn (1979), based on a comparison across individuals of
how much they would be willing to give up in terms of income and time for a

small benefit that they currently did not receive. With data of this sort, it would

 

‘ As remarked earlier, Becker's generalization contains the same predictions as the standard theory
when complete substitutability is possible.

be possible to observe whether the increase in wage affected a shift toward
positively sloped labor supply behavior.

Alternatively, if nonparametric analysis was employed to estimate labor
supply curves, then the finding of a forward bend, like that found in Atkinson et a1
(1981), Hurd (1976) and Kurz et al (1974), could be seen as support for Becker’s
generalization of labor supply. Unfortunately, as pointed out by Heckman
(1993), serious, non-classical measurement error in reported weeks and hours
worked bias the measurement of aggregate labor supply elasticities. If the
influence of measurement error was reduced, then one could conceivably test for
regularities in how labor supply elasticities may change with changing
circumstances. Assuming that intertemporal considerations do not weigh too
heavily on current labor supply, it would be expected that the elasticity of labor
supply would be pro-cyclical, owing to the instrumentally, exogenous variation in
unearned income.

Conclusion
This paper demonstrates that Becker’s generalization of the standard labor

supply modelggenuinely expanded the set of analytical possibilities for labor
supply behavior. It shows that if there are limitations to the extent to which time
and money can be substituted for each other in production of final consumption
goods then negatively-sloped labor supply behavior can be induced by the
diminution of ability to transfer between time and money inputs. This is shown to
be true regardless of the form of preferences. It demonstrates how the standard
theory depends critically upon the assumption that time and money are

completely substitutable for each other.

l5

Bibliography

1. Atkinson, A. B., and Stern, N. H. 1979. “A note on the allocation of time”,
Economic Letters, 3 pg. 119-123.

2. Atkinson, A. B., and Stern, N. H. 1981. “On labour supply and commodity
demands”, in Angus Deaton, ed., “Essays in the theory and measurement of
consumer behaviour in honour of Sir Richard Stone”. Cambridge: Cambridge
University Press, pg. 265-296.

3. Becker, Gary. 1965. “A Theory of the Allocation of Time.” Economic Journal
75 pg. 493-517.

4. Heckman, James J. 1993. “What Has Been Learned About Labor Supply in the
Past Twenty Years?” In “Lessons from Empirical Labor Economics: 1972-1992”,
American Economic Review, 83 (2) pg. 116-121.

5. Hurd, Michael. 1976. “The estimation of nonlinear labor supply factions with
taxes from a truncated sample”, Institute for Mathematical Studies in the Social
Sciences, Technical Report No. 217, Stanford University.

6. Killingsworth, Mark. 1983. “Labor Supply,” Cambridge University Press,
Cambridge.

7. Kurz, Mordechai; Robins, Philip; Spiegelman, Robert; West, Richard and
Halsey, Harlan. 1974. “A cross sectional estimation of labor supply for families in
Denver 1970”, in: Research Memorandum 24, Center for the Study of Welfare
Policy, Stanford Research Institute.

8. Stem, Nicholas. 1986. “On the specification of labour supply functions”, in
Richard Blundell, Ian Walker, eds. “Unemployment, Search and Labour Supply”,
Cambridge University Press, Cambridge, pg. 143-189.

9. Dunn, L. F. 1979. “Measurement of Internal Income-Leisure Tradeoffs.”
Quarterly Journal of Economics, August pg. 173-193.

16

Appendix A

The assumption that time cannot be completely substitutable for money and
money cannot be completely substitutable for time implies that there will
always be a positive money and time costs for all production for final
consumption.

The quantity of final output for Consumption or Leisure, C or L, is a function of

time and money inputs, TC ,MC , TL ,ML. The money-time ratios available for

d ' h g MC 5 d; ML 5 1 h d d
pI'O uctront en are _<_-—-"S an 5—5 . nt estan ar ,

Cobb-Douglass-style production functions, 5C ,5 L1 = 0 (as is the case with pure
’1
leisure) and 6C ,t,‘ L z 00 (as is the case with pure consumption). The more
2 2

general form of production functions considered here allows

4" ,6 ,5 ,6 tobe any positive real numberswhereé $5 and
C1 C2 1’1 1’2 C1 C2

1f," 11 5 6L2 . The case associated with leontief production technology is where

6C = 5C and 511 = :1. . Based on the assumption that C(Tc, MC), L(TL, ML)
1 2 2

are homothetic, we can rewrite the euler's conditions as...

_14tL(W)+I-m PL(W)=BL(W). C. tc(W) + C... Pch)=8c(W)
where 14, Lm, Ci, Cm are the partial derivatives of the leisure and consumption
production functions and tc(w), tL(w), pc(w) and pL(w) are average amounts of
time and money spent producing Consumption and Leisure and gL(w), gc(w) are
continuous, positive functions of the wage. If the production functions were
homogenous then gL(w), gc(w) would be positive constants. So long as a

household or individual has the ability to substitute further between money and

17

time in the production of final goods, the average inputs will adjust themselves for
. . M C .
a change in the wage. But if —-—'— = 5 and .5 < co , the productron
7 . C2 C2

function,(C in this case), will be locally characterized with partial derivatives,
Cm=0 and C.>0. By combining these partial derivatives with the above Euler

Conditions, it is trivial to show that the average time cost of consumption, tc(w),
M
will always be positive. Similarly, if TL = g [.1 and fi L > O, the production
L 1

function, (L in this case), will be locally characterized with partial derivatives,
LPG and L.=O. As before, there will always be a positive pecuniary cost of
leisure. This implies that there will remain positive pecuniary costs to leisure and
consumption, pL(w),pc(w) >0, as the wage approaches zero, assuming some
production is still possible or A20. It also implies that there will remain time

costs to any consumption, tc(w), tL(w)>0, as the wage approaches infinity.

18

Appendix B
Labor Supply Curves under Constant Elasticity of Substitution Preferences
with fixed time costs for Consumption and money costs for Leisure will have
at most 2 local optimas or bends.
To establish that the taxonomy of shapes for labor supply curves is exhaustively

examined in this paper, we look at how many bends can exist for a labor supply

curve. To study these bends, we solve for the equilibrium hours supplied...

(l'flXW'tPLY +fl(p1, -A)(1+W"c)‘
(1-fl)(W+pt)‘(1+W'lc)+fl(W+pr)(l+w-tc)"

 

(1) H(fltA,w:pL’tC):

By differentiating equation 1 with respect to wage and setting the slope equal to
zero and simplifying by removing terms such as the denominator of equation 1

and multiplying both sides by -1, it can be established that

1+w-t

 

fl ’ _ C c 1‘5 w+pL £_
l-fl(pL A)(w+pL) + fl ’C(l+w-IC)

(2) ' l—p -t 1+(p —A)t
(1_pL.1C)(g, w 1. (’+ 45 _ L C)=0

w+pL 1+w-IC w+pL l—pL-IC

is the algebraic expression for the existence of “bends” in the labor supply curve.

1+w-t

To simplify the above expression even firrther, we substitute PW into the

.. I
(3) 11'6fl(pL “/0218 +l—‘F'41C1FE +g(—S—-(A—pL).u)_

(a-1)(1—(A—pL)rC)=o
expression to get...

19

It is important to recognize in the above expression that 1/ p L > u > (C for

(rt—I )
all oo>w>0, and that QL= -——C—<0. Since the left hand side of equation three

allows us to detect whether the labor supply curve will have local minima or not.
Or, whether or not the labor supply curve will bend or change its direction for a
change in the wage offer. If the left-hand side of equation 3 is always negative
then the labor supply curve will be monotonically negatively sloped. The left-

hand side can be guaranteed to be negative, since u>0, if unearned income is

insufficient to cover the cost of consuming leisure all day long, or A — p L <0, and

consumption and leisure are not strong substitutes, or a — 1 <0. Alternatively, the
potential number of bends in the labor supply curve can be limited to one or two if
the second or third derivative of equation 1 is signable for all values of w. This
can also be proven with the first and second derivatives of the right hand side of
equation 3 since the terms removed were all positive and our interest is only in the

signs of the derivatives for the labor supply curves.

If A -— p 1. >0 then the first derivative of the expression on the left-hand

side of equation 3

a

_ l
1__.’B(pL—A)u£"l—l 'Bt -£_l—(—C—+A—

(4) 8( 7— C” "2

 

pL»

is always negative. This signifies that there can be at most one bend in the labor
supply curve if there is sufficient unearned income to consume leisure for the

entirety of the time endowment.

20

If A — pL <0 and >1, the case when <1 was handled earlier, then the

first derivative of equation 4,

_ I
(5) £((£-1)-1—:8F(pL —A)u£ ’ 2 +(£+ 01—74161‘5'2 4.2%)

is always positive. This implies a maximum of two bends in the labor supply
curve when there is not sufficient unearned income to consume leisure for the
entirety of the time endowment and consumption and leisure are substitutable.
This rules out the possibility of more than two bends existing in a labor
supply curve. The existence of positive time costs to all consumption guarantees
that a labor supply curve will be negatively-sloped as the wage offer gets large.
This, in conjunction with the maximum of two bends, ensures the basic shapes a

labor supply curve can take.

21

Appendix C
An Increase in Unearned Income will eventually make Labor Supply Curves
Positively-Sloped for Low Wages.

The main proof showed that if unearned income is insufficient to provide
for spending the entirety of the time endowment in consuming the most time-
intensive bundle of goods available that labor supply will be negatively sloped as
the wage approaches zero. The converse of this is not true. If consumption and
leisure are not substitutable, or -1<0, then the labor supply curve can still be
monotonically decreasing even when unearned income, A, is greater than the cost
of leisure, pL. However, it can still be shown that increasing unearned income
does eventually make the labor supply curve positively sloped for some lower
wage offers.

If we look at the numerator of the first derivative of labor the labor supply

equation,

(-fl2(pL —A)-(1+w-r(.)25 —(1—.6)2 4C -(w+pL)25 +fl(l-fl)-

(1) (w+pL)£(1+w-IC)£-(1—pLzC)-

 

(a w “PFC, A-a _‘+(P1.‘A)’c)
w+pL1+w-IC w+pL l-thC

then, since the denominator is always positive and independent of unearned
income, we can proof the above by showing that for when w->0 there exists an A
where the above will be positive, or there there exists an A where...

-162(pL -A)’(1_16)2’CpL28 +

(2) (A—Zp )t .>0
_. 8 _ . .fi- L C
13(1 fl)pL (1 pL 1C) (PL 1+ I‘PL"C

 

22

In the above, the second two terms that are negative do not include A. The

remaining terms are increasing linearly in A. Since the negative terms are finite,
then there will exist an A > P1. so that the labor supply curve will be positively

sloped for very low wages.

23

Appendix D
The Comparative Statics of how the Exogenous Parameters affect the Shape
of Labor Supply Curves.

Let W... be the wage at which the labor-supply curve bends backwards, or
shifts from positively sloped to negatively sloped as the wage increases, and Wf be
the wage where the curve bends forward, or similarly shifts from negatively
sloped to positively sloped.

Based on the previous proof, we know that both bends will exist when -1

and pL - A >0. Thus, we need to be able to differentiate between the two bends.

This can be done by examining the second order conditions or by totally
. 0 o z o a o
d1fferent1at1ng the above first order condmon w1th respect to wage.

Doing this gives us...

 

 

13 5—1 51 1‘5 - -151

(l) £‘(1_fl(A-pL)'" $+TICH 8 54—3-1"

1C 611

(—2-uaw+(A- pflg’w- —-))

_ 2
, or after substituting in for El: -£:’——tC—)—,
0w l—thC

2 (l—flwg Imam-t )2“..- --pL).6+(1 m-Ct u-l 8)
U ' I (1- mfla— PL C)

Since w, is a local maximum, the second derivative should be positive and
(A — pL )fl +(1- fl) - 1C 41—1—8 > 0. Whereas, since w is a local minimum,
(A - p L )6 +0 — ,3) - 1C 41-1—8 < 0. These inequalities permit us to distinguish

between the two bends in the following proofs of the comparative statics effects

of changes in exogenous parameters.

24

Here we totally differentiate the first-order condition with respect to A to find

8’“i; 19.”;
77A" 6A '
(1) TLBTuE—E-ing-(PL -z‘1)11E lg—’-%"j+87g1CN—E_ g’W—L—g-WZ —O

+8(u—C2311L6A+(A_ pL)S’:——’- 571'— 11)+(l—£)IC

Ol'

aw:fl(ll£fl+(1-fl)£'ll-(1-fl)(g_1)tC)/_al__l
(u-ufl +1, .6) 5((A- p1)" 1p+(1- 3) 1C 11 )

 

The numerator will be negative since the second term in the parenthesis, (l-B)

u, is greater than the third term (l-B)( -1) re and Slim. Then, since

u — ufl + 118/3 >0, we can sign the derivative by signing

(3) (A—pL)u-lfl+(l—fi)-IC .u‘z’g.

Since equation 3 will be positive for wb and negative for Wf by the second order

f
conditions, it follows that —Q >0 and <0.
6A 0A

Qualitatively, this implies that the length of the portion of the labor-supply
curve that is upward-sloping is positively related to the level of unearned income.
Even if to, p1, are set equal to zero this still holds true for the backward bend.

That is labor supply curves will still bend backwards at higher wage levels when
an individual's unearned income is increased. This indicates that the elasticity of

labor supply can vary with exogenous changes in wealth.

Now we totally differentiate the first-order condition with respect to p1, to find

 

9:1, ”I,
6"’L L
_.6 £__fl__ _ 618116111 1_—_,3_ —£-1_@_u__iw_
(1) Wu 81-33(‘01- A)" 5W5117+£ fl (CH aWapL -0
t _
a: 6W 81 61
+e(-1l§2-73-$a7L-+(A—pL)5—w’—ap:——u)+(1—e)zC
01’
(2) aw = —,6(u£,6+(l—fl)c.u-(l—fl)(c—1)t 11C)/5'—’

 

 

51% (u-u,6+u£fl)-£((A—pL)u-1,6+(1—fl)-1C-u 2"8)

The above expression is the opposite of the partial derivative with respect to
unearned income. This gives the implication that changes in the pecuniary price
of leisure has a similar, but opposite, effect to changes in unearned income.
Hence, anything that affects increases the price of leisure, or the minimum cost of
living, would have a similar impact for labor supply as a drop in unearned

income.

26

6w

 

Now we totally differentiate the first-order condition with respect to tc to find a: b ,
C
W
aif O
C
,6 8-1 011 aw 1‘fl -8 1‘16 ‘6—1 611 5W
— — A -— — — + t ——
(1) 5173001 1" 5w 3? 13 " 57‘ c" aw 61C _0
t _ _
_g(%%igV—+(A-pL)%§L-N ')+(1—e)<A—pL)
u C C
or

-3 ‘1 an
(2) aw="(1—.3)(" (l-fl)-fl'a-u +,B(g—1)(A_pL))/5;.
a’C (”"’/3+"gfl)°6‘((r4-pL)u—l,B-(l—)B)«IC-u"2"£)

If A — p L <0,_then the second term in the denominator is negative and the
numerator and the first term in the denominator only need to be signed. If

u — ufl + 115,6 >0 which is more likely to be the case for the forward bend then
the numerator can be signed since [3 u"> (l-B) u — g and the numerator would be

lessthan fl-u" -,B-e-u" +fl(£— l)(A — pL)<0 if >1.
Then, since g—L <0, we have four negatives which makes a positive.

Hence a decrease in the time cost of consumption, when consumption and leisure
are substitutable, will make the wage level at which labor supply becomes
positively sloped become lower.

The rest of the cases do not show any predictions that are independent of
tastes. There does no appear to be a clear impact on the point at which a labor

supply curve bends backwards by a change in the time cost of consumption.

27

Now we totally differentiate the first-order condition with respect to ,B to find

 

 

at 3‘:
6,6’ 513'

(1-13)2(PL A)ug ‘57(pL—A)ug 1%%+1—5%u 8+ '
(I) :0

51-361 u 81%Efi-E(§%%_WL_A)%QP

01'
2 2 2 2 a:

(2) QW—z 11 ((A-PL)" £,fl +(l-fl) 'tC)/€wl—

fl

-fl)/3<u—u/3—z:5fl)-e(<A—pL)2:‘+6/3-<1-m-rC>'

If we assume that u>l and B>l/2 and >1 this represents the forward bend
occurring for the lower range of wages among individuals with a preference for
leisure but a fair amount of substitutability between leisure and consumption.

Based on these assumptions we can show that the denominator is positive since
u - ufl — 115,6 <0. However, for the forward bend

(1- ,B)IC < 11£+1fl - (pL — A) and so it follows that the term in the
numerator,(A — pL )1125 -,B2 +(l — fl)2 4C is less than

_ 23. 2 __ 2_ 3+1 . _
(A PL)“ 13 +(1 3) IC11 fl (12L A) or

fl-(p. -A)u£+1((l-fl)-ug'lfl).
Given the assumptions made earlier, the above upper bound can be shown to be

negative.

28

Thus, the numerator will also be positive and for this particular case, the
wage for which the labor supply curve bends forward will decline with a shift in
preferences toward less time-intensive consumption. Qualitatively, this implies
that leisure-loving, low-wage individuals who behave consistently with locally
negatively-sloped labor supply curves may be induced to change their behavior if
their preferences are altered to favor more money-intensive consumption.

Otherwise, there does not appear to be any obvious impact of a change in

preferences on the shape of the labor supply curve.

29

PAPER 2
On the Measurement and Explanation of Recent Changes in the Male Marriage

Earnings Differential

I. Introduction

Korenman and Blackburn (1994) claim that the Male Marriage Earnings
Differential (NIB/115D)7 declined by ten-percentage points between the years 1967
and 19888. This goes against the Goldin ( 1990, p. 102)’s claim that the MIVIED
has remained "virtually stable" over time. However, inasmuch the causal
explanations for the MMED include increased productivity from being married,
selection into marriage based on earnings ability9, and employer discrimination,
one would expect changing patterns in the division of labor in the household and
marital selection to impact the MMED. The ten percentage point decline in the
MMED, according to Korenman and Blackburn, should allow for us to test
between the specialization and selection explanations for the existence of the
MMED. But their time series analysis is unfortunately flawed since there is a
significant discontinuity in their MMED series. One very likely explanation for
the discontinuity is that the Pre-l976 imputation (or "hot decking") procedures
bias the earlier estimates of the MMED upwards. This data problem leaves the

question of whether the MMED fell unanswered.

 

7 The Male Marriage Earnings Differential (MMED) is the adjusted average difference in earnings
between married and never-married males. Korenman and Neumark (1991) describe the MMED
as being in the 10-40 percent range and argrre that it accounts for about one-third of estimated
gender-based wage discrimination in the United States (e.g. Neurnark 1988).

Koremnan and Blackburn’s claim is based on their successive, cross sectional estimates of the
MMED for white males between 25-54 from the March Current Population Stuvey (CPS).
9 This also includes personal characteristics valued both in the labor and marriage market.

30

Fortunately, a flaw in the earlier imputation procedures is identifiable and
correctable. It causes a number of males with unusually low earnings levels to
appear among never married, full-time/full-year workers, thereby generating
outliers. To remove the outliers’ influence, the paper proposes an innovative form
of a trimmed mean regression designed especially for multivariate regressions.
The process of trimming the mean provides an alternative MMED series for the
year 1967-1996.

The trimmed MMED series permits a reexamination of Korenman and
Blackburn’s time series regression. One can tell whether changing patterns in
marital statusdemographics10 and married female labor force
participation(MFLFPR) are correlated with the MMED. The paper finds a
significant correlation between both marital selection and MFLFPR statistics and
the trimmed MMED for the years 1967-1988. Consistent with the specialization
hypothesis, there is a negative correlation between the married female labor force
participation rate (MFLFPR) and the MMED. However, contrary to the
expectations of Korenman and Blackburn (1994), a decline in the percentage of
males ever married in the sample raises the MMED. Similarly, the rise in the
percentage of divorced/separated males in the sample is correlated with an
increase in the MMED. The joint movement of the MFLFPR and the marriage
demographic statistics tend to cancel out each other’s influence on the MIVIED.

