The Substitutability of Male and Female Engineers in Production
By: Adam Pilz
Abstract: The objective of this paper was to determine the extent to which male and
female engineers are substitutes in production. A Translog Production function was used
to obtain the Hicks Partial Elasticities of Complementarity between male and female
engineers, as well as capital. The data suggest, in four different models, that male and
female engineers are substitutes in production to the extent that a one percent increase in
the quantity of female engineers implies a decrease of .04 percent to 2.33 percent in the
prevailing male wage. From this we assert that competition from female engineers has
very likely had a negative impact on the labor market for male counterparts.
Special thanks is due to Dr. Renna for guiding me through the process of writing this
research paper. Also, to Dr. Stratton for his comments which have expanded my
thoughts as an economist by tying together the theory learned in Labor I and its
application to the scenario presented here. Last but certainly not least, to Alexandra
Antonas who was the inspiration for this topic.
2
Table of Contents
Introduction…………………………………………..4
Theoretical Framework and Analysis……………….. 5
Literature Review…………………………………….7
Procedural Overview………………………………...10
Procedure…………………………………….10
Data Description…………………………….11
Models Including Capital……………...….....11
Models Excluding Capital…………………...13
Results……………………………………………….13
Conclusions………………………………………….17
References………………………………………….. 25
Tables
1………………………………………………19
2………………………………………………20
3………………………………………………24
3
I. Introduction
Engineering has long been a profession dominated by males. Over the last twenty
years, females have entered the field in increasing numbers, nearly doubling their share
of employment from 5.8% in 1983 to 11.1% in 2007.1 Though female representation in
engineering has increased, almost 15% who leave the engineering field cite “Negative
Work Climate Issues” as the primary reason.2 What is the source of this tension for
females in the field of engineering? Female engineers are typically paid less than their
male counterparts.3 Regardless of why the wage differential exists, is the differential
itself the source of negativity towards women? In other words, do male engineers view
their female counterparts as substitutes in production?
If male engineers perceive females as substitutes, then the existence of tension
towards women is not unfounded, they are a source of equivalently skilled, relatively
cheap labor. However, imperfect information may also play a vital role. Suppose for a
moment that female engineers are actually complements to male engineers, but this
information is unknown. Upon discovering the complementarity, male engineers would
actively release such tension in order to retain females in engineering as a means of
increasing their own productivity and wages. In this study, we examine the direct
evidence on the extent to which male and female engineers are in fact substitutes in
production.
Another important source of female attrition from engineering, nearly sixteen
percent, is “Time and Family Related Issues.”4 If male and female engineers are
1
http://www.nsf.gov/statistics/wmpd/sex.cfm#employ
2005 Society of Women Engineer Retention Study
3
http://www.nsf.gov/statistics/seind08/c3/c3s1.htm#c3s14.
4
Ibid.
2
4
substitutes, then the fact that so many women leave engineering occupations is not cause
of disruption for the firm because females who left can be replaced with males who have
similar skills. However, if complementarity exists, then productive synergies are lost by
the attrition of females and male engineers may suffer lesser productivity and wages as a
result.
While there have been numerous studies of substitution among workers of
different groups, none have considered substitution among male and female engineers.
This study may shed light on the causes of tension in the engineering labor market and
reveal if female attrition is removing unique skills from the marketplace. Following a
commonly used technique for studies that look at the substitutability between inputs of
production, this study will employ a Translog Production Function.
Policy implications could be made from a study examining the extent to which
male and female engineers are substitutes in production. If male and female engineers
are found to be complements, perhaps additional awareness programs could be
established to encourage women to enter the field. A 2006 Duke University survey of
American firms that outsource such jobs abroad found that approximately 40 percent
considered the U.S. supply of engineers inadequate.5 Therefore, if male and female
engineers are substitutes, perhaps recruiting efforts should be equally divided among the
two groups.
II. Theoretical Framework and Analysis6
The analysis in this paper assumes that the production technology can be
characterized by the Translog Production Function.7 Firms are assumed to profit
5
http://www.technologyreview.com/article/21859/
The following discussion follows closely from Hammermesh and Grant (1979), Grossman(1982), and the
Handbook of Labor Economics Volume I.
