Other Models of Labor Dynamics

Christopher Taber

Department of EconomicsUniversity of Wisconsin-Madison

March 2, 2014

Outline

1 Kambourov and Manovskii

2 Neal

3 Pavan

Occupational Specificity of Human Capital

Kambourov and Manovskii want to estimate something like thereturns to tenure specification, but allow for occupation andindustry specific human capital

They use the model

log(wijmnt) = β0Emp_Tenijt + β1OJijt + β2Occ_Tenimt + β3Ind_Tenint

+Work_Expit + θit

where

Emp_Tenijt Tenure at the employerOJijt Dummy for first year on the jobOcc_Tenimt Tenure in the current occupationInd_Tenint Tenure in the Current IndustryWork_Expit Total Work Experience

Data

One hard part of this is that they need to get good data onoccupation which is often measured poorly

They use the PSID

They make use of the “PSID Retrospective Occupation-IndustrySupplemental Data Files” which retrospectively get bettermeasures of occupations for the period 1968-1980

They are going to make a distinction between 1, 2 and 3 digitoccupations and industries.

Lets see what that means

The error term in the model is quite complicated with

θit = µi + λij + ξim + vin + εit

where µi is individual effect, λij is job match, ξim is occupationmatch, and vin is industry match (and as usual εit is noise)

This probably means about everything is biased upward

They will deal with this using the Altonji/Shakotko approach

That is, they will use

Emp_Tenijt − Emp_Tenij as an instrument for Emp_Tenijt

Occ_Tenijt − Occ_Tenij as an instrument for Occ_Tenijt

Ind_Tenijt − Ind_Tenij as an instrument for Ind_Tenijt

They do a lot of other robustness checks

Basic results seem robust:

Occupational specific tenure is really importantFirm specific tenure is not importantIndustry specific tenure is somewhere in between

Outline

1 Kambourov and Manovskii

2 Neal

3 Pavan

Neal 1999

Neeal distinguishes between “complex” job switches in whichworkers switch careers from simple job shifts in which workersswitch firms but do not switch careers

He adds uncertainty into our framework: when workers try anew job they don’t know whether they will be good at it or not

He develops a simple model of this and shows that the data isconsistent with the basic predictions of the model: workers firstshop for a career and then shop for a firm within the career

The key components of the model are:

Career match θ distributed F(θ)

Job match ξ distributed G(ξ)

The key restriction of the model is that

to switch careers, you must switch firms, butto switch firms, you do not have to switch careers

He is abstracts from all but the most necessarycomponents-clearly one could make this model morecomplicated if you want.

Assuming that people are paid θ + ξ and that there are nosearch costs in the sense that you can always find a new job ofthe type you want-but you don’t observe the match componentuntil you start working there

You can write the Belman equation as

V (θ, ξ) = θ + ξ + βmax{

V (θ, ξ) ,

∫V(θ, s)dG(s),∫ ∫

V(x, s)dF(x)dG(s)}

where V is the value function and β is the discount factor.

You can think of it in terms of the following figure

Job Mobility among Young Men 241

where V (0, A) is the value of having current matches (0, A) and f is a

discount factor. Equation (1) illustrates that, at the beginning of the next

period, the worker has three options: (i) keep both 0 and 4, (ii) keep her

career match 0 and draw a new firm match, or (iii) draw a new career

match and a new firm match.

Appendix A demonstrates that the worker's optimal policy can be

characterized by figure 1. The variables 0 - and 4* serve as quasi-reserva-

tion values for each type of match, and based on these values, the figure

is divided into three regions. Workers holding a pair (0, 4) that lies in

region A choose to draw a new pair at the beginning of the next period.

Workers holding (0, A) in region B keep their current career match 0 but

draw a new firm match at the beginning of the next period. Workers who

hold (0, 4) in region C cease searching.

Stop

C

Change 0 and 4

A Change 4

B

FIG. 1

Given this search strategy, workers never change careers after changing

firms within a given career. In this model, workers who make simple firm

Note that once you get to region B, you will never go back to A

Once you get to C, you will stay

This has the implication that as workers age, the fraction of jobchanges that are complex should fall

Note also that if we condition on people who have never madea simple job change, the probability that the next job changewill be simple does not depend on age

Neal looks for these implications in the data

Data

He uses the NLSY79 which is great for constructing data on jobchanges and how they vary with occupation and industry

He looks at Males only

The question here is what represents a career

Neal assumes that a complex job change represents both anoccupation change and an industry change

Lets look at the first piece of evidence.

Each observations is a sequence of job changes.

