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THREE ESSAYS ON GOVERNMENT
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THREE ESSAYS ON GOVERNMENT INFLUENCE ON LABOR MARKETS
By

Sang Hyop Lee

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Economics

1998

ABSTRACT
THREE ESSAYS ON GOVERNMENT INFLUENCE ON LABOR MARKETS
By

Sang Hyop Lee

This dissertation is composed of three distinct chapters, all of which detect and
examine the influences of government policy on labor markets.

Chapter 1: While many researchers have sought to estimate government wage
differentials, most of them ignore the issues of unobserved heterogeneity and selectivity
among sectors. That research which has focused on corrections for bias in OLS estimates
does not provide convincing answers to these issues, and yields very different results.
Using the NLSY data set with Geocode supplement, this paper tries to explore sources of
bias of the OLS estimates, focusing on individual unobserved heterogeneity and self
-selection, and seeks to resolve the highly contradictory results in the literature. The main
results point to substantial bias in OLS estimates of government wage differentials due to
individual heterogeneity and self-selection. In particular, the results suggest that self-
selection may be responsible for nearly all of the cross-sectional association between
federal government employment and wages.

Chapter 2: Using the second wave of Malaysian Family Life Survey (MFLS-Z),
this study examines the factors that have contributed to schooling and fertility trends in
Malaysia, focusing on the effect of various policies. By focusing on birth cohort
measures of schooling and fertility at specific ages, it is possible to determine whether the

timing of changes in schooling and fertility decisions, by families in different ethnic

groups, coincides with major changes in policy. The results Show that there is a
substantial increase in the education attainment of ethnic Malay children born after 1960,
which might reflect the fact that children born in 1960 would have begun secondary
schooling just around the time when the Malaysian government began the New Economic
Policy (NEP) in 1971. The results also show the extent to which government policy,
whether willfully or inadvertently, influenced the relative fertility levels of different
ethnic groups in the population.

Chapter 3: Several researchers have used various trend decomposition techniques
to decompose the change in the wage gap between two groups. In contrast to previous
decomposition techniques which are flawed on both conceptual and technical grounds,
this paper provides alternative decomposition methods which have clearer interpretations.
The alternative decomposition is applied to the May CPS from 1983 and 1993. The
results fi'om the empirical application show that the previous decomposition methods
yield substantially lower estimates of the portion due to changes in characteristics, and
therefore higher estimates of the portion due to changes in coefficients. This implies the
conclusions drawn from previous methods might overstate the change in the wage gap

attributable to decline in discrimination.

This dissertation is dedicated to my parents,
who have always encouraged me to do my best.

iv

ACKNOWLEDGMENTS

Without the assistance and encouragement of many people, this work would not
have appeared in its present form.

'My sincerest thanks goes to David Neumark, my mentor. His incredible
expenditure of time spent on my behalf, his technical advice, and his general guidance
made my dissertation possible. He not only gave me valuable comments and suggestions
on my dissertation, but he also helped me to navigate the rough waters of the whole
dissertation process. His help and comments were invaluable.

I owe a special thanks to John Strauss, who is in effect my second mentor. His
continual efforts over the past four years, both as an advisor and teacher, provided the
atmosphere and the incentive that I found indispensable in my graduate research. In
particular, his comments and suggestions on Chapter 2 vastly improved my dissertation.

I also want to express my appreciation to Robert LaLonde, Jeff Biddle, and Jeff
Wooldridge. The analysis in Chapter 1 was especially strengthened by their constructive
suggestions. I am also indebted to Steven Matusz and Ann Feldman for their help in
various stages in my graduate study.

I also cherish the advice and friendship of my fellow graduate student. My thanks

especially goes to Jess Reaser, Heather Bednarek, Kathleen Beegle, and Soomyung Jang.

Finally, I give the largest part of my thanks to my family. My wife, Yangseon,
provided much support that helped move my dissertation forward. Her encouragement,
both as a fellow graduate student and companion, helped prod me whenever fatigue and
laziness overtook me. My children, Jihoon and Sehoon, were patient and sympathetic,
even when I was neglectful in taking care of them. My parents, parents-in-law, and sister
have always supported and encouraged me to do my best. Thanks to all of them for their

love and encouragement.

vi

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... ix
LIST OF FIGURES ......................................................................................................... xi
INTRODUCTION ............................................................................................................ 1
CHAPTER 1
A RE-EXAMINATION OF GOVERNMENT WAGE DIFFERENTIALS
IN THE UNITED STATES ............................................................................................. 6
1. Introduction ....................................................................................................... 6
2. Related Research ................................................................................................ 10
3. Data Construction and Variables ........................................................................ 13
4. Empirical Results ............................................................................................... 16
4.1 OLS Estimation .................................................................................... 16
4.2 Estimates Including Proxy for Ability, and Fixed Effect Estimates ....... 21
4.3 Estimates Correcting for Self-Selection ................................................ 25
5. Conclusion ........................................................................................................ 31
Appendix ............................................................................................................... 45
Bibliography .......................................................................................................... 46
CHAPTER 2
A STUDY OF ETHNIC DIFFERENCES IN FERTILITY AND CHILD SCHOOLING
IN MALAYSIA: THE IMPACT OF GOVERNMENT POLICIES .............................. 50
1. Introduction ...................................................................................................... 50
2. Malaysian Setting .............................................................................................. 53
3. Data and Variables ........................................................................................... 56
4. Methodology and Specification ....................................................................... 61
5. Empirical Results ............................................................................................. 65
5.1 Birth Cohorts .......................................................................................... 65
5.2 Family Characteristics ............................................................................ 66

vii

5.3 Community Characteristics ...................................................................... 68

5.4 Documenting across Birth Cohorts and Ethnic Groups ........................... 71
6. Conclusion ........................................................................................................ 73
Bibliography .......................................................................................................... 91
CHAPTER 3
A NOTE ON DECOMPOSING CHANGES IN THE WAGE GAP
: A CRITICAL COMMENT ON PREVIOUS METHODS .......................................... 94
1. Introduction ...................................................................................................... 94
2. Decomposition of the Change in the Wage Gap ................................................ 95
2.1 A Critique of the Previous Decomposition .............................................. 95
2.2 Two Period Model of Oaxaca's Decomposition ....................................... 99
3. An Empirical Application ................................................................................ 103
4. Conclusion ...................................................................................................... 106
Bibliography ........................................................................................................ 1 12

viii

LIST OF TABLES

CHAPTER 1

Table 1: Summary of Previous Studies by Krueger, and Gyourko and Tracy ............. 33
Table 2: Means and Standard Deviations of Variables ................................................ 34
Table 3: OLS Estimates of Government Wage Differentials ...................................... 35
Table 4: Government Wage Differentials by Occupation Category ............................ 37
Table 5: Proxy for Ability and Panel Data Estimates .................................................. 38
Table 6: Selectivity Bias Correction Estimates ........................................................... 40
Table 7: Sensitivity Analysis (Second Stage Estimates) ............................................ 42
Table 8: Summary of the Results: A Comparison ....................................................... 44
Table A1: Number of Job Switchers and Percentage ..................................................... 45
CHAPTER 2

Table 1: Means and Standard Deviations of Variables ................................................ 75
Table 2: Estimates of Child Schooling (Male Children) ............................................. 77
Table 3: Estimates of Child Schooling (Female Children) .......................................... 79
Table 4: Estimates of Number of Children .................................................................. 81

ix

CHAPTER 3

Table 1:

Table 2:

Table 3:

Table 4:

Table 5:

Examples of Decomposition ........................................................................ 107
Means and Standard Deviations of Variables .............................................. 108
OLS Estimates (Basic Specification) .......................................................... 109
Decomposition Based on Basic Specification ............................................. 110
Decomposition Based on Alternative Specification .................................... 1 11

LIST OF FIGURES

CHAPTER 2

Figure 1: Years of Schooling at Child’s Age 18 ........................................................... 83
Figure 2: Number of Children at Woman’s Age 37 ...................................................... 84
Figure 3: Predicted Schooling at Child’s Age 17: Son’s Birth Cohort ......................... 85
Figure 4: Predicted Schooling at Child’s Age 17: Daughter’s Birth Cohort ................ 86
Figure 5: Predicted Schooling at Child’s Age 20: Son’s Birth Cohort ......................... 87
Figure 6: Predicted Schooling at Child’s Age 20: Daughter’s Birth Cohort ................ 88
Figure 7: Predicted Number of Children at Woman’s Age 32 ..................................... 89
Figure 8: Predicted Number of Children at Woman’s Age 37 ..................................... 90

xi

INTRODUCTION

One of the challenges to economic research is to detect the consequences of
government influence in light of the complex and intertwined world in which we live.
These complexities ofien mask the links between a government action and its effect on
individuals. This dissertation is an attempt to detect and examine this government
influence on labor markets in three different aspects.

Chapter 1, A Re-examination of Government Wage Differentials in the United
States, is an attempt to resolve coflicting evidence in the literature regarding government
wage differentials. In the early 1960’s, a reform of the pay system for most federal
workers in the United States began in an attempt to apply a coherent principle of pay
determination: comparability, which requires government workers to receive wages
equivalent to private sector workers.

However, most of previous studies show a fairly uniform picture; estimates
suggest that wages are 10 to 20 percent greater for federal government workers than
otherwise comparable private sector workers in the United States. Most of these studies,
however, completely ignore issues of unobserved heterogeneity and selectivity among
sectors, with two notable exceptions. Krueger (1988a) uses the fixed-effects approach
and Gyourko and Tracy (1988) introduce selection bias methods to address these issues.

However, the results are not convincing because their analyses rely on either a very small

number of switchers (Krueger) or unconvincing identifying assumptions (Gyourko and
Tracy).

In this paper, I utilize a potentially more appropriate data set (NLSY with
Geocode Supplement) and more compelling identifying assumptions to provide a
comprehensive examination of these questions. The main innovation of this paper is to
give careful attention to constructing convincing identifying variables; the identifying
variables constructed are the percentages of federal, local, and state government
employment in the local labor market when the worker was at age 14. As long as these
variables create exogenous variation, which helps to predict the sectors of current
employment, but do not affect current wages, we can use them as identifying variables.

The results suggest that the implied selectivity correction estimates imply that
OLS estimates are more biased than either the test scores approach or the fixed-effects
approach suggests. Furthermore, the direction of bias under the selectivity correction
estimates is consistent with the results from both the test score approach estimates and the
fixed-effect estimates for each government sector relative to the private sector. One
striking finding is that the federal-private wage differential falls to 2 percent, suggesting
that self-selection might be responsible for nearly all of the cross-sectional association
between federal government employment and wages.

Chapter 2, A Study of Ethnic Differences in Fertility and Child Schooling in
Malaysia: The Impact of Government Policies, examines the factors that have contributed
to schooling and fertility trends in Malaysia focusing on the effect of various government

policies. Along with its rapid economic growth over the last few decades, Malaysia has

also experienced rapid growth in the educational attainment of its population. Moreover,
the shortfall in the education of Malays relative to other ethnic groups has also been
eliminated and even reversed. This fact suggests that the increase in educational
attainment was more concentrated among ethnic Malays than among Chinese and Indians
in Malaysia. Fertility has also declined in Malaysia. However, the fertility decline is
more concentrated among Chinese and Indians. As several researchers point out, this is
in contrast to the trend in fertility of Malays in other multi-ethnic countries, such as
Singapore, where rapid economic growth has apparently lowered Malay fertility much
more drastically.

Most research suggests that government policies might have affected, both
directly and indirectly, the demographic changes in Malaysia. Some researchers have
pointed out the importance of direct government intervention in educational attainment
and fertility decisions. Others emphasize the important role of the policies on labor
market conditions. For example, it is argued that the implementation of the New
Economic Policy (NEP) in 1971 has had an impact on parents’ decisions about fertility
and child schooling through its impact on labor market conditions.

In contrast to previous studies, this study focuses on birth cohort measures of
fertility and schooling across ethnic groups. By truncating fertility and schooling
measures at specific ages, it is possible to determine whether the timing of changes in
schooling and fertility decisions, by families in the different ethnic groups, coincides with

major changes in policy.

The results Show that the Malaysian government has been quite effective in using
its policy tools both as a means to raise overall education levels as well as a way to alter
the schooling distribution among its ethnic groups. In particular, there is a substantial
increase in the pace of educational attainment, especially that of ethnic Malay children
born after 1960, which might reflect the fact that children born in 1960 would have begun
secondary schooling just around the time when the Malaysian government began the NEP
in 1971. The results also show the extent to which government policy, whether willfully
or inadvertently, influenced the relative fertility levels of different ethnic groups in the
population. Results document the widening fertility gap between Malays and other ethnic
groups beginning with the 1935 birth cohort, which is consistent with the explanation that
women born after 1935 were affected by the NEP.

Chapter 3, A Note on Decomposing Changes in the Wage Gap, A Critical
Comment on Previous Methods, re-examines previous decomposition techniques and
their interpretation. Several researchers have used trend decomposition techniques to
decompose the change in the wage gap between two groups. These analyses are
important, since they show how the changes in the means and the coefficients of the
explanatory variables combine to affect the change in the wage gap over time. The
previous results from these analyses suggest that, the proportion of the male-female wage
gap attributable to discrimination declined over time. This is also interpreted as an
evidence that government policy play a role in declining wage gap due to social

discrimination.

This paper argues that the previous decomposition methods are flawed on both
conceptual and technical grounds. In contrast, this paper suggests an alternative
decomposition method which might avoid the shortcomings of interpretation found in
previous treatments. The alternative decomposition is then applied to the May CPS from
1983 and 1993, and the results are compared to the results obtained using the previous
methods.

The results from the empirical application in this two-period model show that the
previous decomposition methods yield substantially lower estimates of the portion due to
changes in characteristics, and therefore higher estimates of the portion due to changes in
coefficients. This implies the conclusions drawn from previous methods may overstate

the change in wage gap attributable to decline in discrimination.

Chapter 1

A RE-EXAMINATION OF GOVERNMENT WAGE DIFFERENTIALS
IN THE UNITED STATES

1. Introduction

In the early 1960’s, a reform of the pay system for most federal workers in the
United States began in an attempt to apply a coherent principle of pay determination:
comparability. The rationale for comparability as a pay policy is relatively simple; since
government is not a profit-making enterprise, there is no market discipline to help guide
pay-setting. Consequently, the government can turn to the private sector—where wages
are disciplined by market forces-for guidance. For example, salaries for most white
collar federal government workers are determined on the basis of comparisons with
private sector pay information contained in the PATC survey, a survey of private sector
wages of professional, administrative, technical and clerical jobs.

However, the PATC survey, as it has been applied, has been criticized on both
conceptual and technical grounds.l For example, because many jobs are unique to the

public sector, the policy of setting public-private pay based on job comparisons is

 

' These criticisms include biases associated with i) the measure of compensation used, ii) the technique of
job comparisons, iii) the scope of the survey universe, and iv) the requirement that pay rates fulfill both
external and internal alignment criteria. See Smith (1977) and Fogel and Lewin (1974) for a detailed
discussion.

questionable. As a result, instead of focusing on the earnings of workers with comparable
job characteristics, most academic researchers have focused on comparisons across sector
of earnings of workers with comparable personal characteristics.

Most of these studies Show a fairly uniform picture; estimates suggest that wages
are 10 to 20 percent greater for federal government workers than otherwise comparable
private sector workers in the United States (Smith (1977), Quinn (1979), Venti (1987),
Krueger (1988a), Moore and Raisian (1991), Katz and Krueger (1991)).2 When the focus
turns to state and local governments, results show that state and local government pay is
at most equal to that of the private sector. Most of these studies, however, completely
ignore issues of unobserved heterogeneity and selectivity among sectors, with two
notable exceptions. Krueger (1988a) uses the fixed-effects approach and Gyourko and
Tracy (1988) introduce selection bias methods to address these issues. However, the
results are not convincing because their analyses rely on either a very small number of
switchers (Krueger) or unconvincing identifying assumptions (Gyourko and Tracy).

Do unobserved individual characteristics matter in estimating government wage
differentials? Is there any good identifying variable to use in a self-selection model?
Does the federal government successfully use higher wages to attract high-ability
workers? The existing literature does not provide convincing answers to these questions.
In this paper, I utilize a potentially more appropriate data set and more compelling

identifying assumptions to provide a comprehensive examination of these questions.

 

2 This persistence of federal-private wage differentials complements another evidence, for example, of job
queues in the federal government sector (Venti(1987), Krueger (1988b), and Heywood and Mohanty
(l995a)).

This analysis will focus on the federal vs. private sector, although wage differentials
between the private and local/state government sector are also addressed.

Several techniques are employed to examine the issues raised above. First, unlike
prior studies, I use test scores as error-ridden indicators of ability, and some variables as
instruments for potential measurement error in test scores. Blackburn and Neumark
(1992) provide a clear discussion of the pros and cons of this approach. For example, this
approach might avoid problems of longitudinal analysis such as the exacerbation of
measurement error from misclassification of workers, and selectivity of sector changers.3
However, the validity of this method depends on test scores being correlated with ability
that is rewarded in labor markets.4 Thus, this approach should also be viewed as
complementary to panel data methods. Because test scores may not capture all of the
heterogeneity, I also employ fixed-effects estimation. However, my sample has four
times the number of switchers as that of Krueger (1988a), and unlike Kreuger’s, it
consists of only males.

Finally, a selectivity bias correction model is used to address the possible
correlation between unobserved factors and Sector of employment. The main innovation
of this paper is to give careful attention to constructing convincing identifying variables;
in particular, I use the percentage of workers in each sector in the local labor market in

which the respondents grew up. The idea is that variation in the sector composition of

employment in the local labor market where the respondents grew up is exogenous to the

 

3 Self-selection of job changers may cause longitudinal estimation of wage gaps to be inconsistent. See
Solon (1988) for a detailed discussion.

