WORKING PAPER
Labor Supply Estimation Biases from
Disregarding Non-Wage Benefits
Matthew Baird
RAND Labor & Population
WR-1079
February 2015
This paper series made possible by the NIA funded RAND Center for the Study of Aging (P30AG012815) and the NICHD funded RAND
Population Research Center (R24HD050906).
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Labor Supply Estimation Biases from Disregarding
Non-Wage Benefits
Matthew Baird
The RAND Corporation∗
February 13, 2015
Abstract
Labor supply models and research underpinned by labor supply decisions typically
assume the agents’ choices are functions of wage and wage offers. However, there is
evidence that these selections are not only wage-driven, but at least in part depend on
non-wage benefits encompassed in jobs and occupations. In this paper, I develop and
estimate a stochastic dynamic model of occupational and job choice, where non-wage
benefits are directly incorporated into the decision alongside wages. A nested model
within this is a wage model, representing common practice in the literature, where
non-wage benefits are disregarded. I separately estimate the full model and the nested
wage model in order to compare the implications of omitting non-wage benefits. Three
analyses are compared: elasticities, economy-wide structural changes in occupations,
and inequality reduction intervention policies. I find that while disregarding non-wage
benefits generally causes biases, there are cases when the two models predict very similar outcomes and have close estimates, such as in occupational-specific elasticities and
job transition elasticities. However, I demonstrate that these special cases are products
of canceling biases, and that the same estimates on subpopulations are biased. These
results suggest that in most cases, ignoring non-wage benefits will bias estimates by
overestimating the importance of wage in the selection process (and so any intervention
or change in wages will be over-emphasized) and by disregarding changes in relative
prices between wage and non-wage benefits, such as happens through changes in wage
taxes or in non-wage benefits. These biases can be severe. The results suggest that
ignoring non-wage benefits in labor supply decisions is appropriate only in the special
case in which subpopulation biases negate each other, which is atypical
∗
I would like to thank Moshe Buchinsky and Maria Casanova for their invaluable and continual help
in this project, as well as Rosa Matzkin, Arturo Harker, Seth Kerstein, Dan Ben-Moshe, Peter Bergman,
anonymous referees at Review of Economics and Statistics, and seminar participants at UCLA, RAND,
Syracuse University, the Bureau of Labor Statistics, and the Census Bureau for numerous helpful comments
and suggestions.
1
Introduction
Assuming that individuals make work decisions based only on wages is a common premise
in both structural and reduced form estimation of labor supply. However, job offers and occupations are bundles of goods which include not only wages, but a set of non-wage benefits.
Not accounting for non-wage benefits that are part of a job offer can potentially lead to biases
in econometric analysis, both in cases when the question is about labor supply decisions or
when labor supply decisions–such as occupation choice, job change, and education–are incorporated in the choice examined. Examples include job lock and the effects of the Affordable
Care Act on job transition rates, changes in programs for occupation retraining (such as in
recessions) and internships, changes in the speed in which firms learn about their employees’
ability, and the outcomes of policies aimed at reducing inequality and poverty.
In this paper, I evaluate the incidence and magnitude of biases that may arise from
not accounting for non-wage benefits in selection. To do so, I develop a dynamic model
of occupation and job choice that incorporates non-wage benefits (for the purpose of this
paper, referenced as the “full model”). The decisions are modeled in order to allow a nested
model, representing the norm in the literature, where selection is made just on wages (“wage
model”). I separately estimate both the full and wage models and contrast the data fit,
labor supply estimates, and policy and event predictions. In addition to including nonwage benefits, other unique modeling contributions of this paper beyond the larger body
of discrete choice dynamic model occupational choice papers (exemplified by Keane and
Wolpin 1997) include: allowing the decision of occupation to be jointly made with the choice
of staying at a firm or accepting a new job offer; and workers and firms both being Bayesian
learners of unobserved worker heterogeneity in occupational specific ability. The models
are estimated from a dataset of young men from the NLSY. I focus on three tests of the
biases: occupational-specific labor supply elasticities,1 inequality interventions, and a large,
structural, economy-wide change in an occupation’s wages.
Estimating a structural dynamic model advances the goals of this paper in several ways.
It allows for direct comparison of the models’ predictions, including in estimating counterfactuals. Also, there is significant evidence that decisions are made by forward-looking
agents, captured by the dynamic nature of the model. For example, Table 1 demonstrates
that workers making the change from white collar to blue collar jobs have significantly lower
wages and non-wage benefits in all categories than their peers, at statistically significant
levels. White collar workers switching might be able to find higher wages and non-wage
1
Occupational specific labor supply elasticities are elasticities on the extensive margin of occupation
choice, viz. the percentage change in the proportion in a given occupation for a one percent change in the
wage.
1
benefits in blue collar jobs. Alternatively, some of them lose their white collar jobs and use
this as an opportunity to switch occupations. There are potential sources of selection bias
in estimating the elasticities and responses when not properly accounting for the occupation
and job decision process, and motivate the use of a dynamic model. By directly modeling
the decision, this paper provides better estimates of the reasons agents transition. Using
a static model, such as in reduced form applications, ignores the dynamic decisions that
workers are making when they choose their occupation and job.2 Another evidence of the
importance of a forward-looking model comes in estimating how much agents would pay to
know which occupation is ex-post optimal.3 In the first post-high school year, agents will pay
on approximately 20% of their wage to know their ex-post optimal occupation. However, a
decade later they are only willing to pay around 5% of their wage. The benefits of knowledge
change over time as workers have less remaining years in the labor force, and entrenchment
occurs as the workers gain occupational specific human capital. Estimating a dynamic structural model allows for many interesting counterfactual tests, which are not possible using
a reduced form model, nor would static models account for the dynamic decisions important to many policies, including direct assessment of the biases from not accounting for the
non-wage benefits.
1.1
Incorporating Non-Wage Benefits
This paper includes four non-wage benefits: health insurance, retirement, the pleasantness
of the work environment, and perceived job security.4 There is also reduced-form evidence
that the non-wage benefits of a job or occupation affect their decisions. Longhi and Brynin
(2010) use data from Britain and Germany, and in both samples find that both job changes
and occupational changes yield positive changes in both wage and job satisfaction, with
job changes across occupation being the best off. Delfgaauw (2007) finds that lower job
satisfaction leads to higher job search, and that the type of dissatisfaction leads to where
workers look for a new job (within the same organization, to a different organization, etc.).
While he doesn’t look at the effect of actually changing jobs or occupation on satisfaction,
he illustrates the reasons why we might expect an increase in satisfaction when the change
is voluntary. Brand (2006) finds workers worse off for non-voluntary job layoffs. Linear
2
See, for example, Parrado et al. (2007), Longhi and Brynin (2010), and Markey and Parks (1989).
The estimation procedure for the willingness to pay is described in Section 5.
4
This paper discusses non-wage benefits and non-monetary benefits, a subset of non-wage benefits. The
difference between non-wage benefits and non-monetary benefits is only evident in health insurance, which
carries both a monetary benefit (the job covers the health insurance payment that otherwise the agent would
have to pay) and a non-monetary benefit (the satisfaction from knowing the employer is taking care of you
and treating you fairly, etc.). Thus, the total non-wage benefits are all of the non-monetary benefits plus
the covering of the health payment.
3
2
regressions on the data used in this paper show that leaving voluntarily leads to higher wages
(Table 2), although staying within the same occupation when switching jobs is correlated
with even higher wages.5 For the non-wage benefits of health insurance, retirement, pleasant
environment, and job security, I observe similar trends (Table 3).
Reduced form and structural estimation models of labor supply have typically relied
on selection on wages alone. In reduced form models, this typically is incorporated using
Heckman correction. For example, Arozamena and Centeno (2006) estimate the returns
to tenure and how it is affected by the business cycle, and Dustmann and Meghir (2005)
use displaced workers data from Germany to estimate the returns to experience and tenure.
Both use Heckman correction with wages being the driving force in selection. One significant
exception is Delfgaauw (2007), who uses Netherlands data to examine how job satisfaction
variables affect job and occupation mobility through regression analysis. Also, there are
many papers which focus on the importance of a single non-wage benefit (for example,
health insurance, geography, and the value of retirement benefits in labor supply6 ), and
demonstrate the importance of that variable. Such papers reinforce the hypothesis of biases
arising from omitting any important non-wage benefits from consideration.
There have also been many structural dynamic models that include occupational choice,
but these models do not typically include non-monetary benefits and the coinciding choice
of job. Keane and Wolpin (1997) estimate a simple dynamic model of occupational choice
also using data from NLSY on young men. Others have followed the use of their discrete
choice dynamic model application to occupational choice, including Lee (2005), Lee and
Wolpin (2006), and Dix-Carneiro (2010), Yamaguchi (2010), and Lee and Wolpin (2010).7
Meinecke’s (2010) model is a dynamic occupational choice model with Bayesian updating
for the individual specific effect on wages, which is also incorporated into this model. One
exception is Sullivan (2009), who tests for the misclassification of occupations and includes
non-wage benefits in a reduced form manner into his structural model.8 . There are also
again several structural estimation papers which focus on a single benefit, such as retirement
benefits, health insurance, and geography.9
5
With two occupations; with ten occupations, log wages are higher if they switch occupations as well.
For example, see Gruber and Madrian (2004).
