Task specialization and market size

Task specialization and size of the market
Evidence from the PIAAC
Lucas van der Velde
Warsaw School of Economics
March 2019
van der Velde Warsaw School of Economics

Introduction
Introduction
As it is the power of exchanging that gives occasion to the division
of labour, so the extent of this division must always be limited
by the extent of that power, or, in other words, by the extent of
the market.
A. Smith (1776)
Research questions
1. Does the division of labour operate within occupations?
2. What drives task heterogeneity within occupations?

Introduction
Motivation
Previous analysis
Literature on the task content of job
→ Workers’ exposure to automation varies by tasks they perform
(Autor et al, 2003; Autor et al, 2006, Acemoglu and Autor, 2011)
→ ↑ Wage inequality within occupations
Social skills
→ Social skills help to explain wage diﬀerences → role of exchange?
(Deming, 2017)
Our intended contribution
Explain diﬀerences in tasks performed by workers within occupation
Heterogeneity analysis

Introduction
A token model of trade of tasks
Each occupation i has a production function that combines R tasks
Yi = (
r in Ri
βr Tρ
r dr)1/ρ
Workers produces tasks according to their ability αj,r and the time spent
on that task lj,r
Tr = αj,r ∗ lj,r
Time constraint: r in Ri
lj,r dr = L

Introduction
A token model of exchange of tasks
Worker starts each period alone and decides
1. To search for a partner or not
2. How much labor to supply to each task
No exchange scenario
Workers pay-oﬀ is the amount produced Yi

Introduction
A token model of trade of tasks
Trade scenario
Expected pay-off in occupation i for a worker j is given by
E(Yi,j ) = (1 − θi ) ∗ (Yi,j ((1 − cj )L)) + θi E(φj,k Yi,jk ((1 − cj )L, (1 − ck )L)))
where
cj L represents the time spent finding a partner
θi is the probability of finding a partner.
φj,k is the share of total output that corresponds to worker j.
φ =
Yi,j ((1−cj )L)
Yi,j ((1−cj )L)+Yi,k ((1−ck )L)

Introduction
The workers’ problem formalized
A worker engages in trade only if
E(solo) ≤ E(trade)
Solving
E(solo) ≤E(trade)
Yi,j (L) ≤(1 − θi )Yi,j ((1 − cj )L) + θi E(φj,k Yi,jk ((1 − cj )L, (1 − ck )L))
Yi,j (L) ≤(1 − θi )Yi,j ((1 − cj )L) + θi E(
Yi,j ((1 − cj )L)
Yi,j ((1 − cj )L) + Yi,k ((1 − cj )L)
Yi,jk ((1 − cj )L, (1 − c
Yi,j (L) ≤(1 − θi )(1 − cj )Yi,j (L) + θi (1 − cj )Yi,j (L)E(
Yi,jk ((1 − cj )L, (1 − ck )L)
Yi,j ((1 − cj )L) + Yi,k ((1 − ck )L)
)
1 ≤(1 − θi )(1 − cj ) + θi (1 − cj )E(
Yi,jk ((1 − cj )L, (1 − ck )L)
Yi,j ((1 − cj )L) + Yi,k ((1 − ck )L)
)
Let b denote the gains of exchange
Yi,jk ((1−cj )L,(1−ck )L)
Yi,j ((1−cj )L)+Yi,k ((1−ck )L)

Introduction
The workers’ problem formalized
Upon rearrangement, a worker will exchange tasks if
θi (1 − cj )(E(bi,j ) − 1) − cj ≥ 0
Workers will trade tasks if
cj is low
θi is high
E(bi,j ) is high

Introduction
Towards an empirical speciﬁcation
In model, gains from trade arise due to specialization
Specialization will be the empirical proxy for trade in tasks
Specialization will increase with
1. social skills →= low cj
2. the density of workers in an occupation in an area → θj
3. the returns to specialization → E(bi,j )

Introduction
Data and method
Program for the International Assessment of Adult Competencies
Survey on skills and tasks collected in 2008-2016
Around 93000 observations from 22 countries
40+ variables describing tasks
Structure of Earnings Survey
Linked employee-employer data for EU countries
+ large sample size, detailed account of occupations
We use waves 2010 - 2014
Occupations are deﬁned using 2-digits ISCO08 codes.

