Work place wage growth and worker retention
by
Paul Bingley,CLS, University of Aarhus, Steve Bronars,University of Texas
at Austin) & Niels Westergaard-Nielsen, CLS, Aarhus School of Business.
Abstract:
There is a substantial volume of indirect evidence which suggests that firms/workplaces
are willing to pay employees more to encourage long-term employment relationships.
Although most new jobs end early, long term employment relationships are common,
and the probability of job separation declines with tenure. However, there is dispute over
the magnitude of the effect of higher tenure on wages, because of self-selection and the
simultaneity of job changes and potential wage growth. This paper provides direct
measures of the effect of wage growth at firm level on employee turnover. We obtain
consistent estimates of wage growth due to tenure and experience for the population of
(19538) Danish private sector plants during 1986-95 employing 10 or more white collar
men. Further, we estimate wage profiles for (405) "competing" employers operating in
the same 2-digit product market (of 27) and located in the same county (of 15) as defined
over the population of (140000) private sector plants employing any white collar men.
Given own and competing wage profiles, agents are assumed to solve an inter-temporal
optimization problem by comparing the discounted present value of the wage costs of
job turnover at all future dates until retirement, assuming turnover is to a competing
employer. Our empirical results are consistent with the hypothesis that firms influence
worker turnover through their wage policies: job separations are a decreasing function of
value of a job with the present employer and an increasing function of the value of a job
with a competing firm. For the first time, we are able to quantify the wage costs of
retaining workers.
1
1. Introduction
In his recent survey, Farber (1999) summarizes a substantial volume of indirect evidence that
suggests that firms are willing to pay workers more to encourage long-term employment
relationships. The empirical evidence surveyed by Farber shows that although most new jobs
end early, long-term employment relationships are common, and the probability of job
separations declines with tenure. It is difficult to obtain consistent estimates of the impact of
higher job tenure on wages, holding constant experience, because job tenure and turnover are
endogenous. Wages increase with job tenure, but there is some dispute over the magnitude of
this effect due to self-selection and endogeneity biases. A plausible explanation of the
evidence on wages and inter-firm mobility is that firms have made investments in specific
human capital, and therefore benefit from wage policies that discourage turnover and promote
job stability. Thus despite the limitations in the empirical literature, Farber concludes that
specific capital models are useful for understanding worker mobility and wage dynamics.
The purpose of this paper is to directly examine the relationship between wage growth at an
employer and the job separation rate at the employer. We obtain consistent (establishment)
firm-specific estimates of the wage growth on the job, due to both tenure and experience, for
male white collar workers in a sample of medium to large employers in Denmark. We also
estimate wage profiles for “competing” employers in the same 2-digit industry and
geographic area of each firm in the sample. Given these estimated wage profiles, we can
compute the expected discounted present value of the wage costs of job turnover (assuming
that workers turnover to a “competing” employer). We then use these estimated wage costs of
turnover to explain differences in job separation rates across employers. Our empirical results
are consistent with the hypothesis that firms influence workers’ job turnover behavior through
their wage policies. The job separation rate is a decreasing function of the expected
discounted present value of future wages in the firm and increases with the expected
discounted present value of expected wages offered by competing employers.
2. Data
The data used in this study originates from the Statistics Denmark IDA Register (The
Integrated Database for Labour Market Research). IDA contains information on labour
market conditions for persons and workplaces in Denmark over the years 1980-1995. The
2
important feature of IDA is that it is possible to associate workplaces with the identity of all
employees at a specific day in November (see Leth-Sørensen, 1998).
The information on employees is quite comprehensive and contains data on wage rates,
number of hours worked, experience, unemployment, demographic variables, education,
region, occupation, unemployment insurance funds, etc. The information on work-places
consists of 5-digit industry codes, (ISIC), plant size, and location (municipality).
Education is measured in years. Individual labour earnings data come from tax records and
incorporate all labour income received in the year by an individual. Firm size is measured as
the number of primary workers in November. A primary worker means a worker that
Statistics Denmark has determined has her/his main job at the workplace.
We are able to identify which workers are hired at a plant and which leave, all measured on a
November to November basis. The limitation is that we are not able to identify those who
have been employed say from December to January the following year. These limitations are
no different from the US LRD data used by Davis and Haltiwanger (1999) for example. The
main difference is, however, that the IDA data allows us to identify the flows of persons
between work places because we also know the identity of persons. We do not observe causes
for mobility, neither do we exploit any information on job changes.