7
See also Aguirregabiria and Mira (2010) and Keane and Wolpin (2008) for a review of these models.
8
Agents’ utility is a function of wages and of factors which aim to capture the non-wage preferences, such
as occupation tenure.
9
For example, Gustman and Steinmeier (2005), Rust and Phelan (1997).
6
3
1.2
Counterfactual Tests and Biases
While the full and wage model yield very similar results in observed data trends (the fit of the
model), labor supply estimates and predictions of policy effects can vary widely between the
two models. The source of the bias in the wage model is that it over-predicts any dynamics
associated with changes in wages and does not account for the trade-off between wage and
non-wage benefits, and the results from a change in their relative prices. I examine three
settings for estimates, and in each find potential biases from using the wage model.
First, I estimate the elasticity of occupational specific labor supply from the simulated
model. The average elasticity of white collar labor supply (the percentage change in workers
in white collar jobs resulting from a one percentage point change in white collar wages) with
respect to a permanent change in wages is estimated to be 5.4, while for blue collar the value
is 2.6. The elasticities for a one year change in wages is substantially lower, at 0.54 and 0.25
for white and blue collar. However, the elasticities are highly variable across age, with the
highest average elasticities for the youngest workers. A decade after high school, the average
white collar elasticity for a permanent wage change is estimated to have decreased to around
2, while the blue collar is estimated to be at half that value. While failing to control for the
non-monetary benefits does not cause serious biases in aggregate (the wage model estimates
are within one standard error deviation of the full model estimates), I demonstrate that for
subsamples, biases do arise and can be severe (over 2 standard errors deviated). The lack of
bias for the aggregate is the product of biases canceling out across the sample–encouraging
for analysis of certain labor supply trends when done in aggregate, while discouraging for
a larger set of analysis underpinned by labor supply decisions. Second, I also perform a
counterfactual of a decrease of blue collar wages of five percentage points and find an overall
decrease of the fraction in blue collar work of 23% for workers who experience the shock
immediately after leaving high school (at the beginning of the model), while the wage model
over-predicts the importance of wage in the decision process (a universal phenomenon for all
tested estimates in this paper). The wage model predicts a 27% decrease. Further analysis
reveals that reasonable permanent changes in any of the non-wage variables could potentially
counteract the 5% wage decrease to maintain similar proportions of workers in blue collar,
emphasizing the importance of their inclusion. Third, I examine predictions of the effects of
an inequality reduction policy, and again find large biases arising in predictable, systematic
ways when non-wage benefits are not included in the model.
The paper proceeds as follows: Section 2 presents the model and Section 3 discusses
the data, assumptions and restrictions made, and stylized trends and statistics in the data.
Section 4 describes the empirical strategy. Section 5 explores the results and the implications,
including the counterfactual studies. Section 6 then concludes.
4
2
Theoretical Model
The model is an extension of previous economic models of occupational choice, with the key
expansion being the inclusion of non-wage benefits. The Roy model (1951) allows workers
to self-select into occupations based on wage-specific skills and the returns to those skills.
One common model used to explain occupation and job transition is a matching model.
Matching models differentiate workers into types (e.g., high skill and low skill) and also
differentiate the labor market into different skill segments, both captured in this model.10
Léné’s model (2011) allows experience and education to be imperfect substitutes for each
other, a feature of my model. Léné’s paper suggests that there is an entry cost to different
labor segments; my model also includes these costs. The search good model (Burdett 1978,
Jovanovic 1979) has transitions that are chosen by workers to improve situations. The model
in this paper is a form of a search good model. Search good models predict lower transition
rates with increased ages. Older workers have had more time to search and find better jobs
and occupations (in terms of overall satisfaction, which will include wage and non-monetary
factors) and stay there.
Keane and Wolpin (1997) estimate a dynamic model of occupational choice using data
from NLSY on young men. Others have followed the use of their discrete choice dynamic
model application to occupational choice.11 Postel-Vinay and Robin (2002) create and estimate a model that examines firm and employee heterogeneity using French data, and look
at equilibrium effects on wages. Meinecke’s (2010) model is a dynamic occupational choice
model with Bayesian updating for an individual-specific effect on wages. Agents have imperfect knowledge about their ability within different occupations, but each period they work
they are able to observe a noisy measurement of their productivity and update their beliefs
about the unobserved portion of their ability. This paper also has agents update their beliefs
about their productivity, but allows firms to update beliefs about the worker’s productivity
as well, and change wage offers according to their beliefs, similar to Felli and Harris (1996)
and Gibbons and Waldman (1999) in theoretical models.
This paper extends these models. Agents choose every period whether to work or attend
school. At the beginning of each period, they receive a bundled offer of wage and nonwage benefits from one firm in each occupation.12 When possible, workers also receive a
10
Examples of matching models include Pissarides (1990), Van Ours and Ridder (1995), Gautier (2002),
Léné (2011), Albrecht and Vroman (2002), and Dolado et al. (2009).
11
For example, Lee (2005), Lee and Wolpin (2006), and Dix-Carneiro (2010)–see also Aguirregabiria and
Mira (2010) and Keane and Wolpin (2008) for a review on these types of models.
12
While the model only includes one job offer from each occupation, this can be viewed as the best job
offer of many job offers. A very bad job offer (below reservation wage, in wage selection models) can be
interpreted as zero job offers.
5
continuation offer from their previous employer in each occupation.13 Agents’ choices are
summarized by the dummy variable dkjt . k is the choice of schooling (k = 0) or work in
occupation k = 1, ..., K. For computational reasons, in the estimation of the model there
are two occupation: white collar (k = 1) and blue collar (k = 2). The division into two
occupations retains many of the trends of interest of a more finely divided categorization.14
j is the choice of a new firm (j = 0) or to stay at the old firm when possible (j = 1). t is the
period.15 By choosing every period to be in school or work in a white collar or blue collar
job, as well as whether to stay at their firm when possible or accept a new job offer, agents
maximize present value lifetime utility
E
T
δ t−1
t=1
K dkjt Ukjt |St
k=0 j=0,1
Ukjt is the per-period utility function. The utility function is constant elasticity of substitution (CES) as a function of wages and non-monetary benefits with an additive random
utility shock and additive utility shifter for starting a new job:
Ukjt =
cρkjt
+
1/ρ
bρkjt
+ Mk ×
K
1(ds1t−1 = 1) + ξkjt
s=1
The wage and non-monetary values differ depending on their choice of dkjt , for occupation/schooling choice k and job decision j in period t. St is a vector of state variables.16 . δ
is the discount factor. ckjt is consumption from occupation k and firm choice j in period t,
while bkjt is a weighted sum of non-monetary benefits from the job. ρ is the CES substitution
parameter. Mk is the entry cost paid whenever a worker starts a new job. ξkjt is a zero mean
normally distributed random shock, with standard deviation σ ξ .
If the agent has no job to return to, then they can either go to school or choose one of
13
I include continuation offers from the firm in other occupations because of trends in the data suggesting
a non-negligible fraction of occupation switches happening within firm; see Figure 1.
14
For example, Tables 2 and 3 show the coefficients from linear regressions of next period’s wage and nonwage benefits on current wage and non-wage benefits and various controls for changing job and occupation,
and whether they were fired. The analysis is performed both at the 2 occupation level (white collar vs. blue
collar) and 10 occupation level. The coefficients are very similar, suggesting that these trends are retained
with only two occupations.
15
For example, if the worker in period t has a job they can return to but accepts instead a job offer in
blue collar, then d00t = 0, d10t = 0, d11t = 0, d20t = 1, and d21t = 0.
16
The state variables in this model are years of post-secondary education, years of occupational experience
in both occupations, years of job tenure, agent beliefs of their occupation-specific productivity, the firm’s
current beliefs of the workers productivity in both occupations, agent AFQT score, firm-employee match
parameter, the indexed non-monetary benefit offer, and whether or not their job includes health insurance
benefits
6
K new job offers, one in each occupation. If they have a job to return to, then they have
the same K + 1 options, as well as K additional job offers at the firm they worked for in the
previous period, one offer for each occupation.17
For schooling, there is no earned wage, so c00t is set equal to a minimum consumption
level chosen exogenously from the model to be the poverty line. b00t is the non-monetary
benefit from schooling.
b00t = θ0B + β ED AFQT
θ0B is a parameter that measures the relative attractiveness of education compared with
working. AFQT is the Armed Forces Qualification Test score, a common measure from the
NLSY for mental aptitude. The extent to which agents receive non-monetary benefits from
schooling differs by mental aptitude as schooling can be easier depending on their ability.
When working at a new job, bk0t (the non-monetary benefit) is given by
NW
bk0t = θkB + β N W Xk0t
θkB is the parameter that measures the relative attractiveness of occupation k against other
occupations and schooling, ceteris peribus. XtN W is a vector of non-wage benefits, such as
whether they offer health insurance, retirement benefits, provide a pleasant working environment, or have good job security. The probability that workers are offered binary benefits,
such as health insurance, is estimated as a logistic regression as a function of the variables
AFQT score, education, and years working. The logistic regression coefficients are estimated
outside the model. The process by which they are selected and their arrival rates are deNW
is the first non-monetary
scribed in Section A.1. ck0t is the consumption from working. X1,k0t
benefit, an indicator variable for whether the worker’s job includes health insurance. β HE is
the average health expense, negative, that must be borne by agents if they don’t have health
insurance. If resulting consumption is below the minimum consumption parameter, agents
receive the minimum consumption level.