’ Furthermore, because these methods also depend on error-ridden measures of ability, valid identifying
assumptions are needed to correct for measurement error.

individual, and therefore generates variation in the probability of sectoral choice. At the
same time, this variation is unlikely to affect current wages. The identifying variables
constructed are the percentages of federal, local, and state government employment in the
local labor market when the worker was at age 14. As long as these variables create
exogenous variation, which helps to predict the sectors of current employment, but do not
affect current wages, we can use them as identifying variables. For example, an
individual who grew up in Lansing (a state capital) might be more likely to work for the
state government sector than one who grew up in Traverse City, Michigan.

However, because the percentage of workers in each sector in geographical areas
may be persistent over time, and because many individuals may remain in the same
geographical area, the percentage of workers in each sector at age 14 may be correlated
with contemporaneous percentage of workers in each sector, which may in turn affect
current wages. To explore this issue, a stronger test is performed by adding the
contemporaneous percentages of workers in each sector as controls in the wage equation.

The results generally point to substantial bias in OLS estimates of government
wage differentials due to individual heterogeneity and selectivity among sectors. The
results from both the test score approach and the fixed-effect estimates indicate that OLS
estimate of the federal-private wage differential is substantially biased upward. The
results of both procedures also suggest that OLS estimate of the state-private wage
differential is biased toward zero, while that of local-private wage differential is biased
away from zero. When the percentages of workers in each sector in the local labor

market are used as identifying variables, the implied selectivity correction estimates

10

imply that OLS estimates are more biased than either the test scores approach or the
fixed-effects approach suggests. Furthermore, the direction of bias under the selectivity
correction estimates is consistent with the results from both the test score approach
estimates and the fixed-effect estimates for each government sector relative to the private
sector. One striking finding is that the selectivity correction estimates of the federal
-private wage differential falls to 2 percent, suggesting that self-selection might be
responsible for nearly all of the cross-sectional association between federal government

employment and wages.

2. Related Research

The overriding concern of bias in estimated government wage differentials has
resulted in two types of approaches; longitudinal analyses and corrections for selectivity
bias. Table 1 summarizes the two prominent research papers by Krueger (1988a), and
Gyourko and Tracy (1988), each of which follow one of the two approaches. As noted in
Table 1, these two papers give very different answers; the OLS estimates of federal
-private wage differential are substantially biased upward in Krueger (1988a), while they
are substantially biased downward in Gyourko and Tracy (1988).5 This contradictory
result is the motivation for further explanation.

Wage models with unobserved heterogeneity allow individuals’ unobserved

characteristics to be correlated (with government status variables. Krueger (1988a)

 

5 The fact that selection depends on the individual unobserved characteristics (a,) in the model of interest
does not introduce a selectivity bias in the fixed effects estimators, since the error term under the fixed
effect does not involve 01,. This suggest that FE and selectivity correction estimates might point in the
same direction, in contrast to the result in Krueger vs. Gyourko and Tracy. See Verbeek and Nijman
(1992) for a detailed discussion.

11

attempts to control for this problem by using matched Current Population Survey data
sets (CPS) and Supplemental Displaced Worker Surveys including sector switchers and
stayers. From longitudinal analyses of these data sets, he concludes that the federal
-private wage differential (0.058 for CPS data, and 0.107 for the Displaced Worker
Surveys) is much smaller than his cross-sectional OLS estimates (0.247 and 0.126).

As Moulton (1990) has noted, however, not many workers actually moved
sectors.6 The standard error of the federal government indicator in the longitudinal
analyses becomes large (0.042 for fixed-effects estimates vs. 0.017 for OLS estimates),
suggesting that it is difficult to precisely estimate the federal wage differential fi'om the
longitudinal analyses given the very small sample of switchers in the data sets and the
potentially large effect of measurement error. Given these problems, Krueger examines
the length of queues for federal jobs assuming that an increase in the wages of federal
workers relative to private sector workers increases the number of applicants for federal
jobs. He also argues that there is a positive relationship between the number of applicants
and the quality of applicants. As he notes, however, this relationship is subject to
alternative interpretations because evidence on the ability of both applicants and
employees for federal government job is very scant.

Wage models with selectivity allow individuals’ selection of sector to be
endogenous with respect to the unobserved individual characteristics which affect wages.

Sectors are not randomly assigned across the population; rather, individuals make their

 

6 In the two surveys he uses, the number of federal-private switchers are 52 for the CPS, and 59 for the
Displaced Worker Surveys. In both cases, these numbers include both men and women, for whom wage
structures, in particular public-private differentials, may differ.

12

own sectoral choice. Depending on how these choices are made, measured wage
differences between workers in different sectors may bias the true wage differential.
Gyourko and Tracy (1988) deal with this problem by allowing for endogenous selection
of government status. By introducing a selectivity bias correction model, they conclude
that the federal-private wage differential with the selectivity bias correction (0.289), the
unconditional wage differential, is much bigger than the wage differential without the
selectivity bias correction (0.188), the conditional wage differential. On the local and
state government level, they also found substantial unconditional wage differentials
(0.181 for local government, and 0.095 for state government), which far exceed the
conditional wage differentials (0.020 and 0.013, respectively).

In any kind of two-stage estimation procedure that corrects for selection bias,
however, most researchers employ some variables in the sectoral choice equation which
they assume are excluded fi'om the wage equation, so that identification need not rest
purely on functional form assumptions via the non-linearity.7 Even though Gyourko and
Tracy use levels of education as a disjointed spline function with break points at high
school and college education for identification including only years of schooling in the
wage equation, this might be unsatisfactory, since educational status might affect wages

independent of years of schooling.8

 

7 As Olsen (1981) argued, we have some intuition about the proper set of explanatory variables to be
included in a regression, but rarely have any intuition about the proper functional form for those variables.
Differing statistical assumptions may lead to different non-linear functions and different estimates of
intrinsic and selection-induced effects. Thus, including the same variables in the regression equations as
well as in the probability model generally leaves the effect of selection unidentified. Also see Schaffner
(1995) for a discussion of this issue.

’ See Card and Krueger (1992) about the specification of the education variable. They found that the
linear-spline specification provides a slightly better fit to the micro data, compared to a conventional log-
linear specification.

13

As mentioned above, I deal with this problem using regional exogenous variation
as identifying information. There is a growing body of literature which uses geographic
differences as a potential source of exogenous variation. For example, Card (1993)
explores the use of college proximity as an exogenous determinant of schooling. He
finds that men who were raised in local labor markets with a nearby 4-year college have
significantly higher levels of education and earnings. When he takes college proximity as
an exogenous determinant of schooling, the IV estimates of the return to education are
25-60 percent higher than the corresponding OLS estimates. A similar idea is used by
Rouse (1995) to control for the endogeneity of choice between a 4-year college and a 2
-year college. She also finds that closer college proximity is associated with higher rates
of college attendance. These approaches might solve the identification problems in two
-stage estimation methods. However, the validity of this method also relies on the
restrictive assmnption that geographic differences (living near a college) have no effect
on earnings apart from the effect through education. In my work, it will be important to
explore the possibility that the sectoral composition of the workforce when individuals

are young affects their later wages.

3. Data Construction and Variables

Two data sets are used. The primary source for estimation is the National
Longitudinal Survey of Youth Cohort data with Geocode supplement (NLSY Geocode).
The NLSY was first conducted in 1979 for individuals aged 14 to 22, with 12,686

respondents. The cohort was re-surveyed every year thereafter. The sample used in this

l4

analysis consists of young male full-time workers who were employed at least once
between 1987 and 1993, but not self-employed. Sales workers, armed forces, farmers and
farm laborers, and private household workers are excluded. To avoid outlier problems,
those who report wages less than one half of the minimum wage, or greater than $100 per
hour (converted to common base year) are also excluded. The assignment of workers to
the different sectors is based on direct responses in the survey to the class of worker
categories.

Most of the previous research has used CPS data for estimation of government
wage differentials. For our analytical purposes, the NLSY data has more useful
characteristics than the CPS. The first advantage of the NLSY is that it contains various
test scores which can be used as indicators of ability. The indicators of ability used are
Armed Services Vocational Aptitude Battery (ASVAB) test scores.9 Because scores may
differ across age groups because of schooling effects, age effects are removed from the
test scores by regressing each test score on a set of eight age dummies, and using the
individual’s standardized residual as their test-score measure.

The second advantage of the NLSY data is that with the Geocode supplement it
includes detailed information on both current residence and residence at age 14. In
particular, I use the 1980 US. Census of Population and Housing data (1980 Census) to
construct variables that might capture exogenous sources of variation in the likelihood of

working in the alternative sectors. This variable construction procedure consists of three

 

9 These tests consist of ten categories: paragraph comprehension, general science, arithmetic reasoning,
mathematics knowledge, word knowledge, mechanical comprehension, numerical operations, electronic
information, auto and shop information, and coding speed.

15

steps. First, by using the Geocode supplement, I identified the state and county of
respondents at age of 14. Second, using the 1980 Census for every state, the level of
federal, local, state goverrunent and private employment in the local labor market
(counties) is measured. Finally, the percentage of employment in each sector is
calculated to construct the employment percentage in each sector at approximately age
14.10 Then, these variables are used as identifying variables which are correlated with
sectoral choice but should not affect wage net of this correlation. I also use 1990 Census
data set to construct contemporaneous percentage of workers in each sector to address the
issue raised above; the percentage of workers in each sector at age 14 may be correlated
with the contemporaneous percentage of workers in each sector, which in turn affect
current wages.

Some other advantages of the NLSY data allow for improvements in the
specification of the wage equation. Researchers who use the CPS must measure
experience by using potential years in the labor force. This specification implicitly
assumes that all years since school were spent in the labor force, which is not necessarily
true. Furthermore, most of the previous research did not control for tenure. However,
government workers are known to have low turnover, and thus high levels of tenure
relative to the private sector (Ippolito (1987)). This fact suggests that the wage gap
estimates that do not control for tenure may bias upward the government wage with

respect to the private sector wage. Because the NLSY data provide information on both

 

1° Of course, this is slightly off because of age variation, which is unlikely to be a problem.

16

weeks worked and tenure, it is also possible to construct both actual work experiences in
the labor market and the years of tenure on the current job.ll

Table 2 shows the means and standard deviations of the variables used in this
analysis. The means of the variables imply that public-sector workers are generally
characterized by higher education and tenure. The percentage of married, non-white, and
union-covered is also higher in the public sector than the private sector. Finally, it is
notable that there is a small but persistent pattern in the percentage in each sector at age
14; the percentage of workers' current sector in the workforce at age 14 is generally

higher for workers' current sector.

4. Empirical Results

4.1 OLS Estimates

In this section, I examine issues regarding the specification in the OLS context.
Specifically these issues include the extent to which one must control for regional
variation, tenure, and occupation. Wage differentials within occupation categories are
then addressed, followed by analysis of the bias in OLS estimates using the test score
approach, fixed-effects, and selectivity corrections. The basic methodological approach

here is similar to that used in other studies. An equation of the form

 

" Another potential advantage of the NLSY data is that it follows workers who move to a new location.
Since the CPS cannot match individuals who change address during the course of the year, the sample is
not completely representative of all workers. Krueger argues that this selection rule is not likely to produce
an important bias in the estimated wage differentials because both joiners and leavers who move to a new
location are eliminated from the sample. However, as he noted, when we estimate wage differentials for
joiners and leavers separately, the coefficients will probably be biased toward zero due to the sample
selection rule of not following workers who move to a new location.

17

(1) Intw.) = 2%... +ifl..,d,-.. + a.
J: _ ,3
is estimated, where X is a vector of individual, regional and job specific characteristics
included as controls, and d’s are a set of dummy variables that take values of one if the
individual is employed in a particular government sector (federal, state, or local
government), and zero otherwise.12 Time subscripts are included to clarify the time at
which the variables are measured. All estimates were obtained using the consistent
variance-covariance matrix estimator of White (1980). The standard errors are thus
robust to heteroscedasticity.

One important issue here is how the detailed regional variables should be included
in the specification. Several researchers have discussed inter-state differences in the cost
of living as a possible contributing factor to the government-private wage differential.
On the state and local government level, Belrnan and Heywood (1995) demonstrate that
failure to consider this inter-state effect might be misleading in the estimation of local
and state government wage differentials.13

In order to examine this issue, I calculated OLS estimates with and without 50

state dummy variables and one for the District of Columbia. Estimates of these

 

'2 As have many researchers, I exclude the postal service sector from the sample and hence from the
federal government. There is a strong motivation for doing this; even though postal workers are also
federal government workers, their wages are set in quite a different manner. See Asher and Popkin (1984)
and Perloff and Wachter (1984) for discussion of the issue of wage comparability for postal workers.

'3 Even though the differences in cost of living in different locations were taken into account, it is expected
that the federal-private pay relationship will not vary with location because the national pay schedules of
the federal government for white-collar workers do not allow for such area differences. However, this
uniform federal wage schedule nationwide has changed since 1990. For example, employees in New York,
Los Angeles, and San Francisco area got 8% geographic adjustments in 1990. See Risher and Fay (1991)
for a detailed discussion.

l8

specifications are reported in columns (1) and (2) of Table 3. The specification of
column (1) includes only three regional dummy variables (North Central, West, and
South), and column (2) includes 50 state dummies and one for the District of Columbia.
Regardless of specifications, one persistent result is worth noting; there exists a highly
significant wage differential of about 11 percent for the federal government relative to the
private sector. On the state and local government level, the estimate of the wage
differential is almost zero for local government and negative 8 to 9 percent for state
government. In particular, the coefficients for state and local government sectors change
by one to two percentage points when we include the state dummy variables, suggesting
that inter-state differences in the cost of living might be a possible contributing factor to
govemment-private wage differentials. I will use the specification in column (2) when I
compare the other estimates with OLS estimates.

As mentioned above, most of the previous research did not control for tenure,
which may result in upward bias of the estimates of the government wage differentials.
To explore this issue, I also performed OLS estimates without tenure variable and its
square. Estimates of this specification are reported in column (3). Compared to column
(2), the coefficients of the government sectors increase by about 2 percentage points,
suggesting that failure to include tenure might bias the government wage differential
upward.

Another set of variables sometimes included in wage regressions are family
background variables such as years of parental schooling. They are thought to proxy

either for home environment-induced variation in productivity or for connections

l9

improving access to premium jobs. The effects of introducing parental schooling into the
wage equation are shown in column (4). The inclusion of these variables has virtually no
effect on the estimated coefficient of the government dummy variables, even though the
coefficient for schooling decreases slightly.

Moulton (1990) argues that estimates of government wage differentials in
previous research do not reflect the true wage differential, because they do not control for
detailed differences in occupations.14 This issue is closely related to the debate regarding
public sector wage determination. Jobs performed in the public and private sectors are
not always comparable, and therefore subjective decisions have to be made as to how a
job should be classified. Some jobs are even unique to the various public sectors.
Consequently, including detailed occupation dummies may be inappropriate because it
might rationalize wage differentials in the government sector. However, it is also true
that less attention is given to the important differences between the sectors in the
distribution of detailed occupations within the major occupational categories. Failure to
include these detailed measures results in treating very different occupations within major
occupation groups as equivalent.

To address this issue, wage regressions are estimated including three-digit
occupation dummy variables to control for different occupational distributions among
sectors. Column (5) of Table 3 reports the wage differentials with these occupational
controls. In particular, the coefficient for federal government dramatically decreases

from 0.105 (OLS estimate) to 0.052. However, this difference results not only from

 

" Gyourko and Tracy (1988) included only one indicator for professional occupations, whereas Quinn
(1979) and Borjas (1980) did not include any occupational variables.

20

differences in the distribution of occupation across sectors, but also from the existence of
some unique jobs across sectors controlled for by occupation dummy variables. To
explore this issue, the wage equation is re-estimated dropping any sectors where the
three-digit occupations cannot be found in all sectors. Columns (6) and (7) present
evidence on this issue. Column (6) reports the wage differential without three-digit
occupation dummies, while column (7) reports the wage differential including the three
-digit occupations. One main finding is that the coefficients for the federal government
indicators change slightly (0.067 to 0.064), suggesting that the results in column (5) are
not because of the differences in the distribution of occupation, but mostly because of the
existence of unique jobs in various sectors, which is not consistent with Moulton’s
argument.ls

An examination of estimates of government wage differentials within occupation
categories can indicate whether wage differentials exist only in certain occupations or are
invariant across occupations. In particular, many researchers have argued that public
sector earnings advantages tend to be larger for workers at lower levels in the
occupational ranking.“5 Based on this argument, Hundley (1991) has shown that public
-private wage differentials tend to decline as occupational skill requirements increase.
Columns (1) through (7) of Table 4 report governmental wage differentials within
occupations. Some consistent patterns can be found in these estimates. First, the federal

-private wage differential is positive and significant in most occupations. Furthermore,

 

’5 This result also implies that these unique jobs seem to have federal government sector wages most out of
line with what is predicted by observed individual characteristics.

'6 See Smith (1977) and Fogel and Lewin (1974) regarding non-discriminatory nature of wage
determination in the public sector.

21

the pattern of relative wage differentials across sectors does not vary across occupations;
the federal government pays the most, while the state governments pay the least.
However, the estimated wage differentials are not invariant across occupations. The
wage differentials between the federal government and private sector are greatest in
operative and labor occupations, but least in professional and managerial jobs. This
finding is somewhat consistent with the argument provided; relatively large federal
-private wage differential for the federal government workers at lower levels in the
occupational ranking, and smaller (but positive) federal-private wage differential for the
federal government workers at higher levels in the occupational ranking. However, this

relationship is not as clear at the local and state government level.

4.2 Estimates Including Proxy for Ability, and Fixed-Effects Estimates

To control for potential omitted ability which may be correlated with the sector of
employment, initially I add to the equations the standardized residual of ASVAB test
scores. These results are reported in columns (1) and (2) of Table 5. In column (1) each
test score is included separately, while in column (2) the average test score is included as
a proxy for ability. The test score approach estimates suggest that the OLS estimate of
the federal-private wage differential is slightly biased upward (compared to column (2) of
Table 3), while that of the local-private wage differential is slightly biased downward.