In this study we are of different reasons only using white collar male workers and have
consequently omitted all blue collar workers. One reason is that wage competition is believed
to be strongest for white collar workers since wages here are to a lesser degree determined by
union agreements. Another reason is that temporary lay offs will play no role for white collar
workers. Furthermore, the replacement ratio from unemployment benefit is relatively low
because all recipients among white collar-workers will be in a wage class where
unemployment benefit is capped, not unlike the rules in the US. While blue-collar workers in
Denmark have little employment protection, white collar-workers have some mandatory legal
rights through a law covering all salaried employees. However, the most important rule is that
the period of notice in case of dismissal increases with tenure and reaches its maximum at 6
months. There are no legal requirement of general redundancy payments etc known from
other countries unless special agreements have been made. Though the data have no
information in this direction, such agreements are reserved a small fraction of top salaried
3
employees. Finally, we have chosen to look at men only, because that diminishes problems
with part time work.
A white collar worker is in this context an employee who is salaried on a monthly basis in
contrast to blue-collar workers, who are in principle paid on an hourly basis.
We can follow each worker throughout her/his employment at the sampled workplace. We
have drawn a 10% sample of all male white collar workers. Table 1 shows summary statistics.
There are altogether 118117 observations on 36941 individuals working in 19538 workplaces.
For each worker we have information on age1, education, tenure at the present employer. The
Table shows that tenure is quite short, since people stay on in their jobs for only 3.9 years but
with a relatively high standard deviation.
Table 1. Summary statistics
Summary Statistics
Coeff
Std.dev.
Age
39.57
10.38
Tenure
3.90
3.40
Educy
12.82
2.38
No of plants 19538
Persons
36941
For each plant we identify “competing plants”. A competing workplace is identified as a
different workplace, which is within the same 2-digit industry code, within the same county
and employing more than 10 white-collar workers. As there are 15 counties and 27 different
industries within the 2 digit industry code that produces 405 different groups of competing
work places.
3. Wage Profiles of Plants
Methodology
1
Used as an indicator of experience. Though we could have used a variable based on the pension point
allocation, it is not considered to be important in this context, since we are interested in the annual increment.
4
There is a substantial empirical literature that attempts to estimate the return to tenure and
experience in wage regressions. Consider the simple wage regression (In our empirical work
we include quadratic terms in ED, EXP and TEN, which provides a better fit of the data, but
does not alter the arguments below):
lnWit = β0 + β1ED1 + β2EXPit + β3TENit + εit
where Wit is the wage of worker i in year t, ED measures a worker’s completed schooling, and
EXP and TEN measure a worker’s labor market experience and job tenure, respectively, and ε
is an error term. Because tenure and job turnover are endogenous, it is unclear that β3 yields a
consistent estimate of the marginal return to an additional year of tenure, holding constant
experience. Even if panel data are utilized, the parameters β2 and β3 can only be individually
estimated by relying on between job-match variation in EXP and TENURE.
If we consider only within job-match wage changes, so that ∆EXPit=∆TENit=1, the return to
an additional year of both tenure and experience is β2 + β3. Following Topel (1991, pages
152-153), least squares estimates of wage changes within jobs will yield a consistent estimate
of within-job wage growth (the sum of β2 and β3). The controversy between Abraham and
Farber, Altonji and Shakotko, and Topel centers around the decomposition of β2 + β3 into the
partial derivatives ∂Wit/∂EXPit and ∂Wit/∂TENit. For our purposes, however, the
decomposition of this total effect into components due to EXP and TEN is unimportant.
We consider M wage regressions, one for each of the employers in our sample, of the form:
lnWijt = β0j + βljEDi + β2jEXPijt+ β3jTENijt + εijt, for j = 1,2,3,...M
where i indexes workers, j indexes employers and t indexes time periods. We measure withinjob wage growth at employer j as the sum of β2j and β3j.We are particularly concerned with
the extent of variation in rates of within-job wage growth (β2j + β3j) between employers. We
do not attempt to explain whether employer j has high within-job wage growth because
∂Wijt/∂EXPijt or ∂Wijt/∂TENijt is particularly high at this employer.
Theory (for example Lazear) predicts that firms which have made greater investments in
specific capital, or that face higher costs of job turnover for any other reason, will choose
5
wage policies which have particularly high values of (β2j + β3j). The wage cost of job turnover
in these firms will be particularly large and, if the theory is correct, we should see lower rates
of job separation at these employers.
