Measuring Aggregate Labor Quality Change Using Firm-Level
Production Functions
Natalya N. Dygalo
The University of Western Ontario
May 23, 2006
Abstract
We propose a method for measuring aggregate labor quality in the economy using estimates of workers’
marginal products obtained from firm-level production functions. Compared to the most widely used
method for measuring labor quality, this method does not assume the equality of the value of the marginal
product of labor and wages and does not assume constant quality within pre-defined demographic groups.
In each time period in the data we estimate the productivity of each cohort in the model relative to the
productivity of a group of workers whose productivity remains roughly stable between consecutive time
periods. Labor quality can be compared between adjacent periods by comparing the productivity of
workers in the economy expressed in reference units in both adjacent periods. We estimate labor quality
for France for the period between 1978 and 1996 using a large matched employer-employee data set. We
find that labor quality has been increasing over the period, with the magnitude of the increase of the
order of 15-30%. These estimates contrast the results for labor quality measures obtained using the most
widely used method, which shows a decline in labor quality in France for the period.
1
Introduction
Being able to measure labor quality and its evolution over time is important for learning about
the underlying sources of economic growth. Ideally, we would like to be able to measure
how the share of output that can be attributed to workers’ labor changes from period to
period to measure labor quality change over time. In practice, instead of measuring workers’
quality by workers’ output, economists and national statistical agencies rely on changes in
the composition of hours worked by sex, education, age, and other characteristics weighted
by relative wages (Jorgenson (2005), BLS (1997)). In this paper I propose a method for
measuring labor quality change by comparing workers’ productivity between periods.
The commonly used measure of labor quality that relies on changes on composition, while
easy to construct, may be removed from the objective of measuring workers’ contribution to
output for two primary reasons. First, relative wages that are used as weights in calculating
the index of labor quality, may not reflect relative productivity between age, education, sex,
and other demographic groups that enter the labor quality index. Recent research has shown
1
that spot market wages may diverge from productivity for older workers (Hellerstein and
Neumark, 2004), and for female employees (Hellerstein, Neumark, and Troske, 1999)1 .
Second, relative wages by education, for instance, may also include returns to unmeasured
workers’ ability, and not represent the direct impact of education on workers’ productivity.
If the composition of workers by ability changes over time within education groups, and
averaged relative wages by education between adjacent time periods are used to aggregate
hours changes between adjacent time periods, then the Jorgenson’s method for measuring
labor quality will not be able to take the change in within-cell labor quality into account (see
Griliches (1970), Griliches (2000), Griliches and Regev (1995)). Within-cell labor quality
change may be due, for example, to the changing quality of education and training, changing exposure to health and social services (Bowlus and Robinson (2004), Bowlus, Liu, and
Robinson (2005), Hanushek and Kimko (2000)).
The method proposed here is as follows. First, I estimate a production technology using firm-level data with labor and capital as inputs, and the labor input disaggregated by
perfectly substitutable groups defined by age (birth cohort), occupation, and sex (the setup
is similar to Hellerstein and Neumark (1995), (2004)2 ). Second, I assume that between the
ages of 46 and 55 workers’ productivity remains stable, or there is a ”flat spot” for workers
between these ages, in terminology of Heckman, Lochner, and Taber (1998) and Bowlus, Liu,
and Robinson (2005). For adjacent periods the age groups are selected in such a way that
workers in age group i are in the age group (i+1) in the next time period. In addition, there
is a flat spot cohort that is between the ages of 46 and 55 in both adjacent time periods (see
Table 1).
Thus, the flat spot cohort’s productivity can be taken as a unit of measurement, or the
productivity of a worker in the flat spot cohort is assumed to be stable between adjacent
time intervals and is normalized to unity. The existence of a flat spot is predeicted by the
human capital theory; workers at some point in their career stop investing in human capital
1 Other studies using matched employer-employee data to compare earnings and productivity are Crepon et al (2002) and
Dygalo and Abowd (2005) for France, Haegeland and Klette (1999) for Norway, Hellerstein and Nuemark (1995) for Israel,
Dostie (2006) for Canada, Kotlikoff and Gokhale (1992) using data for one US firm, Nedoff and Abraham (1981) using personnel
evaluations for US firms, Ilmakunnas et al (2004) for Finland.
2 Hellerstein and Neumark (2004) refer to their method as a method for measuring labor quality in a cross section. The added
value of this project is that I propose a method for comparing labor quality over time.
2
and productivity remains flat until depreciation of human capital causes it to decline (BenPorath, 1967, Becker, 1975, Miner, 1974). The relative productivity of workers in all other
demographic groups is measured from the estimated relative productivity coefficients in the
production function relative to the productivity of the flat spot cohort. To construct an index
of labor quality, relative productivities normalized to the productivity of the flat spot cohort
are multiplied by the proportion of workers (the number of workers) to measure labor quality
change (change in aggregate human capital) and added together across sex, occupation, and
age groups. Chain indexes for adjacent time periods can be multiplied to obtain total quality
change between any two time periods.
The advantages of this method are many: labor quality is measured using actual workers’
output and not wages. The heavily disputed assumption that wages equal the value of the
marginal product is relaxed and so is the assumption of no within-cell quality change. There
are a large number of challenges associated with this approach, some of which are addressed
in the paper. The ability to interpret the change in the estimated relative marginal products
by demographic group as reflecting change in labor quality depends on our ability to account
for other inter-temporal factors that may influence the relative marginal products by age,
occupation, and sex within each time period. A number of robustness checks are performed in
the paper in addition to by now widely used panel data econometric techniques for addressing
some of the issues related to omitted variables, endogeneity bias, and measurement error.
While the results differ in their magnitude between specifications, they tell a consistent
story. The data for the project are matched employer-employee data for France with millions
of workers followed as they change employers between 1978 and 1996, with information available on employers’ capital and labor inputs and output. I find that labor quality increased
over the period, with the magnitude of the upgrade ranging between 15 and 30 percent over
the period, with about 50% of the upgrade due to improving quality within cells defined
by occupation, sex, and age, and the remainder attributed to the shift in composition to
more skilled occupations. This contrasts the conclusions that would be obtained using the
standard labor quality change measure as in Jorgenson (2005), which results in a 3% labor
quality decline over the period. Thus, labor quality change was responsible for a greater
3
share of output change over the period than would be inferred from the standard labor quality measures, and therefore would leave a smaller role for the total factor productivity in
explaining growth in France between 1978 and 1996.