Is this bias statistically significant? To test the null hypothesis that there is no
unobserved ability correlated with each government status variable, I performed a

Hausman type test for each (single) coefficient estimate of the government status

22

variables. The result of the Hausman specification test for the coefficient of the local
government dummy (p-value is zero) implies that omission of the test scores leads to an
omitted variable bias that biases downward the local government dummy. However, it is
not significant for the state government (p-value is 0.63), and marginally significant for
the federal government (p-value is 0.14), suggesting that these estimates are little
different from the OLS estimates excluding the proxy for ability.

Because the test scores are probably error-ridden proxies for ability, using them
may cause measurement error bias in the wage equation estimates, and therefore may be
inadequate according to the role of ability. To allow for this potential measurement error
in test scores, a set of variables is used to instrument for test scores. The set of
instruments includes birth order percentile among siblings and its square term, a dummy
for living with both parents at age 14, and a dummy for living in an urban area at age 14,
which might create variation in individual’s test scores. There is no clear way to test
whether some specific instruments are valid or not. However, since these models are
overidentified, it is possible to use overidentification tests. Column (3) of Table 5 reports
two-stage least squares estimates of this model. Compared to column (2), instrumenting
for test scores leaves the government status coefficient estimate virtually unaffected
except for local government. However, the Hausman test does not imply that
instrumenting for test scores is necessary. In addition, the overidentifying restriction test
statistic (p-value is 0.389) suggests that there is no evidence against the overidentifying
restrictions. In summary, the test scores approach indicates that the wage differential

with respect to the private sector is about 10 percent for the federal government, 1 percent

23

for the local government, and negative 8 percent for the state government, which are quite
close to the OLS estimates.

Because test scores may not capture all of the heterogeneity, unobserved
heterogeneity is addressed using panel data techniques. That is, wages are assumed to be

determined according to an equation of the form

(2) ln(wit) = ifljxjit +iflk+jdjit +ai +3.1

jg] j.1

where the parameter or, represents the time invariant unobserved individual characteristics
such as ability, motivation and/or effort. Because the numbers of switchers are crucial in
this estimation, the numbers and the percentage of sector changes are presented in Table
A1 in Appendix. The rate of sector change is calculated by the sum of switchers between
two sectors divided by the total number of individuals in the same two sectors. For
example, 127 male workers (58 plus 69) in the sample changed sector between the federal
and private sector (sector change percentage is 0.7%).

Column (4) of Table 5 reports the fixed-effects (FE) estimates of the wage
differentials. The FE estimate of the wage differential for federal government workers
decreases by one half (to 0.053), suggesting that the OLS estimate of the federal-private
wage differential is biased upward. The wage differential for state government workers
changes to negative 0.016, suggesting that the OLS estimate of the state-private wage

differential is biased toward zero, while the wage differential for local government

24

workers changes to 0.062, suggesting that the OLS estimate of the local-private wage
differential are biased away from zero. Hausman test (FE vs. OLS) for each (single)
coefficient of the government status variables suggests that the differences in the
estimates are statistically significant for the government status dummy variables for each
sector (all p-values are zero).

As shown in Table A1 in Appendix, the sector change percentage is notably
higher between the state and local government sectors (5.7%). This may result from
more frequent job switches between the two sectors based on similar job characteristics.
However, it is also possible that misclassification occurs more between these two sectors
than any other two sectors. To address the potential problems of misclassification
between local and state government workers, the wage regression is re-estimated
excluding switches between these two sectors. Column (5) reports these estimation
results. The coefficient of the state government dummy falls by 1 percentage point
compared with the previous specification. However, the coefficients of the federal and
local government indicators are almost invariant, suggesting that the above results are
robust.

To make sure the difference in coefficients between OLS and FE are attributable
to unobserved heterogeneity, as opposed to the difference in sample composition between
the whole sample and the sample of changers, wage regressions are re-estimated using
only sector changers (not shown in Table). The OLS estimates based on the sample of
changers are 0.115 for the federal government, negative 0.101 for the state government,

and 0.017 for the local government. Since these estimates are quite similar to the OLS

25

estimates based on the whole sample, it is the FE estimation, not sample composition,
that shifts the estimates.

It is notable that the results of the federal-private wage differential are very close
to those of Krueger. So for this issue, results are robust across the two data sets (the CPS
and NLSY). However, as Table 1 pointed out, the self-selection correction makes a much
bigger difference, posing a puzzle. In the next section, I explore this issue using a self-

selection correction approach.

4.3 Estimates Correcting for Self-Selection

Given an individuals' productivity in various types of work, self-selection may
influence observed wages since a rational individual will select the alternative which
yields the highest value of utility. In our context, self-selection may cause the
disturbance term in the wage equation to be correlated with the error term in the sectoral

choice equation. Thus, a wage equation of the form

h+1

k h
(3) 111(Wi.) = Zfljxijr + Zfllujdjit — Zasps’isir + git
j=l $21

I"

is estimated using the two-stage selection-correction estimation procedure, where os is
the standard deviation of the disturbance in the wage equation, ps is the correlation
coefficient of the two disturbances in the two equations (the sector choice and wage

equations), and the A’s are selectivity parameters. Statistical assumptions are based on

26

Lee (1982), in which the selection of workers into each sector has the structure of a
multinomial logit model, where the error in the log wage regression is normally
distributed, and is also jointly normally distributed with an appropriate transformation of
the errors underlying the multinomial logit model. The probability that each alternative 3

will be chosen can be calculated by the equation

eXP(ZYs)

(4) ProbUi=S] = (1 + Z exp(ZYs))
seS

 

where I, is an indicator of each individual's choice of sector, and Z is the set of variables
in the multinomial logit equation. This probability should depend on the unconditional
(but unmeasured) contemporaneous wage differential associated with each sector for each
individual. This formulation requires that any variable thought to influence the wage
should be included in the sectoral choice equation by way of the wage differentials.
Therefore, any variables in X should be included in Z as well.

What is required to provide compelling identification in the model is a set of
variables that explains variation in the probability of being in a specific sector, but does
not directly affect the current wage. I use the measure of the percentages of workers in
the federal, local, or state government sectors in the local labor market when the worker

was young as identifying variables which are included in Z but should not be included in

27

X.'7 As mentioned above, variation in the local labor market when the worker was young
is exogenous to the individual, and therefore may generate variation in the probability of
sectoral choice that is unlikely to affect current wages.

Equation (3) is estimated in two stages. In the first, I estimate yj by multinomial

logit, and thereby obtain estimates of the selectivity parameters M. In the second, I

consistently estimate SJ and ojpj by OLS afier plugging estimated 5.; into the wage
equation. This substitution implies that the asymptotic variance-covariance matrix
reported by OLS will be biased downward since it does not account for the sampling
variability in the yj. The corrected asymptotic variance-covariance matrix is derived
following the method discussed in Murphy and Topel (1985).

Column (1) in Table 6 presents the coefficients of the first-stage multinomial logit
estimates. The coefficients are reported in the relative risk form. For example, the
estimated coefficient of the non-white dummy in the local government is 1.107,
suggesting the probability that non-white workers will enter the local government sector
is 10.7 percent higher than for white workers. The Chi-square statistic suggests the sector
variables are highly jointly significant in the multinomial logit model. In particular, the
estimated effect of the percentage in the workers’ current sector at age 14 is positive and
significant, suggesting that there is a positive correlation between these variables and

workers’ probability of current employment in that sector. Other coefficients imply that

 

'7 These variables might be correlated with the probability of sectoral choice for various reasons. For
example, the choice of parents' jobs in particular geographical areas will be correlated with the percentage
of employment in those jobs, which in turn may affect children’s choice of jobs.

28

more-educated, married, and non-white workers are more likely to choose public-sector
employment.

Column (2) in Table 6 presents the second-stage estimates of wage equations
based on the first-stage specification (1). The selectivity terms (As) are jointly significant p
at the 1 percent level. The coefficient of the federal government dummy (the
unconditional wage differential) is only 0.034 (and insignificant), suggesting that the
OLS estimate for the federal government is substantially biased upward. On the state and
local government level, the estimates of wage differentials are negative 0.068 for the state
government, and 0.103 for the local government, suggesting that OLS estimates are
biased toward zero for the state government indicator and biased away from zero for the
local government indicator.18 Although the Hausman test does not imply that the
estimates for federal goverrunent and state government are statistically different from the
OLS estimates (p-value is 0.350 for the federal government, and 0.819 for the state
government), the direction of bias is consistent with the results of FE and the test scores
approaches. This is in stark contrast to what we would conclude from the previous
research implementing the FE and selection corrections, as Table 1 should.

The important question posed by the conflicting results in previous research is

whether the conflict is due to the identifying assumptions. Schaffner (1995) demonstrates

 

'8 Another measure, conditional wage differentials, is also presented at the bottom of the column. This
measure differs from the unconditional wage differentials in that it includes the difference in selection
effects among sectors. The selection effect is calculated as the coefficient estimates of A multiplied by the
mean of A. The estimated conditional wage differential between the federal government and private sector
is 0.089. On the state and local government level, the estimates of the conditional wage differentials are
negative 0.098 for the state government, and negative 0.013 for the local government. The conditional
wage differentials are very similar to OLS estimates because the intercept adjusts to control for the
underlying worker selection.

29

that different identifying assumptions lead to quite different estimates. To explore this
issue, I performed a test by using levels of education as a disjointed spline function with
break points at high school and college education for identification, paralleling Gyourko
and Tracy's approach instead of using the identifying variables in my approach. In
contrast to the results in the tables, the results indicate that the OLS estimates of the wage
differential for all government sectors are biased downward (the self-selection correction
estimates are 0.132 for federal government, 0.023 for state government, and 0.157 for
local government). This suggests that it may be the identifying information that gives the
conflicting results of the previous research.

We have seen that the sector composition variables when young are strong
predictors of current sector of employment. The other requirement of these identifying
variables is that they are uncorrelated with the error term of the wage equation. Because
the percentage of workers in each sector in geographical areas may be persistent over
time, and because many individuals may remain in the same geographical area, the
percentages of workers in each sector at age 14 may be correlated with contemporaneous
percentages of workers in each sector, which may in turn affect current wages. To handle
this problem, a stronger specification is estimated by adding the contemporaneous
percentages of workers in each sector as controls in both the sectoral choice and wage
equations. As mentioned, I use the 1990 Census data set to construct contemporaneous
percentages of workers in each sector, just as I use the 1980 Census data set to construct
the percentage of workers in each sector at age 14. Column (1) of Table 7 presents this

estimation result. The coefficients for every government indicator rise by about 3

30

percentage points with respect to the previous specification. However, the pattern of the
results and the direction of the bias is very similar to the original estimates, suggesting
that the above results are robust.

The sensitivity of the results is further tested by estimating additional alternative
specification. To control for individual unobserved heterogeneity and family background
that may be correlated with both wages and sectoral choice, both the test scores and years
of parental schooling are also included in both the sectoral choice equation and the wage
equation. Columns (2) and (3) of Table 7 report the second stage wage equation
estimates first excluding the contemporaneous percentages of workers in each sector, and
then with them. These variables, test scores and years of parental schooling, appear to be
jointly significant in the setoral choice equation, suggesting that selection also occurs
based on individual’s ability and family background. The pattern of the results is similar
to the original estimates, though the biases of state-private and local-private wage
differentials are smaller when test scores and years of parental schooling are included as
control variables. The estimated state-private wage differential is negative 0.071
excluding contemporaneous percentages of workers in each sector, and negative 0.039
with them, while the estimated local-private wage differential is 0.075 excluding
contemporaneous percentage of workers in each sector, and 0.071 with them. Again, the
estimated federal-private wage differential almost disappears (0.023 excluding
contemporaneous percentages of workers in each sector, and 0.035 with them) under the
selectivity correction model, suggesting that self-selection might be the most important

source of bias in the OLS estimation.

31
5. Conclusion

While many researchers have sought to estimate government wage differentials,
most of them ignore the issues of unobserved heterogeneity and selectivity among
sectors. That research which has focused on corrections for bias in OLS estimates does
not provide convincing answers to these issues, and yields very different results. Using
the NLSY data set with Geocode supplement, this paper tries to explore sources of bias of
the OLS estimates, focusing on individual unobserved heterogeneity and self-selection,
and seeks to resolve the highly contradictory results in the literature.

The main results point to substantial bias in OLS estimates of government wage
differentials due to individual heterogeneity and self-selection. Table 8 reports a
summary of these results, comparing to the evidence in the existing literature. As noted,
the techniques employed here provide very consistent results regarding the direction of
bias in OLS. The test score approach suggests that the OLS estimates of the wage
differential are biased upward for federal government employees, biased toward zero for
state government employees, and biased away from zero for local government employees.
The fixed-effects estimates imply that OLS estimates are more biased than the test scores
approach suggests, and in the same direction.

When the percentages of workers in each sector in the local labor market are used
as exogenous variables to predict sectoral choice, the implied selectivity correction
estimates suggest that the direction of bias is consistent with the results from both the
test-score approach estimates and the fixed-effect estimates. These results help to resolve

conflicting evidence in Krueger (1988a) and Gyourko and Tracy (1988). Most important,

32

the federal-private wage differential is close to zero using the selectivity correction
approach, suggesting that self-selection may be the main factor in generating a positive

OLS estimate of the federal-private wage differential.

 

33

Table 1

Summary of Previous Studies by Krueggr, and Gyourko and Tracy

 

 

Krueger (1988a)

Gyourko and Tracy (1988)

 

Data

1. Matched May CPS from 1974-75,
1977-78, and 1979-80

2. Displaced Worker Survey 1984
and 1986

May CPS from 1977

 

Source of Biases

Individual heterogeneity

Self-selection

 

 

 

 

 

in the OLS Esti-
mates
Estimation Fixed-Effects approach Self-selection correction
Technique
Findings The OLS estimates of federal gov- The wage differentials without se-
emment wage differentials are biased lectivity bias correction (the condi-
upward. tional wage differntials) for all gov-
ernment sectors are biased down-
ward.
< Matched CPS >
Conditional Unconditional
OLS FE federal: .188 (.022) .289 (.200)
federal: .247 (.017) .058 (.042) state: .013 (.034) .095 (.175)
state: .062 (.025) .051 (.054) local: .020 (.020) .181 (.132)
Wage Differen- local: .042 (.017) -.038 (.037)
tials
< Displaced Worker Survey >
OLS FE
federal: .126 (.020) .107 (.055)
state: -.010 (.018) -.037 (.045)
local: -.096 (.013) -.044 (.033)
Main Critique lmprecise estimation due to a small Unconvincing identifying assump-

 

number of sector changers

 

tions

 

Standard errors are in parentheses. Conditional wage differential of Gyourko and Tracy are very
close to the OLS estimates.

 

34

Table 2

Means and Standard Deviations of Variables

 

 

Variable Private Local State Federal
Log Wage 1.747 1.844 1.761 2.012
(.491) (.419) (.426) (.405)
Schooling 12.640 13.153 13.967 14.366
(2.259) (2.128) (2.422) (2.333)
Actual Experience 8.256 8.765 8.204 7.580
(3.273) (3 .236) (3 .296) (3.150)
Tenure 3.243 4.323 4.004 3.630
(3.345) (3.504) (3.477) (2.926)
Non White .319 .400 .448 .431
Union .190 .524 .420 .279
Married .473 .570 .550 .487
Father’s Schooling 11.16 11.17 11.44 11.81
(3.558) (3.574) (3.790) (3.977)
Mother’s Schooling 11.04 11.26 11.54 11.90
(2.886) (3.062) (3.021) (2.990)
ASVAB Test Score -.011 -.110 .110 .315
(overall) (.838) (.853) (.835) (.791)
% of Private at age of 14 .010 .042 -.162 -.303
(1.000) (1.021) (.899) (1.037)
% of Local at age of 14 -.010 .127 .024 .089
(.995) (1.014) (1.048) (1.077)
% of State at age of 14 -.009 -.101 .261 .170
(.993) (.958) (1.128) (1.083)
% of Federal at age of 14 -.014 .088 .013 .447
(.981) (1.170) (.788) (1.578)
Number of Obesrvations 18585 1055 786 355

 

Standard errors are in parentheses. Percentage of sectors are standardized with mean zero and

variance of one.

35

 

 

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37

Table 4

Government Wage Differentials by Occupation Catego_ry

 

 

Professional Manager Clerk Craftsman Operative Laborers Service

(1) (2) (3) (4) (5) (6) (7)

Federal .059 .093 .122 .129 .320 .226 .108
(.027) (.043) (.064) (.042) (.093) (.077) (.059)

State -.321 -.008 -.O37 -.070 -.061 -.086 .135
(.034) (.040) (.039) (.037) (.058) (.039) (.026)

Local -.151 -.127 -.019 -.119 .048 -.067 .212
(.030) (.043) (.040) (.032) (.041) (.026) (.021)

Schooling .064 .078 .060 .034 .029 .019 .062
(.004) (.004) (.004) (.003) (.004) (.004) (.004)

Actual Experi- .031 .024 .060 .033 .035 .034 .005
ence (.012) (.012) (.012) (.007) (.009) (.010) (.009)
Experience -.1 1 1 .045 -. l 79 -.045 -.043 -.057 .133
Squared x 10‘2 (.068) (.064) (.074) (.043) (.052) (.058) (.058)
Tenure .047 .050 .069 .047 .055 .040 .073
(.008) (.007) (.009) (.004) (.005) (.007) (.008)

Tenure -.195 -.239 -.344 -.239 -.336 -.232 -.472
Squared x 10‘2 (.062) (.051) (.078) (.039) (.040) (.053) (.068)
Unemployment -.008 -.009 -.019 -.023 -.016 -.016 -.009
Rate (.005) (.004) (.004) (.003) (.003) (.004) (.004)
Union .087 .051 .1 14 .236 .224 .319 .136
(.025) (.028) (.022) (.013) (.013) (.019) (.018)

Non-white -.007 -.049 -.084 -.093 -.065 -.051 -.096
(.021) (.020) (.020) (.014) (.014) (.018) (.018)

Married .130 .1 53 .093 .078 .092 .074 .089
(.017) (.017) (.018) (.011) (.012) (.016) (.017)

R-squared .263 .372 .397 .352 .327 .393 .455
Number of obs. 2768 2509 1778 4538 4197 2352 2639

 

Standard errors are in parentheses. Other independent variables are a dummy indicating an indi-
vidual living in SMSA, 50 state dummies and year dummies. Industry dummy variables are not

included because of the multicollinearity with the government status dummy variables.