6
5
maximizing8 and be in perfect competition in both product and labor markets. Also,
production is characterized by constant returns to scale. A production function is used,
instead of a cost function, because factor quantities are more properly viewed as
exogenous when estimating production models for labor force subaggregates.9
Let the production function be characterized by
Y = F(X1,…,Xn) i=1,…,N
(1)
where F has N factors, or specifically here
Y = F (L1, L2, K)
(2)
where Y is output, L1, L2 are the heterogeneous labor inputs males and females, and K is
a measure of capital stock. The translog production function can be approximated by
lnY = αo +∑ αi lnXi + .5 ∑∑ βij lnXi lnXj
(3)
where αi and βij are technology coefficients and Xi ,is the quantity of factor i. The
assumption of perfect competition allows us to derive factor share equations as done in
the Handbook of Labor Economics.
Si= αo + βij lnL1+ βij lnL2+ βij lnK
(4)
The βij coefficients are interpreted as the effect of factor j on factor i’s share of output. Si
is the share of factor i in production and reflects the following output elasticity equations
7
The tranlsog function is the most popular among the literature of input demand. After testing the tranlsog,
normalized quadratic, and generalized Leontief functional forms Anderson and
Chaisantikulawat (1996) find that preferred functional form appears to be both data and model specific.
Therefore I reduce my choice to the translog largely due to its popularity in the literature.
8
When using a translog production function the appropriate assumption is profit maximization whereas
cost minimization is the appropriate assumption for translog cost functions. Hammermesh and Grant (1979)
9
Also, according to the Handbook of Labor Economics “The studies that treat quantities as exogenous and
estimate elasticities for a variety of disaggregations of the labor force give a better indication of the
substitution possibilities within the labor force disaggregated by age,race,sex than do studies assuming that
factor prices exogenous.”
In the case of the engineering labor market, it is assumed that the labor inputs cannot change vary
rapidly. For instance engineering is characterized by mathematical calculations and specific concept
applications which it may be difficult to learn quickly. Therefore it is assumed that inputs are
approximately fixed and cross-sectional data is used to make this more plausible.
6
∂ lnY / ∂ln Xi = Si =( PiXi / Y )
(5)
and Pi is the price of factor i. When estimating equations that employ the assumption of
profit maximization, the βij coefficients will exemplify a symmetric condition such that
βij=βji.10
Previous works have pointed out that when assuming factor quantities exogenous,
Allen partial elasticities of substitution are inappropriate measures of substitution and that
another measure must be used. We therefore turn our attention to the Hicks partial
elasticity of complementarity. The Hicks elasticity tells us the proportional effect on the
price of one factor given a proportional change in the quantity of another factor, holding
the output price and other input quantities constant.11 It is defined as
Cij = FFij / FiFj
(6)
where Fi is the first derivative of the production function with respect to factor i and Fij
is the second derivative.
Fi = ∂F / ∂Xi
Fij= ∂2F / ∂Xi ∂Xj
(7)
It can be restated in the following form
Cij = (βij + Si Sj ) / Si Sj
Cii =( βii + Si 2- Si)/ Si 2
(8)
where factors i and j are substitutes if Cij is negative and complements if Cij is positive.
In other words, if Cij is negative, an increase in the quantity of j decreases i’s price. If Cij
is positive, then an increase in j’s quantity increases i’s price. Symmetry of the βij
coefficients also allows us to assert that Cij = Cji.
III. Review of the Literature
10
Christensen, Jorgenson, Lau(1973) provide a detailed description of why this is so in their development
of Transcendental Logarithmic Production Frontiers.
11 Sato and Koizumi (1973)
7
Grant and Hamermesh(1981) attempted to estimate how substitutable women are
for young workers. A translog production function is used instead of a cost function
because Grant and Hamermesh assert that factor quantities are more properly viewed as
exogenous than are factor prices. The authors present evidence that when seeking an
estimate of substitution in production among demographic groups, measures of the
capital stock must be included to avoid serious bias. Their estimates of white female
youth substitution imply that the growth of the white female labor force has hurt the
earnings possibilities of young workers.