NW
= 1)
ck0t = wk0t + β HE 1(X1,k0t
and
EXP
educt +
wk0t = exp{θkW +λh +βkAF QT AFQT+β0k
EXP
EXP 2
βk
expert + βk
exper2t +εk0 }
=1,2
17
Workers have a job to return to if they worked the previous period and were not fired. Alternatively,
workers have no job to return to if it is either the first period of the model (they just graduated high school),
they were in school the previous period (college), or they were fired. In the estimation where K = 2, White
Collar and Blue Collar, there are either 3 choices or 5 choices each period.
7
wk0t is the wage offer. θkW is the occupation log wage intercept; β AF QT is the return to
ability (measured by AFQT). λh is a firm-employee match parameter, unique to a firm and
employee. Job offers from new firms come with a new λh that is constant as long as the
agent is working at firm h. λh is distributed normally with variance σ λ . Agents are more
productive in some firms than others and so are better compensated when working for those
firms. If a worker stays with the same firm, then future periods’ wage offers are a function
of the same match parameter. educt is the number of years of post-secondary education, so
EXP
is the return to education. White collar and blue collar occupations will reward
that β0k
education differently. experk is the amount of experience the agent has in occupation k,
EXP
is the
given by the number of years they have chosen to work in that occupation. βk
return to experience in occupation k for an additional year worked in occupation . εk0 is a
random shock, correlated across occupations but not across time or with other variables. If
the workers have a job to return to, they receive continuation job offers. They do not need to
pay the job entry cost for working if they stay. They receive a continuation offer from their
employer in each of K occupations. This can be viewed as a promotion or change of duties
between occupations. Note, between 15-25 percent of White and Blue Collar occupation
changes in the data sample are within firm (Figure 1). Consumption remains a function
of the wage and whether or not they have health insurance. The non-monetary benefits
remain the same if they stay with the same firm; I assume that there is no change in the
non-monetary benefits package offered. This simplifying assumption is helpful in reducing
the state space for estimation purposes. However, the continuation wage offer changes every
period, and is given now by
EXP
educt +
wk0t = exp{θkW + λh + βkAF QT AFQT + β0k
EXP
EXP 2
βk
expert + βk
exper2t
=1,2
+β
T EN
tent + β
T EN 2
ten2t
+
F
ηkjt
+ εk0 }
The continuation wage offer is similar to the initial wage offer, with two important differences.
The first difference is a return to tenure in a firm (the number of years the agent has worked
at the firm) β T EN tent . I include returns to job tenure in the model because of evidence of its
importance in the wage equation and how it affects job transitions.18 The second difference
is firms learn about their workers productivity after each year worked, and adjust their wage
F
is the firm’s estimate. Each worker has some true
offer according to their new beliefs.19 ηkjt
occupation-specific fixed productivity, ηk . ηk is unobserved by the agents and the firms. At
the end of each period, both the agent and the firm they worked for that year observe a
18
19
See Topel (1991) for empirical evidence and Felli and Harris (1996) for theoretical support.
See Gibbons and Waldman (1999) for theoretical support for the inclusion of firms updating beliefs.
8
noisy measurement of ηk , and update their beliefs according to Bayes’ Law. Firms adjust
their wage offers depending on their beliefs concerning ηk . The updating process is detailed
in Section A.2.
At the end of each period, there is a certain probability that a worker is laid off. These
probabilities differ depending on various variables, such as their firm tenure, their education,
which occupation they are in, their occupational experience, and the firms’ beliefs regarding
F
. I model the probability an agent is fired as a logistic regression, and estimate the
ηkjt
coefficients of the logistic regression within the model, depending on the parameters of the
model. The estimation process is explained in Section A.3. The consequences of being fired
are having no continuation offers and bearing the entry cost to work.
The NLSY contains a variable measuring overall job satisfaction on a 1-4 scale, with 1
being the highest report. I use this data to help fit the model, and assume that reports
come from the period utility function, given by whether the report, g, falls between certain
parameter thresholds. The distance between the estimates and observed gkit in each period
and occupation are part of the objective moment function.
gkjt
⎧
⎪
1
⎪
⎪
⎪
⎨ 2
=
⎪
3
⎪
⎪
⎪
⎩ 4
if
if
if
if
Ukjt ≤ q1
q1 < Ukjt ≤ q2
q2 < Ukjt ≤ q3
Ukjt > q3
Given this setup, the value functions for the Bellman equation are as follows:
Vt (St ) = max {Vkjt (St )}
k,j
V00t (St ) is the value function for choosing education:
V00t (St ) = U00t + δE max {Vj0t+1 (St+1 |d00t = 1)}
j
Vkjt (St ) for k = 1, ..., K; j = 0, 1 is the value function for working:
Vkjt (St ) = Ukjt + δE max {πkt V0t+1 (St+1 |dk0t = 1) + (1 − πkt )Vdt+1 (St+1 |dkjt = 1)}
,d
πkt is the probability that the worker is fired from their job (see Section A.3 for details). Individuals will have work careers that last many decades, but this model only examines young
workers. The terminal value function summarizes the future stream of benefits after the
end of the model. The specification is a semi-parametric approximation of the contributions
9
of the expected wage and the non-monetary benefits, summarizing where the workers have
reached. w
kjT and bkjT are the expected log wage and non-monetary benefit, respectively,
in the terminal period for occupation k and firm choice j.
2
kjT +β2T V F w
kjT
+β3T V F bkjT +β4T V F b2kjT +β5T V F w
kjT ×bkjT
VkjT (ST |dkjT = 1) = β0T V F +β1T V F w
3
Data and Summary Statistics
I estimate the model using the National Longitudinal Study of Youth 1979 (NLSY) from
the years that have the pertinent data: 1979-1994. I restrict the sample to agents who
completed high school between the ages 15-20, yielding 14 post-high school years estimated
in the model. These years capture the span of primary interest, when occupations are
decided, early learning happens, and transitions occur. More occupation switches happen
at younger ages, and these decisions can have strong long-run effects. The sample is further
restricted to males, who face less fertility and cultural incentives for leaving the labor force
than females, to agents that do not report being self-employed to improve the reliability
of wage measurements, and to non-military. This results in 2,561 agents in the estimated
model, with varying amounts of years observed for each.
I use the self-reported occupational status to classify occupation.20 Agents are classified
as in school if they report their primary activity for a year as schooling or if their reported
years of education increases. A more detailed description of the methods used, including for
selection of job assignment and transitions, is in the Appendix Section A.4.
Table 4 presents summary statistics associated with this model. The average log wage
is higher in white collar, but so is the variance; job satisfaction is on average better as well
(lower numbers are better, on a scale of 1-4). That more people are in blue collar jobs for
many periods suggests the importance of individual heterogeneity, both of individuals and
jobs. That the average AFQT scores are so different, with white collar workers 14 points
higher on average, or approximately half a standard deviation, reinforces the differences
between the employees in the two occupations.
Figure 3c shows average natural log of real wages by age. Wages are deflated to put wages
in terms of 2005 dollars. White collar workers have similar wages as blue collar workers on
average in younger years, but follow a different trajectory after only a few years. Some
20
I code their occupation as white collar if the 1990 census occupation recoding is under 400 and blue collar
if the occupation code is over 400. This has white collar assigned Managerial and Specialty Occupations;
Specialty Occupations; Technical Support and Sales Occupations; and Administrative Support Occupations.
Blue collar is assigned Service Occupations and Farming; Production, Craft and Repair Occupations; Extraction, Precision Production, and Plant and System Operators; Operators, Laborers and Fabricators; and
Transportation and Material Moving, Handlers, Equipment Cleaners and Helpers.
10
of these white collar workers are finishing up school and joining the work force with higher
wages, pulling up the average. White collar jobs in general have a higher wage growth profile.
There is also sorting into white collar by the highly productive, pulling up the average wage
at a higher rate. Average job satisfaction (Figure 3d) steadily improves (lower numbers)
for both white and blue collar workers, and at about the same rate. However, white collar
workers consistently report, on average, higher job satisfaction. The overall improvement
in job satisfaction may reflect job and occupation sorting into both occupations, as workers
find situations in which they are happy and comfortable more often as more time passes.
Figure 4 presents the trends for the four non-wage benefits used in estimation of this
model. The data is not available for all years for the final three variables; however, enough
years are present to allow for the regressions used in the model. There seems to be an
overall increase in each variable for both white and blue collar, except for perhaps in job
security. Workers are getting into better matches as more time passes. Figure 5 shows
two conditional probabilities. The first is the proportion of job changes that are within
occupation. As workers age, more and more job changes are part of a change in occupation.
Using a dynamic model that includes job offers will help capture the occupation changes
happening. The other plot in Figure 5 shows the proportion of occupation changes that are
within the same firm (the complement being occupation changes that change jobs). This
decreases slightly over time as well, but not as dramatically. Overall, about 20% of workers
that are changing occupations do so within the same job. This could be a promotion or just
a change in duties and responsibilities.