38

Table 5

Proxy for Ability and Panel Data Estimates

 

 

Proxy for ability (l)~(2) TSLS for
average test-

FE (4)~(5)

 

 

 

test-scores average scores Whole Excluding switchers
separately test score sample b/w state and local
(1) (2) (3) (4) (5)

Federal .100 .101 .103 .053 .053
(.017) (.017) (.018) (.025) (.025)

State -.079 -.079 -.080 -.016 -.025
(.014) (.014) (.014) (.017) (.018)

_ Local .017 .013 .007 .062 .066
(.011) (.011) (.012) (.016) (.017)

Schooling .035 .035 .046 .041 .040
(.002) (.002) (.007) (.006) (.006)

Actual Experience .026 .028 .029 .077 .077
(.004) (.004) (.004) (.007) (.007)

Experience -.014 -.018 -.021 -.114 -.l 14
Squared x 10’2 (.022) (.022) (.021) (.023) (.023)
Tenure .052 .052 .053 .036 .036
(.002) (.002) (.002) (.002) (.002)

Tenure -.282 -.282 -.291 -.226 -.228
Squared x 10‘2 (.019) (.024) (.020) (.021) (.021)
Local Unemploy- -.015 -.015 -.015 -.004 -.004
ment Rate (.001) (.001) (.001) (.002) (.002)
Union .197 .201 .199 .095 .095
(.007) (.007) (.007) (.007) (.007)

Married .103 .103 .106 .028 .028
(.006) (.006) (.006) (.007) (.007)
Test Scores .107 .043

Overall

(005)

(040)

39
Table 5 (cont’d).
Hausman Test p-
value for single
coefficient:
Federal .138 .152 .. .000 .000
State .628 .545 .. .000 .000
Local .000 .000 .. .000 .000
Test Average .107
Overidentifying .389
Restriction Test p-
val ue
R- sq uared .433 .430 .424 .3 56 .356
(between) (between)
20781 20781 20676

# of observation 20781 20781
Standard errors are in parentheses. Additional variables are same as in column (2) of Table 3.

In col umn (1), test scores are included separately. In column (5), switchers between the state

 

and local government are dropped.

40

Table 6

Selectivity Bias Correction Estimates

 

First Stage (Multinomial Logit) (1) Second Stage

 

 

(OLS)
Local State Federal (l)’
(Unconditional Wage Differential)
Federal .034
(078)
State -.068
(057)
Local .103
(047)
% of local at age 14 1.021 1.053 1.090
(1.179) (2.641) (3.309)
% of state at age 14 .981 1.063 1.028
(1.375) (5.158) (1.522)
% of federal at age 14 1.011 .999 1.036
(1.003) (.091) (2.866)
Schooling 1.169 1.278 1.144 .055
(8.296) (12.038) (4.908) (.002)
Actual Experience .976 .924 .891 .028
(496) (L465) (L472) (004)
‘PJ<>rn-«~hne L107 L801 L645 4077
(1.256) (6.344) (3.793) (.007)
Married 1.574 1.562 1.052 .112
(6.150) (5.303) (.421) (.006)
Selection Variable:
Lambda 1 (private) -.123
(037)
Lainbda 2 (local) -.077
(022)
Lal‘nbda 3 (state) -.028
(027)
7I~iaxrabda44568aan .017

(.036)

 

41
Table 6 (cont’d).
Chi-square statistic for IVs 4.53 32.44 22.47
F-statistic for lambda 10.70
I-Iausman test p-value for
single coefficient:
Federal .350
State .819
Local .026
(Conditional Wage Differential)
Federal .089
State -.098
Local .. .. .. -.013
t-Sta1:istics are in parentheses for specification (1). Standard errors are in parentheses for specifi-

cation (l)’. Additional variables are same as in column (2) of Table 3. The coefficients in col-
umn ( l) are reported as relative risk form. Since some observations miss their lambdas, the num-

ber of observations slightly decreases to 20691.

42

Table 7

Sensitivity Analysis (Second Stage Estimates)

 

 

 

Including cur- Including test- Includ. current % of
rent percentage scores and fam- sector, test-scores,
of sector ily background family background
(1) (2) (3)
(Unconditional Wage Differential)
Federal .061 .023 .035
(.078) (.076) (.075)
State -.034 -.071 -.039
(.055) (.054) (.053)
Local .140 .075 .111
(.041) (.045) (.044)
Schooling .054 .037 .036
(.002) (.002) (.002)
Actual Experience .029 .027 .027
(.004) (.004) (.004)
Non-white -.078 -.010 -.009
(.007) (.007) (.007)
Married .109 .107 .105
(.006) (.006) (.006)
Selection variable:
Lambda 1 (private) -.056 -.125 -.087
(.032) (.036) (.036)
Lambda 2 (local) -.088 -.060 -.074
(.019) (.021) (.021)
Lambda 3 (state) -.033 -025 -035
(.027) (.025) (.025)
Lambda 4 (federal) .014 .021 .021
(.036) (.035) (.034)
Q‘wll‘rent % of workers in sector yes no yes
est scores no yes yes
all'lily background no yes yes

43

Table 7 (cont’d).
Chi-square statistic for IVs:
in local sector 17.70 4.13 20.56
in state sector 11.83 30.06 10.61
in federal sector 1 1.29 21.98 12.17
F -statistic for lambda 9.65 9.79 8.81
Hausman test p-value for single co-
efficient:
Federal .554 .282 .353
State .41 1 .901 .481
Local .080 .143 .019
(Conditional wage differential)
Federal .099 .086 .091
State -.084 -.096 -.087
_L0<=al -002 -005 .001

 

Sfandard errors are in parentheses. Additional variables are same as in column (2) of Table 3.
S‘nce some observations miss their lambdas, the number of observations slightly decreases to

2069 1.

44

Table 8

Summag' of the Results: A Comparison

 

 

This paper

Krueger

Gyourko and Tracy

 

 

1. NLSY with Geocode

Supplement from

1. Matched May CPS
from 1974-75, 1977-

May CPS from 1977

 

 

 

 

 

Data 1987-1993 78, and 1979-80
2. 1980 and 1990 Cen- 2. Displaced Worker
sus to create identify- Survey 1984 and 1986
ing variables
< Matched CPS >
federal: .247 (.017)
state: .062 (.025)
OLS Esti- federal: .105 (.018) local: .042 (.017) federal: .188 (.022)
mates state: -.080 (.014) state: .013 (.034)
local: .003 (.012) <Disp1aced Worker Survey> local: .020 (.020)
federal: .126 (.020)
state: -.010 (.018)
local: -.096 (.013)
Estimates federal: .100 (.017)
Including state: -.079 (.014)
Proxy for local: .017 (.011)
Abi l ity
< Matched CPS >
federal: .053 (.025) federal: .058 (.042)
- state: -.016 (.017) state: .051 (.054)
FlXed-Effects local: .062 (.016) local: -.038 (.037)
Estimates
<Disp1aced Worker Survey>
federal: .107 (.055)
state: -.037 (.045)
\ local: -.044 (.033)
Estimates federal: .034 (.078) federal: .289 (.200)
ol‘l‘ecting state: -.068 (.057) state: .095 (.175)
Welection local: .103 (.047) local: .181 (.132)

 

 

DErection of
“is under

LS Esti-
m ates

 

 

federal: OLS > test

scores > FE > selectivity

comection
state: OLS < test

scores < selectivity cor-

rection < P E
local: OLS < test

scores < FE < selectivity

correction

 

< Matched CPS >
federal: OLS > FE
state: OLS > FE
local: OLS > FE

<Disp1aced Worker Survey>
federal: OLS > FE
state: OLS < FE
local: OLS < FE

 

federal: OLS < selec-
tivity correction

state: OLS < selec-
tivity correction

local: OLS < selec-
tivity correction

 

tiQua] wage differentials which are very close to the OLS estimates.

StaI'lciard errors are in parentheses. OLS estimates for Gyourko and Tracy are actually condi-

 

APPENDIX

Table A1

Number of Job Switchers and Percentage

 

 

 

To Private Federal State Local Total
From
Private 58 136 177 371
(0.7) (1.3) (1.5)
Federal 69 .. 7 8 84
(1 .2) (1 .4)
State 1 19 8 54 181
(5.7)
Local 123 1 l 5 1 185
Total 31 1 77 194 239 821

Percentage in the parentheses are calculated as the sum of number of switchers between two

sectors devided by total number of observations in those sectors.

45

BIBLIOGRAPHY

‘51

E; -o' .-

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47

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48

Public and Private Sectors, Research in Labor Economics, Vol. 12, pp. 137-172.

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49

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Chapter 2

A STUDY OF ETHNIC DIFFERENCES IN FERTILITY AND CHILD
SCHOOLING IN MALAYSIA: THE IMPACT OF GOVERNMENT POLICIES

1. Introduction

Along with its rapid economic growth over the last few decades, Malaysia has
also experienced rapid growth in the educational attainment of its population. Moreover,
as Figure 1 suggests, the shortfall in the education of Malays relative to other ethnic
groups has also been eliminated, and even reversed. This fact suggests that the increase
in educational attainment was more concentrated among ethnic Malays than among
Chinese and Indians in Malaysia. Fertility has also declined in Malaysia. .However, the
fertility decline is more concentrated among Chinese and Indians (see Figure 2). As
Jones (1990) points out, this is in contrast to the trend in fertility of Malays in other
multi-ethnic countries, such as Singapore, where rapid economic growth has apparently
lowered Malay fertility much more drastically.

Most research suggests that government policies might have affected, both
directly and indirectly, the demographic changes in Malaysia. Some researchers have
pointed out the importance of direct government intervention in educational attainment

and fertility decisions. For example, King and Lillard (1987) examine the extent to

50

51

which the Malaysian government influenced the relative schooling levels of different
ethnic groups in the population. They conclude that Malaysian education policies have
significantly affected the levels as well as the relative distribution of schooling among its
demographic groups. Govindasamy and Da Vanzo (1992) interpret the fertility pattern in
Malaysia as a response to the government pronatal policy, the New Population Policy
(NPP), introduced in 1984. They argue that even though the NPP was not an ethnic-
specific policy, it has been of a greater appeal to the Malays, since they tend to live in
rural areas, have larger families, and are more receptive to political messages. Others
emphasize the important role of the policies on labor market conditions. For example,
Govindasamy and Da Vanzo (1992) and Lillard and Willis (1994) argue that the
implementation of the New Economic Policy (NEP) in 1971 has had an impact on
parents’ decisions about fertility and child schooling through its impact on labor market
conditions. On the one hand, the relatively generous provision of employment
opportunities for Malays may have increased Malays’ educational attainment relative to
other ethnic groups, because their perceived benefit from schooling increased. On the
other hand, among the Malays the tendency to buy more children with rising income
might be less tempered by investment in child quality, since the government bore some of
this burden especially for Malays.

In previous studies, the impact of government policies, like the NEP, has often
been captured by a dummy variable which signals individuals who are potentially
affected by the policy. As Lillard and Willis (1994) point out, however, it is difficult to

prove whether the NEP has played a major role in the noted change, although the trends

52

are compatible with the argument that the NEP has had an important impact on both child
schooling and fertility.

This study examines the factors that have contributed to schooling and fertility
trends in Malaysia focusing on the effect of various policies. In contrast to previous
studies, this study adopts a specific methodology used by Lam, Sedlacek, and Duryea
(1992). That is, this study focuses on birth cohort measures of fertility and schooling
across ethnic groups. By truncating fertility and schooling measures at specific ages, it is
possible to determine whether the timing of changes in schooling and fertility decisions,
by families in the different ethnic groups, coincides with major changes in policy.

The results show that the Malaysian government has been quite effective in using
its policy tools both as a means to raise overall education levels as well as a way to alter
the schooling distribution among its ethnic groups. In particular, there is a substantial
increase in the pace of educational attainment, especially that of ethnic Malay children
born after 1960, which might reflect the fact that children born in 1960 would have begun
secondary schooling just around the time when the Malaysian government began the NEP
in 1971.

The results also show the extent to which government policy, whether willfully or
inadvertently, influenced the relative fertility levels of different ethnic groups in the
population. Results document the widening fertility gap between Malays and other ethnic
groups beginning with the 1935 birth cohort, which is consistent with the explanation that

women born after 1935 were affected by the NEP which began in 1971.

53
2. Malaysian Setting

Malaysia is composed of three major ethnic groups. Malays made up fifty-eight
percent of the population of peninsular Malaysia in 1988, and are considered the
Bumiputra (sons of the soil). Thirty-two percent of the population in 1988 was Chinese,
and less than ten percent was Indian. These ethnic groups differ markedly in
occupational structure and average incomes, as well as other demographic characteristics
and health indicators. Malaysian Chinese, for example, have higher household incomes
on average than Malays, and are more likely to live in urban areas.

The ethnic composition of the Malaysian population reflects the history of
pepulation movements in the 19th and early 20th centuries.1 The discovery of huge
deposits of tin ore in Perak and Selangor in 1850, and the shortage of labor to exploit it,
encouraged the first wave of Nanyang (South Sea) Chinese immigrants. This was soon
followed by the massive importation of cheap labor from India to work in the large
rubber plantations. The new waves of immigrants were encouraged and controlled by the
British, who dictated their location in separate and specific parts of the peninsula. Hence,
there was little intermingling between the majority of Chinese, Indians, and the local
Malays. Occupationally, too, there was segregation, as Malays continued to live off the
land in a subsistence economy, while the Chinese and Indians worked for wages in a cash
economy. The effect of colonialism thus created distinct ethnic divisions, each group

remaining culturally unique, engaged in different economic activities, separated

geographically.

 

' See Snodgrass (1980) for a general historical background of Malaysia.

54

Many government policies may have had a different impact on decisions about
fertility and schooling by ethnic groups. Since its independence from the British in 1957,
the Malaysian government has promoted increased education levels through its many
school-building programs. Moreover, a twin goal of its education policies has been to
redress the lag in education of Malays with respect to the other minority ethnic groups.
To close the schooling gaps among ethnic groups, the Malaysian government took several
policy actions. It promulgated the 1961 Education Act which restricted the medium of
instruction in secondary schools to either Malay or English. In addition, it limited
tuition-free education to Malay language schools and to Malays attending English
language schools. Furthermore, Malay students received a disproportionate number of
government scholarships, which carried the added benefit of virtually guaranteeing
admission to state universities.

From its initiation in 1966, the strategy of the official Malaysian family planning
program began in the cities. It was then extended to smaller towns, and later to the rural
areas. However, as Jones (1990) argues, vigorous family planning information
campaigns have been absent in Malaysia, and this program was conducted in an
extremely low-key fashion. For several reasons, the government might be ambivalent
about programming family planning among the Malays who are concentrated in rural
areas. In a multi-ethnic society, the share of Malays in the population may be of crucial
concern. The government also had to avoid antagonizing religious leaders, who were
seen as pronatalist, hence opposed to contraception in general, or at least opposed to

particular methods. This tendency is dramatically shown in the Malaysian Prime

55

Minister Mahathir’s 1982 speech, which set a population target of 70 million for the
country, five times the size of 1982 population, and heralded a more pronatalist stance.
The New Population Policy (NPP) introduced in 1984 was an outcome of this pronatal
tendency. As Govindasamy and Da Vanzo (1992) argue, this kind of pronatal policy may
have had a greater appeal for Malays, who tend to live in rural areas, and have
preferences for larger families.

In 1971, the Malaysian government introduced the New Economic Policy (NEP)
to eradicate poverty and to close economic and social gaps among ethnic groups in
Malaysia. The first goal of the NEP emphasized increasing productivity and income,
increasing opportunities for inter-sectoral movements, and providing social services, all
within the fi'amework of a rapidly expanding economy. The second was primarily
targeted to reduce inter-ethnic disparities. Laws were passed mandating minimum levels
of Malay ownership in businesses, requiring Malay language certification for government
employment and reserving strict quotas at the university level for ethnic Malays. The
NEP also laid down specifications on the ethnic composition of employment in the
private sector so as to reflect the multi-ethnic composition of the population. Although
no precise targets were stated in their law, the government has not only openly displayed
hiring preferences in the public sector, but has also pressured private enterprises to add
Malays to their payrolls. Thus, Malaysian policy makers have worked on both the returns
and cost side of education to increase the value of education to Malays relative to those of

Chinese and Indian extraction. These policies might have had the effect of reducing

56

incentives for Chinese and Indian families to invest in their children’s education, and

perhaps reducing the incentives to have children at all.

3. Data and Variables

The source for estimation is the Second Malaysian Family Life Survey (MFLS-2),
a survey conducted by RAND and the National Population and Family Development
Board of Malaysia, which was carried out in peninsular Malaysia in 1988-1989. The
MFLS produced retrospective and current household-level data for all household
members, covering conventional measures of demographic variables (fertility, marriage,
migration, mortality, employment, and household composition), as well as other social,
economic, and community-level factors affecting family decision-making.