Borjas(1986) reaches similar conclusions. Borjas attempts to estimate how the
demand for African American labor is affected by changes in the demographic
characteristics of the local labor market. Using a generalized Leontief production
function, Borjas finds that women are strong substitutes for black men in the production
process. Borjas explains that the entry of women into the labor market in the postwar
period may well have prevented the equalization of black and white wage rates and had
negative impacts on black labor force participation. In fact, according to Borjas, much of
the drop in the participation rates of young black men in the postwar period can be
directly attributed to the rapid increase in the number of working women. Furthermore,
Borjas claims that a common problem with current input demand literature, such as Grant
and Hamermesh, is that input supply is assumed exogenous. The justification previously
given was that the supply of any given input factor is fixed at a given point in time.
Borjas explains that although the total stock of a given input may be fixed at a given time,
the distribution across labor markets is likely to be guided by input price differentials and
thus, that supplies should not be treated as exogenous.
8
In a rather different study, Berger(1983) uses a translog production function to
investigate the effects of changes in the composition of the labor force and capital
intensity on the earnings of experienced male workers. He cites a rapid increase in the
number of recent male college graduates relative to experienced males and the decline in
experience male wages as motivation for the study. According to Berger, no previous
study had constructed a model capable of explaining the recent movements in male
earnings in terms of changes in factor proportions. Estimates of elasticities of
complementarity are obtained which indicate that earnings are sensitive to changes in
factor proportions. Berger(1993) differentiates from past studies by disaggregating male
workers by both experience and schooling. He also includes a variable for females. The
increase in female participation is shown to have contributed significantly to the decline
in the earnings of both high school educated young and old workers.
Juhn and Kim(1999) present a model that similarly reveals skilled women being
substitutes for unskilled men. They examine whether increases in female labor supply
contributed to rising wage inequality and declining real wages of less skilled males
during the 1980s using an aggregate demand model. The authors note that much of the
previous literature reports high skilled women to be substitutes for low skilled men but
they hypothesize that the these results are biased because they fail to control for demand
shifts. In fact, when they add demand shifts as separate regressors in their estimation,
Juhn and Kim find that the substitution between educated women and less educated men
disappears. Instead, they find evidence that college educated women are substitutes for
college-educated men and that their entry into the labor market may have actually slowed
the growth in male wage inequality in the 1980s.
9
Most of the previous literature has focused on the substitutability between
different groups of workers that differ on their age, gender, education, and race profile for
the general labor workforce. Not much is know about the substitutability within specific
occupations. O’Connell(1972) looks specifically at the engineering market. He develops
and estimates demand and supply functions for engineers to analyze the complementarity
or substitutability of engineers and other factor inputs. This study is different from the
previous engineering studies in two ways. First, it reduces the heterogeneity arising
when engineers are aggregated, by disaggregating the engineering occupations. Second,
he takes into account the identification problem that occurs because the demand and
supply schedules are functions of wage. This is achieved by constructing separate
demand and supply schedules and estimating them by the method of two-stage least
squares. There are two main findings presented. First is that related occupations
requiring less formal training than engineers tend to be complements and second that
rather considerable changes in relative earnings are unlikely to have a significant impact
on the quantity of engineers demanded.
IV. Procedural Overview
A. Procedure
The share equations listed above was estimated using OLS as is common when
not using the Zellner’s Seemingly Unrelated Regression Model. Previous work has
eluded to biased parameter estimates when a capital measure is not included. Therefore,
two models are to be specified and estimated, one with a capital measure and one
without. Another two models, for a total of four, will be estimated with two different
output measures.
10
V. Description of the Data
The regression calls for data on the prices and quantities of male and female
engineers to calculate the share equations. The cross sectional data was gathered from
IPUMS for 230 Metropolitan Areas in 2007. The econometric specification is
Sik= αo + βijk lnL1+ βijk lnL2+ βijk lnK
(9)
where Si is the share of factor i in production from metropolitan area k. The labor inputs
L1 and L2 are defined as the quantity of male and female engineers in the respective
metropolitan area. The βijk ‘s are interpreted as the effect of factor j on factor i’s share of
output in metropolitan area k. The wage and salary data may bias results since this
measure doesn’t include fringe benefits.