For each of the M plants in our sample, we estimate
lnWaijt = βa0j + βaljEDi + βa2jEXPijt+ βa3jTENijt + εijt
where the superscript a denotes the alternative wage offered by competing employers in the
same 2-digit industry and geographic area as employer j. Note that there are 405 different sets
of competing employers corresponding to the 15 combinations of geographic areas and 27 2digit industry codes in our data. For each set we calculate the mean coefficients representing
the alternative wages.
Results
Table 2 shows the results of estimating plant specific coefficients. The reported figures are
actually mean values of the plant specific βs weighted with the number of employees. The
similar figures are also reported for the competing plants.
Table 2. Plant coefficients to the wage function. Means across plants weighted by number of
employees
Plant
Coeff
const
age
age2
tenure
tenure2
educy
educy2
N
Competing plant
Std.dev. Coeff
Std.dev.
9.3945
9.2918
0.0433
0.0024
0.1080
0.1206
0.0008
0.0001
-0.1178
0.0000 -0.0013
0.0000
0.1331
0.1076
0.0014
0.0001
-0.0108
0.0002 -0.0073
0.0000
0.0054
0.0068 -0.0166
0.0000
0.0018
0.0027
0.0003
0.0002
118117
118117
Table 3 shows the return to an additional year of tenure and experience (for a worker with the
mean characteristics in the sample) at the median employer, and employers at different
percentiles of the distribution of plants with respect to their earnings per worker.
6
Table 3. The return to an additional year of tenure and experience for a worker with plant
level mean tenure and age at employers at different levels of earnings per worker. (In order to
smooth the results plant estimates are averaged over 7 plants around the percentile point.)
Wage distribution
5%
10%
20%
25%
30%
40%
50%
60%
70%
75%
80%
90%
95%
Wage growth
-0.0271
-0.0024
0.0143
0.0183
0.0224
0.0302
0.0444
0.0532
0.0643
0.0756
0.0834
0.1384
0.1581
The entire wage curves for firms at different levels of earnings are depicted in Figure 1.
Figure 1. The earnings profile of typical plants at different levels of the earnings scale
500000
400000
10%
25%
50%
75%
90%
300000
200000
100000
0
1
2
3
4
5
6
7
8
9 10
4. Wage Costs of Turnover
Given the estimated wage profiles for each employer j, and its competitors, we can construct
estimated values of the wage costs of turnover for each individual in our sample. Figure 2
shows the relation between the present values of the wage in the current job and the wage in a
job in a competing plant. The Graph shows that there a substantial interval where the present
value of the wage of the competing plant over the next 5 years is slightly above the wage of
the present plan. In another part of the distribution, PV’s of the present plant wage is clearly
above the competing level. The latter reflects those work places where a good match between
7
employer and employee allows a higher pay. The first part of the distribution reflects cases
where there is only small differences and where there is no great benefit by leaving or staying.
Figure 2. Distribution of Present value of future earnings based on 5 periods
log pv
100000000
10000000
1000000
100000
0
20
40
60
80
100
percentiles
plant
competing plant
However, the expected future wage benefits do also depend on the probability of remaining
with the employer. Similarly, when calculating the expected future wage after having turned
over. Thus, the expected future wage benefits conditional on turning over to a competing
employer depend on the worker’s characteristics (ED, EXP, and TEN), the competing firm’s
wage policy (the β3’s), and the probability of remaining with the competing employer,
conditional on turnover.
To construct the expected future wage benefits of remaining with employer j, we must
compute the probability that a worker, with ‘r years of tenure at employer j, remains on the
job for another year (the survivor rate from τ to τ+l years of tenure at j). We proxy for this
expected future job separation rate by calculating the lagged separation rate for workers with
τ years of tenure in the previous X years.
To construct the expected future wage benefits of separating from employer j, we must
compute the probability that a worker who separates from j and begins working for another
employer and remains with that employer for another year. We proxy for this expected future
job separation rate in competing firms by calculating lagged survivor rates averaged across all
employers in the same 2-digit industry and geographic area over the previous X years. We do
8
it in a similar manner, when we are looking 2 periods ahead. For each period, we take account
of the lagged survivor rates.
We calculate the discounted sum of wage payments in the current and competing employers
over several alternative time horizons using a discount rate of 3%.