In MFLS-2, the Female Life History questionnaire was collected for all women in
three samples: the Panel Sample, the New Sample, and the Children Sample. The Panel
Sample included in the MFLS-2 was a sub-sample of households that could be matched
to MFLS-l, generating a panel of individual-level members.2 The MFLS-l sample
includes ever-married women aged 15 to 49. There were 1,262 primary respondents in
the sample. In the MFLS-Z, 889 of the Panel respondents completed the survey; a
follow-up rate of 70 percent of those eligible. The Child Sample is made up of children
of Panel respondents aged 18 or older. Interviews were conducted with one child, still

living in the household of the Panel respondents, and as many as two children, living

 

2 One issue is that the non-response (both unlocatable and refusals) was not random among the Panel
Sample. For example, the Chinese women in the MFLS-l sample were the least likely to be successfully
re-interviewed (60% of those presumed eligible), while Malays were the most likely to be re-interviewed
(83%). This, in fact, is partly because of the NEP, which provide strong incentives for Chinese to
emigrate. See Hagga et al. (1992) and Strauss and Thomas (1995) for a discussion.

57

elsewhere in Peninsular Malaysia. Children in the Child Sample are selected at random.
There were 499 child respondents living in the household with the Panel respondents, and
597 respondents, living elsewhere in Peninsular Malaysia. The New Sample consists of
women aged 18 to 49 regardless of her current or previous marital status. There were
2,184 respondents in the New Sample. The husbands of both the Panel and the New
Sample respondents were also interviewed provided they were living in the household.
Indians were over-sampled by 100% in the New Sample to allow for sample
representation.

In this analysis, 1 construct two data sets; a women sample and a children sample.
The women sample consists of ever-married women aged 32 or older, who appear in
either the Panel, New, or Child Sample at the time of MFLS-2 survey. After eliminating
1) women aged less than 32, 2) individuals with duplicate reports, 3) individuals with
some missing variables, and 4) whose ethnicity is not Malay, Chinese, or Indian, 1,836
(44% of the women respondents) ever married-women aged 32 years or older remain in
the women sample. There is a question of sample selection in the women sample, since
the women sample consists of only ever-married women, and thus is not representative of
the female population which include both married and unmarried women. A potential
sample selection bias is likely to be more serious for the younger cohorts than for the
older cohorts. However, it should be negligible for the women sample in this analysis

who were aged 32 or older at the time of the survey, because only less than 2% of the

58

women sample (33 women) are not married by this age.3 The children of the women
respondents, aged 17 or older at the time of the survey, provide the children sample.
1,577 (17% of total children) respondents remain in the children sample because it is
restricted in a similar way to the women sample.

I use measures of the following variables in this analysis: fertility, child’s
schooling, household income, other individual and community characteristics. Fertility
variables are represented by the number of children ever born to the woman at age 32 and
37. These variables are calculated from the female pregnancy history in the MFLS-2 data
set. Since each pregnancy history provides information about the woman’s age at the
time of pregnancy and birth outcomes, we can calculate the total number of live births
each woman had by a specific age. Child schooling variables are represented by
cumulative years of schooling completed by the child at ages 17 and 20. Since most of
the children complete their primary schooling at age 12 or 13 in Malaysia, the completed
schooling up to age 17 measures whether the child completed lower secondary schooling
and entered higher secondary level of education. Similarly, the completed schooling up
to age 20 measures whether the child completed higher secondary schooling and entered
post secondary level of education.4 Among the children in the children sample, 214

(13%) children were still enrolled in school at the time of the MFLS-2 survey.

 

3 To examine this issue, the following estimation was also done by just using the New Sample first
excluding never-married women, and then including them. The results are quite similar to each other,
suggesting that the sample selection rule does little to bias the estimation results.

i The Malaysian school system parallels that of Great Britain. The primary level consists of Standards 1
through 6, and begin at age 6 or 7; this is followed by a secondary level which includes Forms 1 through 3
(lower secondary) and 4 through 5 (higher secondary); and post secondary schooling begins at Form 6.

59

Ethnicity is categorized as Malay, Chinese or Indian, identifying the major ethnic
groups found in Peninsular Malaysia. About one percent identified themselves as other
ethnic groups, and they were excluded. As a proxy for permanent income, father’s
(husband’s) earnings are measured in Malaysian Ringgit (1 Ringgit equals US $0.35 in
1988). This is a broad measure of income, which includes father’s (husband’s) market
income, rents and interest, production for home consumption, in-kind, bonuses, transfer
income, and other sources of income.5 Obviously, this measure is a very crude and noisy
measure of permanent income, and assumes that the woman’s labor supply is endogenous
in fertility and schooling investment decisions, while the man’s is not. Furthermore, it
may measure it with systematic error if there is trend growth in incomes. For older
cohorts, it probably overstates permanent income and understates it for younger groups.
For these reasons, estimation results are presented first without the income variable, and
then with it for comparison.

Construction of the community variables is done by matching the female life
history data set to the community data set. The variables are region of residency, school
availability, family planning availability, and electricity availability. The availability of
piped water is also included to capture the level of sanitation. These community
variables measure the overall level of development as well as price and quality for each of
the respondent’s residences. From auxiliary sources, I match information about specific
geographic regions or time periods. First, the Female Life History obtains information on

a variety of topics, including pregnancies, marriage, and migration history. The

 

5 MFLS-Z provides the information about labor and non-labor earnings for each member of household.

6O

migration history provides information about the date of move and her location (state and
district) at each move.6 Second, the community data contains information about the
presence and opening date of schools, clinics, electricity, and piped water supply located
in 398 Enumeration Blocks (E88) and 52 Primary Sampling Units (PSUs). The EBs
represent communities from which the New Sample was drawn, while the PSUs refer to
communities from which the Panel Sample was drawn.7 For these EBs and PSUs, we
know the presence and opening date of the school, family planning programs, and piped
water supply. Unfortunately, while we know the district in which the mother and child
resided, we do not know the PSUs and EBs. To handle this problem, I measure the
proportion of sampled EBs and PSUs within a district that reported having a school,
piped water, and family planning program available at a particular point in time.

These variables are measured at relevant time periods. For example, the primary
school availability in the children sample is measured when a child enters a primary
school at age 6, while the secondary school availability is measured when the child is 12
years old. All the other community variables in the children sample are measured at age
12 of the child. In the women sample, all the community related variables are measured

at the time of marriage. This might be the most relevant time measure, because about

 

6 An important emerging trend in household surveys has been an increased reliance on retrospective
information, especially in developing countries. However, the fact that not all moves are equally well
remembered causes so-called recall bias. For example, closer moves are better remembered, and salient
migrations will be recalled with greater frequency. See Smith and Thomas (1997) for a detailed
discussion.

7 By 1988, PSUs had been replaced by EBs which are smaller than PSUs, and thus no longer existed in
1988. One issue is that the PSUs only reflect the communities of the Panel Sample household (and its
resident Children Sample member) if the household had not moved to a different area. It is because the
high cost of community data collection made it prohibitive to collect community level data for the
additional EBs in which Panel respondents lived in 1988.

61

40% of all women in the sample migrated when they married (relevant community), and
because it is one of the most salient moves (free from the recall-bias). However, it may
also measure it with systematic error, since the time of marriage is not the same across
individuals, and there might be a trend growth in community related variables. Table 1
shows the means and standard deviations of the variables used in this analysis. The
means of the variables imply that Malays are generally characterized by higher fertility
and child’s education. However, the Malays’ parents are characterized by lower
education relative to the other ethnic groups. This also suggests that educational

attainment has increased more for Malays over the past few decades.

4. Methodology and Specification
The methodology employed here proceeds by estimating the following reduced

form relationships. Equations of the form

(1) F=XBF+ZYF+WF5F+3F

(2) S = XBS + 278 + W558 + 88

are estimated, where F is a measure of a woman’s cumulative fertility, S is the child's
cumulative schooling, X is a set of family characteristics, Z is a set of community level
characteristics, and W is a variable specific to mother (F) and child (S), such as birth
cohorts. This reduced form approach reflects the fact that both variables, the quantity of

children (fertility) and the quality of children (schooling), are jointly chosen to maximize

 

62

the household’s utility as constrained by income in the face of existing prices, and are a
function of the same exogenous variables. The equations are estimated with fertility
truncated at age 32 and 37 for women, and with schooling truncated at age 17 and 20 for
children.

One important issue in the specification is the effect of the availability of schools,
clinics, electricity, and piped water on both schooling and fertility. Whether or not there
is a school in the local area is obviously one measure of the cost to parents of sending
their children to school. Since having a school in the community versus not having one
lowers costs for the parents, the correlation between school availability and schooling
levels should be positive. Different measures for school availability are used depending
on the level of schooling. At the secondary level, I include only the availability of a
secondary school, for which the information about the language of instruction is not
available. The language of instruction is also irrelevant at the secondary level for the
most part, since nearly all secondary schools instruct in Malay or English. At the primary
level, however, the presence of primary school in the local area itself is of little
importance, because nearly all of the communities have a primary school. Instead, the
language of instruction might have a more important impact on educational attainment at
the primary level. Therefore, a measure of language instruction in primary schools is
used as a control variable. Different interactions are also used depending on the child’s
ethnicity in order to control for differences among ethnic groups. For example, the
measure of Chinese and Tamil language school availability is interacted with the child’s

own ethnic groups, since Malay and Chinese children are unlikely to attend schools with

63

Tamil language instruction, and Malay and Indian children are unlikely to attend schools
with Chinese language instruction. However, the measure of school availability with
Malay language instruction is interacted with all ethnic dummy variables, since it is
assumed that Chinese and Indian children also attend schools with Malay language
instruction.8

Whether there is a family planning program in the local area is also one measure
of the cost to having children. Program existence and location affect the cost of
contraceptive methods and the accessibility of contraceptive information. There are four
major types of clinics in Malaysia which provide family planning programs.9 I include,
as a control variable, a measure of whether any of these clinics was available. A
sanitation related measure is also important, because it might affect infant and child
mortality. I include a measure of whether piped water was available at the specific time
of interest. The MFLS-2 also includes information about other community variables such
as health clinics. However, I exclude those other variables from the analysis, since those
variables do not provide information about the date of availability.

Another issue is that of the estimating technique which should be employed here.
Although censoring birth histories and years of schooling is not a problem here, OLS

estimates may not be efficient, since both measures are ordered and discrete variables.

 

8 This specification is in contrast to Lillard and Willis (1994). In their sequential-probit model, the school
availability variables are only interacted with the child’s own race regardless of its ethnicity.

9 NPFDB (National Population and Family Development Board, also known as LPPKN) clinics tend to be
located in urban areas, while MOH (Ministry of Health) clinics tend to serve rural areas. LPPKN and
MOH records provide information on what clinic was in the area. F PA (Family Planning Association, also
known as PPK) clinics are voluntary private centers staffed by a qualified nurse and may have a part-tirne
physician. It tends to be located in urban areas. There are also other private clinics. All of these clinics
may provide family planning and family counseling. Some may provide sterilization services.

64

However, preliminary work with ordered-logit or ordered-probit models showed that
OLS regressions behave satisfactorily in the sense that the coefficients were of the same
sign and significance levels as in the two other approaches. Most of all, OLS estimates
are easily interpretable. For these reasons, I employ OLS technique. The OLS estimates
were obtained using the consistent variance-covariance matrix estimator of White (1980).
In addition, I relax the independence assumption in the error term, since it is hard to
believe that individuals of the various clustered units are truly independent. I assume that
only observations with differing households are truly independent. The standard errors
are thus robust to heteroscedasticity, and free from an independence assumption.

A set of estimated parameters of the sample of sons, the sample of daughters, and
the sample of women, is presented in Table 2 through Table 4. The first part of the
regressions in Table 2 uses years of schooling completed up to age 17 as the dependent
variable, specifically using the sample of sons aged 17 years or older. Likewise, the
second part of the table is for years of schooling completed up to age 20 as the dependent
variable. Table 3 presents the same model for the sample of daughters. Table 4 presents
OLS regression estimates for women’s fertility. Similar to the schooling model, the first
part of the regressions uses the number of children born to a woman of age 32 as a
dependent variable, using the women sample aged 32 years or older in 1988. The second
part of the regressions uses the number of children born to a woman of age 37 as a
dependent variable. There are four models. In Model 1, only birth cohorts, ethnicity, and
their interaction terms are included. Mother’s (woman’s) and father’s (husband’s)

education are added as control variables in Model 2. Model 3 is the preferred full model

65

specification, which contains family background, regional characteristics, and parents’
education interacted with ethnicity as additional control variables. For comparison, an
income and its interaction terms with other variables are added as additional variables in

Model 4.

5. Empirical Results

5.1 Birth Cohorts and Policy

To capture the effect of broader shifts in education and population policies as well
as changes in the economy, birth cohort variables are included. In both schooling and
fertility equations, the birth cohorts are included as dummy variables. In the schooling
equation, a child’s birth cohort dummy variable indicating a child born afier 1960 is also
interacted with other variables. This birth cohort dummy variable might suggest the
effect of NEP, since children who were born in 1960 would have begun secondary
schooling just around the time when the Malaysian government began the NEP. In the
fertility equation, the percentage of the years exposed to the NEP is interacted with other
variables. To construct this variable, I set three flag-years, a year at a woman’s age 15, a
year at a woman’s age 32 (and 37), and 1971 when the NEP introduced. The variable is
then calculated as the percentage of the years exposed to NEP between age 15 and 32
(and 37).

The results show that there exists a significantly positive cohort trend in the
schooling equation. It is easily noticeable that the results are quite robust regardless of

various specifications. Furthermore, the coefficient on the 1960 cohort variable

66

interacted with Chinese and Indian ethnic indicators are mostly negative and significant
in the schooling equation, suggesting that the increase in schooling was in favor of
Malay children born after 1960. The results also show that there exists a negative cohort
trend in the fertility equation. The coefficients of the percentage of the years exposed to
the NEP interacted with Chinese and Indian dummy variables appear to be mostly
negative, suggesting that the decrease in fertility was concentrated among Chinese and
Indian women, although some of them are not significant.

Finally, the results show the extent to which cohort effects change when we add
family and community characteristics as additional control variables. In the schooling
equation, while the expanded set of family and community related variables perform in
the expected manner, they do not seem to alter in any significant way the coefficients on
the birth cohort variables. In the fertility equation, cohort effects decline more

substantially, when we add more control variables.

5.2 Family Characteristics

The results generally show that parents’ education has a positive effect on child’s
educational attainment. Even after controlling for other family background
characteristics and regional variables, the effect of parents’ schooling appears to be
strong, suggesting that the results are robust. A significant and negative relationship
between parents’ education and fertility also appears. This is consistent with the notion
that education provides a mother with skills in acquiring and decoding new information,

and thus effectively lower the cost of using more contraceptive techniques.

67

When the effect of income is controlled for, parents’ education still has a positive
effect on child’s educational attainment. Since the effect of income is controlled for, it
reflects only the influence of their tastes and the quality of the home environment on
child schooling. One possible explanation is that more highly educated parents desire
more schooling for their children and will be able to provide a home environment that is
more conducive to greater education of children.

One interesting finding is that the coefficients of the parents’ education variables
interacted with the 1960 cohort variable appear to be mostly negative and jointly
significant in the schooling equation. The results show that the parents’ education is less
important after the NEP, suggesting that the effect of parents’ education on
intergenerational education mobility was diminished after the NEP.

Given controls for residence and parents’ education, results show that higher
-income parents have more highly educated children. The income effect on schooling
increases as the age of truncation increases, suggesting that the income effect is bigger for
children with higher levels of education than for those with lower levels of education.
This might reflect both credit market constraints and higher fees for higher levels of
schooling. The results also indicate that income effect on schooling is greater for
daughters than sons. The income variable has an insignificant, but positive coefficient on
fertility, suggesting that income remains in the range in which both schooling and
children are normal goods. I also interacted the income variable with other variables such

as ethnicity and cohort dummy variable to look at whether there are differences across

68

ethnic groups and cohorts. However, these interaction terms usually do not appear to
have significant effect on either child’s schooling or fertility.

The results show the effect of other family background variables on fertility and
child schooling. The variables such as the number of siblings of mother and schooling of
mother’s parents’ do not appear to affect child’s schooling given controls for parents’
characteristics. However, the number of siblings of a woman has a positive effect on
fertility in the women sample. Finally, the mother’s schooling of a woman (grand
mother) has a significant and negative effect on fertility, but father’s schooling of woman

(grandfather) has no significant effect on fertility.

5.3 Community Characteristics

The estimates of community variables here assume that no correlation exists
between the variable and unobserved component in the outcome. Because some
programs may be placed using criteria that are related to the outcomes being studied
(non-random program placement), this condition is often violated. The treatment for this
potential problem is not addressed here, which needs further analysis.lo

The measures of primary school availability (SRK) with Malay language
instruction are positive for both sexes when interacted with Malay ethnicity. However,
this measure is significantly negative for both sexes when it is interacted with Chinese,
suggesting that Malays benefit from Malay language instruction, but Chinese are hurt by

it. Furthermore, the measures of primary school availability with Chinese language

 

'0 See Strauss and Thomas (1995) for a detailed discussion about this issue.

 

69

instruction are significantly positive for both sexes when interacted with Chinese,
suggesting that the educational attainment of Chinese children is highly sensitive to the
language of instruction. The school availability measures interacted with Indian are not
precise, and may reflect the difficulty of reconstructing variables from retrospective data
based on a relatively small sample of Indians.

The measures of primary school availability with various language instruction are
all positive in the fertility equation, suggesting that the availability of primary schools in
local areas has a positive effect on fertility regardless of its language instruction. Because
of this reason, I included a measure of whether any of these primary schools with various
language instruction was available, and re-estimated the fertility equation. Again, the
SRK variable is positive and significant as shown in Table 4. One possible explanation is
that the existence of primary schools in the local area decreases the shadow price of
schooling, implying that existence of primary schooling may increase fertility.

As expected, the results show that the availability of secondary schools (SMK) in
local areas has a positive effect on child’s schooling, suggesting that the existence of
secondary schools decreases the shadow price of schooling, and thus increase schooling.
However, the availability of SMK has, surprisingly, negative and significant effect on
fertility. This is in contrast to the estimates of SRK in the fertility equation. I do not
provide a clear explanation for this finding, but it needs further analysis.