Another requirement of the model is a measure of output. This study will use two
different measures of output. The first measure is engineering services revenue from the
2007 Economic Census published by the U.S. Census Bureau.12 The model which
employs this measure of output is hereafter referred to as the Revenue Model. The
second measure is theoretical in nature. Under the assumption of perfect competition, the
marginal price charged by firms will equal the marginal cost of that unit. Therefore,
when including a capital measure, total output is equal to the sum of the total cost in each
metropolitan area. The model which employs this output measure is hereafter referred to
as the Factors Model. Table 1 contains the descriptive statistics of the data along with the
respective correlations.
A. Models Including Capital
12
The requirement to be included in the economic census is to be a firm with payroll in business at any
time during 2007. Receipts are a basic dollar volume measure for service establishments of firms subject to
federal income tax. Receipts include gross receipts from customers or clients for services provided, from
the use of facilities, and from merchandise sold in the census year, whether or not payment was received in
the census year.
11
The first two models estimated include a capital figure. The capital figure was
constructed using the Other Professional, Scientific, and Technical Services Current-Cost
Net Capital Stock of Private Nonresidential Fixed Assets as published by the Bureau of
Economic Analysis(BEA) for 2007. The figure was constructed due to the lack of a
published capital figure for engineers and due to the inadequacy of the measures used in
previous work that assumes capital in the services sector is proportional to capital in
manufacturing. Rationale for constructing this measure follows from the BLS work and
output description in Other Professional, Scientific, and Technical Services under which
engineering is categorized.13
The current-cost net capital stock of private nonresidential fixed asset estimates
are presented for detailed industries by asset type. The capital figure consists primarily
of PCs, Storage devices, Pre-packaged software, Custom Software, Own Account
Software, and Office Space. The nature of the data allow for differentiation of capital
levels by engineering subfield while maintaining the assumption that the major input in
engineering production is human capital. For instance, “Electrical Transmission and
Distribution Machinery” is assumed to be the physical capital used by electrical
engineers. This component represents approximately 2.5 percent of the final capital
figure for electrical engineers. Industrial engineers have the largest physical capital
“Industries in the Professional, Scientific, and Technical Services subsector group are establishments
engaged in processes where human capital is the major input. These establishments make available the
knowledge and skills of their employees, often on an assignment basis, where an individual or team is
responsible for the delivery of services to the client. The individual industries of this subsector are defined
on the basis of the particular expertise and training of the services provider.
13
The distinguishing feature of the Professional, Scientific, and Technical Services subsector is the fact that
most of the industries grouped in it have production processes that are almost wholly dependent on worker
skills. In most of these industries, equipment and materials are not of major importance...”
12
component which comprises roughly 11 percent of their total capital. Table 2 contains a
chart of the proposed capital levels by engineering subfield and a further discussion of
this figure.
The independent variables for the model including capital are the natural
logarithms of the quantities of male engineers, female engineers, and capital stock. The
dependent variable is the share of a given input in total output, each share’s intensity.
Recall for both models that the importance of the parameter estimates lies not in the usual
OLS interpretations. In this study, the importance lies in the interpretation of the Hicks
elasticity of complementarity.
B. Models Excluding Capital
The second pair of models is identical to the first but excludes the measure of
capital. This is to acknowledge that the measure of capital stock, while logically
constructed, is still quite arbitrary. Thus, the independent variables for model excluding
capital are the natural logarithms of the quantities of male engineers and female
engineers. The dependent variable is the share of a given input in total output, each
share’s intensity. For both models it is unknown what the complementarities will be
although we could speculate that both male and female engineers will be complementary
with capital due to the highly skilled nature of the profession.
VI. Results
Analyzing empirical estimates of elasticities of complementarity are essential for
predicting the effects of policy changes. Assume for a moment that female engineers are
more complementary with capital than are males, this finding could reveal the outcomes
of different tax policies. For instance, if firms are allowed to use accelerated depreciation
13
methods for capital because of a recession, firms may choose to hire more females
instead of males.