5. Individual Worker Mobility
In the final state we have for each person a net present value of staying and similar for
moving. We have this information for all 140169 observations together with information on
education, tenure, size of plant and ID of individual workers.
We estimate the following logit model:
Prob(Worker i moves from employer j) =
F(γ0 + γ1EDit + γ2EXPit + γ3TENijt + γ4PVWAGEijt + γ5PVWAGEaijt)
PVWAGE and PVWAGEa are the present value of the wage stream if the worker stays at
employer j, and if the worker leaves j for a competing employer, respectively. These present
values are functions of only the worker’s individual characteristics and the firm’s wage policy
parameters including the lagged probabilities of retention in the firm. Because we condition
on all of the worker characteristics in the wage regression in this logit, the only source of
variation in the terms PVWAGE and PVWAGEa is due across-employer differences in the
wage policy parameters. Theory predicts that γ4 should be significantly negative and γ5 should
be significantly positive if employers with high turnover costs seek to lower their job
separation rate through their wage policies.
We have estimated this equation using 3 different methods: LOGITS, OLS and OLS with
fixed effects using the fact that we are observing the same individuals multiple times. Though
OLS is of course not ideal when estimating probability functions, it has clear computational
advantages when we are doing fixed effects estimations. All three methods presents the same
signs, so we have chosen to present only the OLS with fixed effects because this takes
account of unobserved individual effects as well. Furthermore, we have estimated these three
9
functions for different horizons. First for 2 years, then 3 years, 4 years, 5 years and finally 6
years. In principle, we should estimate it for the full horizon until pension.
Table 4. Probability functions of moving from the presents employer.
2 periods
3 periods
4 periods
5 periods
6 periods
ahead
ahead
ahead
ahead
ahead
Coeff. Std.dev Coeff. Std.dev Coeff. Std.dev. Coeff. Std.dev. Coeff. Std.dev.
Const
32.165 0.169 32.177 0.170 32.192 0.172 32.194 0.173 32.198 0.175
-0.021 0.002
-0.026 0.002
-0.031 0.003
-0.035 0.003
lnpvwage
-0.016 0.001
lnpvwageC
0.013 0.005
0.017 0.005
0.020 0.005
0.025 0.005
0.028 0.005
-0.062 0.002
-0.062 0.002
-0.062 0.002
-0.062 0.002
tenu
-0.062 0.002
tenu2
0.003 0.000
0.003 0.000
0.003 0.002
0.003 0.000
0.003 0.000
exp
-0.721 0.005
exp2
-0.001 0.000
educy
-0.031 0.019
educy2
0.002 0.001
lsize
0.007 0.004
y90
-2.974 0.020
y91
-2.217 0.019
y92
-1.532 0.018
y93
-0.732 0.020
nobs
adj R-sq
140169
0.5442
140169
0.5442
140169
0.05443
140169
0.5443
140169
0.5443
Note: The coefficients to EXP, EXP2 etc do only change slightly for further horizons, so they have been omitted
from Table 4.
a
The main variables of interest are LNPWAGE and LNPWAGE . The negative sign to the
expected wage with the current employer means that a higher wage at the current employer
makes it less likely that the person leaves his job. Similarly, we have found that a higher wage
at the competing employer increases the probability of mobility. If we are only allowing the
person to look 2 periods ahead, we find that a 1% increase in salary reduces the probability
that this person leaves for another job with 1.6%. Increasing the horizon to 6 periods increases
the elasticity, so that a one percent salary increase reduces the probability of changing job in
the first period with 3.5%. Visual inspection indicates that these elasticities are asymptotic to
a finite value. Similarly, the coefficient to the competing wage can be interpreted as
quantifying how much extra should be offered to a person to get him to move to a competing
work place.
10
The other coefficients are almost constant for all horizons. The tenure variable shows that the
likelihood of moving decreases over the first 11.7 years of tenure. After that, it increases. This
fits very well with the literature. The coefficients to Exp show that the likelihood of moving is
reduced over the entire working life. Education has also a U-shaped impact. We find that
employees at larger plants - all other things equal – are more willing to leave their jobs.
Finally, we find that the likelihood of moving has been increasing since 1990.
6. Conclusion
The conclusions are the following:
- separations are a decreasing function of the value of the job at the present employer
- Job separations are a an increasing function of the competing wage
-
We have quantified the cost of retaining workers. We have found that the probability
of retaining a worker increases with 2-4% for every time we increase his present value of
earnings.
11