Thus, while the MMED may not be immutable to the changing division of labor

 

'0 Percent ever married and divorced/separated among the males included in the trimmed MMED
sample.

31

in the household“, the countervailing influence of changing patterns in marital

selection help to make the MIVIED appear “virtually stable.”

 

" The regression predicts that the MMED in 1988 and beyond is due mostly to selection.

32

II. Review and Replication of the Korenman and Blackburn Findings.

Korenman and Blackburn investigate the MMED using two data sources,
the March Current Population Surveys (CPS) and the 1970 and 1980 Censuses.
The ten-percentage point decline in the MMED is based on a comparison of the
cross-sectional MMED from the 1968 and 1989 March CPS data sets. The
samples used to construct the earnings differentials are all twenty-two March CPS
data sets collected from the years 1967-1988. The samples consist of white, full-
time/full-year workers between the ages 25 and 54. Korenman and Blackbum‘s
dependent variable is the log of earnings from last year divided by 2080. To
establish the decline over time, Korenman and Blackburn present a series of
figures with the smoothed estimates of the MMEDs and DSEDs12 for black and
white males”. The smoothed series in Figure 1 typifies the smoothed series
Korenman and Blackburn(1994) show. The smoothed series all show a
downward trend.

Figure 1 shows the closeness of the replication to the original MMED
series". Table 1 confirms the closeness of the fit. The reported mean and
standard deviation of the original series are .216 and .034. The corresponding
statistics for the replication are .213 and .032. At the bottom of Table l, a

regression of Korenman and Blackburn’s MMED series on the replication series

 

'2 DSED is Divorced/Separated Eamings Differential.
'3 Their series include both raw and controlled MMED and DSEDs. Raw earnings difl‘erential
include only age dummies along with marital status controls. They smooth with a running three-
year average.

See Appendix 1 for notes on sample construction of the replication series.

33

shows that the replication differentials accurately predict Korenman and
Blackburn’s differentials with a R2 very close to one.

Korenman and Blackburn try to construct consistent measure of the
MMED for each year of datals that would accurately reflect the variation over
time. But, since changes in marital selection and the married female labor force
participation occur gradually“, one would expect the same to be true for the
MMED series. Hence, a way to judge whether a series is consistent is by its
continuity. Aidiscontinuity in a coefficient series, or an outlier, could indicate
that some important differences in the data collection procedures still remain.

Figure 2 shows the importance in looking for discontinuities in any
coefficient series. The alternative smoothed seriesl7 assumes a discontinuity
between the 1974 and 1975 years of the survey”. The assumption of a
discontinuity appears accurate given the semi-smoothed and non-smoothed series’
agreement for these two years. The MMED declines by seven percentage points
between the years 1974 and 1975. The discontinuity in the series suggests that
some differences remain between the pre-1976 and the post-1976 March CPS data

sets”.

 

'5 To do this, Korenman and Blackburn restrict the sample for each year to males employed full-
tirne/full-year during the preceding year. This is necessary since, for the 1968-1975 March CPS
data sets, the hours and weeks worked last year are not recorded. Thus. the standard CPS wage
cannot used as a dependent variable.

'6 See figure 7 for a depiction of the changes in the MFLFPR and the percentages ever married and
divorced/separated in the sample. A significant exception to this is in the year 1981 during a
short, yet severe recession.

'7 See appendix 2 for details of 110w the altemative series is constnrcted.

" As reported in the 1975 and 1976 March CPS data sets.

'9 One way to check whether the discontirnrity is likely to be due to differences across the data sets
is by checking whether the discontinuity is robust across additional series of coefficients from the
same set of regressions. In figures 3-4, similar discontinuities between 1974 and 1975 appear to
be present in both the higher education dummy-variable coefficient series and the white-collar
occupation dummy-variable series. Curiously. the higher education coefficients seem to rise. This

34

III. Explaining the Shift: The Misclassification Problem

As it so happens, the March CPS imputation procedures underwent some
important changes between 1975 and 1976. According to Ed Welniak (1990),
before the 1976 March CPS, the CPS imputation procedures did not use
education, marital status, current labor force status of self and spouse, number of
children, region, and type of residence to impute missing earnings, work .
experience, and longest job information. Instead, the early CPS imputation
procedures look only at a person’s relationship to the head of the household,
gender, race and age. Also, early CPS imputation procedures impute only those
characteristics respondents do not report. A respondent who reports his earnings
from last year but not how many hours or weeks he worked last year would keep
his original earnings while being assigned a work history. To keep original
information allows for inconsistencies in a respondent’s work history. From the
1976 March CPS on, more attention was given to ensure consistency between
earnings and work history”.

If the changes in the imputation procedures were behind the discontinuity
in the MMED series, with the later imputation procedures being more accurate,
then the earlier imputation procedure would have biased the MMED upwards. An

upward bias is not consistent with the omission of marital status in earnings

 

seems to suggest that the outlier low observations biasing the MMED upwards is concentrated
among never married males with higher levels of education. These could be “over-educated”
males who are unable to find full-tinte/full-year employment.

2° Based on the description of the early imputation procedure by Spiers and Knott(1969), it seems
like Earnings-Work Consistency Edits were designed to ensure that non-workers with no income
were not classified as employed. Also a post eamings imputation consistency edit was only nm
for persons who had at least one type of eamings imputed. This means that part-time, or part-year
workers who reported all of their income but not their work-status could be assigned a full-time,
full-year work-status but keep their true work-status.

LOJ
'Jt

imputation in the early imputation procedures since the omission of marital status
fiom the imputation of earnings would bias the MMED downwards“. The
omission of marital status is compensated some by the inclusion of headship
status in the imputation procedures, since, for males, marital status and household
headship are strongly correlated”. Among the data collection changes, the
possibility of inconsistency of information between work-status and earnings
(from here on referred to as misclassification with inconsistent information) is
more likely to contribute to the upward bias in the MMED.

The impact of misclassification with inconsistent information on the
MMED can easily be modeled with a simple equation. To simplify the analysis,
marital status‘and employment status can be reduced to two groups each”. Let

M represent whether an individual is married. Let Ip represent those

misclassified as full-time with earnings that reflect their true work-status.
Similarly, the MMED can be assumed to not differ by employment status“. With
these assumptions, the log-earnings equation, conditional upon being classified as

a full-time worker, become,

 

2' This sort of bias reflects the findings of much recent work on imputation. such as Lillard et a1.
(1986) and Hirsch and Schumachcr (2000). These papers focus 011 110w earnings imputation can
bias the coefficients on characteristics that were excluded from the “Hot-Decking" procedures.

22 One can test the correlation with simple summaries for each year of the 1970-1975 March CPS
data sets of the percentages classified as head of household by marital status and whether or not
full-time/full-year employed. The summary shows that for never married males from three to five
percent of part-year or part-time in the sample are heads and eight to ten percent of full-time/full-
year workers are heads. For married males in the sample. ninety-seven percent of part-time or
part-year males are heads and ninety-nine percent of full-time/fiill-year males are heads. Thus,
regardless of work-status. marital status is highly correlated with headship of household.

2" The divorced/separated category is excluded here and part-time or part-year workers are
grouped as ”part-time” workers with full-time/full-year workers referred to as “full-time” workers.
These simplifications do not affect the analysis of the direction of the bias to the MMED.

2‘ This removes the necessity of looking at M - - I - .
. l p ’1

36

Yi :BOf +BlfMi +00Ip,i +81; (10 <0, 30f >0,Blf>0.

The source of the bias to the MMED here is an omitted variables problem.
Because one cannot distinguish whether an individual’s work-history is imputed
in the earlier March CPS data sets since record was not kept of this information, a

restriction of the sample to individuals classified as firll-time introduces into the
regression outliers. The bias to the estimate of MMED, flAU 25, from the omission

COV (Ip,M)

rs a0 Var (M7 . The bras rs posrtrve srnce 1nd1v1duals whose true status

 

opr

is part-time tend to have lower incomes, or an < 0, and the omitted variable, Ip ,
is negatively correlated with marital status, M26.

IV. An Empirical Examination of the Impact of Misclassification with
Inconsistent Information.

The difiiculty in directly examining the impact afmisclassification.

Ideally, one would want to examine those individuals whose work-status
had been imputed as full-time/full-year and verify the consistency of their
reported'eamings. However, this is made impossible by virtue of the fact that,
prior to the 1988 March CPS, records were not kept of whether or not hours or
weeks last year was reported. As such, one cannot attempt to solve the upward
bias by omitting all observations whose work-status was imputed. Starting with
the 1976 March CPS, earnings are imputed when work-status is not reported. The

Census bureau did not retain records of the original reported earnings until the

 

2’ Estimates of population parameters are distinguished from the population parameters with a
carrot hat in this paper.

26 The higher incidence of misclassified never married individuals with inconsistent information is
due to the significant negative correlation between marital status and an individual’s likelihood to
be part-time/part-year. As shown in table 3, the odds-ratio between married and never married
male workers being classified as full-time/full-year is five to four for the years 1976-1979.

37

1988 March CPS. However, inasmuch as there may be changes over time in
patterns ofnon-reporting between 1974 and 1987 and it is difficult to get records
of reported incomes of non-reporters of work-status, it is difficult to replicate the
impact of the earlier imputation procedure. Because of this, one must consider
the circumstantial evidence for misclassification with inconsistent information.
Predicted Log-Earnings Levels by Mari tal Status

There are other implications of the misclassification of work-history
besides imparting an upward bias to the MMED. These implications are
potentially verifiable empirically. The predicted earnings for both married and

never married workers classified as full-time/full-year27 should be lower than their

A A

true values or; [30f < 30f , 30f + [3 . However, the bras to

<5 +3

1f 0f 1f

never-married workers’ earnings should be more negative, or

for “Bar (Bar +Blf “Bar +511?)-

However, complications do exist in verifying whether earnings levels are
depressed in a given set of years. A marital status group’s earnings change from
year to year along with other individual characteristics that help to determine
earnings levels. Changes in personal characteristics can be controlled for, but one
cannot say with certainty whether variation in an unstable mean is natural or
unnatural. The extent of the bias must be sizeable relative to the normal changes
in the means. Predicting annual log-earnings levels with the mean values of

ersonal characteristics for a articular ear28 controls for ear-to- ear variation
Y Y

 

27 The predicted eamings for never married and married males. 111 this simplified example, are
respectively the intercept and the intercept plus the MMED.
2' Here the year of survey 1975 is used.

38

in personal characteristics. Figure 5 shows the predicted mean log-eamings levels
for married and never married individuals for the years 1969-1978. A comparison
between 1974 and 1975 shows how the predicted log-earnings for never married
males rose from 2.30 to 2.32, and for married males, fell from 2.62 to 2.59. One
can also compare the predicted means for 1969 and 1970.29 Here, the predicted
mean for never-married males fell from 2.36 to 2.32 while for married males it is
constant at 2.36.

To measure the significance of these changes, the predicted mean log-
earnings are first differenced for both series for the years 1969-1978. The median
statistics for the change in predicted log-earnings for never married and married

males are .OO6(.010) and .007(.0164), respectively”. Based on these statistics,
the two and four percentage point declines in the predicted log- earnings for never
married males appear to differ significantly from the normal variation in the
means. However, the changes for married males are not even close to being

significantly negative. From this, the upward bias to the MMED appears to be

 

29 The significant difference between the MMED in 1969 and surrounding years. as shown in the
first column of Table 2-A. suggests that there may be significantly lower levels of
misclassification with inconsistent information in this year. This is confinned by the absence of a
significant difference from between the trirttrtted MMED for 1969 and the surrounding years,
shown in figure 10. It is also shown by the less negative skew of the residual distribution for this
year relative to the surrounding years. as shown in figure 7. The U S Census Bureau reports that,
“The presence of the Census outreach programs have a definite positive impact on the response
rates to CPS and the March supplement. One sunnises that this is because people think that they
are answering the decennial census when it is the CPS instead.” Table 2-C shows that the Basic
and March supplement non-response rates were significantly lower around the time of the
decennial censuses. The improvement in the response rate to both Basic CPS questions and
March Supplements ltas a strong impact on the March CPS since the March Supplement is only
collected from households interviewed with the basic survey. Hence. one can expect the data sets
from the March-CPS decennial surveys to have a higher overall response rate and to contain more
accurate information than otherwise would ltave been imputed. ,

3° These are estimated using a median regression that includes only a constant.

39

due to a disproportionate reduction in the mean log-earnings of never married
males.
Predicted Skew of Earnings Distribution Residuals by Marital Status

However, the misclassification of work-status with inconsistent
information should affect more than the means of the married and never-married
earnings distributions. An outlier’s impact on a distribution is picked up better by
the skew statistic. The skew is a statistic31 commonly used by engineers and
statisticians to help identify the presence of outliers. A skew of zero occurs when
the distribution is symmetric. A negative skew occurs when a distribution
contains a large number of unusually low observations. Averaging over the cube
of the t-statistic makes the skew statistics more sensitive to outliers. The
sensitivity to outliers makes skew statistics more useful than the predicted means
in identifying the influence of misclassification in a distribution. The bias to the

skew statistic should be more dramatic than the bias to the predicted means”.

 

/\
. . . ’7 x.- 1- - . . . ,
3' The skew stattsttc for a sample rs defined as _Z(—17\LL )3 . n . A drstrrbutton s skew

1:1 .
St

sad—fl): 1.

O’
32 A simple example illustrates the skew’s appropriateness for analyzing the impact of
ntisclassification with inconsistent information. Assume the true distribution of log-eamings
conditional on employment and marital status is nonttal. Then. when full-time status is wrongly
imputed, the log-eanrings distribution conditional on being classified as full-time/full-year would
become a mixed normal distribution. The qualitative implications of misclassification on the
conditional, on ntarital status. means and skews of a distribution are robust to what was the initial,
true distribution. The assumption of nonnality is made here for expositional purposes. Figure 6
depicts the distributional consequences of mixing two norntal distributions. The more part-time
workers misclassified as full-time. the more negative. or less symmetric the distribution’s skew
becomes. ~

40

The skew statistic for the residuals of a median regression has the most
potential for reflecting the influence of outliers”. The skew of the residual
distribution can be estimated with the average value of the cube of residual test-
statistic”. The changes in the skew of the married and never-married
distributions between 1967 and 1985 are shown in Figure 7. Consistent with the
misclassification story, the skew for never married males is extremely more
negative prior to 1975 than after 1975. There is no readily apparent discontinuity
in the skew for married males. One discrepancy with expectations is that the
skew for never-married males in 1975 is also unusually negative. However, in
that the MMED for 1975 is comparable to the following years, it is likely that
something else in 1975 is affecting the skew35.

A way to statistically verify that there is a discontinuity in the skew series
is by first differencing both the married and never married series”. The median
statistics for the changes in the skew series are -.24 (.26) and .28 (.81) for married
and never married, respectively as measured by a median regression. The
changes in skew between 1974 and 1976 are -.70 and 4.74 for the married and
never married series. A test-statistic for whether the first difference for never-
married males is significant is (4.74-.28)/.81=5.5. The same statistic for married

males is (-.70-.24)/.26= -1.76. As such, while the reduction in the negative skew

 

’3 A median regression minimizes the sum of the absolute value of the difference between the
observations of the dependent variable and its values as predicted by the independent variables.
Wltile the mean regression is more efficient so long as the data is well behaved. the median
regression will be more robust to the presence of “outliers”. Outliers, here, are taken to be
observations whose values differ from expected values severely because of measurement error.
3‘Dividing the residual by a robust measure of its standard error forms the residual test-statistic.
3’ Additional evidence on the source of this discrepancy and why the trimmed MMED for 1975 is
considered an outlier is given in appendix 3.

36 Here, the years 1969 and 1975 are omitted.

41

for never married is certainly significant, the change in the skew for married
males is in the wrong direction. The skew series is consistent with some never
married full-time/full-year workers with unusually low earnings being behind the
lower mean predicted earnings levels for never married males before 1975”.
Probability of Classification as F 1111- Time/F ull-Year by Marital Status

A direct check for the impact of imputation procedures on work-status
misclassification is to compare the predicted probability of being classified full-
time/full-year’by marital status across time. One can predict the probabilities of
being classified full-time/full-year by marital status for each year from 1969-1978
with a linear probability model and a constant set of means of observable
characteristics”. One would expect to find a discontinuity in the probability
series betweep the years 1974 and 1975. Figure 8 confirms the existence of the
expected discontinuity. The predicted probability of a never married male worker
being classified full-time/full-year drops by 5.5 percentage points. The predicted
probability of a married male worker being classified full-time/firll-year drops by
2.9 percentage points. When the predicted probability of being classified fitll-
time is first differenced, the median statistics for the first differences are
.001(.018) and -.002(.0116) for the never married and married series. The test-
statistics for the decline in the probability of being classified full-time/full-year

between 1974 and 1975 are then -5.5/1.8=-3.l and -2.7/1.16=-2.3. By

conventional standards, the first differences for both married and never married

 

37 A series of predicted mean log-eamings has qualitatively similar implications.
3‘ The same set of year of survey 1975 means used to make the predictions about the mean log-
earnings.

42

males are statistically significant. However, never married workers appear to be
more likely to be misclassified by the earlier imputation procedures.
A Simulation of the Impact of Different Imputation Procedures.

Another simple way to check whether the different imputation procedures
would bias the MMED upwards is with a simulation. Using the 1988B March
CPS, ten percent39 of observed non full-time/full-year male workers can be
selected at random as not reporting their true work-status“. Then, the missing
work-status can be imputed with different hot-decking procedures. First, earnings
are not replaced in a simplified version of the earlier imputation procedure“.
Second, earnings are replaced with the same smaller set of characteristics used for
the imputation procedures. Third, both work-status and earnings are replaced

with a larger set of characteristics. The second set of characteristics used in the

 

’9 The ten percent of part-time or pan-year workers misclassified is based roughly on the findings
of the first attempt at a calibration as presented later.

’0 The ten percent is defined over workers who would be in the sample if they were employed fttll-
time/full-year. The subsample is selected using the sample command from STATA and the seed
1776.

"' Instead of imputing whether someone was full-time or part-time and full-year or part-year
separately, four work-status categories were formed and jointly imputed. In the earlier hot-decking
procedures, most of the categories used for hotdecking of work-status such as color, sex and class
of worker are no. longer relevant because of the restrictions made to the sample. The remaining
characteristics, according to Spiers and Knott(l969). are headship status, amount of earnings and
age. For the hot-decking simulation. three categories are formed for ages 25-34, 35-44, 45-54.
Spiers and Knott(1969) do not report the eantings levels used to form the earnings categories.
Because of this. some assumptions are made here. The cut-off values for eantings differ across
headship-status. Since there are far more heads of household in the sample. it is assumed that
more categories were used to impute their eantings. However. only the lowest eantings categories
are considered here for the imputation of work-status since the observations with inconsistent
information appear to have unusually low earnings as the calibration shows later. The cut-off
value for non-household heads is the median value for all non-head workers. The cut-off value for
household heads is the 12.5 percentile value for all head workers. All observations assigned as not
reporting work-status are classified as falling in the lower earnings category. Another set of
imputations was done where the median value was used for heads and the qualitative impact on
the MMEDs was not very large. The number of heads of households misclassified as full-
time/full-year is higher and the upward bias to the MMED from misclassification is reduced some.

43

imputation procedures is the same group of independent variables used to
generate the MMED”.