Children in Kuala Lumpur (the Capital) area dwellers have significantly higher
levels of schooling for both sexes. A possible reason is that the place of residence

variable might capture the effect of market demand for child labor. For example, in rural

£" .‘ .‘11 Q— --

70

areas, the existence of a market for child labor in farm-related activities and the high
seasonal demand for family labor suggests a high opportunity cost for time spent in
school. The Kuala Lumpur variable also has a negative effect on fertility, which might
reflect the high child rearing costs in metropolitan area.

The effect of family planning availability appears to be negative and significant in
the fertility equation, suggesting that family planning programs may be effective in
spreading contraceptives as well as information. The variable, however, does not appear
to affect educational attainment.

The results show that availability of piped water in a local area has a significant
and negative effect on fertility. A possible reason is that the variable might be negatively
related to infant and child mortality, and therefore fertility. It has been argued that high
infant and child mortality may lead to child replacement and insurance behavior, resulting
in higher fertility. This is the case we see here. The coefficient estimate of the piped
water availability in column (7) of Table 4 is negative 0.275, suggesting that 100
percentage point increase (which equals about 400% increase in availability, since the
average of the piped water availability is 0.252) in piped water availability decreases the
number of children per woman by 0.275. The effect of the piped water supply, however,
does not seem to affect child schooling.

The measure of electricity availability appears to be positive in the schooling
equation, but negative in the fertility equation. This might also reflect that this variable is
strongly related with either the degree of urbanization or overall level of development of

the residence.

 

 

71

I also have attempted to see whether there are ethnic differences in effect of
community characteristics on schooling and fertility. For example, I interacted the
ethnicity dummy variables with community characteristics. However, most of the
coefficients of the interaction terms are insignificant, suggesting that the measures of
community characteristics does not have different impact on schooling and fertility across

ethnic groups.

5.4 Documenting across Birth Cohorts and Ethnic Groups

Using the OLS coefficients presented in Table 2 and 3, we can predict how
schooling attainment has changed across birth cohorts and ethnic groups. I predict these
variables based on means of sample characteristics by each birth cohorts to capture the
net effect of birth cohorts. Model 3 is used for the prediction. Figures 3 and 4 show the
results of predicting each cohort’s schooling based on the coefficients estimated for the
sample of sons. These figures show two truncated measures of cumulative cohort
schooling, with schooling truncated at children’s age 17 and 20. The series for the
predicted schooling is smoothed as three-year moving averages. Looking at Figure 3 and
4, we see that we are able to predict many of the important features of the onset of
Malaysia’s rapid schooling increase. We predict a sharp rise in schooling at exactly the
time what occurred, beginning with the cohorts born in 1952. This might reflect the fact
that children who were born in 1952 would have begun schooling just around the time
when the Malaysian government began to promote increased education levels through its

school-building programs beginning in 1957.

72

However, the trend is not same for all ethnic groups beginning with the birth
cohorts born in 1960. From Figure 3, we see that Malay boys initially had a lower levels
of schooling than Chinese and Indian boys, but the ethnic differentials were completely
eliminated and then reversed with the 1960 birth cohort. The average cumulative
schooling of the 1970 Malay birth cohort is approximately 9 years, suggesting that lower
secondary schooling was almost universal for Malay boys by this birth cohort. Figure 4
shows the same pattern as Figure 3, though these figures more dramatically document the
initial reversal and then widening schooling gap between Malays and other ethnic groups
beginning with the 1960 birth cohort. It reflects the tendency for the increase in
schooling of Malay boys to be bigger especially at the higher secondary and post-
secondary level of schooling than at the lower level of schooling. Figures 5 and 6 show
exactly the same kind of results using the sample of daughters. Once again, we can
capture the timing of a widening gap between Malays and other ethnic groups beginning
with the 1960 birth cohort. The widening gap beginning with the 1960 birth cohort might
reflect the fact that children who were born in 1960 would have begun secondary
schooling just around the time when the Malaysian government began the NEP, which
was favorable to Malays.

Figures 7 and 8 show the results of predicting each cohort’s fertility based on the
OLS regression coefficients estimated for the sample of women. These figures show two
truncated measures of cumulative cohort fertility, with fertility truncated at age 32, and
37. Like the schooling model, the series for the predicted fertility is smoothed as three-

year moving averages. The figures document the fertility decline in Malaysia for all of

73

the measures. The figures also document differences of the fertility trend by ethnicity.
Looking at the figures, we see that Malay women continued to decrease births at a slower
rate than other ethnic groups, as indicated by the steepness of the fertility curve in the
figures. In particular, Figure 8 dramatically documents the widening fertility gap
between Malays and other ethnic groups beginning with the woman’s 1935 birth cohort.
This is consistent with the explanation that Malay women who have been exposed to the

NEP have decreased their fertility less relative to other ethnic groups.

6. Conclusion

Since both schooling and fertility have important impacts on a country's economic
growth and development, both have been major objects of government policies. For
example, broader availability of public schools increases enrollment, and thereby enriches
a country's human capital. The introduction of a family planning program decreases
fertility, and thereby reduces births and maternal mortality risk. Parents’ decisions about
fertility and schooling are also a function of policies which affect the labor market,
. because parents’ perceived economic benefits from education depend on conditions in the
labor market. Based on this argument, this study examines the factors that have
contributed to schooling and fertility trends in Malaysia, focusing on the effect of
policies. In contrast to previous studies, this study focuses on birth cohort measures of
fertility and schooling across ethnic groups. By truncating fertility and schooling

measures at specific ages, it is possible to determine whether the timing of changes in

74

schooling and fertility decisions, by families in the different ethnic groups, coincides with
major changes in policy in any predictable way.

The results generally show that the Malaysian government had been quite
effective in using its policy tools both as a means to raise overall education levels as well
as a way to alter the schooling distribution among its ethnic groups. The availability of
secondary schools in the local area raises child schooling, suggesting that school building
programs in Malaysia might have positive effect on child schooling in Malaysia. The
substantial increase in the pace of educational attainment, which was especially favored
Malay children born after 1960 might reflect the fact that children born in 1960 would
have entered secondary schools just around the time when the Malaysian government
began the NEP. The results also show the extent to which government policy influenced
the relative fertility levels of different ethnic groups in the population. Results docmnent
the widening fertility gap between Malays and other ethnic groups beginning with the
woman’s 1935 birth cohort, which is consistent with the explanation that the fertility of
women, who have been exposed to the NEP, has decreased less for Malays relative to

other ethnic groups.

Means and Standard Deviations of Variables

75

Table l

 

Children sample (1) ~ (4)

 

Women sample (5) ~ (6)

 

 

at age 17 at age 20 at age 32 at age 37
Son Daughter Son Daughter
(1) (2) (3) (4) (5) (6)

Child’s schooling 8.55 8.51 9.02 8.93 Number of 4.26 5.23
(2.05) (2.49) (2.83) (3 .48) children (2.16) (2.52)

(Malays) 8.89 8.72 9.64 9.21 (Malays) 4.47 5.55
(1.92) (2.54) (2.72) (3 .63) (2.14) (2.54)

(Chinese) 8.18 8.29 8.37 8.52 (Chinese) 3 .86 4.65
(2.10) (2.28) (2.82) (3 .29) (2.03) (3 .33)

(Indian) 8.37 8.25 8.83 8.73 (Indian) 4.30 5.39
(2.12) (2.64) (2.81) (3.29) (2.35) (2.65)

Log income 8.52 8.57 8.42 8.41 Log income 8.79 8.70
(.951) (.925) (1.03) (1.01) (.856) (.909)

(Malay) 8.38 8.41 8.31 8.32 (Malay) 8.59 8.46
(.818) (.802) (.926) (.822) (.828) (.861)

(Chinese) 8.68 8.85 8.56 8.53 (Chinese) 9.16 9.06
(1.15) (1.13) (1.21) (1.39) (.798) (.872)

(Indian) 8.62 8.62 8.45 8.55 (Indian) 8.81 8.72
(.843) (.799) (.889) (.952) (.833) (.889)

Mothers’ 2.68 2.69 2.39 2.40 Women’s 4.49 3.63
schooling (2.93) (2.98) (2.84) (2.88) schooling (3.82) (3.63)

(Malay) 2.5 8 2.44 2.25 2.16 (Malay) 4.35 3 .26
(2.85) (2.74) (2.72) (2.58) (3.81) (3.42)

(Chinese) 2.28 2.57 2.02 2.32 (Chinese) 4.45 3.89
(2.83) (3.23) (2.77) (3.34) (3.86) (3.83)

(Indian) 3.73 3.64 3.52 3.23 (Indian) 5.01 4.33
(3.12) (3 .07) (3 .05) (2.86) (3 .78) (3.76)

Fathers’ 4.44 4.54 4.21 4.38 Husbands’ 6.17 5.42
schooling (3 .08) (3.10) (3.10) (3 .28) schooling (3 .69) (3 .65)

(Malay) 4.05 4.14 3 .77 4.00 (Malay) 5.75 4.79
(2.90) (2.94) (2.93) (2.93) (3.67) (3.41)

(Chinese) 4.48 4.49 4.35 4.09 (Chinese) 6.41 5.94
(3.04) (3.07) (3.09) (3.41) (3.73) (3.80)

(Indian) 5 .48 5.99 5.16 6.10 (Indian) 7.16 6.48
(3.45) (3.28) (3.38) (3.65) (3.47) (3.69)

 

Child’s birth

cohort
below 1957
1957-1959
1960-1962
1963-1965
1966-1968
1969-1971

Kuala Lumpur

SMK

Malay SRK

Chinese SRK

Indian SRK

Family planning

Piped water

Electricity

# of observation

(Nhflay)
(Chinese)

(hufian)

.065
.062
.103
.21 l
.300
.260

.050

.163
(212)

.318
(284)

.127
(187)

.067
(095)

.268
(308)

.600
(.314)

.550
(.308)

990
(467)

(344)
(179)

.057
.051
.096
.185
.325
.287

.060

.173
(219)

.344
(286)

.114
(174)

.069
(099)

.287
(299)

.604
(320)

.579
(.296)

687
(356)

(204)
(127)

76

Table I (cont’d).
.105 .094
.100 .085
.167 .159
.343 .307
.285 .355
.060 .056
.152 .146
(.195) (.184)
.309 .321
(270) (270)
.124 .109
(178) (168)
.069 .065
(093) (092)
.229 .240
(283) (275)
.540 .529
(314) (324)
.465 .505
(302) (288)
610 414
(277) (222)
(227) (114)
(106) (78)

Woman’s birth
cohort
below 1935
1935-1940
1941-1945
1946-1950
1951-1955
Kuala Lumpur

SMK

Malay SRK

Chinese SRK

Indian SRK

Family planning

Piped water

Electricity

# of observation

(Malay)

(Chinese)
(Indian)

.121
.124
.189
.244
.322

.079

.102
(171)

.265
(281)

.122
(199)

.063
(096)

.105
(.212)

.3 18
(.299)

.274
(289)

1836
(976)

(567)
(293)

.181
.186
.283
.351

.073

.076
(145)

.236
(265)

.113
(187)

.056
(089)

.064
(.164)

.252
(.268)

.210
(.255)

1228
(628)

(414)
(186)

 

Means are reported, with standard deviations in parentheses. Logincome includes a father’s
(husband’s) market income, in-kind, bonuses, rents and interest, transfer income, and other

sources of income. SRK represents primary schools, while SMK represents secondary schools. I
compute the average only for non-missing values, so the sample size falls slightly for those vari-

ables.

77

Table 2

Estimates of Child Schooling (Male Children)

 

 

Schooling at age 17 (1) ~ (4)

Schooling at age 20 (5) ~ (8)

 

Model 1 Model 2 Model 3 Model 4 Model 1 Model 2 Model 3 Model4

 

, . , , yes yes yes yes yes yes yes yes
:flmcsheczlfiaztgzmw no yes yes yes no yes yes yes
Education interaction no no yes yes no no yes yes
Region & family back. no no yes yes no no yes yes
Income no no no yes no no no yes
(1) (2) (3) (4) (5) (6) (7) (3)
Child’s birth cohort
1957- 1959 1.1 1 1.09 .964 .942 1.35 1.32 1.29 1.28
(.492) (.489) (.483) (.486) (.578) (.567) (.572) (.575)
1960-1962 2.34 2.19 2.17 2.12 3.11 2.87 3.16 3.12
(.749) (.750) (.738) (.720) (.837) (.827) (.833) (.814)
1963-1965 2.78 2.63 2.51 2.36 3.53 3.29 3.42 3.28
(.719) (.719) (.717) (.698) (.799) (.787) (.809) (.785)
1966-1968 2.95 2.71 2.62 2.48 3.73 3.31 3.48 3.36
(.712) (.715) (.712) (.693) (.790) (.784) (.806) (.783)
1969-1971 2.98 2.73 2.65 2.52 .. .. .. ..
(.711) (.715) (.713) (.693)
Chinese 1.02 .941 1.62 1.78 1.06 .939 1.97 2.08
(.673) (.674) (.747) (.749) (.762) (.752) (.902) (.921)
Indian 1.01 .701 .361 .549 1.13 .625 1.34 1.40
(.829) (.831) (1.12) (1.11) (.960) (.962) (1.44) (1.44)
Chinese‘cohort (> -1.81 -1.80 -1.72 -1.63 -2.63 -2.63 -2.56 -2.43
1960) (.686) (.685) (.703) (.688) (.804) (.790) (.821) (.802)
lndian‘cohort (> -1.61 -1.53 -1.62 -1.81 -2.15 -2.11 -2.14 -2.42
1960) (.818) (.814) (.881) (.896) (1 .01) (1.00) (1.11) (1.14)
Mothers’ schooling
Primary .502 .162 .083 .889 .607 .498
(.167) (.707) (.707) (.270) (.934) (.939)
Secondary l .21 .953 .879 2.33 2.68 2.68
(.242) (1.17) (1.23) (.537) (1.95) (2.07)
Fathers’ schooling
Primary .012 .039 -.074 -.422 -.048 -.157
(.305) (.656) (.637) (.400) (.788) (.766)
Secondary .746 2.23 2.16 .968 3 .54 3 .51
(.350) (.692) (.692) (.533) (1.12) (1.18)
Post secondary .491 4.37 4.04 .976 7.09 6.68
(.718) (1.13) (1.15) (1.39) (1.97) (2.00)

78

Table 2 (cont’d).
Mothers’ schooling
*birth cohort
Primary *cohort .244 .242
(.658) (.662)
Secondary*cohort -.136 -.1 85
(1.14) (1.20)
Fathers’ schooling
*birth cohort
Primary *cohort .1 10 .139
(.575) (.565)
Secondary‘cohort -1.56 -1.57
(.613) (.623)
Post secon.*cohort -3.90 -3.86
(1.43) (1.45)
F-test p-value for par-
ent’ schooling*cohort .005 .008
Community variables
Kuala Lumpur .724 .806
(Capital) (.259) (.271)
SMK .696 .759
(.392) (.395)
Malay SRK*Malay .561 .570
(.341) (.333)
Malay SRK‘Chinese -2.59 -2.59
(.669) (.670)
Malay SRK‘lndian .556 .674
(.595) (.584)
Chinese SRK*Chinese 1.90 1.84
(.714) (.717)
Indian SRK‘Indian -.193 -.983
(1.58) (1.52)
Family planning -.145 -.l67
program (.253) (.247)
Piped water -.049 -.081
(.278) (.273)
Electricity .013 .039
(.305) (.307)
Log income .. .167
(.123)
R-squared .097 . 138 .203 .215
# of observation 990 990 990 990

.120
610

.188
610

.375
(853)
4882
(L86)

4396
(716)
4209
(986)
4&44
(2.40)

.052

.747
(485)
.408
(675)
L71
(1544)
4246
(L05)
.944
(L05)
L81
(L21)
4288
(251)
4451
(470)
4333
(506)
.491
(497)

.263
610

.359
(853)
4978
(L99)

4385
(707)
4220
(L04)
4i42
(244)

.034

.874
(493)
.492
(690)
L70
(634)
4247
(L06)
L14
(L06)
L80
(L22)
4273
(2.50)
4488
(472)
4420
(494)
.524
(501)
.233
(196)
.271
610

 

Standard errors are in parentheses. Other variables include ethnic dummy variables interacted
with parents’ schooling and income, mother’s number of siblings, and mother’s parent’s school-
ing. They are jointly insignificant at 5% level. Missing values for presence of father, mother’s
family background characteristics, and community variables were changed to zero, and a dummy
variable was included for each variable indicating the missing values.