The model uses three sets of auxiliary regressions: 1) logit and OLS regressions to estimate probabilities of receiving non-wage benefits or the level of the non-monetary benefits
to model non-wage benefit offers (Table 5); 2) logit regressions to estimate probabilities of
being fired used to estimate firing probabilities (Table 6); and 3) the probability that workers
change jobs regressed on their log wage, non-wage benefits and other controls; the regression
coefficients are part of the minimization criterion, used to help the fit of the model, and in
particular to help with identification of the separate non-wage benefits (Table 7).
4
Estimation
The value functions are solved recursively for the 14 periods. The expectations of the maximum value functions in any given period are estimated using Monte Carlo Simulation:
R r
1 max Vkjt+1 (St+1 |dkjt = 1) |dkjt = 1
=1 =
R r=1 k,j
E max {Vkjt+1 (St+1 |dkjt = 1)} |dkjt
k,j
11
r
Vkjt+1
(St+1 |dkjt = 1) is the value function given specific draws of the random shocks ξ
(random utility shocks), ε (wage shocks), v (measurement error on η ∗ ), as well as shocks
that determine whether they are fired or not and whether they receive different non-wage
benefits or what levels of benefits they receive. I use R = 50 by taking 25 random draws and
using the antithetic variates method to reduce the error. Further, given the large state space,
I use an interpolation technique, as suggested by Rust (1997), by taking random draws from
the state space every period and estimating the value functions at these points in the state
space. I estimate and store the coefficients from a flexible linear regression with quadratics
and certain interaction terms of the state space on the value.21
There are four non-wage benefits of a job: whether it includes health insurance, whether it
includes retirement benefits, overall pleasantness of the job environment, and the perceived
job security. For the first two non-monetary variables, as discrete variables, I estimate a
logistic regression on the NLSY data outside of the model estimation. I estimate the probabilities, uniquely for each occupation, that their job include health insurance, for example, as
a function of their age, age squared, education, AFQT score, age interacted with education,
and age interacted with AFQT score. In the simulations, I take a random uniform draw, and
if the random draw exceeds the probability that, given their state, they would receive health
insurance, then they are modeled as getting a job offer that includes health insurance. The
latter two non-wage benefits are not binary. In the data, they rank the questions (such as
pleasantness of the job) on a scale of 1 to 4, four being they most strongly agree. For these
regressors, I use the same state variables, but use OLS to estimate parameters and offer an
average score for them, given their state. This, plus a normal random shock (with variance
also determined from the data), yields the continuous variable included in their job offer for
these non-wage benefits. The firing probabilities are estimated inside the model, to allow
dependence on the firms’ beliefs for firing. The estimation is described in detail in Section
A.3.
I separately estimate two versions of the model: the full model (as described in Sec-
tion 2) and the wage model (the full model with the removal of non-wage benefits). The
parameters of the models are estimated using simulated annealing on a minimization criterion determined by the method of indirect inference.22 The minimization criterion is the
squared distance between the moments in the data and those predicted by the model in
the simulations. Specifically, the moments are the proportion of agents in schooling, white
collar, and blue collar at each age; mean log wage by occupation and age; standard devia21
Similar in spirit also to Keane and Wolpin (1994); see Aguirregabiria and Mira (2010) for a review of
this methodology.
22
See Gouriéroux and Monfort (1996) for a review on the method of indirect inference.
12
tion of log wages by occupation but not by age; proportion changing occupations by origin
occupation and age; proportion changing jobs by occupation and age; proportion changing
job voluntarily by occupation; average job satisfaction report by occupation and age; the
absolute difference between the reported job satisfaction and the actual job satisfaction; and
an auxiliary regression of whether they changed occupation regressed on the log wage, the
non-wage benefits (health insurance, retirement, job pleasantness, and job security), AFQT
score, education, and age.
ρ (the CES substitution parameter) and the minimum consumption parameter are chosen
exogenously. ρ plays a role both as the elasticity of substitution between wage and non-wage
benefits and the intertemporal substitution between periods. In the case of intertemporal
substitution, there are no savings in my model, so the only consumption smoothing possible is
through choices of occupations and jobs, a rough mechanism that won’t be able to accurately
gauge the substitution preferences. In the case of elasticity of substitution, the indexed nonwage benefits are not directly estimated (because the weighting coefficients are not observed,
but estimated), so the substitution parameter is not separately identified from the weights.
I choose a value equal to ρ = 0.75,an elasticity of substitution between consumption and
non-monetary benefits of 1/(1 − ρ) = 4.23 For the minimum consumption parameter, I set
it equal to the poverty line in the United States (using 1989’s value, inflated into real terms
to match the wage data in the model). The poverty line was 6,310 USD for a family of four
(US Bureau of the Census 1993), which inflated into real 2005 dollars is 9,079 USD. For a
forty hour a week job, worked for 50 weeks in a year, this is equivalent to a 4.54 dollar hourly
wage, which is the minimum consumption parameter value used in this model.
5
Results
Figure 3a presents the true and simulated proportion of workers in each occupation at
different ages. Figure 3b shows the proportion of workers switching occupations, by origin
occupation.24 Figures 3c-3e compare the data trends with the simulated trends for average
wages, proportion changing jobs, and average job satisfaction report. The data trends are
well matched by the model simulations, providing evidence in favor of the model explaining
the data. The wage model similarly matches well, as shown. 95% confidence intervals for
each are given in shaded regions; for the most part, the full model and the wage model have
23
This is based off and consistent with the estimates in Mankiw, Rotemberg, and Summers (1985). I
tested various choices for ρ and found that, after the estimation process, the results did not vary widely.
24
Origin occupation implies, for example, that the line labeled Blue Collar represents the fraction of
workers that were in a blue collar job and switched to a white collar job, out of the working population of
blue collar workers at a given age.
13
overlapping confidence intervals, suggesting that the wage model is similarly able to match
the data moments, and ability to match should not be used as evidence for accuracy, as will
be shown by the difference in predictions. Further, the Wald statistic for the difference in
the restricted wage model compared to the full model is 1.09e+06, for a p-value below 0.01.
Thus, even though the models seem similar on these trends, we reject them as being the
same. The J-test for goodness of fit to the data is 3.24e+05, rejecting the fit of the data at
a p-value below 0.01. However, this is partially due to moments that are not intended to be
represented directly by the model, but to help the fit of the data nonetheless, such as reports
of job satisfaction and the auxiliary regression.
Given utility is a function of wages and non-wage benefits, the means and variances of
the wage and the weighted sum of non-monetary benefits give information about the decision
process of the agents. The estimated mean wages are close in value to the mean indexed
non-monetary benefits, but the standard deviation is approximately three times as large.
The variation in wages will be the driving force behind the occupation and job decisions of
the agents in the model (Table 8).
Table 9 shows the estimated parameters that represent the marginal returns to education,
occupation and experience. As the occupation and job variables are quadratic, the marginal
returns depend on how much experience an agent has.25 As anticipated, white collar jobs
reward workers with higher education at a greater rate than blue collar jobs, at almost three
times as high a return. On the other hand, the parameters suggest that, while white collar
initially has a higher return to own-occupation experience, after only three years the return is
larger for blue collar jobs. The returns for job tenure are high but steeply decreasing with job
tenure. As comparison, Kambourov and Manovskii (2002) show five years of occupational
experience leads to a 12% cumulative increase in wages, and Buchinsky et al. (2010) with
PSID data estimate a return of 3.77-6.33% for each additional year of occupation experience.
The results in this paper estimate are within the range of the other papers across certain
years of job tenure. All of the estimated parameters for the structural model are given in
Table 10.
Using a structural model enables calculation of how much agents will pay to avoid the uncertainty of not knowing the optimal occupation or job to be in for a given period. Estimating
this value serves as a measure of the uncertainty and the potential gains to choosing correctly.
The calculation estimates 1) a worker’s lifetime utility if they knew whether switching or not
was optimal and 2) the worker’s lifetime utility if they didn’t know. From these estimates, I
determine how much money agents would pay in the current period to know for sure which
occupation to be in, i.e. the monetary transfer that would equate the lifetime utility from
25
Experience is represented by X in the table.
14
knowing and from not knowing.26 The youngest workers (just graduating high school) are
willing to pay 19.88% (11.03%) of their wage that year on average to know the optimal
occupation (job) to choose, while fourteen years later they are only willing to pay 4.54%
(3.68%) on average. The sharp decline results from at least three sources: the improvement
in information by the agents of their type, the decreased length of time in which benefits are
accrued, and the entrenchment that occurs later from garnishing the returns to occupation
or job experience. Workers are not willing to pay as much for knowledge about the correct
job, as the benefits from occupational choice last throughout the entire work history, unlike
correct job choice (which only last until they leave that firm). The uncertainty associated
with which occupation to be in, in particular early on, is quite large, and underlines the
importance of understanding the dynamics surrounding occupational transitions for young
workers.
5.1
Labor Supply Decisions
There is a relatively high proportion of the labor force that switch occupations. Kambourov
and Manovskii (2008) use the Panel Study of Income Dynamics (PSID) and estimate the
average annual level of occupational mobility is around 13% at the one-digit level, 15% at
the two-digit level, and 18% at the three-digit level. Markey and Parks (1989) find similar
rates in the January Current Population Survey 1987, and Parrado et al. (2007) also find
a 7% to 11% change at one digit with the PSID. Using the Duncan Index they also find
increasing transition rates over time (through the 1970s and 1980s), increasing from 20.1%
for the 1970s to 26.3% for the 1980s.27 Moscarini and Vella (2003) find higher transition
rates at the three-digit level using the National Longitudinal Study of Youth (NLSY) at
transition rates of 57% to 70% when measuring occupation at a three digit level. In the data
sample used in this paper from the NLSY, the transition rates, at 2 occupations, are higher
than other one-digit levels because the data here is restricted to young men who have been
out of high school for 14 years or less. Young men transition more often than older men, a
trend which this paper will examine.