The remainder of the paper is organized as follows. The next section presents the model
together with the decomposition of labor quality change into parts attributed to within-cell
quality upgrading and to change in composition of the labor input. Section 3 is devoted to
data and implementation, and Section 4 to the presentation of results. Section 6 concludes.
2
A Method for Measuring Aggregate Labor Quality Using FirmLevel Production Functions
We start by assuming that firms produce output according to a Cobb-Douglas technology
using labor and capital as inputs. We assume perfect substitution between workers so that
the aggregate labor input can be expressed in total units of human capital used by the firm
to produce output. The exact amount of efficiency units contained in each of the labor
sub-groups defined by birth cohort, sex, and occupation, is allowed to be determined from
the coefficients of the estimated production technology similar to Hellerstein and Neumark
(2004):
Yit = Ait Lαit Kitβ
(1)
t
Lit = L1it + a2t L2it ... + aMt t LM
it
(2)
where Yit is firm’s output, Ait is a measure of firm’s productivity, Lit is the labor input
expressed in total units of human capital, Kit is capital input, and Mt is the number of groups
of workers within the aggregate labor input Lit in time period t. Coefficients a2t , ..., aMt t are
t
the relative productivities of labor inputs L2it , ..., LM
it with respect to the reference labor
input L1it (to see this, substitute equation (1) into equation (2) and differentiate the resulting
expression with respect to L1it and Ljit , j = 2, ..., Mt ). After taking logarithms and rearranging,
we have the following equation for logged output (Pitj = Ljit /L1it , j = 2, ..., Mt ; Pit1 = 1 −
PMt j
j=2 Pit ):
4
Mt
X
ln Yit = ln Ait + α ln Lit + β ln Kit + α ln(1 +
(ajt − 1)Pitj )
(3)
j=2
We impose restrictions on relative proportions of labor inputs within firms: we assume
that the proportion of labor inputs by each subgroup by birth cohort, sex, and occupation
is the same within all cells defined by the other two classifications. For example, this assumption implies that the proportion female is the same is each occupation/birth cohort
cell. Hellerstein and Neumark (2004) adopt similar assumptions due to data limitations and
find that their qualitative conclusions are unaffected by these restrictions. It remains to be
determined to what extent these constraints affect the results of this paper. We distinguish
between five occupations: managerial employees, professional and lower-level managerial,
service, skilled and unskilled laborers.
Similar equality constraints are imposed on coefficients with equation (3) rewritten as
follows:
ln Yit = ln Ait + α ln Lit + β ln Kit
C
Ot
X
X
j1
+ α ln(1 +
(aj1 t − 1)Pit )(1 +
(aj2 − 1)Pitj2 )(1 + (af − 1)Pitf )
j1 =2
(4)
j2 =2
where C is the number of age cohorts (see Table 1; also see Table A1 for age ranges and
the corresponding cohorts by time period), Ot is the number of occupations (we use five
as described above), and af is the productivity of female workers relative to male workers
(with the proportion of male workers equaling (Pitm = 1 − Pitf )). These restrictions are
somewhat unrealistic since it is well-known that the proportion of workers in managerial
and supervisory positions increases at older ages, and the proportion of females is larger
in services occupations than among unskilled laborers. Each of the sets of proportions by
birth cohort (Pitj1 , j1 = 1, ..., Ct ), occupation (Pitj2 , j2 = 1, ..., Ot ), and sex (Pitf , Pitm ) sum up
to one by construction. From equation (4), the relative productivity of females relative to
males within any cohort/occupation group is the same and equals af . Similar restrictions
are imposed on coefficients with occupations and birth cohorts.
5
The division of labor inputs into cohorts and the ideas underlying the construction of
labor quality aggregates and labor quality comparison between time periods are described
in what follows. In the first stage of the method, I estimate the productivity of cohorts of
workers relative to the reference cohort whose productivity is assumed to remain constant
between adjacent periods. The next step is to estimate the total labor quality expressed in
human capital units, with one unit equaling the productivity of a worker in the reference
cohort. Since for any two adjacent time periods labor quality is expressed in the same units,
we can compare labor quality between adjacent time periods. Chain indexes of aggregate
labor quality can be constructed from indexes for adjacent time intervals.
We define five time intervals in the data as follows: 1978-1981, 1982-1985, 1986-1989, 19901993, 1994-1996. Thus, we have four four-year intervals and one three-year interval. Labor
inputs are subdivided by five occupations 1) managerial - PCS occupation codes starting
with 2 and 3; 2) administrative and lower-level supervisory staff - codes starting with 4; 3)
service occupations - codes starting with 5; 4) skilled laborers - PCS codes 62-65; and 5)
unskilled laborers - all other PCS codes. The second division of labor inputs is by sex, and
the third is by cohort.
I distinguish between twelve cohorts, as shown in Table 1. Table 1 shows cohorts, the five
time periods, and age ranges for each cohort/period cell. I assume that workers’ productivity
remains roughly stable between the ages of 46 and 55, or, in terminology adopted in Heckman,
Lochner, and Taber (1998), there is a ”flat spot” for workers within these age ranges. Such
a flat spot exists according to the human capital theory which suggests that workers stop
investing in their human capital at some age later in their career, and workers’ productivity
that equals to the accumulated human capital over the lifecycle remains flat over the duration
of a number of years. The specific age ranges are taken to roughly correspond to the age
ranges adopted in Heckman, Lochner, and Taber (1998) and in Bowlus, Liu, and Robinson
(2005).
To compute the index of labor quality change using this method, first I deflate the estimated coefficients in adjacent time periods by the coefficients of the ”flat spot” cohort. Then
I express total labor quality by summing the economy-wide proportions of labor inputs that
6
enter equation (4) multiplied by the estimated coefficients a. Since in both adjacent periods
total labor quality is expressed in the same units, or relative to the productivity of a worker
in the ”flat spot” cohort, labor quality change between adjacent time periods is a simple
ratio of labor quality measures expressed in the same units.