79

Table 3

Estimates of Child Schoolig @emale Childrg

 

Schooling at age 17 (1) ~ (4)

Schooling at age 20 (5) ~ (8)

 

Model lMode12 Model 3 Model4 Model 1 Mode12 Model3 Model4

 

(1) (2) (3) (4) (5) (6) (7) (3)
Birth cohort
1957-1959 .863 .823 .529 .405 .867 .861 .462 .318
(.795) (.678) (.662) (.655) (.887) (.775) (.794) (.789)
1960-1962 2.07 1.93 2.53 2.41 2.59 2.36 2.78 2.65
(.865) (.799) (.975) (.991) (1 .01) (.908) (1.19) (1.21)
1963-1965 2.48 2.20 2.80 2.57 3.05 2.59 2.93 2.62
(.770) (.710) (.897) (.926) (.900) (.810) (1.10) (1.14)
1966-1968 2.81 2.50 3.08 2.90 3.08 2.67 3.00 2.72
(.765) (.707) (.906) (.931) (.910) (.821) (1.13) (1.16)
1969-1971 3.24 2.86 3.50 3.25 .. .. .. ..
(.746) (.687) (.880) (.915)
Chinese .915 .664 .955 1.51 .915 .462 1.06 1.54
(.838) (.845) (1 .08) (1.14) (1 .02) (1.06) (1.41) (1.47)
Indian .102 -.684 ' -.702 -.103 .031 -1.25 .473 .962
(1.31) (1.05) (1.13) (1.09) (1.58) (1.07) (1.32) (1.38)
Chinese*cohort (> -1.54 -1.36 -1.26 -1.23 -1.95 -l.59 -1.60 -1.59
1960) (.850) (.850) (.978) (.982) (1.08) (1.09) (1.23) (1.18)
Indian‘cohort (> -.619 -.184 -.034 .405 -.595 .1 13 .276 .348
1960) (1.31) (1.04) (.918) (.905) (1.58) (1 .08) (1.05) (1.09)
Mothers’ schooling
Primary 1.29 2.54 2.42 2.02 2.99 2.78
(.240) (.723) (.747) (.410) (.952) (.988)
Secondary 1.85 3.28 3.01 3.59 4.74 3.74
(.241) (1.23) (1.23) (.509) (1.91) (1.95)
Fathers’ schooling
Primary -.053 .217 .030 -.358 .316 -.053
(.456) (.869) (.853) (.621) (1.07) (1.05)
Secondary .619 .927 .527 .786 1.74 1.23
(.514) (1.06) (1.03) (.785) (1.28) (1.28)
Post secondary 1.60 2.94 3.11 2.65 5.65 3.82
(.694) (1.36) (1.47) (.927) (1.3 7) (1.86)
Mothers’ schooling
*birth cohort
Primary *cohort -1.60 -l .65 -1.09 -1.13
(.698) (.709) (.904) (.909)
Secondary‘cohort -2.07 -2.09 -2.13 -l .73
(1.17) (1.15) (1.83) (1.80)

it]
I

""..d~'—"—'_'

 

Fathers’ schooling

I“birth cohort
Primary *cohort
Secondary*cohort

Post secon.*cohort

F-test p-value for
schooling*cohort

Community variables
Kuala Lumpur
(Capital)
SMK
Malay SRK*Malay
Malay SRK'Chinese
Malay SRK'Indian
Chinese SRK‘Chinese
Indian SRK*Indian
Family planning
program

Piped water

Electricity
Log income

R-squared
# of observation

.091
687

80

Table 3 (cont’d).

.184
687

4230
(829)
4463
(L01)
4221
(L16)

.037

.934
(278)
.447
(569)
.454
(573)
4837
(854)
.675
(963)
L40
(L15)
4570
(L97)
4345
(455)
.093
(384)
.047
(400)

.234
687

4172
(821)
4365
(998)
4280
(L22)

.019

L04
(250)
.536
(548)
.454
(555)
4949
(853)
.378
(973)
L33
(L17)
4141
(2.06)
4270
(447)
.048
(384)
.194
(400)

.216
(.138)

.252
687

.066
414

.205
414

4639
(977)
4847
(L22)
4297
(L19)

.003

.928
(580)
L88
(L32)
.389
(L04)
-L32
(L79)
.408
(L65)
L75
(2.40)
-842
(251)
.115
(849)
4125
(733)
.362
(825)

.268
414

4430
(954)
4954
(L21)
4278
(L62)

.263

L23
(577)
L80
(L30)
.451
(L02)
-L23
(L76)
4064
(L66)
L64
(2.49)
-872
(357)
.294
(816)
4097
(721)
.581
(819)

.455
(261)

.285
414

 

Standard errors are in parentheses. Other variables include ethnic dummy variables interacted
with parents’ schooling and income, mother’s number of siblings, and mother’s parent’s school-
ing. They are jointly insignificant at 5% level. Missing values for presence of father, mother’s
family background characteristics, and community variables were changed to zero, and a dummy
variable was included for each variable indicating the missing values.

a ”-1
l

:4

‘4'

F

 

81

Table 4

Estimates of Number of Children

 

 

Fertility at age 32 (1) ~ (4)

Fertility at age 37 (5) ~ (8)

 

Model 1 Model 2 Model 3 Model 4 Model 1 Model 2 Model 3 Model 4

 

(1) (2) (3) (4) (5) (6) (7) (3)
Woman's birth cohort
1936-1940 -.622 -.540 -.491 -.518 -.594 -.515 -.563 -.561
(.222) (.219) (.221) (.221) (.259) (.258) (.270) (.270)
194 1- 1945 -1.02 -.705 -.622 -.666 - l .04 -.699 -.784 -.781
(.201) (.205) (.209) (.212) (.256) (.264) (.309) (.313)
1946-1950 -1.49 -.978 -.808 -.849 -1.42 -.858 -.905 -.900
(.209) (.221) (.252) (.251) (.295) (.313) (.433) (.435)
1951-1955 -1.69 -.964 -.836 -.873 .. .. .. ..
(.217) (.234) (.307) (.304)
Chinese -.499 -.315 .127 .232 -.099 .041 -.327 .3 53
(.191) (.186) (.271) (.319) (.304) (.298) (.375) (.419)
Indian .381 .679 1.14 1.19 .498 .917 1.24 1.25
(.270) (.266) (.421) (.449) (.450) (.438) (.574) (.600)
Chinese*ratio -.460 -.5 80 .013 .012 -2.07 -1.88 -l .21 -1.19
(exposed to NEP) (.317) (.303) (.344) (.350) (.595) (.577) (.652) (.680)
Indian*ratio -1.00 -l .25 -.437 -.435 -1.28 -1.68 -.906 -.905
(exposed to NEP) (.425) (.402) (.469) (.470) (.884) (.836) (.975) (.985)
Woman’s schooling
Primary -.3 86 . 105 .085 -.506 .040 .033
(.137) (.234) (.234) (.172) (.378) (.379)
Secondary -1 .21 -.203 -.269 -1.46 -.778 -.806
(.167) (.404) (.403) (.242) (.796) (.797)
Husband’s schooling
Primary .147 .142 .109 .332 .307 .300
(.204) (.367) (.269) (.265) (.390) (.392)
Secondary -.505 -1.07 -1.14 -.505 -1.10 -l .13
(.220) (.397) (.404) (.304) (.663) (.670)
Post secondary -.975 -l.54 -1.65 -1.08 -1.42 -1.47
(.259) (.521) (.536) (.347) (.950) (.970)
Woman’s schooling
‘ratio
Primary‘ratio -. 105 -.081 -.193 -.180
(.374) (.376) (.731) (.732)
Secondary‘ratio .039 . 102 1 .13 1.16
(.503) (.505) (1.17) (1.18)

 

Woman’s schooling
*ethnicity
Primary *Chinese

Secondary*Chinese
Primary*lndian
Secondary*lndian

F-test p-value for
schooling*ethnicity

Family background
Woman's number
of siblings
Woman's mother's
schooling
Woman's father's

schooling
Community variables

Kuala Lumpur

(Capital)

SRK

SMK

Family planning

program

Piped water

Electricity

Log income

R-squared
# of observation

.110
1836

82

Table 4 (cont’d).

.187
1836

4864
(260)
-L25
(331)
4512
(453)
-2l4
(492)

.000

.021
(016)
4230
(114)

.000
(117)

4420
(156)
.798
(215)
-L00
(317)
-L15
(238)
4989
(242)
4431
(233)

.252
1836

4854
(260)
-L22
(330)
4529
(467)
-237
(514)

.000

.021
(017)
4236
(114)
4009
(118)

4432
(157)
.803
(215)
-L01
(317)
-L15
(237)
4997
(243)
4427
(234)

.093
(.079)
.253
1836

.117
1228

.188
1228

4881
(335)
-L47
(528)
4528
(596)
-L90
(758)

.022

.026
(025)
4367
(176)
.025
(168)

4405
(248)
.854
(310)
-L24
(497)
-L50
(389)
4275
(419)
4784
(388)

.229
1228

4884
(336)
-L46
(528)
4517
(615)
-L89
(813)

.065

.027
(025)
4369
(176)
.019
(170)

4411
(249)
.855
(313)
-L26
(501)
-L50
(390)
4270
(421)
4792
(390)

.046
(.109)
.230
1228

 

Standard errors are in parentheses. Unlike the schooling equation, I include the SRK as a meas-
ure of whether any of the primary schools with various language instruction was available. Other
variables include ethnic dummy variables interacted with husband’s schooling and income. They
are jointly insignificant at 5% level. Missing values for presence of husband, woman’s family
background characteristics, and community variables were changed to zero, and a dummy vari-
able was included for each variable indicating the missing values.

 

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BIBLIOGRAPHY

 

BIBLIOGRAPHY

Becker, Gary S. (1960), An Economic Analysis of Fertility, in Demographic and
Economics Change in Developed Countries, Princeton University Press.

Brien, Michael J ., and Lee A. Lillard (1994), Education, Marriage, and First Conception
in Malaysia, The Journal of Human Resources, Vol. 29, No. 4, pp. 1167-1204.

de Tray, Dennis (1988), Government Policy, Household Behavior, and the Distribution
of Schooling: A case Study of Malaysia, Research in Population Economics, Vol.

6, pp. 303-336.

Govindasamy, Pavalavalli, and Julie Da Vanzo (1992), Ethnicity and Fertility
Differentials in Peninsular Malaysia: Do Policies Matter?, Population and
Development Review, Vol. 18, No. 2, pp. 243-267.

Hagga, John G., Julie Da Vanzo, Christine Peterson, and Tey Nai Peng (1992), The
Second Malaysian Family Life Survey: Overview and Technical Report, RAND,
Santa Monica.

Hotz, V. J., Jacob A. Klerman, and Robert J. Willis (1997), The Economics of Fertility in
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Jones, Gavin W. (1990), Fertility Transitions among Populations of Southeast Asia:
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pp. 507-537.

King, Elizabeth M. and Lee A. Lillard (1987), Education Policy and Schooling
Attainment in Malaysia and the Philippines, Economics of Education Review,
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Income: the Case of Malaysia, R-2416-AID, RAND, Santa Monica.

Lam, David, Guilherme Sedlacek and Suzanne Duryea (1992), Increases in Women 's
Education and Fertility Decline in Brazil, Research Report No. 92-255,

University of Michigan, mimeo.

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92

Lillard, Lee A., and Robert J. Willis (1994), Intergenerational Educational Mobility:
Effects of Family and State in Malaysia, The Journal of Human Resources, Vol.
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Lucas, Robert E. B., and Donald W. Verry (1996), Growth and Income Distribution in
Malaysia, International Labour Review, Vol. 135, No. 5, pp. 553-575.

Maddala, G. S. (1983), Limited-Dependent and Qualitative Variables in Econometrics,
New York: Cambridge University Press.

Montgomery, Mark, Aka Kouame and Raylynn Oliver (1994), The T radeofi' between
Number of Children and Child Schooling: Evidence fiom Cote d 'Ivoire and
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Panis, Constantijn W. and Lee A. Lillard (1995), Child Mortality in Malaysia: Explaining
Ethnic Differences and the Recent Decline, Population Studies 49, pp. 463-479.

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_S

Chapter 3

A NOTE ON DECOMPOSING CHANGES IN THE WAGE GAP:
A CRITICAL COMNIENT ON PREVIOUS METHODS

1. Introduction

Several researchers have used trend decomposition techniques to decompose the
change in the wage gap between two parts. These analyses are important, since they
show how the changes in the means and the coefiicients of the explanatory variables
combine to affect the change in the wage gap over time. The previous results from these
analyses suggest that, all else equal, the proportion of the male-female wage gap
attributable to discrimination declined during 1970’s (Blau and Beller (1988)). This is
also interpreted as an evidence that government policy play a role in declining wage gap,
due to social discrimination. Stronger evidence of the effect of antidiscrimination
policies has also been obtained for many other countries.1

However, since no specification seems to be clearly better than the other, the
choice of the decomposition technique has been arbitrary.2 This paper re-examines the
previous decomposition techniques, and argues that the decomposition methods adopted

by Blau and Beller (1988), Wellington (1992), and O’Neill and Polachek (1993) are

 

' See Blau and Kahn (1995) for a discussion.
2 See Wellington (1992) for a discussion.

94

95

flawed on both conceptual and technical grounds. In contrast, this paper suggests an
alternative decomposition method which might avoid the shortcomings of interpretation
found in previous treatments. The alternative decomposition is then applied to the May
CPS from 1983 and 1993, and the results are compared to the results obtained using the
previous methods.

The results from the empirical application show that the previous decomposition
methods yield substantially lower estimates of the portion due to changes in
characteristics, and therefore higher estimates of the portion due to changes in
coefficients. This implies the conclusions drawn from previous methods may overstate
the change in the wage gap attributable to decline in discrimination. In section 2, the two
-period decomposition method is derived from single-period decomposition. Its
implications are also discussed. Section 3 presents an empirical application. Section 4

summarizes the paper.

2. Decomposition of the Change in the Wage Gap
2.1 A Critique of the Previous Decompositions

The most common forms of the decomposition are developed by Blau and Beller

(1988), Wellington (1992), and O’Neil and Polachek (1993). Let lIl(Wmt) and ln(wa) be
the means of the log of male (m) and the log of female (1) wages. If the wage model is
estimated separately by sex, then the means of the log wage gap can be expressed as the

following form

96

 

(1) ln(wmI)—1n(wn)= Y... {am-Z. I3.

where in“ and Ya are vectors containing the means of the variables, and [3m and [3,.

are the estimated coefficients. The subscript t represents the time at which the variables

 

are measured. Let the time increment be measured as, A,1n(w) = ln(w:) — ln(w: - 1) ,
AR: Y, —I(-,_, , and A43 =8, —[3,_,. Given the equation (1), the change in the wage gap,

At ln(wm) — A. 1n(wr) has taken the following forms

(2) Blau and Beller<1988): (6...-.Afim— {Swain(Y..-.A.I3..—3<'.-.A.é.)+a
(3) Wellington (1992): (6.... AK.- Ii. AIR.) + (Y... AIL-Y.-. A43.)

(4) O’Neill and Polachek (1993): (Emu‘xm— SAY.) + (imAfim—iufm + a.

where in and it are vectors containing the means of the variables pooling two periods

for males and females, while Em and E, are the means of the estimated coefficients
pooling two periods for males and females. In each of these, the first term has been
interpreted as the change in the wage gap due to a change in characteristics, while the
second term has been interpreted as the change in the wage gap due to a change in
coefficients (discrimination). Notice that the above equations look very similar to each
other. The only difference between (2) and (3) is that the first term of (2) is evaluated at

base year coefficients, while that of (3) is evaluated at current year coefficients.

 

 

97

Similarly, the difference between (3) and (4) also results from the different time at which
the variables and coefficients are measured. One common problem in both (2) and (4) is
that the sum of the first term and second term is not equal to the total change in the wage
gap. The last term (a and a’) in their decompositions has no clear interpretation.
Although the at term does not appear in equation (3), the (3) has different (and probably
more serious) problem. It does not answer why the changes in the characteristics are
evaluated at current year coefficients, while the changes in the coefficients are evaluated
at base year characteristics. In addition, there seem to be more important flaws in these
decompositions both on conceptual and technical grounds.

First, although Wellington (1990) argues that she employs these kinds of
decomposition in the spirit of Oaxaca’s (1973) decomposition, these decompositions are
far from the spirit of Oaxaca’s decomposition. Let’s consider Oaxaca’s single-period
decomposition model. In a single period earnings function, Oaxaca shows that we can
decompose the wage gap between two groups into differences in the means and
differences in the coefficients including the constant term. Given equation (1), the means

of the log wage gap can be decomposed in two ways. That is

 

(5) ln(wm)-ln(wr)= fimAgx+3§AgI§

01'

 

(6) ln(wm) — ln(wr) = {3,133+}; Agfi

 

98

where Agi= Rm- 7, , Ag13= [Tim—[3,. The first term of either (5) or (6) is the part ofthe
wage gap due to the different characteristics of males and females, and the second term is
the part of the gap due to different coefficients. If in the absence of discrimination males
and females receive identical returns for the same characteristics, and differences in
wages would therefore be due only to differences in characteristics, then this second term
can be interpreted as the wage gap due to discrimination. For the time being, assume that
in the absence of discrimination the male wage structure would prevail at both time t and

3

t-1. It is the assumption made in using (5). Oaxaca’s one-period decomposition then

can be calculated at both time t and t-1 , which have the following form

 

(7) In(Wmt) - ln(wa) = [3m ASK: 4’th Agfit

 

(8) In(Wmt - l)-Ifl(Wfi -I)= fimt-IAth-l+ifl-1Agfi"l

where subscripts t and t-l are the times at which the variables are measured. Now notice

that we never get the previous decomposition forms by using Oaxaca’s decomposition
method, since neither [3,, nor [3“ appears in the first term of the right hand sides in both

(7) and (8). Similarly, we would get the same result if we started with [3,. and [3“ as
non-discriminatory wage structure.
Second, a calculation (interpretation) problem with the previous decomposition

can be demonstrated using a relatively simple example. Suppose the change in

 

3 Wage structure describes the array of prices set for various labor market skills.

99
characteristics over time is same for both males and females, but that there is an initial
difference in the level of characteristics between males and females (that is AtYm = £1.71: ,

but Kim-113211 - 1). In addition, assume that the change in coefficients over time is same

for both males and females, and that there is no difference in the level of coefficient

between males and females (that is Atém= Afir , and [3 — [3M , and therefore [3,," =

"H _
[3,. ). In this case, the previous decomposition methods suggest that the change in the
wage gap is totally due to change in coefficients (discrimination), when this is clearly not
what has occurred. It does not answer why an initial difference in the level of
characteristics leads to the change in the wage gap totally due to change in coefficients,
but not due to change in characteristics.4 In the next part, I consider alternative

decomposition methods which have a clearer interpretation.

2.2 Two-Period Model of Oaxaca’s Decomposition

Let’s subtract (8) from (7) side by side. Then, we get

(9) Atln(Wm)‘Atln(Wf)= [‘3 A 32‘ " fimt—lAgY'—l] + [iaAgé‘ ‘ Yfl—lAgéi‘d

mtg

The right hand side of equation (9) can be transformed into the following form.