The occupational specific labor supply decision is made with agents forward-looking.
I perform a series of tests where workers receive a one percentage point increase in their
26
Specifically, I solve for the transfer τ that equates ((wc − τ )ρ + bρc )1/ρ + ξc + EVc = VU C , where subscript
c are the variables for when the agent is certain about which occupation/job is better ex post, and U C is the
lifetime utility from when they are uncertain. Note that τ is bounded below by zero (by the certain situation
being a special case of the uncertain situation) and above by wc (as they can’t give more than their whole
wage, as there are no savings in this model).
27
The Duncan index is the sum across occupations of the absolute values of the change in the percentage
of employment.
15
wage offers for occupations and jobs, testing both a temporary (one year) increase and a
permanent increase.28 The effects I measure are the resulting elasticities of occupational
specific labor supply (for example, the percentage change in the proportion in blue collar
work) and elasticities of job changing. The elasticities should be positive for occupation:
increases in the wage should induce more workers to opt for that occupation or job. The
elasticities for job changes should be negative: a higher wage offer in the current job induces
less switching. I separately estimate elasticities for the two models: the wage model, where
selection is made only on wage offers (representing the norm in the literature, as discussed
in Section 1), and the full model, which includes wage and non-wage factors in utility.
Table 11 presents the average elasticities of occupational-specific labor supply for the
full model (which incorporates wage and non-wage benefits into the decision process) and
the wage model, which is separately estimated. Standard errors are in parantheses. The
wage model is nested within the full model by shutting down the role of non-wage benefits.
The elasticities (averaged over time) for permanent wage changes are higher for white collar;
white collar jobs are more attractive for their wage benefits, so that increasing these has a
larger effect than for blue collar, for which wage is also important, but non-wage benefits
play a larger role. Further, for a typical white collar worker with higher education, white
and blue collar jobs are more substitutable, resulting in the larger elasticities. Further,
permanent wage increases have approximately ten times as large an effect as temporary
wage, with a longer horizon over which the benefits are accrued. Table 12 presents the job
change elasticities with standard errors. For both sets of elasticities, the wage model does
remarkably well in estimating similar elasticities as the full model, especially considering
both models were estimated separately and have separate model parameters. The estimates
fall within each other’s confidence intervals easily.
To investigate the lack of bias, we will focus our attention on the occupation-specific elasticities. These elasticities are the averages over time. However, the agents act very differently
depending on their age, due both to the changes in how substitutable the occupations are
based on their occupational experience levels and the shorter horizon over which benefits are
accrued. The estimated elasticities for the full model and wage model are in Figure 6. There
is a sharp and secular decrease in the estimated elasticities with respect to permanent wage
changes.29 The transition rates will vary largely on age, and so the estimated effects depend
on the age composition of the working force, and the entry and exit levels of workers will be
much higher for younger workers. A researcher interested in understanding economy-wide
28
A permanent increase for occupational elasticities lasts the duration of the working life; a permanent
increase for job elasticities lasts the duration of working for that employer.
29
While not presented here, the elasticities for temporary wage increases have a flat profile over age.
16
responses to wage shocks should understand the age distribution in the occupation, and
further, should not use the averages in this paper, which only accounts for young workers.
Comparing the full and wage model shows that, for elasticities, the wage model does
remarkably well. This is particularly true for blue collar elasticities, even across different
ages, while white collar elasticities tend to be underestimated when using the wage model
for early ages. I hypothesize that the estimators are largely unbiased because the biases
cancel out. For example, a worker in a job with high non-wage benefits would tend to be less
responsive to wage changes, so would have a lower elasticity. Estimating the wage model on
such individuals would overestimate the elasticities. On the other hand, a worker in a job
with low non-wage benefits would be more responsive to wage shocks than on average, so the
wage model would underestimate the elasticities. On the other hand, a worker with low nonwage benefits would tend to be highly responsive to wage changes (high elasticities), so that
the wage model would underestimate the elasticity for such individuals. On average, given
that workers are both above and below average non-wage benefits in even proportions, the
biases will by and large cancel out. If that is true, the results would be biased if the sample of
individuals at any given age not in the occupation examined do not have individuals evenly
above and below the average non-wage benefit. Specifically, for the elasticity of white collar
to underestimate for young workers (as is observed), the distribution of young agents not in
white collar would be disproportionately composed of workers with low non-wage benefits.
Further, not accounting for non-wage benefits, workers will chose education solely based on
future wages, and not for the high or low non-wage benefits that will be borne. For workers
of high ability, the full model estimates that education is more enjoyable (higher non-wage
benefit) than many jobs of average non-wage benefits. This could also contribute to the bias.
One way to test this hypothesis of canceling biases is to separately estimate the elasticities in the simulations for those with high non-wage benefits and those with low non-wage
benefits. Specifically, for every person-year in the full model simulation, I separately estimate the decisions with a one percentage point wage increase using the wage model and
using the full model, and then advance the simulation using the full model decision while
saving the non-wage benefit index for each person-year. Aggregating across non-wage benefits yields, as before, relatively unbiased estimates (that is, the wage and non-wage model
predict the same average elasticity). However, if we separate into, for example, the top 25th
percentile of non-wage benefit workers and the top 25th percentile, biases start to arise.
Table 13 presents the estimated elasticities for the subgroups. For the bottom quartile, the
wage model severely underestimates the elasticities (as hypothesized). For the top quartile,
the white collar elasticities are roughly equivalent, but the blue collar elasticities are overestimated, as hypothesized. The wage model parameter estimates are not within the 95%
17
confidence intervals of the full model in these cases. The over- and under-estimates of the
elasticities for blue collar demonstrate why the results shown in Figure 6 are unbiased, while
the white collar has a slight downward bias for the wage model (as the bottom quartile is
underestimated, but the upper quartile is roughly unbiased, aggregating to a downward bias.
These results verify the hypothesis that, while a wage model generates unbiased overall elasticities, elasticities for subgroups (which can be any subgroup that doesn’t uniformly average
the non-wage benefit spectrum) will be biased.
5.2
Counterfactual: Non-Wage Benefit Compensations
To illustrate the importance of non-wage benefits in the decision process of workers and
potential biases, I apply the model to a case in spirit similar to the decline of manufacturing
in the United States. Typically viewed as a shock to labor demand for blue collar workers,
we can analyze the situation in terms of labor supply response to the demand shock in
this model that incorporates not only wages but non-wage benefits. Consider an economywide blue collar wage deterioration of five percentage points. Figure 8 shows the resulting
proportion in blue collar jobs. Each line represents the resulting proportion depending on
what age the workers were when the wage change happened. The results suggest not only
a relatively large decrease in the proportion in blue collar work, but that the effect depends
strongly on the age of the worker, with younger workers making larger initial changes, with
that gap never fully recovered by the end of the model. Shocks to the wage in an occupation
will disproportionately affect younger cohorts of workers, with these effects persisting to the
end of those workers’ careers.
Consider the wage shock happening in the first period after high school. Table 14 reports
the effects of this labor demand shock to wages. The wage model yields results in many
cases different than the full model, predicting a sharper decline in overall wages and blue
collar employment, as the effects of wage change are not partially absorbed by the non-wage
benefits. I then estimate the level of non-monetary benefits necessary to induce the preshock levels of blue collar employment. The results, along with the coefficients on the nonmonetary variables included for comparison, are in Table 15. Most temporary changes would
be insufficient: if no blue collar workers had health insurance or retirement, giving all workers
both health insurance and retirement, but for just one year, would not compensate for the
five percentage point reduction in the wage. On the other hand, the results suggest that
giving all blue collar workers without health insurance or retirement benefits permanently,
if the fraction of workers without those benefits was over half, would be approximately
sufficient to return to the pre-shock levels. Alternatively, the results are roughly in line with
18
a permanent one point increase in job security or pleasantness of environment for everyone
would be enough as well.
5.3
Counterfactuals: Inequality Intervention
This paper investigates one further counterfactual, a policy change. Consider that a government is interested in reducing consumption inequality through increased minimum consumption (the minimum consumption guaranteed by the government) and potentially financed
through a wage tax. The models are tested for various increases in the minimum consumption (ranging from an increase by a factor of 1 to 2), and with various taxes (from zero to
14%). This paper focuses on the biases arising from using a wage model in place of a full
model; however, it should be noted that naı̈ve policy predictions that assume no dynamic
response (in this case, no changes in occupation or job given the new minimum consumption
or wage tax) are severely biased, as expected.