The elasticities of complementarity are calculated using the mean values of each
factor share from Table 1 and the regression coefficients in Table 3. Recall that factors
are substitutes if Cij is negative and complements if positive and our symmetry conditions
provide that Cij = Cji.
14
In the Factors and Revenue Models the signs of complementarity are similar. In
most cases, the estimated elasticities are fairly large relative to their standard errors,
which supports the hypothesis that factor prices are sensitive to changes in male-female
labor force composition and capital intensity. Previous research has suggested that if one
coefficient in the system has a very large standard error, this will be reflected in all
estimates derived from a production function. It does not appear that this will present any
problems in this study. Given that the models including capital appear more theoretically
relevant,14 and that previous work has stated that exclusion of capital stock measures may
lead to serious bias, the following discussion will focus primarily on those models
including capital.
Initially, we set out to examine the evidence on the extent to which male and
female engineers are substitutes in production. The evidence suggests that female
14
There is a theoretical discrepancy in the factors model when looking at the own elasticity of
complementarity for males without a capital stock measure. The positive sign implies that for a given
metropolitan area, as the proportion of male engineers rises, their wage increases when holding the output
price and other input quantities constant. No other theoretical discrepancies appear in terms of the own
elastisicities of complementarity.
15
engineers are indeed substitutes for their male counterparts. In fact, the data suggest that
a one percent increase in the quantity of female engineers in a given metropolitan area
will decrease the male wage from .14 percent in the factors model(FM) to .88 percent in
the revenue model(RM). Therefore, the existence of tension towards women is not
unfounded, as they are a source of readily substitutable, relatively cheap labor.15 We can
make some assumptions about tax policy from this finding. If the government were to
implement policies designed to increase employment in the field of engineering, it
appears that females may find more employment opportunities than males. Even though
females appear to be substitutes for males in production, additional male entrants appear
to have a larger negative effect on the prevailing male wage than that of additional female
entrants. Notice the own wage elasticity of complementarity for male engineers ranges
.277 percent(FM) to 1.13 percent(RM).
The most striking observation is the magnitude with which female entrants hurt
the prevailing female wage. The data suggest that a one percent increase in the quantity
of female engineers in a given metropolitan area will decrease the female wage anywhere
from 6.8 percent(FM) to 10.3 percent(RM). According to this data we would suspect that
the group most likely to resist the entrance of additional females into engineering would
be that which consists of established female engineers.
The data indicate that male and female engineers are complementary with capital.
This is not surprising considering the highly skilled nature of the engineering profession.
A remarkable observation is the difference in magnitude of complementarity between
capital with male and female engineers. The data imply that a one percent increase in the
15
See http://www.nsf.gov/statistics/issuebrf/sib99352.htm for a discussion of the pay gap between male and
female engineers for 2003. This trend appears to remain in 2006 from authors own calculations from data
derived using SESTAT Data Tool. http://www.nsf.gov/statistics/sestat/
16
capital stock of a given metropolitan area will increase the male wage from .07
percent(RM) to .16 percent(FM) whereas the female wage will increase 2.01
percent(RM) to 4.44 percent(FM). This indicates that women who will have relatively
fast gains in wages are those who are employed at firms that are accumulating capital
relatively quickly compared to other firms and who have low levels of females relative to
other inputs.16 Therefore if the government were to implement policies which are meant
to increase the capital stock of the engineering field, women at firms quickly increasing
their capital stock would benefit significantly. The finding that females are more
complementary with capital than males is consistent with the findings of
Hammermesh(1981). This may be due to differences in capital use by male and female
engineers. For instance capital can only raise worker productivity insofar as workers
become capital intensive themselves. Given equal intellectual ability but an increased
attention span women may be able to reap larger increases in productivity from capital
than male engineers, thereby increasing their wages to a larger degree. 17
VII. Conclusions
Females have nearly doubled their share of employment in engineering
over the last twenty years. When such an increase is made, the potential effects on those
already in the engineering labor market could be substantial. In this study, we examine
the direct evidence on the extent to which male and female engineers are in fact
substitutes in production. Such an attempt may also help to determine if the attrition of
16
This is because firms will seek to equalize the marginal productivity per dollar spent on each input. Thus
a firm with a relatively large number of females may decrease female employment and wages if their mix
of inputs is not optimal.