It is important to allow for the possibility that the decision to not report
work-status is endogenous. Hence, earnings of non-work-status reporting males
may be systematically different from most part-time or part-year workers. This is
important when simulating the impact of the early imputation procedures since
the reported eamings’ level affects the magnitude of the bias to the MMED.

Since the reported earnings were unavailable, an alternative approach is used to
examine this possibility. In the simulation, all non-reporters are assigned the
same earnings level according to whether they are a head or non-head. Two sets
of earnings are assigned for the same simulation of the early imputation
procedure. The initial value assigned is the median earnings, by headship status,
for part-time or part-year workers"3 . This represents the case where non-reporters’
earnings do not systematically differ from part-time or part-year workers. The
second set of earnings assigned to non-reporters is lower and allows for the
possibility that non-reporters’ earnings differ from the average part-time/part-year
worker“.

The results of the simulation are summarized in Tables 2A and 2B.
Overall, the results of the simulation confirm the inherent difficulty of direct
observation of whether misclassification caused an upward bias to the MMED.

The first two rows of Table 2A show that the early imputation procedure raises

 

‘2 The same seed, 1000, is used in all three imputation procedures. .
‘3 The assignment of this value represents the case where non-reporters’ eantings do not
systematically differ from part-time or part-year workers.

44

the proportion of the sample full-time/full-year by 2.6 percentage points for never
married males, 1.7 percentage points for Divorced/Separated and .7 percentage
points for the Currently Married. Similarly, the proportions of full-time/full-year
males misclassified are 3.5 and .8 respectively for never married and married
males. As shown earlier, it is the combination of the difference in the incidence
of misclassification by marital status and inconsistent information that biases the
MMED upwards as shown in columns 2, 3 and 4 of row 3 of Table 2B.

However, the extent of the bias is dependent on the earnings levels of non-
reporters and the percent of non-reporters in the sample. Column 3 shows that
when the average earnings levels for non-reporters are the same as the median
value for partytime/part-year workers that the misclassification biases the MMED
upwards by only one percentage point. This bias is considerably lower than the
observed seven-percentage point drop in the MMED series, even with a sizeable
fraction of non-reporters in the sample. Hence, the misclassification with
inconsistent information hypothesis may only explain the bias to the MMED if
non-reporters’ earnings were unusually lower than the typical part-time or part-
year worker’s earnings. Alternatively, when non-reporter’s earnings are assumed
to be substantially lower there is an upward bias of three and a half percentage

0 - S
pornts, as shown 1n column 44‘.

 

“ The rule used here is derived from the later calibration. The mean earnings for full-time/full-
year workers, disaggregated by headship status. are scaled downwards by exp(-2).

‘5 Further comparison with earlier findings is made by looking at how different imputation
procedures impact the skew of the residual distribution. Rows 4, 5 and 6 show the different skews
by marital status before and after each imputation procedure. The comparison between the skews
in column 3 and 4 is especially interesting since in column 3 the skews do not differ substantially
from the non-imputed sample. while in column 4 the skews are considerably larger across all three
marital status groups. As shown by figure 7. there is no evidence that the skew for married males
is biased downwards in the earlier years. This could be because some peculiarity of the early

45

The MMEDs in the fifih and sixth columns of Table ZB show that the
MMED falls some, but does not change significantly when earnings are imputed
along with work-status. This is true regardless of whether one controls for
headship and age or all of the characteristics used in the MMED regression.

A Reconciliation of the Different Tests for Misclassification.

The different tests for misclassification with inconsistent information pose
a slight puzzle. While the earlier imputation procedure seems to be associated
with a higher probability of both married and never-married males being
classified firll-time/full-year, there is no evidence in the series of residual skews
and predicted means for significant misclassification with inconsistent
information of married males during the earlier years. A possible reconciliation of
this puzzle is that work-status mis-classification with inconsistent information is
less likely to occur for married than never-married males. Since there are more
male heads of the household than non-heads, the number of earnings categories
used for the early imputation procedures may differ by headship status. If
additional earnings categories used for heads of households resulted in fewer non-
reporters with very, unusually low inconsistent information then this would help
to reconcile the evidence from the tests for misclassification with inconsistent

information.

 

imputation procedures (such as a larger number of earnings categories being used for heads of
households) may have prevented misclassification of work-status for lteads of households.

46

V. Calibrating the Percentages Misclassified and the Extent of the Bias

Reasonable levels of misclassification should be able to explain the
entirety of the upward bias to the MMED. A concrete sense of what levels of
misclassification with inconsistent information would explain the bias is possible
with a calibration of the equation(s)

110,1- =(1’pmc,i)'“T,i +pmc,i '“mc,i In this equatron, the observed

. . . . 45 .
overall mean, no i , for marrred and never marrred groups, 1ndexed by 1=m, rt 15
I

the weighted average between the “true” overall mean", “T i , and the mean
I

value ofobservations misclassified with inconsistent information, p A

are ,i '
calibration of these equations determines the predicted true MMED,

”Tan — ”T,nm and the extent of the upward bias,

. “O,m - ”Omm) ' (“Tm ' “Tmm )'
However, to predict the overall means requires a way to predict the

percentage of observations misclassified with inconsistent information, p m C ,i ,

and the value of 11 To better determine both of these values, one must

mc,i'

narrow down the portion of the sample likely to contain the misclassified

 

‘6 A consistent, though complicated. notation is used throughout this section. The Greek
symbol, 1.1 , is used .to represent means. The letter p is used to represent proportions. The

subscript O consistently refers to observed values. The absence of an O in the subscript for a
mean or proportion implies the “true” value of what the mean or proportion would be without the
misclassification problem. The subscript Tr stands for the sub-sample of observations that would
belong in the lower portion of a trim. The subscript mc stands for the misclassified observations.
The subscripts FT, PY represents observations whose work-status is classified as full-time/full-
year and part-time or part-year.

47

observations with inconsistent information. Observations identified as belonging
in the lower portion of a residual-based trim"8 are judged as likely to include the
entirety of the misclassified observations.

What the relegation of all of the outliers to a sub-sample would do is relate

the observed means for the sub-sample observations, “Tro i , as weighted
. I

averages of the mean values of misclassified observations and what true mean

value of the sub-sample would be in the absence of misclassification, or

49

”Troy =(1-ai)"uTr,i ”’1' 4’ch
To complete the calibration, one must predict the values of

and r1 - for both married and never married groups.

—a-- mc,.t

pmc:,i I pTrO,i
Since there are two equations with six unknowns, a solution will only require four
additional assumptions. Two different approaches will be used here to calibrate
the bias to the MMED.

The first two assumptions are predictions about the “true” means of the

sub samples, or “Tr i . To predict these values, the log-eamings of observations
I

for the years 1970-74 and 1976-1978 are pooled together into two groups. Then,

the differences in log-earnings stemming from differences in ages between the

 

‘7 Or, the mean in the absence of the misclassification of work-status problem.

’3 After estimating a median regression 011 the entire sample. one squares the residuals and uses
them as a dependent variable itt another median regression to estimate the hetero-skedastic
variance of all the observations. Observations whose residuals are more than 2.58 standard
deviations below zero are likely candidates for misclassification. This is done for the years of
survey 1970-1974 and 1976-1978

‘9 “1' here is the proportion in the sub-sample that are misclassified with inconsistent information.

48

two periods are removed”. There are two groups for both married and never
married full-time/full-year workers; one for before and one for after the change in
the imputation procedures. Out of each group, four statistics are observed“: the

mean log-eamings for all observations in the marital status group, no i t 52; the
I I

mean log-earnings for the lower-trimmed sub-sample, ”Tim 1' t ; the percentage
I I

of the overall sample of full-time/full-year workers in the lower-trimmed sub-

sample, pTrO i t; and the proportion of workers in the sample classified as full-
time/fitll-year, p FTO,i ,t' A prediction for the value of ”Tr ,i , 1 is 'uTrO,1',2 ,

the observed mean for the trimmed sample during the later period. This assumes

_ 53
that “TrO,i , 2 — “T131 , 1 '

It is inappropriate to assume that the proportions in the trimmed sub-
sample, in the absence of the misclassification problem, would be the same across

the two periods, or pTr,i , l = pTrO,i I 2. Figure 9 shows that the percentage

in the lower trimmed sub-sample rises over time. An alternative assumption is
that the proportion of observations in the lower trim would be equal across marital

status in the absence of misclassification, or that

p p (l-am)pTrO,m :(l-anm)pTrO,nm'

Tr,m _ Tr,mn’

 

5° The log-earnings for the later group are regressed on a ftrll set of age dummies. Then, the mean
proportions for each age group in the years 1970-1974 is used to predict what the log-earnings for
the later period 1976-1978 would have been 111 the absence of age differences.

5' Although, sampling weights are used for comparison of the regressions across time, sampling
weights are not used for the calibration.

’2 The subscript i denotes marital statrrs (111 or run) and the subscript t denotes period 1 or 2. The
absence of a time subscript either denotes period 1 or that the time subscript is irrelevant.

’3 Since there is no longer a misclassification problem in the years after 1975, one can estimate the
“true” mean log-earnings for the earlier sub-sample with the later mean log-earnings value.

49

For the final assumption, two approaches are taken here. The first
approach is to assume that the proportions of part-time or part-year males

misclassified as full-time/full-year, p PYm C i , are equal across marital status”.
I

For this assumption some additional notation is needed. Let the percentage of
married or never married males misclassified as full-time be

res ectivel . One can decom ose the ro ortions of
pmc’ml pmc’nma p y p p p

workers classrfied as full-time w1th the equation pFTO,i = pFT,i + pmc,i .
This allows us to define the proportion of part-year or part-time workers

. . p ' . .
m15classrfied, pPYmc as equal to mC%-PFT i). The assumptton then 15
I

that,

Pmc ,m' : Pmc,nm
( ’PFTO,m’me,m) (l—PFTOmm—me/nm

Then, by substttuttng 1n 0’. - pTrO,i for p m c,i , one gets the system of four
equations,
(1)0m'llmc,m '1” (1 “ant)UTr,m :pTrO,m

(2) anm 'Umcmm + (1 ’ arm?) “Trmm : “TrOmm

 

5‘ This assumes that greater numbers of never-married males are misclassified because a larger
percentage of never married than married males are part-year or part-time. There is no reason to
believe a differential propensity to be ruisclassified exists across marital status.

3) (l—am)pTrO,m _(1_anm)pTrO,nm

P
TrO,m _
(4) “m

(1 - PFTO,m _ ampTrO,m)

anm pTrO ,nm
(PP F TO ,nm TanmpTrO ,nm)

With the solutions to the above equations”, one can solve for the true

overall mean log-earnings for each group, “T i , the proportion of full-time

workers misclassified, p and the proportion of the part-year or part-time

mc,i ’

sample misclassified, p P Ym C .5 6

The second approach to completing the calibration is to assume that no
married males were misimputed with inconsistent information. This assumption

is supported strongly by the evidence from the predicted means and skew series.

 

“mc . = ((l-pFTO,m)pTrO,nm’(1-pFTO,nm)pTrO,m) “Tr,i +
’1 (l-pFTO,i) (pTrO,nm-pTr0,m)
Prro ,1 (pFTO ,m ‘Prro ,nm) “no ,1
(l-pFTO,i) (pTrOmm'pTrOnn)

55

a _ (l-pFTO ,i) (pTr0,nm'pTrO ,m)
1 (Prro,m “PFr0,nm)Prro,i

. where i=nm. 111.
56 - - -

To do tlus requires the formula “0,1 - pmc’i -pmc’i + (1 - Pmc,i )“T,i'
One can then manipulate the decomposition formula to solve for the true overall mean
”"251 =(“0,1 - mrnc,i "pmc,i ) / (1 - pmc,i )'

This gives the solutions to the three variables listed above as...

' ' ' ' = — . B nthis
Thts assumption 1mplres that, pmc,nm pTrO,nm pTrO,m asedo

alternative assumption, another prediction for the bias to the MMED can be
found.
The Results of the Calibration

Table 3 summarizes the statistics and predictions described above for both
approaches at calibration. Since the observed means are 2.638 and 2.329, the
observed raw MMED for the years of survey 1970-74 is .309. The observed raw
MMED for the years of survey 1976-78 is .180. The MMED appears to fall by
12.9 percentage points. However, when the percentage of part-time or part-year
workers misclassified with inconsistent information is assumed to be equal across
marital status groups then the true MMED is predicted to be .262 with a 4.7
percentage point bias to the MMED. This calibration also predicts that two and
four percent of the married and never-married full-time/full-year worker samples
are misclassified. However, since the percentage of observations in the lower
trim for married males is lower in 1970-1974 than 1976-1978, it is not likely that

two percent of male full-time/full-year workers are misclassified with inconsistent

 

(l'pFTO,i) (pI‘rO,nm'pTrO,m)

 

 

 

 

pmc,i - (pFTOIm-pFTOmm) '
piI'rO, nm - pTrO,m

pPYmc =( ) r r;

pFTO,m pFTO,nm pTr0,nm p Tr0,m

("0,1 -pTrO,i ' pTrO,i) (prrom - pFTOmm)
"T i 2r ) (1 ) ( )+
I pI-"'.I‘0,m pFTO,nm pFTO, .i pTr0,nm pTr0,m
. 1- - 1 -
”Tr, .1” pFTO,nm)pTrO,m ( pFTO,m)pTrO,nm)

- .. 1- ..

(pFTO,m pFTOmrn) ( pFTO, i) (pTrO,nm pTrO,m)

information. Thus, the likelihood of misclassification with inconsistent
information is not equal across marital status.

When the entirety ofthe misclassification problem is assumed to be
concentrated among never married males, the predicted bias to the raw MMED is
(.309 - .247) = .062. Almost half of the 12.9 percentage point decline in the raw
MMED between these two periods is due to misclassification”. This calibration
estimates that only 2.29 percent of never married workers are misclassified as
full-time/full-year with inconsistent information. The rate of misclassification of
part-time or part-year workers is then only 6.84 percent. These estimates appear
reasonable given that to report one piece of information and not report another
piece of information seems likely to be a rare, but important, event. The
calibration also shows that while there is a real decline in the MMED between the
two periods, it is not from a decrease in the earnings of married males. Instead,
the earnings of never married males employed full-time/full-year rise between the
two periods.

VI. An Alternative Robust Approach to estimating the MMED

The previous section shows that the existence of low outliers among
never-married males could bias the MMED upwards for the years prior to 1975.
These observations cannot be directly removed since the CPS does not keep track

of whose work-status was imputed during this time. Hence, to investigate

 

’7 When the predicted true value of the trimmed sub-sample for never married males is adjusted
downwards some to allow for the fact that the mean log-eantings rose some between the two
periods, the bias to the MMED falls by .001 or .002 points. However. if most. but not all of the
biased observations. are captured itt the trim then the estimate of the bias here will be biased
downward. This is unlikely to be too severe as the comparison of the descriptive regressions for
the 1.96 him and 2.58 trirtt 111 Table 5 shows that precious little is gained in reduction of the bias
due to misclassiftcation by tightening the trirtt.

'Ja
w

whether the MMED changes over the years 1967-1996”, one needs an alternative
estimate of the MMED that is robust to the bias caused by outlier observations. A
simple approach to remove the influence of unusually low log-earnings values is
with a residual-based, trimrned-OLS regression.

The idea for a residual-based, trimmed-OLS regression is very simple.
Ordinarily trimmed estimators exclude a certain percentage of the extreme values
of the dependent variable that are judged as likely to be due to mis-measurement.
In a multiple regression framework, exclusions based on extreme values of the
dependent variable are difficult to justify since what would constitute an extreme
value varies across individuals. Even if a worker’s reported log-eamings, or log-
wage, were unusually low or high for their characteristics, it may still be within
some broad range of acceptable log-earnings. Thus, a trim based on the values of
the dependent variable may not remove all outliers.

Thus, it is necessary to base a trim on residuals, not values of the
dependent variables. As shown by Bollinger and Chandra (2001), a trim based on
arbitrary cutoff values of the dependent variable will likely bias the estimators.
Instead, which observations are trimmed should be chosen based on the quantiles
or standard deviations of a residual distribution. However, if there are outliers in
the data then precautions need to be used measure that the outliers do not
influence the grim. First, one should use a median regression to generate the
residuals. This is because a median regression is more robust to the presence of
outliers and its residuals are more likely to reflect the extent the outlier differs

from the norm. Second, one should allow for the possibility of heteroskedasticity

 

’8 The alternative specification detailed in appendix 2 is used here for the trimmed means.

.1

U1

when estimating the standard errors or quantile values for the residual
distribution. This is because what is an unusually high or low residual may vary
with observable characteristics. Without controls for heteroskedasticity, an
unusual proportion of individuals with a higher variance in earnings59 will be
excluded from the sample. This is particularly relevant for the estimation of the
MMED since there is heteroskedasticity in earnings across married and never
married males. Third, if the trim is based on the standard deviations, then the
estimates of the heteroskedastic standard deviations need to be made from a
median regression with the log of the square of the residuals as the dependent
variable“. The standard deviations of the residual distribution are then based on
a transformation“ of the predictions made from the median regression. The
residual trim based on standard deviations excludes an observation from the
ordinary least squares-regression if the observation’s residual is more than x
standard deviations away from 0. A trim based on quantiles requires the
estimation of two quantile regressions with the residuals from the median
regression as dependent variables“. To trim x percent of the sample, the first
quantile regression is estimated at the 100-x/2 level and the second quantile
regression is estimated at the x/2 level. Observations are trimmed if their residual

is either less than or greater than the lower or greater quantile. However, a trim

 

’9 For example, when a heteroskedastic variance equation was regressed without controls for
marital status, the trinuned MMED values dropped by fifiy percent.

6° For the heteroskedastic variance regression. the same specification as the final regression is
used. The log of the square of the residuals is taken to ensure that the dependent variable is not
winsorized at zero.

6' It is acknowledged here that the exponent of one half of the expected value of the log of a
residual squared is not a consistent estimator of the standard deviation. However, it should not be
that far off and is suitable for the purpose of trimming.

OJ.
Ur

based on quantiles does not remove as much of the discontinuity in the MMED.
This could be because the inclusion of additional observations as fiill-time/full-
year workers with low earnings levels affects the measurement of the quantiles.
Because of this, a trim based on standard deviations, rather than quantiles, is used
here.

In figure 10, a comparison is made between the untrimmed MMED series
and a trimmed MMED series where the trim excludes from the sample all
observations 2.58 standard deviations away from zero“. Because of selection
into marital status, married and never married males’ residual distributions are
likely to be asymmetric. As such, one can expect the trimmed OLS estimates of
the MMEDs to legitimately differ some from the untrimmed MMED estimates“.
However, the trimmed MMEDs will be more robust to the bias considered earlier.
As long as the outlier observations are more than 2.58 standard deviations from

their predicted medians, they will no longer influence the MMED.

 

‘2 With, of course. the same full set of regressors used in the quantile regression as would be used
in the estimation of the robust standard deviations.

‘3 A trimmed series at 1.96 standard deviations is also examined. The 2.58 trim and the 1.96 trim
consistently removes approximately ten and twenty percent of the sample, respectively. A
comparison of the Post-76 Intercept irt the second and sixth columns of Table 5 shows that the
1.96 cutoff trim does not significantly reduce the bias. Also. Table 4 shows that the year-to-year
variation in the series with a 1.96 cut-off is greater. rtot smaller. than the other trimmed series.
This appears to be counter-intuitive. lt tums out that the nature of trim makes the tighter trim less
reliable as is shown later. Bollinger and Chandra (2001) quote Stephen Stigler as having
concluded from his studies of the benefits of trimming 111 the natural sciences that the ten-
percentage point trimmed mean is the most reliable estimator. As such. the cutoff value of 2.58

a pears to be reliable.