Chain indexes of labor quality can be constructed by multiplying period to period indexes
j2
of labor quality change. If P̃itj1 , j1 = 1, ..., M and P̃it+1
, j2 = 1, ..., M are economy-wide
proportions of labor inputs in time periods t and (t + 1) in equation (3) and ã are the
coefficients a divided by the coefficients with the ”flat spot” cohort in periods t and (t + 1),
then the labor quality index between periods t and (t + 1) can be computed as follows:
PM
it,t+1 =
j2
j2
j2 =1 P̃it+1 ãt+1
PM
j1 j1
j1 =1 P̃it ãt
(5)
Using equation (5), we can compute the chain indexes between period t and (t + n) by
multiplying indexes it,t+1 , ..., it+n−1,t+n :
it,t+n =
n
Y
it,t+j
(6)
j=1
To investigate the source of labor quality change, I decompose the total quality change
between adjacent time periods into the proportion attributed to changing relative marginal
products ai and the proportion attributed to changing composition of labor input P̃i 3 :
PM
PM
it,t+1 = 1 +
j=1 āj 4Pj
PM
j1 j1
j1 =1 P̃it ãt
j=1
+ PM
P̄j 4aj
(7)
j1 j1
j1 =1 P̃it ãt
j
j
P̃it
+P̃it+1
ãjt +ãjt+1
j
j
,
4P
=
P̃
−
P̃
,
ā
=
, and 4aj = ãjt+1 − ãjt . We can refer to
j
j
it+1
it
2
2
PM
āj 4Pj
γ1 ≡ PMj=1 j1 j1 as the proportion of the overall quality change attributed to the change in
j1 =1 P̃it ãt
PM
P̄j 4aj
composition by age, sex, and occupation, and to γ2 ≡ PMj=1 j1 j1 as the portion attributed
j =1 P̃it ãt
where P̄j =
1
to the change in within-cell marginal productivity, or within-cell quality4 .
3 Equation
and
PM
4 We
PM
(5) implies it,t+1 =
j2
j2
j2 =1 P̃it+1 ãt+1
−
PM
j1 =1
P
PM
j
j
j2
j2
j1 j1
P̃it1 ãt1 + M
j2 =1 P̃it+1 ãt+1 − j1 =1 P̃it ãt
PM
j1 j1
j =1 P̃it ãt
j1 j1
j1 =1 P̃it ãt
=
PM
j=1
1
āj 4Pj +
PM
j=1
PM
=1+
j2 =1
P̄j 4aj .
have it,t+1 = 1 + γ1 + γ2 ≈ (1 + γ1 )(1 + γ2 ) if we ignore the cross product (γ1 γ2 ).
7
P
j2
j2
j1 j1
P̃it+1
ãt+1
− M
j1 =1 P̃it ãt
PM
j1 j1
j =1 P̃it ãt
1
,
Estimation of equation (4) presents a number of challenges. The role of possible biases
due to omitted variables, endogeneity of labor and capital, and due to measurement error
have to be extensively investigated. The objective is to estimate the relative productivity
coefficients between occupations, age groups, and genders ai to allow meaningful comparison
of labor quality over time using indexes defined in equations (5) and (6). Estimation methods
used in this study are discussed in the next section.
3
Estimation
After adding an independently and identically distributed additive error term, I estimate
equation (4) using nonlinear least squares with additional controls for industry and allowing
the intercept to vary between time periods. Coefficients a in equations (3) and (4) represent
relative marginal productivities between the specified groups of workers by birth cohort, sex,
and occupation, if there is no omitted variable bias or bias due to endogeneity or measurement
error. Some of these assumptions will be addressed in the empirical section of the paper.
4
Data and Implementation
The data for this project require information on firm’s inputs and output to estimate the
production function in equation (4) as well as information on firm-level composition of employment by sex, occupation, and birth cohort. The data are matched employer-employee
data for France, with a longitudinal workers’ employment history file with information on
workers demographic characteristics and salaries matched to a firm-level survey with information on firms’ production inputs and outputs. The match between the two files, the worker
history file with identifiers by worker, firm identifiers and year of employment, and firm-level
file with identifiers by firm and year, is conducted using firm identifiers and year.
The source of information on the firm level composition of employment by sex, birth
cohort, and occupation is “Déclarations annuelles des salaires“ (DADS) administered by
INSEE (Institut National de la Statistique et des Etudes Economiques) in the years between
1976 and 1996, with the exception of 1981, 1983, and 1990. The data are a 1/25 subset of all
8
workers in the French economy, with the exclusion of civil servants. The sample includes all
workers born in October of even-numbered years, and the data are from mandatory reports
provided by employers. Self-employed workers are included in the data, but we cannot
identify them.
For each worker-year record the following information is available: the identity of the
employing firm (the data are aggregated to the level of the firm from establishment-level
data), full-time status, the number of days paid, a measure of annualized compensation,
occupation, the industry of the employing firm, workers’ age and sex. Each record is identified
by a person identifier, firm identifier, and year. The full data set with observations identified
by person, firm, and year of employment contains 15,424,755 observations, with 1,142,736
firms and 1,951,334 workers. Since the data for firms is available only starting in 1978, the
DADS sample excluding 1978 and 1979 contains 13,949,578 observations, and information
on X unique firms and Y unique workers (Table 2).
The source of firm-level information is the annual survey “Enquête annuelle d’entreprises“
(EAE) available for the years between 1978 and 1996. Employer-level information includes
the firm identifier, the four digit industrial affiliation, employment, capital, and sales by year.
The sampling frame for this data set is described in INSEE documents, and larger firms were
sampled with a larger probability than smaller firms. An approximate sample weight was
constructed for the data to be representative by firm size (the weight was not used in the
current set of estimations). Two-digit industry capital and value added deflators were available separately from INSEE for the period under investigation. The deflators were obtained
from the INSEE macroeconomic time series data (Banque de données macroéconomiques).
Information on the composition of workers at the firm/year level by sex, occupation,
and twelve birth cohorts in DADS was merged with information on firm-level inputs and
outputs by year and firm identifier. The estimating sample was further reduced due to some
firms missing information on sales, capital, and/or employment. Finally, the sample of firms
was further restricted to firms with at least two matched workers. Table 2 contains the
description of the merged sample of workers and its comparison to DADS for 1978-1996.
The empirical specification divides the data into four time intervals: 1978-1980, 1982-1985,
9
1986-1989, 1991-1993, and 1994-1996.