17
G. Becker, Hubbard, and Murphy(2009) show that IQ scores are nearly identical for young boys and girls
and that females are more likely to have a higher GPA in college than males. They also show that girls
have higher non-cognitive abilities than do boys and claim these abilities yield increased preparation,
organization, and attention levels. We suggest here that increased attention, organization, and preparation
may increase the productivity gained from using engineering capital(computers, software).
17
females from engineering is removing unique skills from the marketplace.
Substitutability is implied to the degree that a one percent increase in the quantity of
female engineers in a given metropolitan area will decrease the male wage anywhere
from .14 percent to .88 percent holding output price and other input quantities constant.
The estimates derived imply that the dramatic growth of females in engineering has had a
relatively small effect on the earnings of male engineers. That being said, competition
from female engineers has very likely had a negative impact on the labor market for male
counterparts.
There are many potential sources of error in this study. To name a few:
production in the engineering labor market may not be accurately characterized by the
Tranlsog Production function, the capital measure constructed may not reflect true capital
levels for engineers, and exogeneity of quantity supplied may be a false assumption.
Further replication of this study should be completed to ascertain a more solid foundation
of knowledge as to the substitutability or complementarity of male and female workers in
the engineering labor market.
18
Table 1.
Defintions:
Male Share Rev, Female Share Rev, Capital Share Rev- are variables that assume the
shares of each input are best described by their relation to 2007 Economics Census
published by the U.S. Census Bureau.
LnM, LnF, LnK- are the natural logarithms of the quantities of the respective input.
Male Share Factors, Female Share Factors, Capital Share Factors- are variables that
assume the shares of output are best described by their relation where marginal cost equal
marginal benefit.
19
Table 2.
The capital figure was constructed using the Other Professional, Scientific, and
Technical Services Current-Cost Net Capital Stock of Private Nonresidential Fixed
Assets as published by the Bureau of Economic Analysis(BEA) for 2007. Defintions of
20
the components of this measure are provided at the end of this explanation. It consists
primarily of PCs, Storage devices, Pre-packaged software, Custom Software, Own
Account Software, and Office Space. Since Engineers only represent a portion of those
classified in the Professional, Scientific, and Technical Services category, the total dollar
value of PCs, Storage devices, Pre-packaged software, Custom Software, and Own
Account Software was divided by the number of people in this category, arriving at a
dollar value of these capital pieces per capita. The calculation is
(Total value of Software related Capital)
(Number of people in Prof., Sci., Tech. Ser.)
Then two other components were added, one representing the office space occupied and
the other representing specialized equipment. Office Space as reported by the BEA is
“Office space including medical buildings” and a per capita figure is derived as above.
The BEA also reports asset figures for specialized machinery and equipment. The
categories used and the corresponding engineering subfields they are attributed to are:
Internal Combustion engines(Mechanical), Special industrial machinery(Industrial),
Electric transmission and distribution(Electrical) Aircraft(Aerospace), Other construction
machinery and Construction tractors(Civil), Other(any subfield not previously specified,
divided evenly). A representative calculation is
(Total value of Special industrial machinery)
(Number of people in Prof., Sci., Tech. Ser.)
The total number of people in Professional, Scientific, and Technical Services was used
to maintain consistency with the calculation for software capital and remove the arbitrary
steps that would be needed to break this number done further.
21
The total capital Figure is the sum of the two above calculations. The assets
figures for specialized machinery and equipment comprise 2.5 to 11 percent of the total
capital figures.