A trimmed mean only shares the same asymptotic mean with the regular mean when the error
distribution is symmetric. If the distribution of ability were symmetric but there is cutoff point for
whether an individual becomes married then the distribution for manied males would ltave a
positive skew and tlte distribution for never-married males would ltave negative skew. This
would make the trimmed MMED estimate “biased.” However, if the nature of the difference
between the trinuned and non-trimmed MMED is stable. then the trimmed series should still allow
for a valid examination of the changes in the MMED over time.

56

Table 5 summarizes a descriptive econometric comparison of the
untrimmed MMED series and the trimmed MMED series. The untrimmed
MMED regression’s Post-1975 intercept shift shows a significant seven-
percentage point decline. The trimmed MMED regression’s equivalent statistic
shows a three-percentage point decline. The trim takes off an average of 4.2
percentage points from the pre-1975 MMEDs. Figure 10 confirms a reduction in
the discontinuity in the series“. Also, the MMED for 1969 is no longer unusually
lower than its surrounding years in the trimmed MMED series. But, when the
Post-1975 intercept is removed from the regression, the fit does fall and, as shown
in columns four and five ofTable 5, shifts in intercept in 1975 and 1989 still
explain a good portion of the MMED series variation over the years 1967-
199666.67.

Figure 11 shows a “raw” version of the trimmed MMED that includes
only age controls along with the alternative MMED. The comparison between the
two series is done as a test for the robustness. The two series appear to mimic
each other pretty strongly. The Raw MMED series varies more and is on average

lower than the Controlled MMED series.

 

‘5 For tlte calculation of the smoothed series. the 1975 trimmed marriage earnings differential is
not used. These observations were shown to be outliers in Table 5. Smoothed backward
extrapolations are made based upon the contiguous years.

‘6 One possible reason for the decline from 1967-1974 to 1975-1988 is that the later hot-decking
procedures routinely impute the eantings of never-married males with fewer personal
characteristics. As Lillard et 31. point out smaller groups. like never-married males. are more
difficult to find a match based 011 all of the criteria used for imputation. As such, the quality of the
match is not as good. Since Never Married Males are more likely to have their earnings from last
year imputed, they are more likely to be assigned the higher eantings of a married male, or the
higher eantings associated with some orher characteristics correlated with marital status. An
artificial increase in the mean eantings of never-married males would bias the MMED downward.
‘7 1989 is when the imputation procedures changed for the second time. This could have lead to a
reduction in a downward bias due to a disproportionate number of never married males earnings

VII. Econometric Analysis of Trimmed MMED Series

The same strategy as Korenman and Blackburn (1994) can be used to test
whether the trimmed MMED series’ variation over the years 1967-88 is
explainable by the changes in selection and specialization“, with the necessary
caveats about the difficulty of identifying causality from a time series regression
and an acknowledgement that the independent regressors’ may be somewhat
endogenous. Hence, the influence of changes in specialization can be identified
by the Married Female Labor Force Participation statistics for females age 25-34
from all races (MFLFPR)69. The influence of changes in marital selection can be
identified with the percentage of males ever married or currently
divorced/separated in the sample”. A potential change in the relationship
between the MMED and the MFLFPR and Marital Status Selection statistics in
1981 is controlled for with a spline-fit". Then, any remaining systematic

differences in the MMED between the 1967-1974 and 1975-88 periods can be

 

being imputed with a smaller set of characteristics. This bias is controlled for in the regression
analysis with intercept shifts between the periods.

‘3 The regression MMED values are weighted ltere by the inverse of their standard errors squared.
‘9 The MFLFPR statistics are froru the Labor Force Statistics Derived from the CPS, 1948-1987
(BLS Bulletin 2307). The statistics for the remaining years were not made public and are from the
Bureau of Labor Statistics.

7° Korenman and Blackbum appear to have used the proportion of never ntarried males classified
as Full-Year. Full-Time Workers irt their samples to identify the impact of selection. This is not a
good measure for the same reasons that led to the bias in the marriage earnings differentials.

The percentage of males itt the marital status groups in the sample reflects the changing
composition of full-time/full-year workers 111 the sample and the population. If an increase in the
MMED is consistently due to a reduced percentage of married ntales with lower-earnings in the
sample and these individuals are not getting married then the coefficient of the percentage ever
married in the time series regression should be negative. Similarly, if the distribution of married
males declines in its means because several higher ability males are consistently selecting out of
marriage the coefficient on the percentage divorced/separated would be negative. By controlling
for both the percentage ever married and divorced/separated. one allows for the decision to not
marry or to select out of or back into marriage to have different influences on the MMED.

7' As noted by Korenman and Blackbum (1994). there is widely believed to be a strong change in
marital patterns in the US in 1981. The change may ltave been due to a change permitting “no-

controlled for'with an additional shift parameter”. Figure 12 shows the changes
in the independent regressors over the time period. Table 6 shows the results of
the regressions”.

After finding the best fit for the mean regressions, a median regression is
estimated. Out of sample predictions are made for both the mean and median
regressions. The median regression is preferred based on its superior out of
sample predictions as shown in table D-l in appendix D. Figure 13 shows that the
median time-series regression predicts the variation in the trimmed MMED fairly
well for the years 1967-1994. The regression result provides evidence that
changes in selection and specialization exert countervailing influences on the
observed MMED for this period. An increase in the proportion of younger
married females working outside the home is negatively correlated with the
observed MMED. Likewise, a decrease in the percentage of ever-married males
and an increase in the percentage of currently divorced/separated males in the
sample are correlated with an increase in the MMED. From the regression
results, the larger magnitude of the change in the MFLFPR appears to be
responsible for the earlier decline in the trimmed MMED. Overall, the MMED
does not change that much in level“. However, the appearance of stability in the

MMED over time does not imply the absence of a change in the composition of

 

fault” divorces. No-fault divorce laws make it is easier to get a divorce when one of the parties in
a marriage objects to the divorce.

7’ The inclusion of this control does not affect the qualitative implications of the regression
analysis. ,

73 The time series regression with the trimmed MMED estimates as a dependent variable is
weighted by the inverse of the square of the standard errors of the MMED coefficients.

7‘ This is especially the case after controlling for remaining differences between 1967-1974 and
1975-1988 as shown in the fourth and fifth colunm of Table 3. Over thirty percent of the variation
in the thirty years can be controlled for by intercept changes between the three periods.

U1
\0

the MMED. The extent to which there is a change can be checked by a
comparison between the years 1967 and 1988. The MFLFPR nearly doubled,
rising by 68.6-35=33.6 percentage points between the two years. Since the
coefficient on the MFLFPR is -.45, the regression predicts that the MMED would
have fallen by fifteen percentage points between the two years. It would have
gone fi'om twenty-four percentage points in 1967 to nine percentage points in
1988, ceteris paribus. Since the trimmed MMED in 1988 is measured at 18.3
with an upward correction of 2.8 percentage points”, it appears that an additional
twelve percentage points of the MMED in 1988 is due to changes in marital
selection.
Comparison of Findings for the C ontro/led and the Raw [VIA/{ED Series

The direction of the influence on the MMED from changes in the
MFLFPR and marital status selection statistics appears to be robust for the Raw
MMED regressions as shown in table 7. However, while the spline-fit
dramatically improved the fit for the Controlled MMED-m, the spline-fit is less
important for the Raw MMED. But, as shown in figure 14, the basic predictions
still hold. The predicted MMED, when the MFLFPR is extrapolated beyond
1988, is too low and the predictions made with a fixed MFLFPR fit with the
observed MMEDs better. Also, when the MFLFPR is held fixed at its value in
1988, the predicted MMEDs for the earliest years in the sample are far lower than

the observed MMEDs. The time series regression’s prediction that the causality

 

7’ The correction upwards is based on there being a negative downward bias to the MMED
estimated after 1974. This bias is picked up by an intercept shift in the time series regression.
75In 1981, a change in the percentage of males divorced/separated becomes associated with an
even stronger change in the Controlled MMED.

60

of the MMED has changed is observed for the raw MMED, as well as the
controlled MMED.
An Investigation into the Nature of the Changes In Marital Selection

Given that the predictions for the impact of changes in the selection into
and out of marriage on the MMED are indeterminate, it would be enlightening to
check whether or not changes in the distributions of earnings ability or age of
marriage contributed to the observed changes in the percent ever married or
divorced/separated. To do this, a comparison is made for the years 1967 and 1988
of the probabilities of being married conditional on not currently being
divorced/separated or the probabilities of being currently divorced/separated
conditional on having been married. Figures 15-18 and Table 8 show the results
of estimated probits with log-eamings and its square and cube and age dummy
variables as the independent variables for each year”.

Figures 15-16 show the‘predicted probabilities of being married for 1967
and 1988. Immediately apparent is that the probability of marriage for younger
males is significantly lower in 1988. For the older age ranges, though, the
probabilities of being married are comparable across the two years, as shown in
Table 8’s summary of the predicted probabilities of being married by age group.
Table 8 reports the mean predicted probability of being married and the standard
deviation conditional on age. The variation in the predicted probabilities
conditional on age reflects the importance of differences in earnings ability. This

is because only age and earnings are included as controls in the probits. Table 8

 

61

shows that the variance in the probability of being married across the age groups
has not changed significantly between the two years. This indicates that the
primary reason for the decline in the percentage of males ever married in the
sample is because of the postponement of marriage. Since earnings rise with age,
an increase in the post-ponement of marriage would increase the positive
correlation between marital status and earnings. Hence, the postponement of
marriage could explain why the decline in the percentage of ever-married males in
the sample appears to be correlated with an increase in the MMED.

Figures 17-18 show the predicted probabilities of being divorced/separated
for 1967 and 1988. In both years, it appears that the probability of being currently
divorced/separated initially rises with age and then falls back to its original level.
The overall probability of currently being divorced/separated has risen across all
age levels, but more so for the midrange of ages. Table 8 shows that the amount
of variation in the predicted probabilities of being currently divorced/separated
conditional on age has grown considerably. Hence, an increase in the variation in
earnings ability has contributed strongly to the probability of being currently
divorced/separated. Thus, endogenous selection out of marriage appears to be at
least in part responsible for the positive correlation between the growing

percentage of currently divorced/separated workers in the sample and the MMED.

 

77 The samples for the probits were based on the relevant subset of the samples used for the
estimation of the 2.58 Cutoff, Trimmed MMED.

62

VIII. Conclusion

It appears that the MMED did not decline by ten-percentage points. A
Replication ofKorenman and Blackburn’s MMED series from 1967 to 1988
demonstrates the existence and significance of a non-trivial data-problem in the
1968-1975 March CPS data sets. Once the nature of the data problem is
identified as owing to a concentration of low outliers among never married males,
one can construct a consistent MMED series by removing the influence of the
outliers. To do this, the paper proposes and executes a residual-based trim. The
trimming technique improves the estimation of the MMED by removing the
noisiest portion of the sample.

Recent papers on “hot-decking,” such as Lillard et al. (1986), criticize the
way the CPS imputation procedures beginning with the 1976 March CPS data sets
replace all of the original valid work-history information. The main problem with
the imputation procedures were their failure to keep record of the original
reported values of earnings, work-status last year and information about the most
recent job. This paper demonstrates that, while pertinent original information
should never be discarded, it is possible that an inconsistent official work-history
may also be a significant source of bias.

By identifying the likely source of the bias in the original MMED series
and constructing an alternative MMED estimator, the original objective for
constructing a series of coefficients— to test the relative importance of the

selection and specialization hypotheses for the changes in the MMED— becomes

63

possible. The regressions from the years 1967—1988 shows that both variations in
the percentage of males ever married and the younger married female labor force
participation rate appear to influence the MMED series-’8. A dramatic increase in
the proportion of younger married females in the labor force is correlated with a
decline in the MMED. However, the decline of the observed MMED associated
with the increasing MFLFPR is checked by changes in the composition of the
samples by marital status. The decision of younger males to post-pone marriage
and the selection of predominantly lower ability males out of marriage raise the
observed MMED. The regression results imply that the MMED has come to
signify more the impact of marital selection and less the increased earnings

associated with being married.

 

7‘ This is true for both controlled and raw MMED series.

64

Bibliography

Blackburn, McKinley and Korenman, Sanders. 1994. “The Declining MMED.”
Journal of Population Economics 7(3): 249-70.

Bollinger, Christopher and Chandra, Amitabh. 2001. “Iatrogenic Specification
Error: Cleaning Data Can Exacerbate Measurement Bias.” First Draft, July 9,
2001 as presented at the 2001 Joint Statistical Meetings.

Comwell, Christopher and Rupert, Peter. 1997. “Unobservable Individual
Efi‘ects, Marriage and the Earnings of Young Men.” Economic Inquiry 35(2),
285-294.

Gray, Jeffrey S. 1997. “The Fall in Men’s Return to Marriage: Declining
Productivity or Effects of Changing Selection?” Journal of Human Resources
32(3): 481-504.

Goldin, Claudia. 1990. “Understanding the Gender Gap, An Economic History of
American Women,” New York, Oxford University Press.

Hirsch, Barry T. and Schumacher, Edward J. 2000. “Earnings Imputation and
Bias in Wage Gap Estimates” Unpublished, February.

Korenman, Sanders and Neumark. David. 1991. “Does Marriage Really Make
Men More Productive?” Journal of Human Resources, 26(2), 282-307.

Lillard, Lee; Smith, James P. and Welch, Finis. 1986. “What Does One Really
Know About Wages? The Importance of Nonreporting and Census Imputation.”
Journal of Political Economy 94(3): 489-506.

Nakosteen, R. A. and M. A. Zimmer. 1987. “Marital Status and Earnings of
Young Men: A Model with Endogenous Selection.” Journal of Human Resources,
22(2), 248-68.

Spiers, Emmett F. and Knott, Joseph J. 1969. “Computer Methods to Process
Missing Income and Work Experience Information.” ASA Proceedings of Social
Statistics Section, 289-297.

Welniak, Ed. 1990. “Effects of the March Current Population Survey’s New

Processing System on Estimates of Income and Poverty”, unpublished paper from
the 1990 ASA convention.

65

Figure 1
Comparison of Smoothed and Non-Smoothed
Original and Replication of Korenman and Blackburn's
Male Marriage Earnings Differential Series
——9— Korenman and Blackburn's MMED—a— Replication of Original MMED

30*

 

 

 

 

I 1 fl r l r f I I l
67 69 71 73 75 77 79 81 83 85 87
Year of Survey

66

Figure 2*
Alternative Series for White Male Marriage Earnings Differential
0 Alternative MMED series Alternative MMED series, Smoot

 

 

 

 

O O
30~ \
\ o
(I)
E O
E, o o
g
o
(I)
3’ 25a
s o O 0
iii JJ\\ Ga
0
.g \O\\ o 0% \Q/
(U \. /
2 O
2 \/ o
g 20 a
O
I I l l I l l I l l l l l l l
67 69 71 73 75 77 79 81 83 85 87 89 91 93 95
Year of Survey

 

' A discontinuity between 1974 and 1975 is assumed for the smoothed differential by making
1974 and 1975 effectively endpoints. The three-year moving averages here and in the rest of the
paper are weighted according to their standard errors. A linear time trend is assumed for the
estimates and the errors in measurement are assumed to be independent. Based on these
assumptions, for a series of coefficients X, Y and Z that has standard errors x, y and z, the
smoothed estimate of Y is ((x"2+z"2) Y+2*y"2*(X+Z))/(x"2+z"2+4*y"2); the smoothed estimate
of X, a left endpoint, is ((4‘y"2+z"2) X+2 x"2 Y-x"2 Z)/(x"2+z"2+4‘y"2); the smoothed estimate
of Z, a right endpoint, is ((4*y"2+x"2) 2+2 z"2 Y-z"2 X)/(x"2+z"2+4"y"2). Standard Errors or
smoothed estimates are calculated by assuming the independence of the consecutive year’s
standard errors. These equations are all calculated by picking the best linear unbiased estimator
based on the assumptions listed above.

67

Figure 3
Trends in Education Coefficients Over the Years 1969-1981

 

 

 

 

 

 

 

+ Years of Education 12 & 16
o—--Years of Education 9-11 & 13—15 & 17-18
75 -
2 7o — /W
:2 65 — )1" o
5 °
g 50 - W/
.1 0
g) 50 T w +
g 45 " +
18 40 1 o o
g" 35 ‘ 9_ 0 \o___/ O o
5 30—1 0”? 0 0 + + + +
g 25 ‘ ._ - + + M
'8 20 — o o
g _j/°———o-——/
if] 15 T w it)” 0 0
1O - °
5 _
T l l l l l l
69 71 73 75 77 79 81
Year of Survey

68

White Collar Earnings Differentials

 

Figure 4
Trend in White-Collar Coefficient over Time

 

 

18 —
O o
—1 fi\-\ //
16 , \w/ 0
0/,
14 T O
o
O
12 O /—\/
,/
10 — O
o
I I I I I I f
69 71 73 75 77 79 81
Year of Survey

69

Figure 5
Comparison of Predicted Mean Earnings in 1987 Dollars for F ull-Time/F ull-Year
Workers by Marital Status
—e— Mean Log ‘Wage‘. Never-Married—a— Mean Log 'Wage'-.25. Married

2.4 "

N N
w o:
a: on
g 1
\\
\\‘ t
f/

B\.
/.

Average Log-Wage
/
/

i3
/
\
f
/

l
x.

N
(A)
l

 

 

 

l
70 72 74 76 78
Year of Survey

70

Figure 6
Probability Density Functions for Normal and Mixed Normal Distributions with
parameters

{Mean 1, Variance 1, Mean 2, Variation 2, Proportion of Distribution 2}
{SI 1’ 2! 2' O}
0.4

0.3
0.2

0.1

2 4 6 8 10

{5, 1, 2, 2, 0.25 }

0.3 :-
0.25
0.2
0.15

0.1

 

 

2 4 6 8 10

{5, 1, 2, 2, 0.5}

0.2 ;
0.15 '
0.1 .

0.05 ’

 

 

10

71

 

Figure 7
Comparison of Average Skew of Residuals from Median Regression by Marital
Status

Never-Married Skew. Smoothed
Married Earnings Skew, Smoothed

o Never-Married Earnings Skew
D Married Earnings Skew

 

 

 

; 0“
o
6‘;
c W
.9 D
‘5
.o
'5
.2 _
o '5 ,
In //
g) 0
m o .
11.1 o /
”5 o
2 -10-
3
(n
8
2 O
‘63
3
.0
a?
-15

 

 

 

I I I l I I I I I I
67 69 71 73 75 77 79 81 83 85

Year of Survey

72

Figure 8

Comparison of Probability Employed Full-Time/Full-Year by Marital Status for

Earnings Last Year

Employed Males

—e—— Prop. Full-Time Never-Married —8— Proportion Full-Time Married-.1

 

 

 

.8 ‘
EL
.75 4 cu
SCI /B/B\
\ 13’ \\E]
.65 ‘ \\‘M/\\
\‘k
.6 a \
.55 ‘
I l l T I I I l l l
59 7O 71 72 73 74 75 76 77 78

Year of Survey

73

 

Percentage of Sample Trimmed 2.58

.1 - a/X
//
.08 a \ N"
b,

'06 _ W
. / k
\k/
.04 — /\
E j
1'
.02 -

Figure 9
Comparison of Proportions of Sample Trimmed
because Residual was too High or too Low by Marital Status.