From Table 2, the estimating sample contains slightly less than half of all observations in
DADS for 1978-1996, slightly better paid workers and more full-time workers than in the full
sample. Notice that the proportion of part-time workers has been increasing over time. The
total number of observations is larger in 1986-1989 because this time interval contains four
years of data compared to all other time intervals with three years of data. After taking this
into account, the number of worker-year observations has been increasing over time which
reflects population growth and changes in workforce participation. The sample is reasonably
well-representative by age and residence in Ile-de-France.
Table 3 describes the sample of firm-year observations used in estimating equation (4)
compared to the full EAE sample fo firms. The sample of firms contains about half of all
firm-year observations in the full EAE dataset: 504,858 out of 1,516,123. The most important
difference is that the firms in the sample are larger by all available measures: they are larger
in terms of employment, sales, and capital, and there are about 22 percent of all firms in the
sample with over 150 employees compared to the full EAE dataset which has only about 11%
of such firms. On average, firms’ employment composition by demographic characteristics
in equation (4) was computed using 8.2% of all employees. There are about 75% of firms
with 3 and more matched employees from DADS, and 35% of firms with 6 or more matched
workers.
Table 4 presents the distribution of workers in the sample compared to DADS and the
distribution of firms in the sample compared to EAE by industry. The industry classification
in Table 4 is a NAP40 classification with 38 industries. The codes were changed after 1983,
but a cross-walk between time intervals provided by INSEE was used to make NAP40 codes
consistent between all years in the data. Compared to all workers in DADS, the sample
contains fewer workers in construction and homebuilding, services to individuals, financial
and non-profit services, and a larger fraction of workers in manufacturing, in particular in
trucks and auto industries, electrical materials and electronics. There is a larger fraction
of workers employed in firms providing services to firms in the sample compared to DADS.
Compared to the full sample in EAE, the sample of firms used in estimating equation (4)
10
contains fewer firms in construction and home building and in financial services, and a larger
fraction of firms in non-food wholesaling, food retailing, and transportation services.
Table 5 presents the composition of firm-level employment by birth year cohort, sex, and
occupation for the average firm in DADS and in the sample of firm-years used to estimate
equation (4). First, the proportion female is slightly lower in the sample because the sample
contains a larger fraction of manufacturing workers and there are fewer females employed in
manufacturing. Second, the proportion female increases from 38 to 44 percent over the time
period spanned by the data in DADS, and only from 32 to 33 percent in the sample. Third,
the average firm-level proportion of workers employed in service occupations is lower in the
sample than in DADS which is due, once again, to a larger fraction of manufacturing firms in
the sample and a lower fraction of firms from the service sector. Finally, the sample reflects
the average firm-level composition in DADS by cohort reasonably well.
5
Results
Table 6.1 presents the estimated coefficients with logged capital, labor, occupation and sex
in equation (4). The results in Tables 6-7 were obtained using nonlinear least squares. In
addition to variables shown in equation (4), the estimated equation contains controls for
40-digit industry and year effects.
From Table 6.1, the coefficients with logged employment and capital sum up to almost
one. While the Wald test of equality to exactly one is rejected (Wald Test 1), the rejection
is probably due to the large sample of firms - over half a million. The Wald test of equality
of the sum of capital and labor coefficients to 1.005 (Wald Test 2) is not rejected, and the
estimated production technology, therefore, is very close to exhibiting constant returns to
scale.
From Table 6.1, female employees are about 15% less productive than males. Skilled laborers are about 13% more productive than unskilled workers. Workers employed in service
occupations are about 30% more productive than unskilled workers, while managerial and
lower-level supervisory workers are 50% and 240% more productive than unskilled laborers
11
respectively. These coefficients are in line with the usual estimates for this type of specification of production technology with perfectly substitutable labor inputs obtained with data
for France (Crepon et al, 2002) and other countries (Hellerstein and Neumark (1995) for
Israel, Hellerstein, Neumark, and Troske (1999) and Hellerstein and Neumark (2004) for the
US, Haegeland and Klette (1999) for Norway, and Dostie (2006) for Canada).
The coefficients with cohorts are presented in Table 6.2. The reference category by cohort
was chosen in such a way that workers in the reference category are 34-39 years old during
the period (age ranges are in square brackets in the table). The general pattern within each
time period is for the productivity to peak during workers’ late twenties and early thirties,
and for older and entry-level workers to have lower productivity than during the peak years.
Thus, the age-productivity profile within a given cross-section appears to be concave, and
increasing during younger ages and then declining.
Table 6.3 tests the hypothesis of stable age-productivity profile between time periods.
The test compares coefficients with the same age ranges across different time intervals. for
most age ranges the age-productivity coefficients differ between time periods. This finding
suggests that either there are forces that are unaccounted for in the simple model in equation
(4), there are different biases between time periods, or that the age-productivity structure
actually changes between time periods. For now we will disregard possible challenges from
the quality of the estimated equation - the specification will be tested more below, and focus
on the hypothesis that the age-productivity profile does not remain stable over time.
One potential source of the different coefficients between time periods would be differential
labor quality between cohorts. Workers born in different years acquire different vintages of
education and undergo different styles of training. Differences in accumulated human capital
between cohorts within cells defined by occupation, sex, and age together with differences
in other factors such as the quality of healthcare between cohorts may explain the results in
Table 6.3 of unstable age-productivity structure over time.
To further investigate this possibility, I present a series of Wald tests in Table 6.2 that
test for the equality of differences between coefficients between adjacent cohorts. If the age
differences between adjacent cohorts do not overwhelm differences in labor quality, then we
12
would expect to find roughly stable differences between relative productivities for adjacent
cohorts across all time periods in the data. Except for cohorts that are in their younger ages
and are probably in the most intensive stages of human capital accumulation, the differences
between adjacent cohorts tend to be very stable over time offering some support for the
hypothesis that different age-productivity structure between time periods may be partially
due to different quality between cohorts.
Thus, within-cell quality changes with cells defined by age, occupation and sex are probably important, and we will probably see change in aggregate labor quality between time
periods using the labor quality index in equations (5) and (6). The results of labor quality
calculations are presented in Table 7. Using the coefficients in Tables 6.1 and 6.2, labor quality showed an approximately 5% increase for between the first four time periods: 1978-1981,
1982-1985, 1986-1989, and 1990-1993. Labor quality remained stable between 1990-1993 and
1994-1996.