Figures 9-11 show the predicted percentage change in the Gini coefficient for consumption,
wage, and non-wage benefits, respectively, for the wage and full models.30 For each point,
the minimum consumption level is increased by a factor given by the parameter scale, and
a wage tax is imposed equal to various tax rates. The model is simulated again and the
Gini coefficient is re-estimated, and then the baseline model Gini coefficient is compared
with the new Gini coefficient. The purpose of the intervention is to decrease consumption
inequality through raising the minimum consumption guaranteed; Figure 9 shows that this
was accomplished. Higher minimum consumption guarantee and higher wage taxes both
serve to decrease consumption inequality. However, while the predictions of the wage and
full model are similar, they are not identical. Universally, the wage model predicts smaller
reductions in consumption inequality. One reason for this is seen in Figure 10, where the wage
model vastly over-predicts the increase in wage inequality, dampening the overall effectiveness
of the intervention. The wage and full models both capture the distortion that happens as
individuals below but near the new poverty line more often choose not to switch to better jobs
or occupations than before (which increases wage inequality), as well as the incentive for highproductivity workers to receive more education early on with higher guaranteed consumption,
leading to higher future wages (and thus also increasing wage inequality). However, the wage
model overstates the importance of the wage dynamic, and doesn’t account for the change
in the relative benefits of wage and non-wage that arises from the wage tax. Accounting for
non-wage benefits, high earning workers on the margin will switch from higher paying jobs
to slightly lower paying, but better non-wage benefit jobs, dampening the spread of wage
30
The Gini coefficient is a common measure of inequality, equal to the fraction of the population above
the Lorenz curve but below the 45 degree line. Higher values represent greater inequality.
19
inequality and leading to a greater success of the intervention. This is reinforced by the
expansion of non-wage inequality with no change in the minimum consumption guarantee
but an increase in the wage tax. The change in the Gini coefficient for non-wage benefits
is more complicated with large changes in the minimum consumption parameter, where a
reduction in non-wage benefit inequality is predicted. This is likely due to the incentive at
the bottom of the wage distribution for workers to choose jobs with much better non-wage
benefits and lower pay if neither pay are above the new minimum consumption guarantee,
leading to a contraction of the non-wage benefit distribution.
The bias from using the wage model in place of the full model is larger for larger increases in the minimum consumption guarantee and for larger changes in the wage tax. As
the specifics of this set of counterfactuals are manufactured, this paper does not focus on
the specific magnitudes of the bias here, but instead emphasizes the point that predictions
surrounding the effect of large policy interventions will be biased if estimated using a model
based solely on the wage incentive, especially if the relative prices of wage and non-wage
benefits has been changed (here, for the bottom of the wage distribution through the increase of the consumption guarantee, and for the remainder of the population through the
wage tax).
6
Conclusion
Understanding the process by which workers choose their occupation and the associated
elasticities and the importance of non-wage benefits has many important applications. Examples examined in this paper include evaluating labor sector changes from the supply side,
such as in the decline of manufacturing in the United States, and understanding the impact
of the decisions on various policies such as inequality and poverty interventions. Dynamic
structural models are capable of predicting changes from new policies. However, previous
research estimating dynamic structural models of occupational choice have ignored non-wage
benefits and the joint choice of occupation and firm, and reduced form investigations ignore
the joint incentives of wage and non-wage benefits. By adding them into the model used
in this paper, I am able to show the bias generated when workers are assumed to make
occupation and job transitions based solely on the wages and expected future wages.
Ignoring non-wage benefits does not significantly bias the estimated effects of wages on
occupation transitions. However, this is due to biases canceling out across the non-wage
benefit spectrum. The results in this paper suggest that there are situations, therefore,
in which a labor supply model based on selection on wages will yield unbiased estimates.
However, this is only true under certain conditions. In particular, the aggregate bias will
20
depend on the sign and magnitude of the bias in each subpopulation and on the size of each
subpopulation, and it is only in very particular cases of biases going in different directions
with similar magnitudes for which biases will not be significantly large.
Many analyses will not meet either criterion. The examples of the deterioration of blue
collar wages and the inequality intervention policy analysis demonstrate the resulting biases.
However, both criteria must be met, as demonstrated in the example of the occupationalspecific labor supply elasticity for a subpopulation in jobs with poor non-wage benefits. The
first criterion is met, as biases do have the potential to go in either direction, but criterion
two is not met, as the bias for the subpopulation of interest go in the same direction. As
shown, the biases here can be as large as a factor of 2.39 (blue collar, bottom quartile of
non-wage benefits), substantial deviations. The results of this paper offer estimates of the
elasticity of labor supply for white and blue collar for young workers, which can be useful
when predicting labor supply sector changes. The paper also provides a useful framework
for researchers to estimate the effects of various policies, and estimates the size of the bias
by either ignoring strategic response altogether or from ignoring non-wage benefits. Future
research can apply a model that incorporates non-wage benefits to questions of job lock,
training, or changes in the speed of learning for firms.
A
A.1
Appendix
Non-Wage Benefit Estimation
For binary variables, I assume that
P r(benefitks = 1) =
f (α0ks + α1ks AFQT + α2ks yr + α3ks t + α4ks tAFQT + α5ks t × yr + α6ks t2 )
k denotes the occupation, s which benefit, yr = exper , the years in the work force,
and t is the number of period (number of years since graduating high school). f (·) is a logit
function, and α’s are estimated using maximum likelihood outside of the model using NLSY
data. Then, in the model, a random uniform variable is drawn, and if the value exceeds
the probability that a worker with their characteristics, then their job offer includes that
non-wage benefit. In my model, there are two benefits that are binary: health insurance
benefits offered and retirement benefits offered.
For continuous non-wage benefit variables,
21
benefitks =α0ks + α1ks AFQT + α2ks yr + α3ks t
+ α4ks tAFQT + α5ks t × yr + α6ks t2 + uks
uks is a normally distributed random shock. These α’s are estimated using OLS outside
of the model using NLSY data, as well as the variance of the residuals. In the model, I take
a random normal draw and estimate their benefits, given their characteristics. Two variables
in my model are on a scale of 1-4 (how pleasant the job environment is and the level of job
security, and are assumed to represent an underlying continuous variable, as described.
A.2
Bayesian Updating
I assume that both the agents and the firms that they work for learn about a fixed ability
parameter specific to each worker and occupation, given by ηk∗ . All learners start with a
zero mean prior. At the end of every working period, workers and firms observe a noisy
measurement of ηk∗ for the occupation k worked in, and update beliefs according to Bayes’
Law. This is comparable to each period, workers and firms observing the productivity of each
worker and differencing out all contributing factors to the productivity, such as education and
experience. All that is left after the differencing is ηk∗ , or fixed ability, and other unobservables
assumed to be orthogonal to ηk∗ .
From this, workers and firms are able to get a better sense of the productivity of the
worker. Firms adjust wage offers accordingly. While firms’ lowering wages might seem odd,
there is evidence of real wage decreases in firms, and the wage offer could still be growing,
F 31
. The beliefs of the workers about their own
but at a slower rate given a negative value of ηkt
productivity matter insofar as workers form expectations about their future wage streams
based on what they expect the firms to learn about their own ability. A worker with a
low productivity parameter in occupation k might choose to avoid job offers from firms in
occupation k, expecting the firms to learn about their poor ability and lower wage offers in
the future and lower their wage offer accordingly without the worker being able to gain the
returns to firm tenure or a good match parameter value.
The updating is based on the work of Ansley and Kohn (1983). Every period, firms
and workers receive a noisy measurement of ηk∗ given by ηkt = ηk∗ + vt . Assume that the
noise shocks are independently and identically distributed across individuals and time, but
∗ ).
possibly correlated across occupations, and given by vt ∼ N (0, Ω). Let η ∗ = (η1∗ , ..., ηK
31
see McLaughlin (1994) and Card and Hyslop (1997) for empirical evidence, and Gibbons and Waldman
(1997) for theoretical support.
22
Then, at the beginning, each agent receives a draw from η ∗ ∼ N (0, Σ). The agent uses
Bayesian updating according to the following rules. Let the agent have an initial prior on
η ∗ be given by η0 ∼ N (0, Σ). Meinecke (2010) demonstrates how by the independence of
η ∗ and vt , given an observation of ηkt , and recognizing that only one ηkt is observed each
period, for one occupation (dt is a vector on indicator variables for which occupation they
work in in period t)
ηt+1 = ηt + Gt dt (ηkt − ηkt )
t d (dt (Σ
t + Ω)d )−1
Gt = Σ
t
t
t+1 = Qt Σ
t Qt + Gt ΩGt
Σ
Qt = I K − Gt
The estimation of the wage fixed effect can be estimated given a wage history and occupational choice by these rules.
A.3
Firing Probabilities
The probability that an agent is fired is given by
F
P r(f iredkjt = 1) = f (zkjt γ Z + γ η ηkjt
+ ekjt )
I model f (·) as a logistic regression. The coefficients γ Z and γ η are estimated using
maximum likelihood. zkjt contains a worker’s firm tenure, their education, which occupation
they are in, and their occupational experience. These variables are all observed in the
F
is not observed in the data.
data, as is whether or not the worker is fired. However, ηkjt
F
, so that γ can
Examining the wage equation, however, suggests a strategy for estimating ηkjt
be estimated. The wage equation can be generalized as
OB OB
F
β + λh + ηkjt
+ εkjt
ln(wkjt ) = Xkjt
OB
where Xkjt
are the observable wage variables.32 λh is the firm employee match, and εkjt is
a random shock. Note then, if we isolate the observable portions
32
AFQT, educt , expert , exper2t , tent , and ten2t .