——8— Never-Married, Lower Trim ——a— Never-Married. Upper Trim
—9— Currently Married, Lower Trim——-—- Currently Married, Upper Trim

    

 

 

 

T E j I 7 l I I I I I T I I I
67 69 71 73 75 77 79 81 83 85 87 89 91 93 95
Year of Survey

74

Male Marriage Earnings Differentials

30“

25—

20"

 

15*

Figure 10
Comparison of Trimmed with Non-Trimmed OLS
Male Marriage Earnings Differential Series

0 Alternative MMED series
0 Trimmed MMED series 2.58

 

 

o O
\\ 01/,
/o

O o

C] O
\, 0’
D E] \\ o/j 11: \o/ Cl
\\ //—/ h\ O\\, O
\
131 El \\ Q‘\

are? ‘0/ EZ/fl/fl
\ j/fl

 

Cl

Alternative MMED series. Smooth
Tn'mmed MMED 2.58, Smoothed

. rm. . In

.7/

 

 

l I I F I I l I I I I I I
67 69 71 73 75 -77 79 81 83 85 87 89 91
Year of Survey

75

I I
93 95

Male Marriage Earnings Differentials

 

Figure 11
Comparison of Trimmed OLS
Male Marriage Earnings Differential Series

0 Raw Trimmed MMED series
0 Trimmed MMED series 2.58

 

Raw Trimmed MMED, Smootne
Trimmed MMED 2.58, Smoothed

 

 

 

25-
O
O
O D
I A O 0
Dig, W0 9‘3, /-—/o/\
\‘D\ O ,//\\\i \\ O 0/0 /\
‘1 "V \ DJD Q / lo
20— I/ a \\ o .0 ,0 )4
\91 C] \ O/ \// {D
\U
0 U\\ \\\// O O D,/ \
22 O /
a 08.0 /
‘ CI
\ /
\\ M / O
\ /D /
15“ CV %
C]
D
o
I I I I I I I I l I E l l l I
67 69 71 73 75 77 79 81 83 85 87 89 91 93 95
Year of Survey

76

 

I aux-w

Figure 12

Independent Regressors Used in the MMED Time Series:

Married Female Labor Force Participation Rate(MFLFPR)
for Women Ages 25-34, all Races;

Percentage of Ever-Married Males in the 2.58 Trimmed Sample
of Full-Time/Full-Year Workers;
Percentage of Divorced/Separated Males in the 2.58 Trimmed Sample

of Full-Time/Full-Year Workers.

—e——NFLFPR ——e—%Ever-lVariedinSarple-20
———a—%Divorced/Sepa'aed+30

OMQe—Jug flgU/D/BW o
Wm
60 fl fig W0

 

 

Mir-

‘r-m (36.5.5

 

!l

 

77

Figure 13
Comparison of Observed and Predicted Male Marriage Earnings Differentials

0 Trimmed MMED series 2.58—— Trimmed MMED 2.58, Smoot
—9— Predicted Trimmed MMED —5— Predicted MMED MFLFPR Co

30‘

257

207

15—

107

Male Marriage Earnings Differential

 

 

 

 

l l I l l
(517 619 7'1 7‘3 7'5 7'7 7'9 8'1 8'3 85 87 89 91 93 95
Year of Survey

78

 

Figure 14
Comparison of Observed and Predicted Male Marriage Earnings Differentials
(Age Only Controls)

0 Raw Trimmed MMED series Raw Trimmed MMED, Smoothe
——8— Predicted Trimmed Raw MMED—a— Predicted Raw MMED, FLFPR fi

 

 

Raw Male Marriage Earnings Differential

25—
O

O D "'\,D

D //’D/B\,\\

”my \ w
204 O \'\\\

o o \ O D O o A
.D /f\) / F
\ O / A A O
W / A” A
. A?
15—« A A- / a
- E3 . .0
)4; ‘ a/y
A . '
T\ 7
10‘ H \‘\, 43
a A \f/
/ A
41/
AM
A

5..

 

 

 

D I I I I I I | I I I I I I I
67 69 71 73 75 77 79 81 83 85 87 89 91 93 95
Year of Survey

79

Figure 15
Predicted Probabilities of Being Married by Age and Log-Earnings
Year 196779

 

Predicted Probability of being Married
Conditional On Not Being Divorced/Separated

 

 

25 35 45 55
Age

 

79 Tables 15-18 are constructed with the predictions from the ols regression of Currently Married,
or Currently Divorced/Separated on the log-wage, its square and cube and age dummies. The
sample used for Tables 15-16 is the same as that used for the estimation of the 2.58 Cutoff,
Trimmed MMED for the years 1967 and 1988. The sample used for Tables 17-18 is the same as
that used for the estimation of the 2.58 Cutoff, Trimmed MMED for the years 1967 and 1988
excluding never-married observations.

80

Figure 16
Predicted Probabilities of Being Married by Age and Log-Earnings

Year 1988

go 8
luv 0
g 00

.23 00
Q8 0 0
£8
Allin—6080 Q

 

All—avg
go 0
Q8 0 OO
guOQu O 0
g 0 O O
.2250 O O
IEHBOQQ O OO
2:5. 0000

 

£88588 0

Ego O 8

ECO O O O

.fiSOBUOOO O OO 0
g 0 00

0 £58966 0

O AIHfluHNUOAXUOUQU O

LariazZ... OOC

 

 

g 000 O O

55

Age

25

 

 

 

3658938020 933 “oz :0 63550
85.2 33 5 2:389“. 8553

81

Figure 17
Probability of Being Divorced/Separated Conditional On Having Been Married

Year 1967

O 00 Ogi

O OO 8 0 0% 8i
0 O O 888i

OO O 899i

0 OO gggxi

O O O 608i

 

 

Age

35

25

 

 

BEm comm 9.3m c0_mco=_ucoo
855 868.95 52:0 £52.05

82

Figure 18
Probability of Being Divorced/Separated Conditional On Having Been Married

Year 1988

 

45
Age

35

 

 

 

3:5 :25 9:5 :0 .mcoEucoo
.855 $68.95 5.3.0 £323

83

Descriptive Statistics for Replication of Korenman and Blackburn.

Table 1A

Years 1967-1996.

 

 

 

 

 

 

 

 

Original Replication Replication
1967-1988 1967-1988 1967-1996
Marriage .216 .213 .211
Coefficients L034) (03 2) (.028)
Table 18

Summary of Comparison of Replication with
Korenman and Blackburn’s Reported Time Series Results.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependent/ O . . . .
Independent rrgmal . Replicanon of .
V . Korenman and Blackburn Senes Korenman and Blackburn Senes
anables
Year 67-88 67-88 67-88 67-88 67-88 67-88 67-88 67-88
Sample
:33. -.42 -.62 -.293 -. 169 -.39 -.58 -.312 -.l64
(.07) (.12) (.23) (.173) (.07) (.10) (.21) (.104)
(Trend-14)" .59 .222 .57 .264
I(Year>80) (.28) (.36) (.26) (.325)
Post-76 -3. l 7 -3.96 -2.62 -3.57
Intercept (1.98) (1.49) (1.80) (1.37)
Adjusted R2 .61 .67 .70 .71 .62 .69 .70 .71
Table 1C

Results from the Regression of Korenman and Blackburn’s Marriage Earnings
Difi‘erential Series on the Replication Marriage Earnings Differential Series

 

 

 

 

 

“tilfizgldém Coefficients/Statistics
Iléephcatron of 1.0671
orenman and ( 0412)
Blackburn '
-1.203
Constant (339)
Adjusted R2 970

 

 

 

 

' The trend variable is equal to 1 during Year of Survey 1967.

84

Table 2A
Summary of Sample Statistics For Simulation of Early Imputation Procedures

using Data from 1988B March CPS

 

Percentages
/Groups

Never Married

Divorced or
Separated

Currently Married

 

% of Sample
Full-Time/Full-Year
Before Imputation

.712

.748

.847

 

% of Sample
Full-Time/Full-Year
After Imputation80

.738

.765

.854

 

% of Overall
Sample Assigned
Non-Reporter
Work-Status

.040

.030

.015

 

% of
Full-Time/Full-Year
Workers
Misclassified6

 

 

.035

 

.023

.008

 

 

Table 28
Summary of Alternate Hot-Decking Procedure’s Impact on the MMED

using Data from 19888 March CPS

 

 

 

 

 

 

 

 

 

 

 

- - Work- Work-
(3111:3333: ‘35 None Staxzrgnlv Stafiizrghlv Status and Status and
p ' ° Eamings Earnings
Characteristics Head-Ship. Head-Ship. . same
Used for None Age and Age and Heals-Selim, 83:52];
Hot-Decking Eaniings Earnings g MMED"
.232 .244 .2688? .227 .228
MD (.010) (.010) (.011) (.010) (.010)
Residual Skew
. -6.67 -5.99 -1 1.67 -5.20 -6.65
Never Married
Residual Skew
Divorced/Separa -2.93 -3 .04 -8. 19 -2.55 -2.98
ted
Resfizgiesgew -3.72 -3.71 -6.23 -3.67 -3.65

 

 

 

3° These percentages reflect the values from the simulation of the early imputation procedures.
8' The same controls used in the main regression for estimating the MMED are used as 110t-
decking characteristics. The only exception is that ages are grouped into three categories, ages 25-

34, 3544, 45-54.

‘2 The difference between the MMEDs shown in the third and fourth columns is in the earnings
value assigned to non-reporters. 1n colunm 3. the eantings are the mean eamings for heads and
non-heads who are part-year or part-time workers. In column 4. the earnings are exp(-2) times the
mean earnings for heads and non-heads who are full-time. full-year workers. The second set of
earnings values is considerably lower than the first and is based on the calibration results.

85

 

 

Table 3

Statistics Used for Calibration of Misclassification of Work-History

 

Years 1970-74

Years 1976-79

 

Married

Never-
Married

Married

Never-
Married

 

Overall
Means

2.638

 

2.329

2.648

2.468

 

 

Observed
Raw MMED

.309

.180

 

Sub-Sample
Means '

1.798

1.162

1.778

1.423

 

Proportion of
Sample in
Sub-Sample

.0555

.0784

.0628

.0673

 

Proportion of
Workers
Classified as
Full-Time

.823

.688

.792

.640

 

Proportionfi
Misclassified
Approach I

.0207

 

.0436

 

 

Percentage of
Part-Year
Workers
Misclassified

.088

 

Predicted
True Overall
hdeans

2.663

 

2.401

2.623

2.443

 

 

Predicted
Raw MMED

.262

.180

 

Bias to
MMED

.047

 

Proportion“
Misclassified
Approach 11

.0229

 

Percentage
Part-Year
Misclassified

.0684

 

Predicted
True Overall
Means

2.638

 

2.391

2.623

2.443

 

 

Predicted
MMED

.247

.18

 

Bias

 

 

.062

 

 

 

‘ Predicted Proportion of Full-Time/Full-Year Workers.

86

 

Table 4

Summary of Alternative MMED Series

Descriptive Statistics

 

 

 

 

 

 

 

 

 

 

Years 67-88 Years 67-96
Excluding 75 Excluding 75
Untrimmed OLS 24.81 24.31
MMED (3.59) (3.21)
Untrimmcd OLS
MMED Standard (11'3” (11%?)
Errors ' '
Trimmed
OLS mo (220647; (220 '1676)
2.58 Cutofl‘ ' '
Trimmed
OLS MMED .854 .840
2.58 Cutoff (.053) (.052)
Standard Errors
Trimmed
OLS MMED (22°12?) (22° 2473)
1.96 Cutoff ‘ ‘ ‘
Trimmed
OLS MMED .755 .744
1.96 Cutoff (.044) (.045)
Standard Errors
Trimmed Raw 18.05 18.54
OLS MMED (2.91) (2.75)
Trimmed Raw
mm 3.2:, 3.22.
Standard Errors ' °

 

 

 

87

 

Table 5
Descriptive Regressions

 

 

 

 

 

 

 

 

 

 

lOOfIndep Nontrimm Trimmed Alternative Trimmed Alternative
Vanable ed MMED Series MMED Series
MMFD Cutoff 2.58 Cutoff 1.96
Series
Sample 67-96 67-96 67-96 67-96 67-96 67-96 67-96 67-96 67-96
Years
Year/10 0.0892 -1.22 .464 .91 .. -1.08 .433 1.35 _
(0.274) (3.41) (1.87) (2.99) (3.69) (2.02) (3.14)
Year"2/ -0.l76 0.5 12.5 -.90 __ 0.40 1.2 -1.2 _
100 (0.688) (0.9) (.57) (.90) (0.90) (0.6) (.89)
Post-76 -7.21 -2.6 __ -214 -3.05 -2.46 _ -1.93 -3.00
Intercept (1.77) (2.18) (1.86) (.84) (2.36) (1.96) (.91)
Post-89 .. __ __ 4.83 1.95 .. _- 5.59 2.08
Intercept (1.53) (.79) (1.61) (.85)
Year=1969
outlier -541 -1.94 -1.95 -1.85 __ .1.44 -1.45 -1.34 _
. (1.78) (2.28) (2.30) (1.95) (2.48) (2.48) (2.05)
intercept
Yeafil975 .
outlier 1.1 -1.23 -2.35 -1.89 -.821 -3.34 .44 -4.1 -2.87
. (2.11) (2.51) (2.35) (2.15) (2.09) (2.72) (2.53) (2.26) (2.24)
intercept
£91m“ .712 .132 .117 .369 .304 .128 .125 .402 .316

 

 

 

 

 

 

 

 

 

 

88

 

 

Summary ofT

Table 6
ime Series Regressions

of 2.58 Cut-Off, Trimmed MMEDS on Descriptive Statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.58 Cut-Off, Trimmed MMEDS
Years 1967-1988
Inde endent ‘ +
v1.2.1.1... Means (1) (2) (3) (4) (5) (6) (7)
MFLFPR“3 52.7 -0.398 -0.662 .327 .0525 .0571 .055 -0.45
(11.38) (0.260) (0.349) (.31) (0.305) (.328) (.254) (.059)
MFLFPR“
23.5 -.061 .181
”W193” (31.91) " " " (0.377) (.627) " "
Percentage
Em 3: ed 88.25 -0214 0.122 -.098 -.74 -.954 -0.697 -.741
Elie: (3.60) (.40) (0.498) (.485) (0.544) (0.709) (0.458) (.086)
Married
Percentage
of
Employed 30.60 -- -- __ __ .57 -- -
‘Ever- (41.4) (1. 16)
Married"
(Yeor>1981)
Percentage
Empatoved 7.07 0.87 1.06 .847 1.57 1.56 1.70 1.53
a i (
Divorced! (2.62) (0.87) (0.88) (8)6) (1.16) (1.1)) (.77) (0.19)
Separated
Percentage
°f 242
Employed 3.60 -- -- .- 2.27 2.21 2.08 (0'20)
Divorced/ (4.88) (1.63) (1.68) (1.09) '
Separated“
(Year>l981)
““9198” .364 __ -- -- -22.1 -85.6 -240 -28.82
(.49) (16.1) (130) (10.2) (1.77)
“6391974) .636 __ __ -.816 -l.89 -1.92 -1.83 -2.77
(.492) (1.81) (1.44) (1.48) (1.32) (.30)
(Year=l975) .045 -2.38 -2.57 .200 -1.76 -1.71 -1.79 -1.46
(.213 (1.63) (1.63) (1.87) (1.36) (1.4) (1.30) (.16)
Trend 11.5 .. 0.571
(6.5) (0.508) " " “ " "
D.W.
Statistics - 1.71 1.81 1.74 2.62 2.61 2.62 2.24
Adjusted
R2/ - 0.514 0.522 .490 0.745 0.729 0.763 0.614
Pseudo R2

 

 

 

 

 

 

 

 

 

 

 

* Median Regression Specification.
'3 Married Female Labor Force Participation Rate.

89

Table 7

Summary of Time Series Regressions of Trimmed Raw

@ge Controls Only) MMEDs on Descriptive Statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.58 Cut-Off Trimmed Raw MMEDS
Years 1967-1988
Inde ndent +
v.52... Means 0) <2) <3) <4) (5) (6) (7)
MFLFPR“ 52.7 .0372 -0686 -.166 -0.633 -0.651 -0.498 -0.466
(11.38) (0.253) (0.331) (.287) (0.306) (.332) (.261) (.788)
MFLFPR“
23.5 .327 .417
““9193” (31.91) " " " (0.374) (.629) " "
Percentage
Em 2f ed 88.25 .157 .564 .491 -.088 -.168 -0.316 .460
Elie? (3.60) (.389) (.475) (.448) (0.541) (0.713) (0.47) (1.24)
Married
Percentage
of
Employed 30:60 __ __ -- __ .2 12 -- --
Ever- (41.4) (1.16)
Married“
(Year>l981)
Percentage
Empfiiyed 7.07 .881 1.10 .815 2.73 2.73 1.99 1.97
Divorce d/ (2.62) (.851) (0.84) (.83) (1.16) (1.2) (.79) (2.56)
Separated
Percentage
°f 186
Employed 3.60 __ __ __ -.355 -.381 .668 (3 69)
Divorced] (4.88) (1.62) (1.69) (1.11) '
Separated“
(Year>1981)
““9198” .364 __ -- __ -211 -44.7 -10.6 -3.24
(.49) (15.9) (130.2) (10.36) (35.0)
(“391974) .636 __ __ .232 .321 -3.22 -3.58 .479
(.492) (1.67) (1.42) (1.47) (1.34) (3.36)
(Year=l975) .045 -1.81 -2.03 -.741 -.482 -.464 -.323 -.071
(.213 (1.63) (1.59) (1.76) (1.37) (1.423) (1.342) (1.804)
Trend 1 1.5 -- “-636 -- --
(6.5) (0.484) " " "
D.W.
Statistics - 1.76 2.00 1.94 2.70 2.67 2.58 1.96
Adjusted
R2/ - 0.752 0.766 .765 0.865 0.854 0.867 0.711
Pseudo R2

 

 

 

 

 

 

 

 

 

 

 

* Median Regression Specification.
8‘ Married Female Labor Force Participation Rate.

90

 

Table 8A

Summary oflmportance ofEarnings for
Probability of Being Married or Divorced/Separated
For the Years 1967 and 1988

 

 

 

 

 

 

 

 

 

 

 

 

Regression Probability of Being Married' Probability of Being
Divorced/Separated+

Year 1967 1988 1967 1988
Log-Wage -.011 .34 -.53 -.24
(.026) 4.1 l) (.34) (.13)

Log-Wage7 1.2 -1.0 1.5 .69
/100 (1. 1) (.47) (1.4) (.52)
Log-Wage} -.20 .12 -. 17 -.08
/1000 (. 154) (.064) (.20) (.07)
Pseudo R2 .106 .159 .049 .027
Sample Size 13279 12395 12813 13351

Table 8B

A Table Summary of Changes in Means and Dispersion of Probabilities of Being
Married or Divorced/Separated
For the Years 1967 and 1988

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P . Probability of Being Married, Probability of Being
r01)" . +
Divorced/Separated
Period Year 1967 Year 1988 Year 1967 Year 1988
Group Nev? Married Nev.“ Married Married Lollicger Married Loliiger
Mamed Married Married Married
Age .77 .81 .45 .48 .02 .015 .081 .096
25 (.09) (.07) (.08) (.07) (.013) (.007) (.036) (.059)
Age .89 .93 .84 .85 .023 .024 .114 .137
3 5 (.045) (.046) (.048) (.046) (.017) (.005) (049) (.058)
Age .92 .95 .91 .93 .042 .054 .120 .140
45 (.06) (.03) (.05) (.03) (.022) (.043) (.044) (.047)
Age .90 .945 .92 .965 .020 .020 .080 .097
54 (.074) (.038) (.056) (.037) (.016) (.010) (.041) (.052)

 

 

' Conditional on not being Divorced/Separated and being part of the sample used to determine the
2.58 Cutofl', Trimmed MMED.
+ Conditional on having been Married and being part of the sample used to determine the 2.58
Cutoff, Trimmed MMED.