He groups by the total number of job changes and documentsthe fraction consistent with the pure model (i.e. no complexchanges following simple changes)

You can see that the results are not precisely the two stagemodel, but they are much closer than you would expect bychance

Next an observation is a single job change

He groups by the number of simple changes since working inthe current career (and by education)

Key thing is that (for example) for high school graduates forwhom this is there first firm in the career, the chances that thenext switch is complex is 69%

However, for those who underwent a previous job switch in thiscareer, it is only 22%

The next tables are similar, but we group by experience

One concern is that this could be about career specific humancapital rather than about search.

Neal addresses this with the following Table

While the strict version of the model is not precisely true, thedata is broadly consistent with the idea.

Outline

1 Kambourov and Manovskii

2 Neal

3 Pavan

Career Choice and Wage Growth

Pavan implements a structural extension of Neal’s model

Like Neal he uses a similar definition of Career change.

Data

He also uses the NLSY79

Individuals born between 1957 and 1964Representative males (with some restrictions to simplifysample)Different definitions of career

(3 digit) occupation and industry change (t − 1, t) to(t + 1, t + 2)occupation and industry change t to t + 1occupation t to t + 1industry t to t + 1

He then does something similar to what Komogorov andManovskii do, but for career

(using his four definitions of career)

Structural Model

he : general human capitalθc : career specific human capitalεt : firm specific human capital

All three variables are initially drawn from a normal

h1 ∼N(µh1,σ2h)

θ1 ∼N(0, σ2θ)

ε1 ∼N(0, σ2ε)

as in Neal, you draw a new θ when you switch career and anew ε when you switch firms

Don’t get to see those variables unless you actually move

These things evolve

he =h(e, h1)

θc =µθ + α1 (h1 − µh1) + θc−1 + uθc

µθc ∼N(0, η2θ)

εt =µε + α2 (h1 − µh1) + εt−1 + uεt

µεt ∼N(0, η2ε)

Wages are

log(wect) =δ′Xe + he + θc + εt

econometrician observes wages measured with iid normalmeasurement error

Utility

Let

He be hours workedKe(He) disutility of work

U = log(weHe)− Ke (He)

=δ′Xe + he + θc + εt + log(He)− Ke (He)

First order condition for He implies

1H∗e

=K′e (H∗e )

Dynamics

Every period I receive an offer in a different career andanother in the same careerSeparate from firm exogenously at rate pf

When that happens with additional probablity pc he mayalso have to switch career

Value Function

This gives the value function

V(h1, e, θ, ε,Xe)

=δ′Xe + he + θc + εt + log(H∗e )− Ke (H∗e )

+ β(1− pf )VNS(h1, e + 1, θ, ε,Xe+1)

+ βpf pcVSC(h1, e + 1,Xe+1)

+ βpf (1− pc)VSF(h1, e + 1, θXe+1)

Where

VNS(h1, e + 1, θ, ε,Xe+1) = max{E(

V(h1, e + 1, θ′, ε′,Xe) | θ, ε

),

E(

V(h1, e + 1, θ′, ε1,Xe) | θ

)− Cf ,

E (V(h1, e + 1, θ1, ε1,Xe))− Cc}

and

VSC(h1, e + 1,Xe+1) =E (V(h1, e + 1, θ1, ε1,Xe))− Cc

VSF(h1, e + 1, θXe+1) = max{E(

V(h1, e + 1, θ′, ε1,Xe) | θ

)− Cf ,

E (V(h1, e + 1, θ1, ε1,Xe))− Cc}

Estimation

Pavan solves this model by Maximum Likelihood

(Much much easier said than done, see his paper for details)

Wage Decompositions

The model is complicated

To understand it better Pavan does three different wage growthdecompositions

Remember that we can write

log(wect) =δ′Xe + he + θc + εt

The X′s he uses don’t change over time so

log(we+1c′t′)− log(wect)

=he+1 − he + θc′ − θc + εt′ − εt

=he+1 − he + (θc′ − θc) 1(c′ = c + 1

)+ (θc′ − θc) 1

(c′ = 1

)+

+ (εt′ − εt) 1(t′ = t + 1) + (εt′ − εt) 1(t′ = 1)

=he+1 − he + (µθ + α1(h1 − µh1) + uθc) 1(c′ = c + 1

)+ (θ1 − θc) 1

(c′ = 1

)+ (µε + α2(h1 − µh1) + uεt) 1(t′ = t + 1) + (ε1 − εt) 1(t′ = 1)

(there is a typo in the paper)

Do this decomposition for three different cases

1 People who stay at the same job2 People who stay in the same career3 Everyone

Altonji and Shakatko approach

This suggests there is a return to firm tenure, but Altonji andShakotko didn’t

So what is the reason?

Pavan simulates data from his model and repeats theprocedure on the simulated data

This suggests that this is not a good way to do this and wereally need structural models