23
F
OB OB
F
F
= ln(wkjt ) − Xkjt
β = ηkjt
+ λh + εkjt = ηkjt
+ νkjt
η̃kjt
F
In other words, we can think of observing a ηkjt
with measurement error νkjt = λj + εkjt .
OB
F
. This is a measurement
Given β , which are parameters of the model, we can estimate η̃kjt
F
error affected measure of ηkjt . I estimate the logistic regression of firing using zkjt and the
measurement error affected η̃kjt . The measurement error causes attenuation bias in γ η and
η unbiased. φ
consistent estimates of γ Z . Let φ be the bias correction scalar that makes φ × γ
is another parameter of the model to be estimated within the search of the model. I choose
the φ, along with all of the other parameters of the model, to match all of the moments the
best.
A.4
Data Selection Procedure
Various methods have been used to code when an occupation has been changed and what
an individual’s occupation is. The most common and natural definition is when there is
a change in the reported occupation (for example, as used in Kambourov and Manovskii
(2008) and Parrado et al. 2007). Mellow and Sider (1983) argue that there is a great
deal of misclassification in occupation. They match self-reported occupation in the CPS
with employer records and find only 58 percent match rates at the three-digit level and
81 percent at the one-digit level. Mathiowetz (1992) does a similar matching and finds a
higher match rate at 87% at the three-digit level. Longhi and Brynin (2010) argue that this
is unreliable, overestimating transitions when interviewees change their report when they
actually haven’t changed their occupation. They only record an occupation change when
both a new occupation code is recorded and a change of job is also recorded. They find
that this significantly decreases the measured amount of occupational transitions, and argue
that this is the measure that should be used. However, this underreports changes, because
some occupation changes are clearly within firms. I allow for occupation changes within
firms, such as through promotion. Sullivan (2009) uses the job that is recorded in the most
number of weeks as their occupation. I use the definition of what the agent reports as their
primary occupation each year, where possible, to link the job to the wage and non-wage
benefits reported annually. The misclassification issues in this paper are less severe because
occupation is restricted to blue collar and white collar jobs.
The first restriction imposed is that the interviewee is male and observed from at least
age 18 in the data. I drop those that report they are self-employed. The most consequential
decision I had to impose on the data interpretation process is the selection of which of their
24
various reported jobs each period was their primary job, and how long they had been there.
Some years and for some variables they reported their current job, and this was used as the
most reliable classification. However, some years and some variables did not report current
occupation; instead, the agents reported on up to five jobs they had held this year. The
following rules, in order of the priority of the rule (rules with better, i.e. lower, priority
numbers overruled potentially conflicting assignments from worse priority numbers) were
used to select which was their primary current job, and thus to assign wage, tenure, and
non-wage benefits for that job.
1. The first in the priority list that they say they are still in or do not record a stop date
2. If there is none from step 1, set equal to occupation with most recent stop date
3. If there is no stop date for any, choose highest priority occupation listed
4. If no occupations are listed that year, but difference in tenure across the two periods
is greater than 52 (stayed at same job) and occupation is the same tenure before and
after is the same, set occupation in the intermediate (missing year) equal to that value
The following rules were used for assignment (again, in order of priority) of whether they
changed their job or not, conditional on their working that period
1. The job chosen has a recorded stop date in that year
2. If the job chosen next period is not the earliest start date next period...
3. The next year has an occupation with the same occupation number and larger tenure
but is not job X
4. The next year’s tenure is less than tenure in the current year + 25
5. They record they are no longer there
6. Change to not changed job if past year and future year suggest the same job throughout
With all of these methods, I performed numerous inspections of the raw data to see if
the assignments from the rules reflected what I would intuitively assume happened on a case
by case level, and found it to be reliable.
25
A.5
Model Parameters
βkAF QT : log wage return to ability (AFQT) score for white collar (k = 1) and blue collar
(k = 2)
β ED : non-monetary marginal benefit for higher ability to education (AFQT score)
EXP
βjk
: linear term in the log wage returns to experience in schooling (j = 0), white collar
experience (j = 1), and blue collar work (j = 2), having different returns in white
collar jobs (k = 1) and blue collar jobs (k = 2)
EXP 2
βjk : quadratic term in the log wage returns to experience in white collar experience
(j = 1), and blue collar work (j = 2), having different returns in white collar jobs
(k = 1) and blue collar jobs (k = 2)
HE
β : health expenditure payments
βjN W : non-monetary return for benefits health insurance (j = 1), retirement (j = 2),
pleasant environment (j = 3), and job security (j = 4)
β T EN : linear term in the log wage return to the job tenure
β T EN 2 : quadratic term in the log wage return to the job tenure
βjT V F : coefficients in the terminal value function: a constant (j = 0), expected wage (j = 1),
expected wage squared (j = 2), expected non-monetary benefits (j = 3), expected
non-monetary benefits squared (j = 4), and an interaction between expected wage
and expected non-monetary benefits (j = 5)
Mk :
job entry cost for occupation k
Ω:
variance-covariance matrix for the shock to wages for white collar and blue collar
qj :
job satisfaction report thresholds, j=1,2,3
ρ:
CES utility parameter
Σ:
variance-covariance matrix for the unobserved ability that agents and firms update
beliefs on (this also effects the speed of learning)
σλ:
firm-employee match parameter variance
σξ :
variance of random utility shocks
B
θk :
non-monetary benefits intercept for schooling, white collar, and blue collar
W
θk :
log wage intercept for white collar (k = 1) and blue collar (k = 2)
26
A.6
Tables
Table 1: Average Job Characteristics, White Collar
Stayed in White Collar
Switched to Blue Collar
ln(wage)
2.63358
2.31904
Health Ins.
0.88584
0.75956
Retire.
0.73706
0.60201
Pleasant Env.
3.40171
3.13167
Job Secure
3.31054
3.02509
Table 2: NLSY Sample Regressions on Next Period Log Wage to Compare 2 and 10 Occupations
2 occupations 10 occupations
ln(wage)
0.532***
0.531***
(0.0159)
(0.0159)
Change Occupation
0.0223
0.0331***
(0.0162)
(0.0123)
Change Job
-0.0670***
-0.0752***
(0.0128)
(0.0132)
Period
0.0372***
0.0391***
(0.00171)
(0.00182)
Change Job × Period
-0.0120***
-0.0107***
(0.00167)
(0.00171)
Change Occupation × Period
-0.00230
-0.00575***
(0.00214)
(0.00157)
Left Voluntarily
0.102***
0.101***
(0.0103)
(0.0131)
Left Voluntarily × Change Occupation
-0.0338**
-0.00980
(0.0170)
(0.0138)
Period is the Number of Years After High School
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
27
Table 3: Regressions on Non-Monetary Benefits
Change Occupation
Change Job
Period
Change Job × Period
Change Occupation × Period
28
Left Voluntarily
Left Voluntarily × Change Occupation
Health Inst−1
Retirementt−1
Pleasant Env.t−1
Health Ins.
2 Occs
0.00147
(0.0234)
-0.108***
(0.0208)
0.00595***
(0.000992)
-0.00755***
(0.00216)
0.00237
(0.00262)
0.0888***
(0.0137)
-0.0172
(0.0204)
0.453***
(0.00786)
Health Ins.
10 Occs
0.0483***
(0.0168)
-0.121***
(0.0211)
0.00774***
(0.00118)
-0.00623***
(0.00219)
-0.00396**
(0.00184)
0.0933***
(0.0161)
-0.0120
(0.0158)
0.453***
(0.00786)
Retire.
2 Occs
0.0617
(0.0684)
-0.0389
(0.0520)
0.00717***
(0.00219)
-0.00948*
(0.00493)
-0.00438
(0.00658)
0.0881***
(0.0190)
-0.0182
(0.0325)
Retire.
10 Occs
0.0692
(0.0437)
-0.0533
(0.0529)
0.00883***
(0.00253)
-0.00814
(0.00502)
-0.00625
(0.00415)
0.0932***
(0.0227)
-0.0137
(0.0241)
0.612***
(0.00825)
0.612***
(0.00825)
Pleasant Env.
2 Occs
-0.0545
(0.135)
0.0121
(0.118)
0.0135
(0.0356)
0.0414
(0.0521)
-0.000677
(0.0653)
0.0273
(0.0742)
0.0236
(0.120)
Pleasant Env.
10 Occs
0.106
(0.110)
-0.0354
(0.119)
0.0348
(0.0408)
0.0638
(0.0530)
-0.0554
(0.0526)
0.181*
(0.0928)
-0.209**
(0.0959)
0.350***
(0.0285)
0.352***
(0.0280)
Job Securet−1
Period is the Number of Years After Graduating High School
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Job Secure
2 Occs
0.0449
(0.163)
0.0450
(0.131)
0.0263
(0.0397)
-0.135**
(0.0618)
0.0285
(0.0767)
0.257***
(0.0871)
-0.0830
(0.130)
Job Secure
10 Occs
0.202
(0.127)
-0.0277
(0.135)
0.0412
(0.0453)
-0.116*
(0.0636)
-0.0357
(0.0620)
0.420***
(0.113)
-0.256**
(0.112)
0.283***
(0.0307)
0.282***
(0.0306)
Table 4: Summary Statistics
ln(wage)
ln(wage), White Collar
ln(wage), Blue Collar
AFQT
AFQT, White Collar
AFQT, Blue Collar
Change Occs
Change Job
Change Job Voluntarily
Job Satisfaction
Job Satisfaction, White Collar
Job Satisfaction, Blue Collar
Mean
2.41
2.57
2.32
48.08
59.56
38.97
0.16
0.36
0.65
1.74
1.64
1.79
Std. Dev. Min.