91

 

Appendix A
Description of Replication of Korenman and Blackburn’s MMED Series

Korenman and Blackburn construct their time series of cross-sectional
MMEDs for fiill-year/full-time, white workers using the 1967-1988 March CPS
samples. Their dependent variable is the log of an individual’s earnings in 1987
dollars divided by 2000. The sample is restricted to workers whose dependent
variable is greater than one and who report no personal self-employment income85
and are not employed in agriculture or fisheries and wildlife, private household
service, or welfare and religious service“. A constant-real-value top code equal

to the real value of the lowest top-code is applied to the earnings data. MMEDS

 

"Mrs” :-

are then estimated, without sampling weights”, with three categories of marital
status: never married, currently married88 and divorced or separated”. Other
controls include 29 age dummies, 18 education dummies, 10 industry dummies,
one white-collar dummy, 8 region dummies and dummies for whether the
respondent's residence is outside an SMSA or in a central citygo. The industry and

white-collar dummy variables were more difficult to replicate since the two-digit

 

'5 Koremnan and Blackbuni remove individuals with positive values of personal income from self-
employment. In the later. altemative specification only indin‘duals who report zero personal
income last year from self-employment are in the sample.

'6 The two—digit codes for industry last year were used to form the industry dummy variables.

37 The alternative MMED series uses sampling weights to ensure that differences in targeted
sampling do not atTect the MMED series.

'8 Currently married includes the category. manied spouse absent.

'9 Widowers are excluded from the sample.

9° The age, education. and region dummies were easy to define based 011 standard reported
characteristics including the nine census regional divisions. For the place of residence variables,
there is an additional category in later years for respondents whose MSA status is not identifiable.
Since Koremnan and Blackburn do not report this category, individuals in this category were
included with those living inside the SMSA.

92

classification of major industry"1 and occupations‘2 last year changed twice over

the 1967-1996 period”.

 

9' The ten industry dummy variables were condensed from the many two-digit industry last year
codes.

92 Occupations chosen to be included in the white-collar status were those that were listed first
among the two-digit occupation codes. They include professional. medical and salaried managerial
occupations and clerical. sales occupations.

93 It changed between the 1975 and 1976. 1982 and 1983 March CPS Surveys.

. ' |

Appendix B
Description of Additional Changes made to form the Alternative MMED
Series

For an alternative series spanning the year 1967-1996, the specification
needs to be adjusted to ensure consistency in the MMED series and to account for
additional changes made in sample construction. One of the biggest changes in
the data sets that affects the estimation of the MMED is how years of education
are reported. From 1992 on, instead of asking how many years of education
someone has, the CPS surveys ask about degree completion. To make a
consistent series, six education categories are formed for each year”. Besides the
change in the education dummy variables and the restriction of the sample to
exclude individuals with negative values of income from self-employment and the
use of sampling weights, the additional change to the regression specification is
the formation of fourteen industry categories”.

The changes made in the formation of the data set are that sampling
weights are now used to control for year-to-year differences in targeted sampling.
Also, one no longer needs to drop individuals whose wage is less than one dollar

since the trim will take care of these values. Finally, instead of imposing a

 

9‘ The first category consists of individuals with less than nine years of education. The second
category consists of individuals with some high school education but not a high school diploma, or
nine to eleven years of education. The third category consists of individuals with a high school
diploma and with or without some college education. but no college diploma. or twelve to thirteen
years of education. The fourth category consists of individuals with an associate degree or who
went to a technical college with individuals who report fourteen to fifteen years of education. The
ftfih category consists of individuals with a bachelor degree. or sixteen to seventeen years of
education. The sixth category consists of individuals with a post-bachelors degree or who have
eighteen years of education. ’

95 The Industry categories are: Construction. Mining. Manufacturing Transportation and
Communication and Utilities and Postal Workers. Wholesale. Retail. Banking/Finance and
Insurance and Real Estate. Business and Repair Services. Personal and Entertainment/Recreation
Services except Private Household. Medical and Health Services (excluding Hospitals), Hospitals,
Educational Services, Other Professional Services. Public Administration.

94

 

consistent low top-code across the years, the log-earnings are consistently
imputed for top-coded respondents. These changes are made to take into
consideration the findings of Bollinger and Chandra (2001). Bollinger and
Chandra find that using arbitrary values of the dependent variable to trim or
censor observations likely introduces more bias than it removes. As such, since
the underlying distribution does not stay fixed when a fixed censor value is
imposed, it may dampen the true year-to-year variation in the MJVIED.

An alternative approach is to impute the values of top-coded
observationsgé. To do this a simple assumption is made. The upper half of the
log-earnings distribution is normally distributed. The median log-earnings value
is found. A variable is created where all observations whose log-earnings have
values less than the median log-earnings value are assigned the median log-
earnings value. Then, a Tobit is estimated with the median values being the lower
censor point and the top-coded values being the upper censor point. After the
Tobit regression, one calculates the expected value of the log-eamings for top-
coded observations under the assumption that the Tobit distribution is accurate
and that the true values are above the assigned values. The top-coded
observations are then assigned the predicted true log-eamings. This approach
maintains a consistency across the years by simultaneously correcting for the

changing real values of the top-code and underlying log-earnings distribution.

 

9‘ The current dollars levels of top-codes vary a fair amount across the data sets from 50,000 to
75,000 to 99,999 to the last couple of years where there is no fixed top-code but a number of
values above 100,000. In the imputation procedures, for all of the data sets. any observation
whose current dollar value is above 99.999 is reset to 99.999 before imputation. This allows for
consistency across the years.

an.“ .r P‘.‘ "

 

{'1‘ LI' 5.2"6’1

Another advantage is that one can test the accuracy of the normal distribution

assumption for the top half of the earnings distribution”.

 

97 This is quite easy to do. Isolate the observations at or above the median so that all the
observations can be expressed as ,u MED + a) . where a) Z O. For all the observations where

w > 0 , additional observations can be created with the values ,1: ME D - a) . This guarantees a

symmetric distribution and that if the upper half of the log-eantings distribution is normally
distributed then the constructed distribution will be nonnally distributed. A box-cox test for
normality can then be estimated 011 the constructed distribution. The box-cox tests 011 the
transfonned upper half of the log-eantings distribution for fitll-timc/full-year white males ages 25-
54 for the years 1967-1996 fails to reject the null hypothesis at the five percentage point
significance level that the constructed log-earnings distribution was significantly different from
the normal distribution. The full log-eantings distribution of full-time/full-year males for every
year did differ very significantly from the nonual distribution.

96

 

Appendix C
Description of Why the 1975 Trimmed MMED is considered an outlier.

The year 1975 appears to be an outlier as it deviates strongly from the
overall downward trend between 1974 and 1976 in figure 10. In figure 9, the
percentage of never-married males excluded in the lower portion of the trim in
1975 is comparable with the earlier years. However, the figure below shows that
the unusually low trimmed MMED for 1975 is because of how another form of
measurement error affects the trimming process for 1975. The average
heteroskedastic variance for both married and never married males is unusually
low for the year 1975. When the heteroskedastic variance is biased towards zero
with the distributions having a negative skew, the result is that a disproportionate
number of lower observations, particularly‘in the never-married sample, are
excluded in 1975.

What would bias the variance downward? The 1976 March CPS data sets
is the first set where precise hours and weeks worked last year are asked of
respondents. If a larger number of respondents refuse to give their true work-
history for this year”, as is shown to be the case in figure 2 of this appendix, then
one would impute both their work-history and their income from last year. If the
imputed incomes, on average, were more average incomes then the variance of
log-earnings would be biased downwards by an unusually large number of

imputations.

 

9' Perhaps, because of the way the question was phrased.

97

 

is... ..- .« 4 _'

Mean Heteroskedastic Variance

 

O

 

Figure C-l
Comparison of Average Heteroskedastic
Standard Deviations by Marital Status

Never-Married Earnings Variance——— NeverMarried Variance. Smoothed
Married Earnings Variance

 

Married Earnings Var.. Smoothed

 

 

 

 

1 l 1 1 j l 1 1
67 69 71 73 75 77 79 81
Year of Survey

98

Figure 02
Trends in the Proportion of Observations
by Marital Status with Imputed Earnings Last Year.
—9— % in Never-Married Sample—e— % in Married Sample

.2 r R /B\E1

_L
‘1
U"
L
\T
/
\

/
_... "1

 

E/\\
\\
.125 — / 1

2f

/

//

M
V

 

 

_i.
1
CD

 

 

1 1 l T
72 74 76 78
Year of Survey

Percentage of Sample with imputed Income from Last Year
a
l
81- 4

99

 

Appendix D
Comparison of Accuracy of Prediction between the Median and Mean
MMED 1967-1988 Time Series Regressions.

As shown in tables 6-7, the preferred, final specification is estimated with
both a mean and median regression. To distinguish which regression is better, a .
prediction is made for the years 1989-1994 for both regressions. The regression
results show that the 2.58, trimmed MMED regression predicts better out of
sample than the 1.96, trimmed MMED regression. The correlation between the
predicted and actual MMEDS is negative for the latter trimmed series.

An explanation for the inaccuracy of prediction using the 1.96, trimmed
series is because of the measurement error in the estimated standard errors. When
the trim is tighter, the measurement error in the standard errors is more important
since the density of the residual distribution is higher. As such variation in the
standard errors may introduce noise to the trimmed MMED99.

Table D-l

Summary of Median Regression Assessments of Accuracy of Predicted Trimmed
2.58 Controlled MMEDS for the years 1989-1994.

Tl

if}. c l

 

 

 

 

 

 

Dependent Trimmed 2.58 Trimmed 1.96 Trimmed 2.58 Raw
Variable MMEDS MMEDS MMEDS
Predicted

MMED Series .816 -.163 -.318
Mean (.795) (.677) (2.68)

Regression

Pseudo R‘ .023 .154 .003
Predicted

MMED Series .707 -.235 1.085

Median (.681) (.436) (1.01)
Regression

Pseudo R‘ .085 .141 .382

 

 

 

 

 

 

100

.'h ...-. K." ° .‘

 

Has the Male Marriage Earninlgipgrifferential’s Causality Changed?
A Historical Over-View of the Literature.
1. Introduction.

The Male Marriage Earnings Differential (MMED)’S sizeable and
Significant nature was first set out by Hill (1979) over twenty years ago. Since
then, the bulk of research on the MMED centers on inferring the direction of the
causality between marriage and higher earnings rather than its magnitude'00 or its

. . . . 10'
vanation across time 01' COUIIII’ICS .

Papers have tried to show that marriage
causes earnings to rise and form the MMED or that selection into marriage based
on earnings ability is responsible for the MMED'OZ. Yet these stories are not
mutually exclusive and together may explain the MMED. Moreover, the relative
importance of the different potential causes of the MMED may differ across time
or location with different patterns in sex roles and marriage.

To determine the relative magnitudes of the various effects causing the

MMED vary across time, the return to years of marriage after controlling for fixed

 

99 The noise in the standard error estimation is more significant when the underlying residual
distribution is not symmetric. In this case, and variation in the level at which the mean is trimmed
leads to variation in the asymptotic mean. This seems likely to be the case with the MMED.

'00 Korenman and Neumark (199 l )’s 10-40 percent range no longer appears to be an accurate
description of reality. The only MMED reported in this paper that is near 40 percent is in
Nakosteen and Zimmer (1987). The size of their MMED could be specious due to the inclusion of
males ages 18-22 in their sample. This group of young, mostly unmarried males earnings will be
lower than the earnings of older married males. Moreover, among younger males in more recent
samples, Gray (1997) finds MMEDS statistically Significantly less than 10 percent. As such, a
better range for the MMED would be 5-25.

'0' Goldin (1990) declares that the MMED has been virtually stable. Similarly, Schoeni (1990)
fails to find significant systematic differences in the MMED across developed countries.

'02 The best way to determine the direction of causality of the MMED is by simultaneously
controlling for differences in unobserved ability with fixed effects and how many years someone
has been married. The fixed effects pick up part of the effect from selection and the years married
show whether earnings grow with how long someone has been married. The longitudinal MMED

101

 

effects from Gray (1997) and Stratton (2002) are reexamined. Gray (1997)
compares the longitudinal estimates of the MMED and the return to years of
marriage with the NLS and NLSY. Stratton (2002) similarly looks at longitudinal
estimates of the MMED and the return to years of marriage/cohabitation using
data from the National Survey of Families and Households (N SFH). The return to
years of marriage, in Gray (1997), is significantly greater than zero in the earlier
but not the later cohort. However, the cohorts in Gray (1997) have returns to
years of marriage that do not differ statistically Significantly from each other. To
confirm a change in the return to years of marriage, a residual-based trim is used
to reexamine Gray (1997) and Stratton (2002)”)3. Then, the trimmed longitudinal
returns to years of marriage are compared to each other and other papers’
estimates to verify whether the return to years of marriage is declining. After
looking at the longitudinal evidence, other studies that investigate the prevalent
direction of causality behind the MMED with different methods104 are compared
by when their data sets are collected. A meta-analysis of the MMED across age

groups and by periods when the data was collected is then estimated.

 

 

 

is examined along with controls for years of marriage and its square and, in most studies, years
divorced.

'03 The residual-based trim is estimated using Gray (1997) and Stratton (2002)’s original data sets.
The trim is based on the residuals from a median regression. This is because one can tell whether
an observation’s reported log-wage is aberrant by its residual. The residuals from a median
regression are used since “outliers" due to measurement error are less likely to affect the estimates
of a median regression.

Stratton’s sample is altered to allow for better comparison with other studies. Instead of using all
males between the ages 18 and 65, the sample is restricted to observations between the ages 25
and 54.

'04 There are other techniques used that either help to distinguish between the competing causal
explanations or provide evidence for or against one of the two hypotheses. However, because the
number of papers is small with a fair amount of variation in techniques and sample selection, one
can only directly compare the longitudinal MMEDS with controls for years of marriage across the
studies. However, the qualitative implications of the different studies as to the causality behind
the MMED can be considered.

(‘2‘ 2

 

In general, the qualitative comparisons of the remaining papers are
consistent with the findings of the longitudinal studies. In more recent years,
there is less evidence for the causal effect from being married to having higher
earnings and more evidence for higher earnings increasing the likelihood of being
married. To find a change in the predominant direction of causality with no
evidence of a change in the cross-sectional estimates of the MMED illustrates the
reduced form of observed cross-sectional MMEDS. These naive estimates are not
useful for determining underlying structural causality, or tracing out the effects of
a change in structural causality. Additional information is needed to infer
whether the direction of causality has changed. But, the evidence accumulated in
this paper does indicate that when social structures such as sex roles, marital
behavior, divorce law and etc. change, economic relations will also change.

II. Reinvestigation into Gray (1997)

Gray (1997) uses young men aged 24-31 in 1976 or 1989 from the
National Longitudinal Study of Young Men (N LS) and National Longitudinal
Study of Youth (NLSY) to test whether there has been a change in the causality of
the MMED over time. Table 1 compares the results of the non-trimmed and
trimmed versions of an alternate specification of Gray (1997) 105. In the second
row, we see that 15 or 15.7 percent of the sample is removed by a residual-based

Him“. In the third row, we see that there is a low adjusted R-squared for the

 

'05 Gray (1997) includes the existence of dependents in the regression as does Comwell and
Rupert(1997), Akerlof(l997) and Korenman and Neumark (1991). However, as couples are likely
to wait to have children until they can afford them and the variable is partially collinear with
marriage, it is not included in the specifications run here. Generally, the Sign of the variable goes
very close to zero when one controls for fixed effects and years of marriage.

'06 The specification used is a slight variation on Gray’s original cross-sectional specification.
Changes include how five education category dummies are included in the regression. The

103

 

rpm“ .v‘.1'.'a
1
1

linear probability regression over whether an observable is trimmed or not can be
predicted based on observablesm. The linear probability regression serves as a
safe-check that observations are not being systematically excluded from the
sample by the trim.

The impact of the trim is apparent by a comparison of the standard errors
for the trimmed and non-trimmed samples. For the longitudinal estimates of the
MMED without controls for years of marriage, the standard error goes from .30 to

.21 and .25 to .15. The standard error is around a third lower than its previous

. Nadiaplluuuo- '-“.\.. -

 

 

categories include less than nine years of education, less than twelve but greater than eight years
of education, twelve years of education, less than sixteen but greater than twelve years of
education, sixteen years of education and greater than sixteen years of education. Also whether or
not dependents are present in the household is not included in the specification. This variable is
omitted because of its endogeneity and correlation with marriage.

The specification described above is first used for a median regression. Only the
residuals are considered from the median regression. Then, a mean, individual, fixed-effects
regression is estimated with the median regression residuals as the dependent variable. The
residuals from the fixed-effects regressions are then used for the trim. The reason for the two
steps is because of the limit on number of variables in STATA and how fixed effects has not been
programmed for median regressions.

Then, an estimate is made of the conditional median log-variance of the residual
distribution by regressing two times the log of the absolute value of the fixed effects regression’s
residuals on the same independent variables used in the original median regression. The
specification used in the median log-variance regression is the same as that used in the original
median regression. Predicted log-variances are made for all observations. The predicted values
are exponentiated and then the square root is taken to arrive at a set of robust estimates of the
conditional standard deviations of the residual distributions. Robust is here used to refer to how
the influence of outliers on the standard errors is reduced relative to what would be the case if a
mean log-variance regression was used to estimate standard deviations. Then, all observations
whose residuals from the residual fixed effect regression are more than 2.58 standard deviations
away from zero are removed from the sample.

'07 The same variables as the Gray Specification without the dependents variable are included in
the median regression. The linear probability for being trimmed excludes year dummies. The
purpose of this linear probability is to make sure that the trim does not disproportionately remove
observations from the sample based on any observable characteristics. This is a safe guard against
the trim causing additional bias to the observed coefficients through an endogenous attrition of the
sample. It makes sure that the controls for heteroskedasticity in the trim are working to ensure that
the cut—off values for the trim are consistent across observable characteristics. This is particularly
relevant for estimation if there are asymmetries in the earnings distribution, since to trim too
deeply because of the underestimation of the standard deviation for a particular group will
exacerbate the inevitable bias caused from trimming an asymmetric distribution.

104

Is

 

value. Although, the gains in efficiency seem to be higher for the NLSY than the
NLS‘O".

There is now a statistically significant change in the change in the return
to years of marriage between the two cohorts'og. However, with the NLS, 2.3 of
the original 12.0 non-trimmed cross-sectional MMED is attributable to years of
marriagel 10. 9.7 percentage points are attributable to selection for the earlier
period. In the NLSY, none of the 9.8 non-trimmed cross-sectional MMED can be
directly attributed to years of marriage. This indicates that the cross-sectional
MMED may have fallen primarily because of there no longer being a return to
years of marriage.

III. Reinvestigation into Stratton (2002)

Stratton (2002) looks at the MMED and the difference in earnings
between cohabiting males and single, non-cohabiting males. It uses data from the
1987-88 and 1992-94 waves of the NSFH. Her original sample is restricted to
white, non-hispanic men under the age of 65 and at least 18. Tables 2 and 3

llland

summarize the findings from looking at Stratton’s original sample
additional samples. Stratton, in her original sample, finds a significant cross-

sectional MMED and Cohabitating earnings differential. Stratton also finds a

 

'08 This is shown by how a larger portion of the sample is trimmed and how the adjusted R-squares
rises more because of the trim.

'09 In a regression where the two cohorts were estimated simultaneously, the restriction that the
return to years of marriage and years of divorce had not changed between the two cohorts was
rejected at the 5% significance level.

”0 Trimming the mean does reduce the MMED. However, if this reduction is because of
asymmetries in the log-eamings distributions conditional on marital status and the asymmetries
are due to endogenous selection then the trim reduces the influence of selection on the MMED.
111 Only observations found in both waves are included in the cross-sectional regression, unlike in
Stratton (2002). This tends to raise the MMED but the overall qualitative implications are not
changed.

105

I-“ .