Definitions(taken directly from source):
Other Professional scientific and technical services consists of accounting, tax
preparation, bookkeeping, and payroll services; architectural, engineering and related
services; specialized design services; management, scientific, and technical consulting
services scientific research and development services; advertising and related services;
and other professional, scientific, and technical services. Excludes Legal and computer
systems design and related services.18
Current-cost valuation estimates of net stocks and depreciation reflect the prices
of the given period. For instance, the estimate of the net stock for 1997 reflects the value
of the stock expressed in the prices that would have been paid for those assets if they had
been purchased at the end of 1997. Similarly, the 1925 net stock estimate reflects the
value of the stock in 1925 expressed at the prices that would have been paid for them if
they had been purchased in 1925.19
In principle, the current-cost net stock is the market, or replacement, value of the
stock; that is, the value for which the assets in the stock could be bought or sold in that
year. In equilibrium, this market value will equal the present value of all expected future
services embodied in existing assets.
18
19
http://www.bea.gov/scb/pdf/2009/11%20November/1109_fixed.pdf
http://www.bea.gov/national/pdf/Fixed_Assets_1925_97.pdf
22
Fixed assets are produced assets that are used repeatedly, or continuously, in the
processes of production for more than 1 year. BEA’s estimates cover structures,
equipment, and software, but not cultivated assets such as livestock or orchards.20
20
http://www.bea.gov/national/pdf/NIPAhandbookch1-4.pdf
23
Table 3.
The βij coefficients are interpreted as the effect of factor j on factor i’s share of output.
24
References
Anderson, D. P., Chaisantikulawat, T., Guan, A. T. K., Kebbeh, M., Lin, N., &
Shumway, C. R. (1996). Choice of functional form for agricultural production
analysis. Review of Agricultural Economics, 18(2), 223-231.
Becker, G., Hubbard, W., & Murphy, K. (2009). Explaining the worldwide boom in
higher education of women. Unpublished manuscript.
Berndt, Ernst. "Modelling the Simultaneous Demand for Factors of Production." In The
Economics of the Labor Market, edited by Z. Hornstein et al. London: Her Majesty's
Stationery Office, 1980.
Conrad, C. A. (2001). Racial trends in labor market access and wages: Women. In N. J.
Smelser, W. J. Wilson & F. Mitchell eds (Eds.), America becoming: Racial trends
and their consequences. volume 2 (pp. 124-151). Washington, D.C.: National
Academy Press.
Christensen, L. R., Jorgenson, D. W., & Lau, L. J. (1973). Transcendental logarithmic
production frontiers. The Review of Economics and Statistics, 55(1), 28-45.
Ehrenberg, R. G., & Kuh, C. V. (2009). Doctoral education and the faculty of the
future. Ithaca and London: Cornell University Press.
Grant, J. H., & Hamermesh, D. S. (1981). Labor market competition among youths,
white women and others. The Review of Economics and Statistics, 63(3), 354-360.
25
Grossman, J. B. (1982). The substitutability of natives and immigrants in production.
The Review of Economics and Statistics, 64(4), 596-603.
Hansen, W. L., Moser, C., & Brown, D. (1967). The economics of scientific and
engineering manpower. The Journal of Human Resources, 2(2), 191-220.
Hamermesh, Daniel S. "The Demand for Labor in the Long Run." In Handbook of
Labor Economics, vol. 1, edited by Orley C. Ashenfelter and Richard Layard, pp.
429-71. Amsterdam: Elsevier Science Publish-ers, 1986.
Humphrey, D. B., & Moroney, J. R. (1975). Substitution among capital, labor, and
natural resource products in american manufacturing. The Journal of Political
Economy, 83(1), 57-82.
Juhn, C., & Kim, D. I. (1999). The effects of rising female labor supply on male wages.
Journal of Labor Economics, 17(1), 23-48.
Kooreman, P. (2009). The early inception of labor market gender differences. Labour
Economics, 16(2), 135-139. doi:10.1016/j.labeco.2008.07.002.
O'Connell, J. F. (1972). The labor market for engineers: An alternative methodology.
The Journal of Human Resources, 7(1), 71-86.
Oostendorp, R. H. (2009). Globalization and the gender wage gap. World Bank
Economic Review, 23(1), 141-161.
26
Rosenbloom, J. L., Ash, R. A., Dupont, B., & Coder, L. (2008). Why are there so few
women in information technology? Assessing the role of personality in career
choices. Journal of Economic Psychology, 29(4), 543-554.
doi:10.1016/j.joep.2007.09.005.
27