0.56
-4.28
0.58
-3.14
0.52
-4.28
28.60
0.00
27.14
0.00
26.11
0.00
0.37
0.00
0.48
0.00
0.48
0.00
0.72
1.00
0.69
1.00
0.73
1.00
Max.
10.57
8.67
10.57
100.00
100.00
100.00
1.00
1.00
1.00
4.00
4.00
4.00
N
22,312
7,784
14,528
2,561
8,090
14,973
18,488
26341
8,617
22,338
7,946
14,392
Table 5: Fringe Regression Results (Logit: 1-4; OLS: 5-8)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
afqt
0.0000
-0.0004 -0.0039 -0.0005 -0.0024 -0.0030
0.0078
(0.0032) (0.0018) (0.0062) (0.0046) (0.0020) (0.0012) (0.0022)
educ
-0.2797 -0.1033 -0.8357 -1.3113
3.3696
3.1219
2.7865
(0.2096) (0.0996) (0.6122) (0.4115) (0.1245) (0.0701) (0.1413)
period
-0.1983 -0.2615
0.1557
0.0933
0.0860
0.1291
0.0925
(0.0639) (0.0622) (0.0855) (0.1062) (0.0666) (0.0802) (0.0756)
period2
0.0010
0.0006
0.0008
0.0004
0.0004
0.0003
-0.0008
(0.0004) (0.0002) (0.0006) (0.0004) (0.0003) (0.0002) (0.0004)
period × afqt
0.0232
0.0335
-0.0063
0.0034 -0.01120 -0.0172 -0.0111
(0.0067) (0.0070) (0.0079) (0.0101) (0.0087) (0.0109) (0.0098)
period × educ 0.4054
0.2063
0.2330
0.1943
-0.0398
0.0222
0.0170
(0.0485) (0.0247) (0.1170) (0.0830) (0.0440) (0.0284) (0.0500)
constant
-0.0235 -0.0113 -0.0106 -0.0070
0.0045
-0.0036
0.0034
(0.0030) (0.0016) (0.0058) (0.0042) (0.0041) (0.0027) (0.0047)
1: Health Insurance, White Collar; 2: Health Insurance, Blue Collar
3: Retirement, White Collar; 4: Retirement, Blue Collar
5: Pleasant Environment, White Collar; 6: Pleasant Environment, Blue Collar
7: Job Security, White Collar; 8: Job Security, Blue Collar
29
(8)
-0.0003
(0.0013)
3.0695
(0.0757)
-0.0147
(0.0866)
0.0004
(0.0002)
0.0057
(0.0118)
-0.0125
(0.0307)
-0.0016
(0.0029)
Table 6: Probability Fired Coefficient Results
afqt
educ
job tenure
period
period × afqt
period × educ
period × job tenure
period2
constant
(1)
(2)
-0.00502 -0.01165
-0.23962 0.19378
-0.11367 -0.12823
-0.00026 0.00063
0.01195 0.00010
-0.08491 -0.07752
0.00541 0.00504
0.02428 0.00144
-0.30643 -0.07687
Table 7: Auxiliary Regression Results: OLS Regression of Probability Changed Job
log wage
educ
health insurace
retirement
pleasant surroundings
job security
afqt
period
constant
-0.08849
0.00811
-0.12590
-0.06962
0.01435
-0.09661
-0.00000
-0.02299
1.09905
Table 8: Average Means and Standard Deviations of Wages and Non-Monetary Benefits
Mean
Wages
12.766
Non-Wage Benefits 14.655
Standard Deviation
7.663
2.475
Table 9: Marginal Returns to Work Experience
Returns
Returns
Returns
Returns
to
to
to
to
Educ
White Collar Experience
Blue Collar Experience
Job Tenure
White Collar
Blue Collar
0.12704
0.04961
0.07521-0.01125 X -0.17644+0.02797 X
-0.08890+0.00424 X 0.03422+0.00315 X
0.15252-0.02639 X
30
Table 10: Parameter Values
Parameter
θ0B
θ1B
θ2B
β ED
β1N W
β2N W
β3N W
β4N W
Ω11
Ω22
Ω12
Σ11
Σ22
Σ12
EXP
β01
EXP
β11
EXP
β21
EXP
β02
EXP
β12
EXP
β22
M1
M2
θ1W
θ2W
β1AF QT
β2AF QT
σξ
β T EN
σλ
q1
q2
q3
β HW
β T EN 2
EXP 2
β11
EXP 2
β21
EXP 2
β12
EXP 2
β22
β0T V F
β1T V F
β2T V F
β3T V F
β4T V F
β5T V F
φ
Full Model
-1.954
-0.272
1.901
0.066
1.835
2.022
1.634
1.662
0.172
0.020
0.057
0.004
0.177
0.027
0.127
0.075
-0.089
0.050
-0.176
0.034
-1.961
-0.009
1.677
1.875
0.003
0.002
11.449
0.153
0.009
-8.857
-4.050
47.460
-0.001
-0.013
-0.006
0.002
0.014
0.002
8.089
10.395
17.072
-0.852
0.001
-0.469
0.770
SE
Wage Model
(0.983)
(0.236)
(0.317)
(0.020)
(0.433)
(0.351)
(0.182)
(0.223)
(0.036)
0.082
(0.007)
0.056
(0.011)
0.052
(0.000)
0.038
(0.010)
0.043
(0.002)
0.037
(0.006)
0.108
(0.009)
0.071
(0.009)
-0.082
(0.008)
-0.003
(0.013)
-0.096
(0.004)
0.038
(0.408)
-1.953
(0.047)
-0.298
(0.029)
1.519
(0.036)
1.917
(0.001)
0.006
(0.001)
0.002
(0.595)
10.137
(0.011)
0.160
(0.008)
0.010
(801.965)
-2.973
(260.595)
-2.672
(2.141)
25.051
(16.697)
-0.024
(0.001)
-0.013
(0.001)
-0.005
(0.001)
0.004
(0.001)
0.003
(0.000)
0.001
(70.101)
16.906
(8.447)
8.316
(1.984)
8.697
(0.426)
(0.001)
(0.131)
31
(25.397)
1.563
SE
(0.020)
(0.017)
(0.015)
(0.013)
(0.005)
(0.010)
(0.004)
(0.010)
(0.012)
(0.005)
(0.008)
(0.004)
(0.458)
(0.053)
(0.042)
(0.019)
(0.001)
(0.000)
(0.377)
(0.010)
(0.007)
(4.592)
(2.300)
(0.636)
(20.841)
(0.001)
(0.001)
(0.001)
(0.002)
(0.000)
(104.724)
(4.508)
(1.395)
(177.827)
Table 11: Elasticities of Occupational Specific Labor Supply
White Collar Permanent
Blue Collar Permanent
White Collar Temporary
Blue Collar Temporary
Full Model
5.4429
(0.6256)
2.6165
(0.4001)
0.5399
(0.1659)
0.2529
(0.0821)
Wage Model
4.8580
(12.6098)
2.4439
(12.5897)
0.5305
(1.6026)
0.2594
(3.0139)
Table 12: Elasticities of Job Changes
White Collar Permanent
Blue Collar Permanent
White Collar Temporary
Blue Collar Temporary
Full Model
-3.4138
(0.5512)
-2.5499
(0.8927)
-0.9284
(0.4729)
-0.9151
(0.4647)
Wage Model
-3.0294
(5.3435)
-3.1675
(7.0867)
-0.8697
(0.7204)
-0.9286
(1.5126)
Table 13: Elasticities of Occupational Specific Labor Supply
White Collar
Wage Model
Full Model
Blue Collar
Wage Model
Full Model
Bottom Quantile
7.01
(1.33)
10.82
(1.19)
3.97
(4.29)
7.87
(2.12)
32
Top Quantile
5.30
(1.29)
5.62
(1.86)
1.77
(0.19)
0.58
(0.18)
Table 14: Percentage Changes in Blue Collar Trends from a 5 Percentage Point Wage Decrease
Proportion in Blue Collar
Job Satisfaction
ln(Wage)
Proportion Changing Jobs
Proportion Changing Occupations
Full Model
-23.43
0.57
-2.78
1.50
21.53
Wage Model
-27.20
0.58
-3.09
1.90
20.25
Table 15: Manufacturing Wage Shock Counterfactual: Non-Monetary Benefits Necessary for
Pre-Shock Employment
% Change in Proportion in BC
-23.42
Temporary Non-Wage Necessary 7.43
Permanent Non-Wage Necessary 1.08
Coefficients on Non-Monetary Benefits
Health Insurance
Retirement
Job Security
Pleasant Environment
33
1.835
2.022
1.634
1.662
A.7
Figures
Figure 1: NLSY Sample, Conditional Proportions of Job and Occupation Transitions
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Figure 2: Predicted Average Fraction of Wage Willing to Pay for Knowledge of Ex-Post
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Figure 3: Data vs. Simulated Trends
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(b) Proportion Changing Occupations
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