 

 

 

significant return to years of marriageI [2 and evidence that the return to years of
cohabitation is only positive for males who are long-terrn cohabitersl '3.
However, Stratton’s sample includes very young males ages 18-24. This
group is very young with correspondingly low earnings. They also have a very
low likelihood of being married. The correlation between experience and marital
status is made more positive by the inclusion of this group in the sample. The
strengthening of the correlation between experience and marital status increases
the magnitude of bias transferred from the experience coefficientsl '4 to the
marital-status coefficients. The inclusion of younger, unmarried males will tend
to bias the MMED upwards. Because of this, the sample is restricted to males
ages 25-541'5. Some of Stratton’s findings are sensitive to the change in the
sample and specification1 ‘6. There no longer is a Significant cohabitation earnings

differential and there is no longer any significant return to years of marriage.

 

"2 Stratton (2002) only lists the results from regressing the log of years of marriage plus one. This
paper regresses years of marriage and its square to maintain continuity with earlier papers. 1n the
original Stratton sample, neither of the years of marriage and its square are individually
statistically significant, but together they are statistically significant.

”3 The years cohabited is negative but its square is significantly positive so that after two years of
cohabitation there begins to be a positive return to years cohabited.

"4 The experience coefficients are biased in part by endogenous selection out of employment.

"5 Older males are unlikely to be never married and also are excluded. There also is a selection
effect from endogenous retirement for older males that can be avoided by not including the oldest
males.

”6 Stratton’s original specification included education, experience, experience squared, tenure,
tenure squared, tenure and tenure squared interacted with the second wave, years not employed,
residence in SMSA, a second wave interaction with SMSA, South, Active in Union with wave
interaction, children present, wave dummy, eleven industry dummies, seven occupation dummies.
Children present, years not employed are too likely to be endogenous. The new specification
omits children present, years not employed. and all the wave interactions used above. Most of the
wave interactions are not significant and no a priori reason for why they should be included is
given. Instead of education, education cohorts for years less than nine, less than twelve more than
eight, twelve years, less than sixteen more than twelve, sixteen years, more than sixteen years of
education. These cohorts are interacted with wave dummies. This is because of the rising return
to education. Only the dummy variable for sixteen years of education is significantly greater in
the second wave.

106

 

in c‘

 

When a residual-based trim' '7 is run on the modified Stratton sample, the
cross-sectional and longitudinal MMED both become statistically significantly
different from zero. It also becomes more apparent that controls for years of
marriage and years cohabited do not explain any portion of the longitudinal
MMED. This confirms the findings of Gray (1997) that there does not appear to
be a return to years of marriage in the late eighties.

IV. A Comparison of the Findings of Longitudinal Studies

Table 4 summarizes the findings of longitudinal studies of the MMEDl '8.
The findings are summarized in the form of the cross-sectional MMED,
longitudinal MMED and the longitudinal MMED after controlling for years of
marriage and divorce. Unfortunately, the first paper, Comwell and Rupert (1997),
is not comparable to the other studies since it includes tenure at current job and its
square in its final longitudinal regression that measures the return to years of
marriage. Otherwise, Korenman and Neumark (1991) and Trimmed Gray (1997)
Al 19 are very similar in their findings of a significant return to years of marriage
after controlling for fixed effects'zo. Both Akerlof (1997) and Gray (1997) B find
a lower MMED and a lower return to years of marriage in the National
Longitudinal Survey of Youth (NLSY). Akerlof (1997) uses data drawn from an

earlier set of years than Gray (1997) B. There still is a positive return to years of

 

”7 The same residual-based trim used to analyze Gray (1997) earlier in the paper.

”8 The coefficients from the MMED and dependents variable are added together for Comwell and
Rupert (1997), Korenman and Neumark (1991), Akerlof ( l 997). The standard errors presented are
estimated by taking the square root of the sum of the squares of the reported standard errors for the
two coefficients. This is a conservative estimate of what would be the MMED and its standard
error if the dependents variable was not included in the specification.

”9 There are two time periods where Gray (1997) estimates the MMED. The first from 1976-
1980 and the second is from 1989-1993.

'20 Both papers use the National Longitudinal Survey of Young Men for their papers.

107

5‘ 1"-

 

\n“!

81.“.

 

marriage in Akerlof(1997) but it is lower than in Korenman and Neumark(199l ).
Then in Gray (1997) B. there does not appear to be any return to years of
marriage. The MMEDS from Stratton (2002)!” are somewhat higher than the
other papers. However. this caould be because ofendogenous sample attritionm.
ln Stratton (200), the signs on years of marriage and its square are the wrong
direction and the MMED rises, instead of falling, when controls for years of
marriage are added. Altogether, there appears to be a downward trend in whether .
the MMED rises with years of marriage. i

To further investigate whether the causality of the MMED has changed,

 

the rest of the paper compares the findings of investigations into the causality of j
the MMED by the time periods when the data is collected. Then a meta-analysis
is done to test whether the MMED has fallen after controlling for differences in
the age group used to estimate the MMED.
IV. Earliest Studies.
The earliest study by Hill (1979) consists of verifying whether the MMED
is still significantly positive after one adds additional controls to the earnings
regression. Hill (1979) finds that the MMED remains significantly positive and

even rises with the number of controls. Hill, after demonstrating the existence of

 

'2' These MMEDS are from the modified sample and specification.

'22 Later, when a meta-analysis of cross-sectional MMEDS is measured based only on observations
from the first wave, the MMED estimated from the NSFH is comparable to the other cross-
sectional estimates, after controlling for age of sample and a shift after 1980. When both waves
are used to estimate a cross-sectional MMED, it is considerably higher than the other cross-
sectional MMEDS.

108

a MMED that is unexplainable by observable characteristics. poses the question
as to its source123 .

However, one cannot infer the cause(s) of the MMED from a solitary
cross-sectional estimate. More information is needed. Kenny (1982) first
incorporates multiple observations from the same individuals to obtain more
information about the effect of marriage on earnings. As summarized in Table 5,
Kenny (1982) tests whether earnings rise at a different rate before or after a man
is married. He finds that earnings tend to rise at a higher rate after marriage than
before marriage. Bartlett and Callahan (1984)’s later finding of greater income
growth among continuously married males provides support for Kenny’s finding.
While Bartlett and Callahan’s finding by itself is not convincing because of the
obvious selection story, it is consistent with Kenny’s finding that earnings rises
faster during marriage.

Kenny (1982) interprets the increased rate at which earnings rises after
marriage as evidence for Becker’s theory that married males are able to
accumulate more market-oriented human capital'24. However, as Korenman and
Neumark (1991) observe, Kenny’s finding is also consistent with the employer
favoritism model. Both papers argue that there is evidence in favor of marriage
increasing productivity versus employer favoritism. The evidence in favor of
increased productivity from marriage is based on the supposition that employer

favoritism would increase the level of earnings of married males and not increase

their earnings growth rate. The counterfactual to this argument is that if

 

123 After posing the question, Hill gives her econometrically unsubstantiated assessment that the
MMED is due to employer favoritism toward married males.

109

“'45.”.
2‘.

 

 

employers are favoring married males primarily through an increased number of
promotions then the impact of favoritism would be a higher growth rate of
earnings. Korenman and Neumark (1991) go further to Show that married
workers are more likely to be more productive. Married workers receive higher
performance ratings from their supervisors. Their increased chance of promotion,
thus, corresponds to their higher performance ratings'zs. Regardless though, to
find a higher growth rate during married years does suggest that the MMED is not
completely due to the selection of males with higher earnings into marriage.

V. Studies Based on Data Collected during the Seventies.

Table 6 summarizes the major findings of studies using data drawn during
the Seventies. The paper using the earliest data set, Nakosteen and Zimmer
(1987), runs the first test of the endogeneity of marital status. Nakosteen and
Zimmer (1987) finds that it is unable to reject the exogeneity of marital status.
Their instrumental variables estimate of the MMED is marginally higher than the
OLS estimate of the MMED. As such their paper does not provide convincing
evidence for the claim that the observed MMED is the causal effect from
selection into marriage based on earnings abilitym’.

The remaining three papers briefly discussed earlier examine the NLS data

set with fixed effects and measures of married/divorced years. They include:

 

'24 The increased productivity would be based on the household division of labor.

'25 Implicit here seems to be an argument against discrimination based on the theory of
discrimination set out in Becker (1957). Becker argues that if a firm did have discriminatory
tastes or supervisor’s performance ratings reflected more than the actual productivity of workers
that in a competitive market a firm would not be profit maximizing. Competition from non-
discriminatory firms would likely put such firms out of business or result in a change in
ownership.

'26 Nakosteen and Zimmer (1987) use the statistical insignificance of the 1V MMED statistic to
claim that there is no evidence for the household specialization/employer favoritism hypotheses.

llO

 

1‘...

 

Korenman and Neumark (1991 ). Gray (1997) and Cornwell and Rupert (1997).
Both Korenman and Neumark (1991) and Gray (1997) find a significant return to
years of marriage during the seventies for white males in America. However. the
similar findings are with the same data set for the same years and so the two
studies cannot be said to be independent of each other. Korenman and Neumark
(199]) goes further and looks at an additional data set taken from the records of a
company personnel database. The analysis of the data set indicates that there is a
significant MMED but that the differences are mostly due to a concentration of
married males in higher job grades. Married men receive higher performance
ratings and as such are more likely to qualify for promotions. AS with Kenny
(1982), the increasing levels of income during years of marriage support the
household specialization/employer favoritism hypotheses.

Comwell and Rupert (1997) use the same NLS data set to reexamine the
findings of Korenman and Neumark (1991). They lengthen the panel data set so
that it includes observations from 1971 so as to include additional changes in
marital status. Contrary to Korenman and Neumark (1991), Cornwell and Rupert
(1997) do not find a significant return to years of marriage after controlling for
fixed effects. However, their paper neglects to consider additional implications of
their extension of the panel data set. There are changes in their data set from
Korenman and Neumark (1991) that could provide alternative explanations of the

different findingsm.

 

127 These include a smaller sample size and the inclusion of years of tenure variable in the
specification. Korenman and Neumark (1991) show that, since marital status affects turnover
likelihood, the variable is endogenous. The inclusion of tenure at current job in a regression
would bias downward the return to years married.

11]

 

 

The biggest change involves the effect ofthe inclusion of non-spouse
dependents in their regression. Both Korenman and Neumark (1991) and
Comwell and Rupert (1997) include the dummy variable in their specification.
Cornwell and Rupert find a significant correlation of .052 (.019) in their fixed
effect specification. On the other hand, Korenman and Neumark do not find a
significant correlation, .02 (.02), between having dependents and earnings. The
negative correlation between significance in marital status and significance in
presence of dependents across the two papers could be related to the collinearity
between the two variables. Cornwell and Rupert (1997) show in their Table 1 that

there is a strong collinearity between the two variables for the later years in the

 

panel'zg. However, in 1971 , the year that Cornwell and Rupert add to the panel,
only 73 percent of married males have dependents. Herein lies an explanation for
the differences between the two papers. Since married males that have non-
Spouse dependents are likely to be older and the decision to have or not have
children can depend on their affordability, married males with dependents are
likely to have higher earnings than married males without dependents, which
makes the non-spouse dependent dummy variable is endogenous and biased
upwards in the earnings equation. The positive correlation between the non-
spouse dependent dummy and the married dummy leads to a transfer of bias to the
MMED. The MMED becomes biased downwards. One can check whether or not
the inclusion of the dependents variable is affecting the MMED by adding the

coefficients for the married and non-spouse dependent dummies for both papers

 

’28 They report 85, 89 and 92 percent of married males have non-spouse dependents in the years
1976, 1978 and 1980. Only 3, 6, l l and 9 percent of never married males report having

112

 

and comparing the point estimates. For Comwell and Rupert, the sums of the two
coefficients are .135 and .108 for the cross-sectional and fixed-effects estimates.
For Korenman and Neumark, the sums of the same two coefficients are .15 and
.08. The differences in the sums of the two coefficients are well within their

likely standard errorsm.

Because of this exigency, Comwell and Rupert (1997)
does not contradict Korenman and Neumark (1991)’s finding of a return to years
of marriage. Thus, it seems that the MMED, in all likelihood, did rise with years

of marriage during the seventies.

VI. Studies based on Data Collected during the Eighties/Nineties.

 

However, an examination of Tables 7 and 8 Show that, after the seventies,

there is less evidence in favor of the specialization/favoritism hypotheses.
Nakosteen and Zimmer (1997, 2001) both show with the PSID that selection into
marriage based on earnings ability during the eighties is important. Similar to
Gray (1997), Jacobsen and Rayack (1996) Show that both the MMED and the
negative correlation between hours worked by spouse and a male’s earnings are
dampened when one controls for fixed effectsm. Loh (1997) directly tests a
number of the predictions of the theory that marriage enhances productivity.

These include tests of: whether higher hours of work by wives lead to a decline in

 

dependents in the relevant four years, 1971, 1976, 1978, 1980.

'29 The standard error of the differences between the sums is greater than .02 for the cross-
sectional estimates and greater than .03 for the longitudinal estimates. This is based on a
comparison of the standard errors for the individual coefficients. One must also remember that
there are also differences in the two data sets.

'30 Unfortunately, like Gray (1997), Jacobsen and Rayack (1996) does not report the relevant
information about their 1V estimation technique. As such, one cannot assume it is reliable. Gray
(1997) does report that a significant negative correlation between hours the spouse works accounts
for the decline in the MMED. However, this is not robust to changes in specification and the
instrumental variables of child less than six does not pass the test for a valid instrument and the
remaining correlation between the instruments and the hours worked by spouse is not strong
enough for the 1V results to be reliable.

113

the earnings of males. whether cohabitation prior to marriage leads to higher
earnings ceteris paribusl3 1, whether self—employed males who are married have
higher earnings than not married self-employed malesm. In all cases. no
evidence is found for the productivity-enhancing hypothesis. Hersch and Stratton
(2000) use the information from the National Survey of Families and Households
to test whether variation in hours spent in housework explain part of the MMED.
They find that, while there is a negative correlation between a male’s earnings and
hours spent in food preparation. controls for the hours spent in housework do not
affect the MMED. Hersch and Stratton (2000) do not find direct evidence that the
extent of specialization in household production has a Significant causal effect on
market earnings. Stratton (2002) finds that when younger males ages 18-24 are
included in the sample there is a Significantly positive cross-sectional correlation
between cohabiting and earnings. The earnings of males in long-tenn
cohabitation relationships also seem to rise with time. However, these findings
are not robust to when the sample is restricted to include only males ages 25-54.

The change in the sample shows that there is no significant difference in earnings

 

'3 ' When a couple chooses to cohabitate, this allows for the same marriage specific specialization
in human capital investment as may occur during marriage. The human capital model predicts
that, after controlling for years of actual marriage, the additional time spent in cohabitation Should
increase the MMED.

'32 If married men have higher earnings then both salaried and self-employed married men should
have similar higher earnings. Otherwise, one might expect from an employer-discrimination
model that married self-employed men may not be better off than never married self-employed
men. Loh shows that, conditional on being self-employed, married men make less than never
married men. The finding of a marriage penalty for self-employed men is robust to the inclusion
of a selection correction for being self-employed. Loh does not look into whether the marriage
penalty is robust to differences in specification. Self-employed is not interacted with any other
term besides marriage. Other terms included in the regression that are not interacted with being
self-employed are education, tenure, tenure squared and age. With tenure, we would expect that a
self-employed worker would not need a Lazearean implicit contract with himself over time. If
married males were more likely to be salaried workers with this type of long-tenn contract, then

114

 

between older cohabiters and never-married non-cohabiters and no return to years
cohabited. This corroborates the findings of Loh (1997) that there are no higher
earnings associated with cohabitation. Akerlof (1998) exploits the details of the
NLSY to establish that large differences in behavioral patterns exist across males
by marital status. The differences in traits, such as likelihood to get intoxicated or
incarcerated, may contribute to the selection hypothesis to the extent they are
valued both in the marriage and labor markets.

Chun and Lee (2001) is the only recent paper that claims to find evidence
against the importance of selection in the later yearsm. Chun and Lee (2001)
estimate a switching regression between married and never-married states.
However, Chun and Lee (2001) finds that controls for the endogenous selection
do not change the MMED. This implies that the characteristics used to identify
the decision to become married do not also lead to higher earnings. Chun and Lee
(2001) also find evidence that there is a negative correlation between
unobservables in the marriage and earnings equations. One would expect that if
unobserved differences in earnings ability also are important in the selection into
marriage that there would be a positive correlation between the error terms in both
equations. Hence, for the error terms for these two equations to have a negative
correlation does complicate the selection story. Yet, it does not disprove the
selection storym. This is because there is more than one possible selection story.

It also may be possible that multiple selection stories for marriage can coexist.

 

there would be a negative bias to the interaction of marriage and self-employed. As such, the
comparison across groups of workers is not convincing.
"‘3 Their data set is collected in 1998.

115

 

IK
I

 

An additional selection story could be where higher ability males. once freed from
previous social constraints, select not to marry. One can easily explain why this
could be the case. As Becker (1973) notes in his treatise on the family.

“Nothing distinguishes married households more from singles households
or from those with several members of the same sex than the presence, even
indirectly, of children. Sexual gratification, cleaning. feeding. and other services
can be purchased, but not own children: both the man and woman are required to
produce their own children and perhaps to raise them(p.818).”

Given the centrality of production of children as an economic rationale for
marriage and the time-intensive nature of child rearing as well as the indivisibility
of children, one can easily posit that some high-income males will prefer not to
have children. As such, the incentive for marriage may not exist for themm.
There could be a non-linearity in the relationship between earnings ability and
propensity to become married.

Tentative evidence that the average earnings of never-married males has
risen in recent years is found using the same data set used in the second paper of
this dissertation. Graph 1 shows that in the years of survey 1995 and 1996, the
MMEDI36 begins to decline relative to its predicted levels from the years 1967-
1988. Graph 2 shows that the decline of the MMED is paralleled with a similar
decline in the Divorced/ Separated earnings differential (DSED). The parallel

between the two series’ declines is likely due to an increase in the average

earnings among never married males. If this trend continues to exist in 1999 then

 

'34 Moreover, if it did refute the selection hypotheses then how would one account for the

longitudinal estimates of the MMED being lower than the cross-sectional estimates of the
MMED?

'35 This is particularly the case if employer favoritism toward married males in the past is no
longer the case.

”1’ This actually is the trimmed MMED. A similar form of trim is employed in Wetzell (2002) as
is used to reexamine Gray ( 1997) and Stratton (2002).

116

 

it likely affects Chun and Lee’s data. One can postulate that the inclusion of a
fraction of higher ability males as never married would increase the group’s
average earnings. This would then reduce the MMED and potentially make the
correlation between the error terms for marital status and earnings equations
negative.

The key point is that Chun and Lee (2001) do not disprove the selection
story. Their findings can be reconciled with the earlier finding of evidence in
papers like Nakosteen and Zimmer (1997, 2001) in support of selection as one of

the factors causing the MMED. To reconcile this finding, an additional, theory-

 

based selection story is given. Then with the help of this story, the deviation of
the two last MMEDS in the series constructed by Wetzell (2002) from the pattern
that prevails in the previous twenty-eight years is explained and extrapolated as
likely to still apply in more recent years.
VII. Summary of Meta-Analysis of Cross-Sectional MMEDS

The main, or average, Cross-Sectional MMEDS for eleven of the reported
studies are reported in table 9. These MMEDS are grouped with the mid-range of
the sample’s age evaluated at the mean year when the data was collected and a
dummy variable for whether the data was collected after 1980. A median
regression with the Cross-Sectional MMED as the dependent variable is then
estimated with the age and when the data set was collected as independent
variables. The regression shows that the cross-sectional MMED does rise with
the age of the group and that there is a Significant four-percentage point decline in

the Cross-Sectional MMEDS estimated on data sets collected after 1980. The

117

median regression establishes that Nakosteem and Zimmer’s estimate of the
MMED is an outlier. When a mean regression is estimated on the rest of the
sample, the same results are found.
VIII. Conclusion

The above comparison of the results of studies across time confirms that
the MMED has changed. The relative importance of the sources of the MMED is
not fixed. The finding of a significant return to years of marriage in Kenny
(1982), Korenman and Neumark (1991) and Gray (1997) A, and Akerlof (1997)
show that there was a significant causal effect from marriage to higher earnings.
But the Significance of the causal effect of marriage to earnings for the existence
of the MMED appears to have declined in importance, as illustrated by Gray
(1997) B and the modified version of Stratton (2002). The decline in the
importance of marriage for earnings is supported by how a meta-analysis shows a
decline in the Cross-Sectional MMEDS after 1980. In addition, a survey of
several more recent studies that look at the predictions of the specialization
hypothesis fail to find strong support for its contribution to the MMED. Lastly,
several more recent papers do find strong support that selection into and out of
marriage in more recent years is correlated with earnings ability. Thus, it seems
that the MMED, in more recent years, is less due to marriage increasing earnings
productivity than increased earnings productivity increasing the likelihood of

being married.