The total quality change over the period amounted to about 14%. Using the decomposition
in equation (7), about 50% of the total quality change was due to changing composition of
the labor force over time, and the remaining 50% was due to quality upgrading within cells
defined by age, sex, and occupation. The standard errors with the labor quality measures for
adjacent time periods (columns (4) and (5) in Table 7) are sufficiently precisely estimated to
dismiss concerns that the estimated differences are entirely due to random variability.
An immediate concern may be that the sample of firms changes over time and the estimated quality upgrade may be due to differences in the sample composition and not to true
quality changes. While the following exercise of selecting firms that are observed in all years
in the data is not completely valid, the results are also presented in Table 7. The exercise
is not completely valid because the sub-sample of firms observed in all years in the data
contains larger firms and the sample is no longer representative of all firms in the French
economy. Still, the results are given in Table 7 and they indicate an about 30% total quality
upgrade over time. Thus, the finding of a quality upgrade does not depend on different
firms sampled in different time periods. The finding of rising labor quality using the method
presented here contrasts with the usual finding of declining labor quality in France between
13
the early 1980’s and the mid-1990’s using methods commonly used by national statistical
agencies (e.g., Jorgenson (2005)).
6
Conclusion
The paper proposes a method for measuring labor quality change by comparing the portion of
output that can be attributed to labor between time periods. This is a major departure from
the current method used by national statistical agencies that measures the change in labor
input by comparing hours weighted by relative wages between adjacent time periods. The
method presented here departs from the two main assumptions of the conventional method,
the assumptions that have been challenged in recent research: 1) the assumption that wages
equal the value of the marginal product of labor, and 2) that within-cell labor quality with
cells defined by gender, age, education and other characteristics remains unchanged over
time.
The method estimates relative productivity using a production function with perfectly
substitutable labor inputs by age (cohort), sex, and occupation. The ability to compare
labor quality over time depends on the assumption that there exists a flat spot during certain
ages when the productivity remains stable between adjacent time periods. The age range
was chosen to be between 46 and 55. Then the quality of all labor inputs in two adjacent
time periods can be expressed in terms of the productivity of the flat spot cohort whose
productivity is assumed to be the same in both time periods, and an index of labor quality
can be constructed and labor quality compared between adjacent time periods.
In this project the data are from a large matched administrative employer-employee data
set for France for the period between 1978 and 1996. The estimated labor quality using the
method developed in the paper increases over the period spanned by the data by a magnitude
of 15-30%. While the exact quality change figure varies between estimation methods, the
results indicate a labor quality upgrade over the period and therefore a smaller role for the
total factor productivity change in explaining growth in France between the late 1970’s and
the mid-1990’s. In addition, about half of the labor quality change was due to labor quality
14
upgrading within cells defined by occupation, sex, and age. These results differ from the
conventional labor quality measures used by national statistical agencies which indicate a
labor quality decline, and not an increase, of about 3%.
References
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Reference to Education, New York, National Bureau of Economic Research; distributed
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Bowlus, A. J., Liu, H. & Robinson, C. 2005. Human Capital, Productivity and Growth.
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Bowlus, A. J. & Robinson, C. 2004. Technological Change in the Production of Human
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Crepon, B., Deniau, N. & Perez-Duarte, S. 2002. Wages, Productivity, and Worker Characteristics: A French Perspective. Manuscript.
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Lifecycle: Evidence from Employer-Employee Data on Earnings. Manuscript.
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University Press.
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Griliches, Z. 2000. R&D, Education, and Productivity, Cambridge and London: Harvard
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Haegeland, T. & Klette, T. J. 1999. Do Higher Wages Reflect Higher Productivity? Education, Gender and Experience Premiums in a Matched Plant-Worker Data Set, in
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Nations, American Economic Review 90(5): pp. 1184–1208.
Heckman, J. J., Lochner, L. & Taber, C. 1998. Explaining Rising Wage Inequality: Explorations with a Dynamic General Equilibrium Model of Labor Earnings with Heterogeneous Agents, Review of Economic Dynamics 1(1): pp. 1–58.
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112.
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with heterogeneous labor: Evidence from a new matched employer-employee data set.
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Characteristics: Evidence from Plant-Level Production Functions and Wage Equations,
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Ilmakunnas, P., Maliranta, M. & Vainiomaki, J. 2004. The Roles of Employer and Employee
Characteristics for Plant Productivity, Journal of Productivity Analysis 21(3): 249–276.
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Jorgenson, D. 2005. Information Technology and the G7 Economies, Revista di Politica
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Kotlikoff, L. J. & Gokhale, J. 1992. Estimating a Firm’s Age-Productivity Profile Using the
Present Value of Workers’ Earnings, Quarterly Journal of Economics 107(4): 1215–42.
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of experience, Journal of Human Resources 16(2): 186–216.
Mincer, J. 1974. Schooling, Experience, and Earnings, New York, National Bureau of Economic Research; distributed by Columbia University Press.
17
Table 1. Cohorts, time periods and ages
Birth Year\ Time Period
1978-1981
1982-1985
1986-1989
1990-1993
1910-1920
58-81
X
X
X
1921-1928
50-59
54-63
58-67
X
1929-1932
46-51
50-55
54-59
58-63
1933-1936
42-47
46-51
50-55
54-59
1937-1940
38-43
42-47
46-51
50-55
1941-1944
34-39*
38-43
42-47
46-51
1945-1948
30-35
34-39*
38-43
42-47
1949-1952
26-31
30-35
34-39*
38-43
1953-1956
22-27
26-31
30-35
34-39*
1957-1960
18-23
22-27
26-31
30-35
1961-1968
16-19
16-23
18-27
22-31
1969-1980
X
X
16-19
16-23
Notes: 1) the flat spot is between age 46 and 55;
2) the reference group in the estimating equations is between age 34 and 39 (denoted as "*");
the coefficient (relative productivity) with the reference cohort is normalized to one
3) the data DADS contain information for workers born in October of an even-numbered year
4) X - the cohort is not included in this year (its proportion is assumed zero)
1994-1996
X
X
X
58-62
54-58
50-54
46-50
42-46
38-42
34-38*
26-34
16-26
Table 2. Descriptive Statistics for Workers
Time Interval
Variable
1978-1980
1982, 1984, 1985
1986-1989
1991-1993
1994-1996
Age
Logged compensation
Full time
Ile-de-France
Observations
Age
Logged compensation
Full time
Ile-de-France
Observations
Age
Logged compensation
Full time
Ile-de-France
Observations
Age
Logged compensation
Full time
Ile-de-France
Observations
Age
Logged compensation
Full time
Ile-de-France
Observations
DADS
Mean
34.539
4.007
0.822
0.285
2,322,435
34.997
4.046
0.792
0.281
2,224,398
35.018
4.030
0.735
0.280
3,368,644
35.337
3.986
0.695
0.272
2,986,837
35.848
3.880
0.675
0.257
3,047,264
1,076,340
1,853,134
13,949,578
SD
12.227
0.837
0.383
0.451
11.718
0.907
0.406
0.449
11.381
0.966
0.442
0.449
11.329
1.118
0.460
0.445
11.191
1.245
0.468
0.437
Sample
Mean
36.088
4.189
0.917
0.247
919,394
35.530
4.160
0.829
0.287
994,606
35.106
4.141
0.758
0.299
1,402,544
34.814
4.100
0.721
0.286
1,235,914
35.254
4.016
0.712
0.272
1,251,219
105,157
1,060,641
5,803,677
SD
12.203
0.676
0.276
0.431
11.529
0.863
0.376
0.452
11.217
0.945
0.429
0.458
11.181
1.131
0.449
0.452
11.032
1.201
0.453
0.445
Unique Firms
Unique Workers
Total Observations
Notes: 1) Data source: DADS, 1978-1996
2) The sample contains all worker-year observations employed in firm/years (504,858 obs.)