(10) I6..-.(A.¥m-A.ir)+A.3<’.A.fi.I HY.-. (Afi..-A.fi.)+A.é.A.‘X}I

OI'

 

‘ We would get an exact same result if we instead assumed that there is an initial difference in the
coefficient, but not in the characteristics.

 

100

(11) I3..<A.im—A.Yr)+A.Y.-.A.I3..I HY. (A.é..—A.Ii.)+A.I3.-.A.3<‘.I

(a) (b) (C) (d)

This form clearly show how the change in the wage gap over time can be
decomposed into four parts. Consider (11) only. The term (a) represents the change in

the wage gap due to a change in the characteristics evaluated at males’ current year

A

coefficient. It is evaluated at males’ coefficient, [3,“, , since we temporarily assumed that
in the absence of discrimination the male wage structure would prevail at both time t and
t-l. This form implies that if characteristics of males increase faster than those of
females, then the wage gap increases due to a change in characteristics as long as the
coefficients attached to characteristics are positive. The term (b) is an adjustment term,
which implies that if there is a difference in the level of characteristics between males and
females, then there exists a change in the wage gap due to a difference in the level of

characteristics, even if the change in the female and male wage structure is the same.

Notice that neither [3,. nor [3“ appears in both terms (a) and (b), since we assumed that
in the absence of discrimination the male wage would prevail at both time t and t-l.
Similarly, the term (c) represents the change in the wage gap due to a change in
coefficients. The term (d) is again an adjustment term, which implies that if there is a
difference in the level of coefficients between males and females, then there exists a
change in the wage gap due to a difference in the level of coefficients, even though men

and women experience the same change in characteristics.

101

Table 1 demonstrates several examples of this decomposition, which show the
importance of these adjustment terms in this analysis.5 Case I is the assumption which
we made to show a calculation problem in the previous decompositions. Notice that how
a difference in both change and level of characteristics (coefficient) leads to the change in
the wage gap due to differences in both change and level of characteristics (coefficient).

Now suppose that in the absence of discrimination the female wage would prevail
at both time t and t-l. It is the assumption made in equation (6). A corresponding

decomposition is of the form

(12) Iii. (Aim-ARI) + Ag'X‘.-.A. (3.] + [7... (Aim—A43.) + Agii.-. Aim]

which has a similar interpretation as equation (11). Again, it is noticeable that only
coefficients of females appear in the left hand side, since we assumed that, in the absence
of discrimination, the female wage would prevail at both time t and t-l.

However, the validity of these new decomposition also hinge on the rationale of
their assumptions: that is, in the absence of discrimination, the male (female) wage
structure would prevail at both time t and t-l.

The two decomposition methods above do not guarantee the same result, because
different wage structure assumptions are used in the alternative decomposition methods.
Neumark (1988) argues that the non-discriminatory wage structure should be derived

from a theoretical model of discriminatory behavior, and shows how different

 

’ By using similar examples, Blau and Kahn (1995) demonstrate the importance of wage structure in
explaining the international differences in the male-female wage gap.

 

 

102

assumptions about employers’ discriminatory tastes lead to Oaxaca’s estimators. A

corresponding decomposition based on his argument is of the form

(13) [heir/W)+A.$<’..A.BI +II‘X..(A.é.-A.fi)+ Y. (Axis—A43.» +

(a)’ (b)’ (C)’

{(firm-1-f3t—I)AI7m+(13t-I-§n-I)AI7r}]
(d)’

In this decomposition, terms (a)’ and (b)’ represents a change in the wage gap due
to characteristics evaluated at the current year non-discriminatory wage structure.
Similarly, terms (c)’ and (d)’ can be interpreted as the part due to coefficients. If it is

assumed that in the absence of discrimination the current male wage structure would
prevail at both t and t-l, then SH: [3%, , [3; [3m , and (13) reduces to (l l). Ifinstead it
is assumed that in the absence of discrimination the current female wage structure would
prevail at both t and t-l, then BM: [3“ , [3,: [In , and (13) reduces to (12). Thus, (11)
and (12) are two special cases of (13), and the critical issue is the choice of f3, and [3H ,

the non-discriminatory wage structure at each time period, and therefore A43. Also

notice that both (a)’ and (b)’ does not depend on either coefficients of males or
coefficients of females. Neumark (1988) proposes that this estimator of the non-

discriminatory wage structure can be implemented simply, as the coefficients estimated

 

r-— —"

103

from the log wage regression for the whole sample, using predicted wages from the log
wage regression as the dependent variable.6

Notice that equation (13) also show how a difference in both changes and levels
of characteristics (coefficients) leads to the change in the wage gap due to a difference in
both changes and levels of characteristics (coefficients). In the next part, I examine how

different decomposition methods lead to different results.

3. An Empirical Application

In this section, alternative decomposition methods are applied to the May Current
Population Survey (CPS) samples from 1983 and 1993. To simplify the discussion, the
sample is restricted to white, full time, year round, private sector workers. Individuals in
agriculture, forestry and fishery, and personal service industries are dropped. Hourly
wages are used as the wage variable in order to control for the change in hours worked
between genders over periods. Table 2 presents descriptive statistics for the data set in
1983 and 1993. The log wage gap in 1983 was 0.355, implying that female wages are
70% of the male wages in 1983. The wage gap falls to 0.251 by 1993, implying that
female wages are 78% of the male wages in 1993. The mean value of schooling is higher
for males in both periods, which is partly due to males being older on average.

In order to compare the alternative decomposition with the previous
decomposition, I construct the following specification. A basic wage equation of the

form

 

6 See Neumark (1998) pp. 283-89 for a detailed procedure.

 

104

(14) MM) = XIB + 8i

is estimated without industry or occupation dummy variables, where X is a vector of
workers’ characteristics.

Table 3 reports the OLS estimates for the basic form of the log wage equation.
The coefficients in these estimations are used in the calculation of decomposition. It is
noticeable that the coefficients for the schooling variable increase over time. However,
they increase faster for females than males, suggesting that this variable might play a role
in decreasing the wage gap through the change in the coefficient effect. The coefficients
for the marital status dummy variable increase for females, but decrease for males,
suggesting that this variable also might play a role in decreasing the wage gap through the
change in the coefficient effect.

Table 4 presents a comparison between the previous decomposition and the
alternative decomposition methods for the basic specification. At the bottom of the table,
the change in the wage gap attributable to each variable is added up, in order to
summarize the result. Results show that the new decomposition produces more or less
lower estimates of the percentage of the wage gap due to coefficients (therefore higher

estimates of the percentage of the wage gap due to a change in characteristics). Using

[3,," as the male wage structure, it is estimated that 39% of the change in the wage gap is
due to characteristics, while using Blau and Beller's (similarly Wellington’s) method

leads to an estimate of 22%. The adjustment terms are in parentheses. They markedly

105
vary by assumptions on wage structure, implying a potentially important role for wage
structure at each time period in decomposing the change in the wage gap.

Table 5 presents results for alternative specifications which consider changes in
the employment distributions of males and females across industries and occupations.
The first specification in Table 5 includes the portion due to changes in the employment
distributions of men and women across industry. Based on the argument by Macpherson
and Hirsch (1995), the second specification considers the effect of sex segregation due to
a change of differences in gender density in specific occupation and industry. The last
specification includes the portion due to changes in the employment distributions of men
and women across industry and occupation. Occupation and industry dummy variables
are for one digit 1980 code.

Some results are easily noticeable from Table 5. First, when these variables are
added as additional control variables, the portion due to characteristics rises substantially
in both previous decompositions and alternative methods. This might reflect the shift in
industry and occupation structure and relative demand for labor over time. Second, the
rise in the portion due to changes in characteristics is substantially higher when we use
the alternative methods. This implies one cannot arbitrarily choose a decomposition
method without considering its differences from other alternatives, since they lead to
quite different interpretation; the conclusions drawn from previous methods may
overstate the change in the wage gap due to decline in discrimination. Third, as Neumark
(1988) points out in a single-period model, the estimates using (1 1) (male wage structure)

and (12) (female wage structure) do not provide any range for the non-discriminatory

 

 

106

wage structure in the two-period model, either. However, unlike Neumark's single period
model, the estimates based on non-discriminatory wage structure are not necessarily
more sensitive than the estimates based on (1 l) and (12) to differences in the distribution

of characteristics across men and women.

4. Conclusion

Although several researchers have used trend decomposition techniques to
decompose the change in the wage gap between two groups, their decomposition methods
are flawed on both conceptual and technical grounds. In contrast, this paper suggests an
alternative decomposition method which might avoid the shortcomings of interpretation
found in previous treatments. The alternative decomposition is then applied to the May
CPS from 1983 and 1993, and the results are compared to the results obtained using the
previous methods.

The results from the empirical application in this two-period model show that the
previous decomposition methods yield substantially lower estimates of the portion due to
changes in characteristics, and therefore higher estimates of the portion due to changes in
coefficients. This implies the conclusions drawn from previous methods may overstate

the change in the wage gap attributable to decline in discrimination.

I“.

107

Table 1

Examples of Decomposition

 

 

Assumptions on Characteristics

 

Assumptions on Coefficients

 

 

 

 

 

 

 

Cases
Assumptions Results Assumptions Results
Change: same due to a change in Change: same due to a change in co-
1 (At in, = At 32,) characteristics = 0 (At [3m = At (if) efficient = 0
. - difference in levels 0f difference in levels of
Level. dIfferent .
(Y I $32“ I) characteristic 1: 0 Level. same coefficient = 0
mt - -
(Brut-1: Bit-l)
Change: different due to a change in Change: same due to a change in co-
[1 (At Xm ¢ At x.) characteristics at 0 (At 6m ___ At 13‘) efficrent = 0
Level: same dti‘fference in levegs of Level: same difigrence in levels of
(imt -1 =-)—(-fl _ I) c aracterrstrcs — A A coe rcrent — 0
(Bmt-l = Bfl-l)
Change: different due to a change in Change: same due to a change in co-
m (At in] at At Yr) characteristics ¢ 0 (Atfim = At 131) efficient = 0
Level: same dir‘iference In levegs of Level: di fferen t drffgence to levels of
(7m: _ l = in _ I) c aracterrstrcs — A A coe rcrent at 0
(Brut—l f Bit-I)
Change: same due to a change in Change: different due to a change in co-
1v (AtX-m = At 2.) characterrstrcs = O (Atfim at At 3f) efficient at 0
Level: different drilfference in levels of Level: same difference in levels of
(Ymt _ I #3:“ _ 1) c aracterrstrcs ¢ 0 A A coefficrent - 0
(Burt-l = Bit-l)
Change: same due to a change in Change: different due to a change in co-
V (At Km = At if) characterrstrcs = 0 (Atfim at At fir) efficrent at 0

 

Level: different
(YmI-I¢3(’n-I)

 

difference in levels of
characteristics at 0

 

Level: different
(Bmt-l 7:13:14)

 

difference in levels of
coefficient at 0

 

Only one variable case is considered.

 

108

Table 2

Means and Standard Deviations of Variables

 

 

 

1983 1993
Total Male Female Total Male Female
log (wage) 6.415 6.551 6.196 6.772 6.876 6.625
(.497) (.495) (.414) (.528) (.538) (.476)
Schooling 12.92 12.98 12.81 13.12 13.14 13.10
(2.56) (2.74) (2.25) (2.40) (2.54) (2.20)
Age 36.91 37.45 36.05 37.73 37.95 37.41
(12.25) (12.18) (12.32) (11.21) (11.28) (11.09)
Experience 19.00 19.47 18.24 19.60 19.81 19.31
(12.83) (12.73) (12.96) (11.50) (11.46) (11.55)
Married .655 .719 .551 .633 .681 .565
Union .209 .259 .129 .130 .171 .071
Central City .206 .195 .224 .189 .185 .195
In SMSA .373 .385 .354 .395 .396 .393
# of observation 7165 4421 2744 7569 4448 3121

 

Means are reported with standard deviations in the parentheses. Age is included only for com-
parison between groups. Experience is calculated by a formula, age - schooling - 5. This vari—
able construction implicitly assumes that all years since school were spent in the labor force,
which is not necessarily true. This is a common problem we face when we use the CPS data.

 

109

Table 3

OLS Estimates (Basic Specificatiory

 

 

 

 

1983 1993
Total Male Female Total Male Female
Constant 4.90 5.02 4.99 5 .03 5.12 5.00
(.012) (.042) (.055) (.010) (.048) (.060)
Schooling .074 .070 .068 .098 .094 .098
(.001) (.002) (.003) (.001) (.003) (.004)
Experience .03 1 .037 .024 .029 .032 .026
(.001) (.002) (.002) (.0004) (.002) (.002)
Experience x 10-2 -.O48 -.058 -.o39 -.044 -.046 -.046
(.001) (.004) (.005) (.001) (.004) (.005)
Married .144 .157 .011 .128 .146 .033
(.004) (.015) (.015) (.003) (.016) (.015)
Union .223 .158 .181 .197 .147 .125
(.004) (.015) (.022) (.004) (.018) (.029)
Central City .051 .023 .097 .071 .043 .1 18
(.005) (.018) (.019) (.004) (.019) (.021)
In SMSA .125 .120 .112 .113 .094 .149
(.005) (.015) (.017) (.003) (.015) (.017)
R-squared .7701 .3157 .2055 .8597 .3319 .2782
# of observation 7165 4421 2744 7569 4448 3121

 

Standard errors are in the parentheses. In the log wage regression for the whole sample, the de-
pendent variable is fitted log wages from the separate wage regression. Other variables include 8
regional dummy (state division categories in the CPS) variables. Occupation and industry
dummy variables are not included.

 

 

_II"__7I1

110

Table 4

Decomposition Based on Basic Specification

 

 

 

(2) (3) (4) (5)
O’Neill & New Method: New Method: New Method:
Polachek Male wage Female wage Non-
structure structure discriminatory
wage structure
Schooling (total=-.O94)
Characteristic -.012 -.009 (.001) -.009 (.002) -.010 (.001)
Coefficient -.083 -.085 (-.002) -.085 (-.002) -.084 (-.001)
Experience (total=-.134)
Characteristic -.016 -.029 (-.003) -.017 (.000) -.024 (-.003)
Coefficient -.1 17 -.105 (.009) -.117 (.003) -.110 (.006)
Exp. Square (total=.1 10)
Characteristic .012 .015 (.004) .008 (-.001) .012 (.002)
Coefficient .097 .094 (-.001) .102 (.005) .098 (.003)
Married (tota1=-.026)
Characteristic -.006 -.009 (-.001) .002 (.004) -.009 (-.002)
Coefficient -.020 -.017 (.002) -.028 (-.005) -.017 (.001)
Union (total=-.001)
Characteristic -.006 -.006 (-.003) -.011 (-.007) -.009 (-.003)
Coefficient .004 .005 (.004) .010 (-.001) .008 (.002)
Central City (total=.002)
Characteristic .003 .000 (-.001) .002 (-.002) .001 (-.001)
Coefficient -.001 .002 (.002) .001 (.000) .001 (.001)
In SMSA (total=-.028)
Characteristic -.004 -.003 (-.001) -.003 (-.000) -.004 (-.001)
Coefficient -.024 -.024 (-.001) -.025 (-.001) -.024 (.001)
Region (total=-.032)
Characteristic .000 .000 (-.002) .001 (-.004) .000 (-.004)
Coefficient -.031 -.032 (.001) -.032 (.001) -.032 (.002)
Change due to
Change in Charact. -.038 -.020 -.011
Difference in Charact. .. -.003 -.008 -.032
Total -.028 -.041 -.028 -.043
(%) (26.9%) (39.4%) (26.9%) (41 .4%)
Change in Coeff. . -.074 -.075 -.075
Difference in Coeff. .. .011 -.001 .014
Total -.O76 -.063 -.076 -.061
(%) (73.1%) (60.6%) (73.1%) (58.6%)

 

The change in the wage differential, Aln( Wm) - Aln(w;) = -0.104 over the period of 1983-1993.
Occupation and industry dummy variables are not included.

 

'L

111

Table 5

Decomposition Based on Alternative Specification

 

 

Decomposition (1) (2) (3) (4) (5)
Wellington O’Neill & Male wage Female wage Non-
(Blau & Polachek structure structure discriminatory
Specification. Beller) would apply would apply wage structure
Including industry
dummies
Change in Charact. -.032 -.025 -.031
Difference in Charact. .. .. -.023 -.015 -.026
Total -.032 -.019 -.056 -.040 -.056
(%) (30.8%) (18.3%) (53.8%) (38.5%) (53.8%)
Change in Coeff. -.060 -.067 -.060
Difference in Coeff. .. .. .012 .003 .011
Total -.072 —.079 -.048 -.064 -.048
(%) (69.2%) (76.0%) (46.2%) (61 .5%) (46.2%)
Macpherson & Hirsch:
(Including FEM)
Change in Charact. -.035 -.022 -.045
Difference in Charact. .. .. -.043 -.020 -.033
Total -.027 -.032 -.O78 -.O42 -.078
(%) (25.6%) (30.7%) (75.2%) (40.3%) (75.0%)
Change in Coeff. -.033 -.059 -.051
Difference in Coeff. .. .. .008 -.003 .016
Total -.077 -.O72 -.026 -.062 -.036
(%) (74.4%) (69.4%) (24.8%) (59.8%) (25.0%)
Including occupation
and industry dummies
Change in Charact. -.046 -.023 -.053
Difference in Charact. .. .. -.044 -.063 -.032
Total -.031 -.036 -.090 -.086 -.085
(%) (30.3%) (34.8%) (87.1%) (83.0%) (81.7%)
Change in Coeff. -.025 -.008 -.037
Difference in Coeff. .. .. .012 -.010 .020
Total -.072 -.O67 -.013 -.018 -.017
(%) (69.7%) (65.2%) (12.9%) (17.0%) (28.3%)

 

The change in the wage gap, AID(Wm) - A ln(w1) = -0.104 during 1983-1993. FEM is the ratio if

female to total employment in a worker’s occupation and industry.

BIBLIOGRAPHY

BIBLIOGRAPHY

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