118

 

Bibliography

Akerlof, George A. 1998. “Men Without Children.” The Economic Journal 108,
pg. 287-309.

Bartlett and Callahan. 1984. “Wage Determination and Marital Status: Another
Look.” Industrial Relations 23 (1): 90-96.

Becker, Gary. 1957. “The Economics of Discrimination.” Chicago.

Becker, Gary. 1973. “A theory of marriage: part 1.” Journal of Political
Economy, 81, 4, July/August, pg. 813-46.

Blackburn, M and Korenman S. 1994. “The declining marital-status earnings
differential.” Journal of Population Economics, 7, pg. 247-70.

Chun, Hyunbae, and Lee, Injae. 2001. “Why Do Married Men Earn More:
Productivity or Marriage Selection?” Economic Inquiry 39 (Spring) pg. 307-319.

Comwell C. and Rupert PG. 1997. “Unobserved Individual Effects, Marriage,
and the Earnings of Young Men.” Economic Inquiry 35 (Spring) pg. 285-94.

Gray, J. S. 1997. “The fall in men’s return to marriage: declining productivity
effects or changing selection?” Journal of Human Resources, 32 (Summer) pg.
481-504.

Hersch and Stratton. 2000. “Household specialization and the male marriage wage
premium.” Industrial & Labor Relations Review 54 (1) pg. 78-94.

Hill, Martha S. 1979. “The Wage Effects of Marital Status and Children.” Journal
of Human Resources, 24 (Fall) pg. 579-94.

Kenny, L. W. 1983. “The accumulation of human capital during marriage by
males.” Economic Inquiry, vol. 21 (April), pg. 223-31.

Korenman, S and Neumark, D. 1991. “Does marriage really make men more
productive?” Journal of Human Resources, vol. 26 (Spring), pg. 282-307.

Jacobsen and Rayack. 1996. “Do Men Whose Wives Work Really Earn Less?”
American Economic Review 86 (2) pg. 268-273.

Loh, E. S. 1996. “Productivity differences and the marriage wage premium for
white males.” Journal of Human Resources, 31 (Summer), pg. 566-89.

119

 

Nakosteen, R. and Zimmer. M. 1987. “Marital status and earnings of young
men.” Journal of Human Resources, 22 (Spring) pg. 248-68.

Nakosteen, R, and Zimmer, M. 1997. “Men, Money and Marriage: Are Higher
Earners More Prone than Low EarnerS to Marry?” Social Science Quarterly, 78,
March, pg. 66-82.

Nakosteen, R, and Zimmer, M. 2001. “Spouse Selection and Earnings: Evidence
of Marital Sorting.” Economic Inquiry 39 (Spring) pg. 201-213.

Schoeni, Robert. 1990. “The earnings effects of marital status: results for twelve
countries.” Population Studies Center Research Report, University of Michigan,
March pg. 90-172.

Stratton, Leslie. 2002. “Examining the Wage Differential for Married and
Cohabiting Men” Economic Inquiry 40 (Spring) pg. 199-212.

Wetzell, David, 2002. “On the Measurement and Explanation of Recent Changes

in the Male Marriage Earnings Differential.” Paper two in Dissertation, Michigan
State University.

120

 

 

 

Table 1

Summary of Trimmed Versions of Gray (1997)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample NLS - NLSY -
e T e Z
°/o of Original ASL R. Of f % of Original ASL R. Of
Trim Sample Pro ability 0 Sample Pro ability of
. . . Berng . Being
Statistics Trimmed Trimmed Trrmmed Trimmed
.150 .0041 .157 .0023
Type of Non- . Non- .
Sample Trimmed Trimmed Trimmed Trimmed
Cross-
Sectional .4200 .5068 .3525 .4651
Adj. R2
.120 .096 .098 .096
MMED (.017) (.015) (.014) (.012)
Longitudinal
Adj. R2 .7757 .9052 .6989 .8948
.091 .066 .022 .056
MMED (.030) (.021) (.025) (.015)
Longitudinal
w. Controls
Years of .7770 .9061 .6986 .8949
Marriage
Adj. R2
.063 .043 .007 .042
MMED (.032) (.022) (.026) (.016)
Years of .027 .026 .008 .004
Marriage (.009) (.006) (.009) (.005)
$31,122:: —. 142 -.1 12 -.069 -.069
Squared/100 (.043) (.029) (.051) (.031)

 

 

121

 

 

 

Table 2A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Comparison of Descriptive Statistics Stratton (2002)137
Sample .Stratton’s Wetzell’s Sub-Sample
Original Sample Males Ages 25-54
No. of Individuals 1358 1209 1017
Type of Sample Non-Trimmed Non-Trimmed Trimmed
Real Wage 1992 8 15.85 16.63 16.52 17.64 16.55 17.29
Log Wage 2.62 2.62 2.67 2.71 2.69 2.73
Married 73.2 77.5 78.3 80.9 79.4 81.9
Divorced. 9.0 11.7
Widowed. Separated 8'0 I 1’9 8'7 l 1'0
Cohabiting 3.3 5.2 3.9 4.2 3.5 4.1
Has Cohabited 25.6 32.2 28.8 33.9 28.9 33.3
Years of Marriage 11.7 16.0 12.2 17.0 12.3 17.1
Age 36.28 42.0 37.3 43... 37.4 43.3
Education 13.88 13.92 14.08 14.13 14.13 14.17
Table ZB
138

Summary of Reexamination of Stratton (2002)

 

 

 

 

 

 

 

 

 

 

 

 

Sam 1e Stratton’s Wetzell’s Sub-Sample
p Original Sample Males Ages 25-54
Type of Sample Non-Trimmed Non-Trimmed Trimmed'”
RI .3905 .3451 .4790
.198 .218 .201
MMED (.049) (.055) (.042)
Longitudinal R" .845 .833 .938
.085 .062 .069
MMED (.044) (.057) (.036)
Longitudinal R" .846 .835 .938
.085 .081 .080
MMED (.044) (.060) (.036)
. .004 -.001 -.006
Years of Marriage (.008) (.010) (.005)
Years of Marriage .010 .027 .026
Squared/100 ( .022) (.024) (.014)

 

 

 

 

 

 

'37 The means are weighted by sample weights. Cross-sectional MMEDS are estimated with
sampling weights, but sampling weights were not permitted by STATA for XTREG, fixed effects.
'38 There is an upwards bias to the cross-sectional MMED caused by the sample attrition between
the two periods for the NSFH. When the MMED is estimated from the first wave alone it is .143
(.033).

'39 The Adjusted R2 from the linear probability regression of whether or not an observation is
trimmed is 0.0179. This is a little higher than usual and indicates that males with less than high-
school education were more likely to be trimmed. To disproportionately trim a portion of the
sample causes bias if the underlying distribution is asymmetric. For example, if controls are not
made for marital status a disproportionate percentage of never married males are trimmed from the
sample. This is because there naturally is a wider variance in earnings for never married males.
But, because the earnings distribution for never married males is negatively skewed, to trim too
many never-married males reduces the MMED significantly. As it is, never married and
divorced/separated males have a four percentage point greater likelihood of being trimmed. This
may not be enough of a difference to alter the MMED Significantly.

122

Table 3

Summary of the Impact of Cohabitation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stratton’s Wetzell’s
Sample Original Sample Subsample
Males Ages 25-54
Type of Sample Non-Trimmed Trimmed
R" .3930 .4797
.230 .203
MMED (.049) (.044)

. . .113 -.014
Cohab1t1ng (.068) (.054)
Previously -.024 -.030
Cohabited (.026) (.025)

Longitudinal Rj .845 .938
.080 .062
MMED (.047) (.037)

. . -.020 -.O48
Cohabrtmg (.050) (.039)
Previously -.001 -.010
Cohabited (.047) (.034)

Longitudinal Rt .848 .938
.080 .059
MMED (.048) (.037)

. . .041 -.048
Cohabiting (.054) (04])
Previously .047 -.012
Cohabited (.048) (.035)

. .0080
Years Married (.0084)
Years .012
Marriedz/IOO (.022)
. -.022 .0025
Years Cohabited (.018) (.0142)
Years .012 .086
CohabitedZ/IOO (.022) (.127)

 

 

 

 

II."
!

 

Table 4

Summary of Returns to Years Married from

Longitudinal MMED Studies With Controls for Years Married.

 

 

 

 

 

 

 

 

 

Cross- . .
Time Age Data Section Longrtudrnal
Span Range Source Married Married Yeags 3110052
1971, A868
(31:31:21, 1976, 19-29 NLSY .135 .099 .033 -.005 -.03
1991;”, 1978, in M (.028) (.032) (.028) (.006) (.03)
( ) 1980. 1971
Koren- 197 6 Ages
man 1978’ 24-34 NLSY .15 .08 .03 .022 -.096
Neumark 1980, in M (.03) (.036) (.03) (.009) (.034)
(1991) ' 1976
Trimmed 1976 Ages
Gray 1978, 24-31 NLSY .096 .066 .043 .026 -.112
(1997)A 1980. 1n M (.015) (.021) (.022) (.006) (.029)
1976
By
1985
Akerlof 1984- Done NLSY .109 .04 .018 .016 -.15
(1998) 1991 With (.026) (.024) (.020) (.007) (.05)
Educ-
ation
Trimmed 1 937- 95%;:
Modified 1988, in NSFH .201 .069 .080 -.006 .026
Stratton 1992- (.042) (.036) (.036) (.005) (.014)
1988
. Ages
hanged :33? 24-31 NLSY .096 .056 .042 .004 -.069
(199.03 1993: 1;?” (.012) (.015) (.016) (.005) (.031)

 

 

 

 

 

 

 

 

 

 

 

 

'40 Years Married and its square.

'4' Unlike the other papers, Comwell and Rupert include tenure at current job and its square in
their specification. Also see text about the consequences of the inclusion of dependents dummy.
Only longitudinal results are reported with years of marriage as a dependent variable.

124

Table 5

Summary of Earliest studies based on data collected before 1970.

 

 

 

 

Authors/ Time Range Age Range Source of Data Estimated Principal

Publishing of Earnings of Data Set Set MMED Finding

Date Information

Lawrence Before Ages 30- Retrospective 17-20 Monthly

Kenny 1969. 40 Monthly Data earnings rise

(1983) more quickly
when a male is
married

Bartlett and 1966-1977 Ages 55- National 20-32 Continuously

Callahan 64 Longitudinal married men

( 1984) Survey of have higher

Older Men earnings

growth

 

 

 

 

 

 

125

 

 

 

Table 6

Summary of MMED Studies based on Data Collected 1970-1980.

 

 

 

 

 

 

 

 

 

Authors/ Time Range Age Source of Cross- Principal Finding
Publishing of Earnings Range of Data Set Sectional
Date Information Data Set MM ED
Cornwell 1971, 1976, Ages 19- National 13.5”" No positive return
and Rupert 197 8 and 29 in Longitudinal to years married
(1997) 1980. 1971 Survey of after one controls
Young Men for tenure.
Nakosteen 1977 Ages 18- Panel Survey 37-41'” Correcting for the
and Zimmer 24 of Income endogeneity of
(1987) Dynamics marital status fails
to reduce the
MMED from its
OLS level. The test
for endogeneity of
marital status is also
inconclusive.
Korenman 1976, 1978 Ages 24- National 15 There exists a
and and 1980. 34 in Longitudinal positive return to
Neumark 1976 Survey of years married after
(1991) Young Men controlling for fixed
effects.
Jeffrey Gray 1976, 1978 Ages 24- National 12.0 Replicates
(1997) and 1980. 31 in Longitudinal Korenman and
1976 Survey of Neumark (1991)’s
Young Men finding of
significant rise in
MMED with years
of marriage
Korenman 1976 Not White male 1 1.9"” MMED associated
and Given managers and with higher
Neumark professionals performance ratings
(1991) from a single and greater/lower
firm likelihood of
promotion/tumover

 

 

 

 

 

 

 

 

I-

IV—

"2 The MMED is found here by adding the coefficient on marital status to the coefficient on the
dummy variable for non-spouse dependents, when the non-spouse dependent variable is included
in the regression. This is relevant for Comwell and Rupert (1997) and Korenman and Neumark
(1991). The lower MMED is the one associated with the longitudinal analysis, the higher MMED
is from the cross—sectional.

”3 The lower estimate is the OLS estimate and the higher estimate is the 2SLS estimate.

'4‘ This includes precompany experience and its square, company service and its square, region
and education dummies.

126

Table 7

Summary of MMED Studies based on Data Collected 1980-1989.

 

 

 

 

 

 

Authors/ Time Range Age Source of Estimated Principal Finding
Publishing of Earnings Range of Data Set MMED
Date Information Data Set
Nakosteen 1984, 1986. Younger Panel Survey -- Shows that traits
and Zimmer 1988 Males of Income that predict future
(1997) Dynamics earnings predict
well the transitions
into and out of
marriage.
Nakosteen 1983, 1985, Singles Panel Survey -- Shows that there
and Zimmer 1987, 1989 who of Income exists a positive
(1987) become Dynamics correlation between
married wage regression
in the unobservables
next between singles and
period. future spouses.
Jacobsen 1984-1989 Younger Panel Survey -23, 5,1 1"" Shows that
and Rayack waves. Males of Income instrumental
(1996) Dynamics variables or fixed
effects removes or
dampens the
MMED and the
negative correlation
between wife’s
hours of work and
earnings. Taken as
evidence against
specialization.

 

 

 

 

 

 

 

 

”5 MMED for not self-employed. Lowest value is the instrumental variables estimate, middle
value is fixed effects estimate, and highest value is the OLS estimate.

127

Table 8

Summary of MMED Studies based on Data Collected 1984-1998.

 

 

 

 

 

 

 

 

Authors/ Time Age Source of Estimated Principal Finding
Publishing Range of Range of Data Set MMED
Date Earnings Data Set
lnfonnation
George 1984-1991 Completed National 10.9 Never Married Males
Akerlof education Longitudinal are more likely to
(1998) by 1985; Survey of engage in non-
Age 24-31 Youth socially productive
in 1989 behavior.
Eng Seng 1990 25-33 National 9.1 Finds that a series of
Loh (1997) Longitudinal tests do not support
Survey of marriage as
Youth productivity-
enhancing. '46
Hersch and 1987-1988, 18-59 National 9.4-1 1.0 Shows that the hours
Stratton 1992- 1994 Survey of of work in the
(2000) 18- 6 5 Families and household, while
and Hersch Households 17.0 negatively correlated
(2002) with earnings, do not
appear to affect the
magnitude of the
MMED.”7
The cohabitation
earnings differential
is only significant for
long-tenn cohabiters.
Jeffrey 1989, 24-31 in National 9.6 Shows that the
Gray 1991, 1993 1989 Longitudinal MMED no longer
(1997) Survey. Survey of rises with years of
Youth marriage, as was the

 

 

 

 

 

 

 

 

”6 Finds that the extent of wife’s labor force participation does not affect the MMED. Finds that
self-employed, married men earn less than self-employed, never-married men and that men who
cohabited with their wives before marriage do not have higher MMEDS than men who did not

cohabitate with their wives before marriage.
Married males, whose wives do not work, do about two hours less housework than never

147

married and married males with spouses who work. Formerly married males work on average
about three hours more than married males. However, overall, the magnitudes of hours worked
do not differ that greatly among housework by marital status. The negative correlation between

hours worked with earnings is primarily driven by food preparation time. This correlation may be

due to males with lower market earnings being more likely to invest in food preparation human
capital. The direction of causation may be the opposite direction.

128

 

 

 

case in the seventies.

 

 

Hyunbae
Chun and
lnjae Lee
(2001)

 

1998.

 

Ages 18-
40

 

March CPS
Supplement

 

11.7-12

 

Estimating a
switching
regressionI48 does not
alter the MMED
significantly. There
is a slight negative
correlation between
unobservables in the
marriage and
earnings equations.

 

 

' The 1999 March CPS Supplement was used. Unlike earlier studies, all races are pooled in the
same sample here. A dummy variable for whether someone is black is included in the

s ecification. The sample is also restricted to never married and married males.

' 8 The switching is between the married and never-married statuses.

129

 

 

Table 9A

List of Values Used for Meta-Analysis of Cross-Sectional MMED
across Age Groups and Over Time

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MidRange of Age Years Data
Study over Years MMED Collected>1980
Kenny (1983) 35 .185 0
Bartlett and Callahan
7
(1984) 59.5 .._6 O
Comwell and Rupert ., q
(1997) -9...5 .135 O
Nakosteen and
7 fl
Zimmer (1987) 7' “’7 0
Korenman and .
Neumark(199l) ’1 '15 0
Non-Trimmed
7 7
Gray(l997) A "9'5 'l"0 0
Akerlof ( l 997) 26 .109 l
Non-Trimmed
7
Gray(l997) B “9'5 '098 1
Eng Seng Loh (1997) 29 .091 1
Modified
Hersch and Stratton 39.5 .143 l
(2002)'
Hersch and Stratton
7
([997) 41...5 .11 1
Chun and Lee (2001) 29 .1 185 1
Table 98

Summary of Meta-Analysis of Changes in Cross-Sectional MMED

 

MMED dependent variable/
Independent Variables

Median Regression

Mean Regression
Excluding Nakosteen and

 

 

 

 

 

 

Zimmer( 1997)
100*Age .386 .425
(.081) (.068)
100*Period (Year>l970) -3.98 -4.25
(2.30) (1.24)
100*Constant 3.04 3.89
(3.84) (2.65)

 

 

' This includes all observations ages 25-54 in the regression in the first wave. Lower educated,
Never married males experienced a disproportionate rate of attrition in the second wave. The
upward bias from the endogenous attrition appears to be six percentage points.

 

 

 

Male Marriage Earnings Differential

Figure 1
Comparison of Predicted and Observed Trimmed MMED

o Trimmed MMED series Smoothed, Trimmed MMED
—B—-—- Predicted Trimmed MMED

 

 

 

 

30 r
/
25 ~ 0
13.4,
8A8 4 /
/:/ / 0 \\e/ O

20 8 ”>6 \

° \
15 "

l I l l r

87 89 9‘1 93 95

Year of Survey

131

Figure 2
Comparison of the Trimmed MMED and DSEDMQ series
For Years of Survey 1991-96

 

 

 

E ——e—— Trimmed MMED series ———e—— Trimmed DSED series

E

g 25 — g

5 w/

in

O)

E 20 -

8 \

U

2 \U

S

m

8 15 —

a)

i

O \

..>.

g 10 .4 /g/‘a \\
9/8/

S \e

d)

D

9

9 5 ‘

1’ 1 1 1

g 91 93 95

Year of Survey

 

"9 DSED stands for the Divorced/Separated Earnings Differential.

132

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