used in constructing labor inputs in the estimated the production function
(or workers employed in firms in years with matched firm-level information from EAE,
firms with at least two matched workers to the firm, valid capital, employment, and sales)
3) Logged real annualized compensation (1980 FF) includes employer and employee taxes
4) Ile-de-France is the area in and around Paris
5) Observation counts refer to worker-year observations
Table 3. Firm-Level Variables
Variable
Period
Mean
3.965
3.863
3.772
3.901
3.933
8.012
7.695
7.617
7.643
7.756
9.581
9.570
9.659
9.732
9.785
6.9
69.8
12.2
6.8
4.4
100.0
EAE
SD
0.946
0.975
1.023
0.888
0.916
1.594
1.891
1.971
1.826
1.854
1.254
1.331
1.306
1.259
1.304
Obs
173,344
201,406
293,200
202,750
187,519
115,121
132,482
214,337
279,710
284,738
173,730
198,313
267,804
203,607
188,315
Mean
4.487
4.414
4.356
4.201
4.250
8.307
8.020
8.089
8.196
8.369
10.222
10.201
10.225
10.033
10.101
2.1
56.4
20.0
13.0
8.5
100.0
Sample
SD
1.077
1.095
1.044
0.968
0.987
1.619
1.933
1.972
1.794
1.855
1.259
1.356
1.355
1.319
1.365
Logged Employment 1978-1981
1982-1985
1986-1989
1990-1993
1994-1996
Logged Real Capital 1978-1981
1982-1985
1986-1989
1990-1993
1994-1996
Logged Real Sales
1978-1981
1982-1985
1986-1989
1990-1993
1994-1996
Firm Size
<21
(employees)
21-75
76-150
151-350
351+
Total
Percent of workers
matched per firm
0.082
Distribution of the
2
26.35
number of
3
18.42
matched workers
4
12.13
per firm
5
8.07
6+
35.03
Total
100.00
The total number of
firm/years
1,516,123
Notes: 1) The sample is a subset of firms in EAE with at least 2 matched workers and valid
observations for employment, capital, and sales
2) Capital is measured at book value in the beginning of the period
3) Data source: EAE, France 1978-1996
Obs
75,580
82,762
116,916
119,263
110,337
75,580
82,762
116,916
119,263
110,337
75,580
82,762
116,916
119,263
110,337
504,858
Table 4. The Composition of Workers and Firms by Industry
Sample of Firms DADS Sample of Workers
Industry
EAE
Agriculture
0.50
0.04
0.02
0.01
Milk and Meat
1.79
2.37
0.95
1.84
Other Agriculture and Food
2.61
3.51
2.37
2.91
Mining
0.01
0.01
0.07
0.15
Oil and Natural Gas Production
0.09
0.09
0.20
0.44
Electricity, Natural Gas Distribution, Water
0.24
0.21
0.84
1.90
Steel, Ferrous Metals
0.28
0.40
0.68
1.29
Non-Ferrous Metals
0.17
0.23
0.29
0.62
Construction Materials
1.70
1.48
0.82
1.12
Glass
0.23
0.30
0.34
0.64
Chemical and Artificial Fibers
0.44
0.58
0.69
1.40
Pharmaceuticals
1.11
1.55
1.10
2.22
Metal Working and Foundry
5.18
4.89
2.50
3.23
Mechanical Construction
4.71
4.86
2.63
3.79
Electrical Materials and Electronics
2.58
3.00
3.04
5.71
Trucks and Automotive
0.89
1.20
2.19
4.52
Shipbuilding, Aerospace, Arms
0.27
0.36
0.76
1.53
Textile and Apparel
4.51
4.81
2.56
3.52
Leather and Shoes
0.88
0.93
0.51
0.74
Lumber and Furniture
3.46
3.09
1.69
1.85
Paper and Carton
0.89
1.15
0.63
1.15
Printing and Publishing
2.58
2.37
1.51
1.87
Rubber and Plastics
1.68
1.89
1.18
2.06
Construction and Home Building
13.65
10.55
8.17
6.95
Food Wholesaling
3.85
3.48
1.50
1.69
Non-Food Wholesaling
9.17
10.21
4.31
5.15
Food Retailing
3.73
4.85
3.73
5.68
Non-Food Retailing
4.18
3.82
4.72
3.85
Automotive Sales and Repairs
3.75
4.12
1.97
1.56
Restaurants and Tourism
2.18
2.70
4.61
2.36
Transportation Services
5.57
6.73
4.65
6.46
Postal/Telecommunications
0.05
0.04
0.64
0.57
Services to Firms
10.64
10.06
13.42
16.59
Services to Individuals
3.45
3.19
11.91
3.83
Real Estate and Leasing
0.92
0.90
0.61
0.71
Insurance
0.17
0.00
0.91
0.02
Financial Services
1.67
0.01
2.17
0.01
Non-Profit Services
0.24
0.05
9.11
0.06
Total
100.00
100.00
100.00
100.00
Notes: Data Source EAE and DADS, France 1978-1996
The sample of firms includes firms with at least two matched workers and valid observations for
capital, sales, and employment. The sample of workers includes all workers observed working
in the sample of firms. The proportions are out of the total number of firm-years and worker-years.
Table 5. The Composition of Firm-Level Employment by Occupation, Sex, and Cohort
DADS: Mean Firm-Level Proportions
Sample of Firms
Category
Labor Input
1978-1981 1982-1985 1986-1989 1990-1993 1994-1996 1978-1981 1982-1985 1986-1989 1990-1993 1994-1996
Cohort
1912-1920
4.16
4.17
[58-81]
[58-81]
1922-1928
9.92
6.51
2.86
11.78
6.95
2.33
[50-59]
[54-63]
[58-67]
[50-59]
[54-63]
[58-67]
1930-1932
6.60
5.82
4.37
1.88
7.46
6.54
4.56
1.65
[46-51]
[50-55]
[54-59]
[58-63]
[46-51]
[50-55]
[54-59]
[58-63]
1934-1936
6.62
6.14
5.26
3.92
2.21
7.25
6.59
5.54
4.04
2.08
[42-47]
[46-51]
[50-55]
[54-59]
[58-62]
[42-47]
[46-51]
[50-55]
[54-59]
[58-62]
1938-1940
6.54
6.18
5.63
4.83
3.99
6.95
6.62
5.84
5.06
4.15
[38-43]
[42-47]
[46-51]
[50-55]
[54-58]
[38-43]
[42-47]
[46-51]
[50-55]
[54-58]
1942-1944
7.71
7.33
6.82
6.18
5.65
8.01
7.78
7.15
6.39
5.91
[34-39]
[38-43]
[42-47]
[46-51]
[50-54]
[34-39]
[38-43]
[42-47]
[46-51]
[50-54]
1946-1948
10.93
10.09
9.51
8.86
8.36
11.24
10.94
10.13
9.19
8.71
[30-35]
[34-39]
[38-43]
[42-47]
[46-50]
[30-35]
[34-39]
[38-43]
[42-47]
[46-50]
1950-1952
12.91
11.21
10.38
9.78
9.41
12.66
11.82
11.02
10.23
9.90
[26-31]
[30-35]
[34-39]
[38-43]
[42-46]
[26-31]
[30-35]
[34-39]
[38-43]
[42-46]
1954-1956
14.59
12.09
10.78
9.85
9.50
13.67
12.51
11.40
10.40
10.03
[22-27]
[26-31]
[30-35]
[34-39]
[38-42]
[22-27]
[26-31]
[30-35]
[34-39]
[38-42]
1958-1960
15.61
14.76
12.89
11.22
10.69
13.77
14.59
13.24
11.75
11.26
[18-23]
[22-27]
[26-31]
[30-35]
[34-38]
[18-23]
[22-27]
[26-31]
[30-35]
[34-38]
1932-1968
4.42
18.87
27.98
27.48
25.31
3.03
14.84
26.40
27.97
26.66
[16-19]
[16-23]
[18-27]
[22-31]
[26-34]
[16-19]
[16-23]
[18-27]
[22-31]
[26-34]
1970-1980
3.34
15.26
24.01
2.26
12.90
20.78
[16-19]
[16-23]
[16-26]
[16-19]
[16-23]
[16-26]
Sex
Proportion female
38.33
40.93
42.18
44.20
44.40
31.59
34.05
34.64
33.66
33.08
Occupation Managerial and
Professional
5.70
7.28
8.90
11.20
12.17
4.29
6.53
8.17
9.49
10.44
Lower-Level
Supervisory
12.74
14.68
15.95
16.35
16.46
14.16
15.95
16.73
16.91
17.19
Service
29.10
31.03
31.46
31.62
31.44
18.64
23.07
24.24
20.57
19.88
Skilled Laborers
30.63
27.03
25.36
22.95
21.69
36.69
30.81
29.19
31.17
31.09
Unskilled Laborers
21.82
19.98
18.33
17.87
18.23
26.22
23.64
21.67
21.86
21.40
Notes: Source: DADS 1978-1996
The column proportions within categories defined by occupation and cohort do not always sum to 100%
Age ranges for the cohort-year cell are in square brackets.
Table 6.1. Coefficients with Sex, Occupation, Labor, and Capital
Variable
Coefficient
SE
Female
0.860
0.004
Managerial and Professional
2.405
0.016
Lower-Level Supervisory
1.509
0.009
Service
1.277
0.007
Skilled Laborers
1.133
0.006
Unskilled Laborers
Logged Capital
reference
0.224
0.001
Logged Employment
0.782
0.001
Wald Test 1
35.90 (0.001)
Wald Test 2
0.29 (0.589)
R-Square
0.777
The Number of Observations
504,858
Notes: Data source: DADS matched with EAE, 1978-1996,
additional covariates include year and industry dummies by NAP40
industrial classification; the model was estimated using NLLS.
Wald Test 1 tests for the equality of the sum of the coefficients
with logged employment and capital to one, and Wald Test 2 - to 1.005
(p-value in parentheses). Both tests have 92 degrees of freedom.
Table 6.2. Production Function Estimates: Coefficients with Cohorts
Variable
1978-1981 1982-1985 1986-1989 1990-1993 1994-1996 Wald Test P-Value
Cohort
1912-1920
0.835
X
X
X
X
(0.030)
[58-81]
1922-1928
0.925
0.892
0.968
X
X
0.43
0.808
(0.024)
(0.023)
(0.031)
[50-59]
[54-63]
[58-67]
1930-1932
0.917
0.870
0.932
0.910
X
4.79
0.188
(0.027)
(0.024)
(0.024)
(0.034)
[46-51]
[50-55]
[54-59]
[58-63]
1934-1936
0.998
0.927
0.928
0.942
0.805
11.73
0.020
(0.029)
(0.025)
(0.022)
(0.024)
(0.029)
[42-47]
[46-51]
[50-55]
[54-59]
[58-62]
1938-1940
0.951
0.908
0.960
0.954
0.902
1.76
0.780
(0.029)
(0.024)
(0.023)
(0.023)
(0.023)
[38-43]
[42-47]
[46-51]
[50-55]
[54-58]
1942-1944
reference
0.987
0.999
1.001
0.934
4.22
0.378
(0.024)
(0.022)
(0.022)
(0.021)
[34-39]
[38-43]
[42-47]
[46-51]
[50-54]
1946-1948
1.075
reference
1.020
1.025
0.938
3.56
0.468
(0.028)
(0.020)
(0.020)
(0.019)
[30-35]
[34-39]
[38-43]
[42-47]
[46-50]
1950-1952
1.027
0.997
reference
0.973
0.910
1.68
0.794
(0.026)
(0.022)
(0.019)
(0.018)
[26-31]
[30-35]
[34-39]
[38-43]
[42-46]
1954-1956
1.070
1.009
1.009
reference
0.938
22.16
0.000
(0.027)
(0.022)
(0.019)
(0.018)
[22-27]
[26-31]
[30-35]
[34-39]
[38-42]
1958-1960
1.049
0.989
1.025
1.082
reference
4.05
0.399
(0.026)
(0.020)
(0.019)
(0.020)
[18-23]
[22-27]
[26-31]
[30-35]
[34-38]
1962-1968
1.062
1.007
1.008
1.090
1.022
18.80
0.000
(0.038)
(0.020)
(0.016)
(0.017)
(0.015)
[16-19]
[16-23]
[18-27]
[22-31]
[26-34]
1970-1980
X
X
0.912
1.010
0.863
(0.030)
(0.018)
(0.014)
[16-19]
[16-23]
[16-26]
Notes: Data source: DADS matched with EAE, 1978-1996, additional covariates include year and
industry dummies by NAP40 industrial classification; the model was estimated using NLLS.
Standard errors are in brackets under the coefficients, and age ranges are in square brackets.
The Wald Tests test for the equality of the differences between coefficients for adjacent cohorts
(the difference between the current cohort's coefficients and the coefficients of the following cohort)
for all periods available for the two adjacent cohorts. For example, the test for adjacent cohorts
born in 1922-1928 and 1930-1932 the Wald test is in the line for cohort 1922-1928 and the test
is for the equality of the following differences: coefficients in 1978-1981 (0.925-0.917), coefficients
in 1982-1985 (0.892-0.870), and coefficients in 1986-1989 (0.968-0.932). The degrees of freedom
for the test equal to 93 minus the number of time periods with valid coefficients in both adjacent
cohorts (for most cohorts, this number is 88 (=93-5)).
Table 6.3. Wald Tests for Stability of the Age-Productivity Profile Between Periods
Age Range 1978-1981 1982-1985 1986-1989 1990-1993 1994-1996 Wald Test
[58-63]
0.910
0.805
5.57
(0.034)
(0.029)
[54-59]
0.932
0.942
0.902
1.60
(0.024)
(0.024)
(0.023)
[50-55]
0.870
0.928
0.954
0.934
7.03
(0.024)
(0.022)
(0.023)
(0.021)
[46-51]
0.917
0.927
0.960
1.001
0.938
8.41
(0.027)
(0.025)
(0.023)
(0.022)
(0.019)
[42-47]
0.998
0.908
0.999
1.025
0.910
27.84
(0.029)
(0.024)
(0.022)
(0.020)
(0.018)
[38-43]
0.951
0.987
1.020
0.973
0.938
10.37
(0.029)
(0.024)
(0.020)
(0.019)
(0.018)
[34-39]
reference reference reference reference reference
[30-35]
P-Value
0.018
0.450
0.071
0.078
0.000
0.035
1.075
0.997
1.009
1.082
12.40
0.006
(0.028)
(0.022)
(0.019)
(0.020)
[26-31]
1.027
1.009
1.025
0.39
0.821
(0.026)
(0.022)
(0.019)
[22-27]
1.070
0.989
6.00
0.014
(0.027)
(0.020)
Notes: The age range for years 1993-1996 is shorter than for other periods by one year:
for example, the age range 46-51 is 46-50 for 1993-1996.
The Wald test tests the equality of all coefficients within a given age range.
See notes to Tables 5.1 and 5.2; the coefficients are from Table 5.2.
Standard errors are in parentheses.
The degrees of freedom equal 93 plus one minus the number of coefficients in the row:
for example, the test in the first row has 93+1-2=92 degrees of freedom.
Source: DADS matched with EAE, France 1978-1996
Table 7. Labor Quality Change between 1978-1991 and 1994-1996
Period 1
Period 2
Flat Spot Cohort Labor Quality in (1) Labor Quality in (2)
(1)
(2)
(3)
(4)
(5)
Results based on coefficients in Table 6
1978-1981
1982-1985
1929-1932
1.328
1.384
(0.027)
1982-1985
1986-1989
1933-1936
1.299
1.357
(5)/(4)
(6)
% within Cumulative Change
(7)
(8)
1.042
37.7
1.042
1.045
50.8
1.089
1986-1989
1990-1993
1937-1940
1.312
1.384
1.055
70.1
1.148
1990-1993
1994-1996
1941-1944
1.318
1.306
0.991
N/A
1.138
Results for firms observed in each year in the data
1978-1981
1982-1985
1.017
1982-1985
1986-1989
1.091
1986-1989
1990-1993
1.100
1990-1993
1994-1996
1.071
Notes: Standard errors (delta method) in parentheses
In column (7), percent within refers to the portion of period to period labor quality change that is due to quality upgrading within cells
by age, sex, and occupation (see equation 7 in the text). The decomposition of labor quality change between period 1990-1993
and 1994-1996 is not reported because there was almost no quality change between the periods
Data Source DADS matched to EAE, France 1978-1996
Table A1. Age Ranges and Corresponding Cohorts by Time Period
Age Range
1978-1981
1982-1985
1986-1989
1990-1993
14-19
61-68
61-68
69-80
69-80
18-23
57-60
61-68
61-68
69-80
22-27
53-56
57-60
61-68
61-68
26-31
49-52
53-56
57-60
61-68
30-35
45-48
49-52
53-56
57-60
34-39
41-44
45-48
49-52
53-56
38-43
37-40
41-44
45-48
49-52
42-47
33-36
37-40
41-44
45-48
46-51
29-32
33-36
37-40
41-44
50-55
21-28
29-32
33-36
37-40
54-59
21-28
21-28
29-32
33-36
58-63
10-20
21-28
21-28
29-32
1994-1996
69-80
69-80
69-80
61-68
61-68
57-60
53-56
49-52
45-48
41-44
37-40
33-36