Introduction
Data and method: On the task content of jobs
Which tasks...?
Follow Lewandowski et al (2018)
Data-driven approach to replicate O*NET measures in PIAAC
Characterize occupations in routine, non-routine and skill use.
Tasks
Routine Non-R. Analytical Non-R. Personal Manual
Filling forms Reading news Supervising Physical tasks
Change order of tasks reading professional titles Presenting
Solving problems
Programming

Introduction
Data and method: Measuring specialization
Task data are measured on ordinal scale
Eg. How often did you perform task t? Never, ..., Every day
Lewandowski et al (2018) dichotomize variables → information loss.
Build on Walesiak’s (1999) index
Measures distance between two jobs based on ordinal variables
It uses information only on the relation >, <, = between responses
Specialization = average distance to all other workers in occupation
i in the country j.

Introduction
Walesiak’s Index
distj,k =
1
2
∗(1−
N
t=1(1(lt.j = lt,k ) − 1) + J
h=1
N
t=1 sgn(lt,j − lt,h)sgn(lt,k − lt,h)
( J
h=1
N
t=1 sgn(lt.j − lt,k ))2 ∗ ( J
h=1
N
t=1 sgn(lt.j − lt,k ))2
)
Elements
N
t=1(1(lt.j = lt,k ) − 1) sums the diﬀerence between two workers
J
h=1
N
t=1 sgn(lt.j − lt,h)sgn(lt,k − lt,h)
whether workers j, k deviate in the same direction against all workers
( J
h=1
N
t=1 sgn(lt.j − lt,k ))2 ∗ ( J
h=1
N
t=1 sgn(lt.j − lt,k ))2
geometric average of diﬀerences between j,k and all others

Introduction
Model operationalization: RHS variables
Remember our condition for exchange in tasks
θi (1 − cj )(E(bi,j ) − 1) − cj ≥ 0
We operationalize these variables as follows
1. ˆθ is proxied by the average share of workers with the same ISCO
code as respondent across ﬁrms. (Source: EUSES)
2. 1 − cj is proxied by workers’ literacy skills (higher literacy, easier to
communicate). (Source: PIAAC)
3. E(bi,j ) is controlled for using workers’ and job’ characteristics.

Results
Main specification
We estimate the following regression
distj,i,c = β0 + β1
ˆθi,c + β2
ˆ(1 − c)j + X β + γi + γc + j
where
disti,j,c is the measure of specialization (based on Walesiak index)
ˆθi,c is a measure of the probability to find a trading partner
(1 − c)j measures costs of finding a partner
X β worker characteristics
γi , γc Occupation and country fixed effects

Results
Initial regressions
(1) (2) (3) (4)
Share Firm -0.0058*** -0.0029*** -0.0031*** -0.0048***
(0.001) (0.001) (0.001) (0.001)
Literacy skills -0.0031*** -0.0056*** -0.0049*** -0.0051***
(0.000) (0.000) (0.000) (0.000)
Occupation FE Y Y Y
Individual Y Y
Job Y
N obs. 29,238 29,238 29,238 29,238
R2
0.008 0.042 0.048 0.052
Notes: all regressions include country fixed effects. Robust standard errors pre-
sented in parenthesis. Individual includes controls for age, gender, education
level, marital status. Jobs includes additional controls for industry (4 codes), size
of the firm, and whether it is a public worker. ***, **, * denote significance at
the 1%, 5% and 10% level.

Results
Non-linear eﬀects
Is the relation between specialization and ˆθi,c non-linear?
Predicted values and 90% CI
Perhaps, but...
Non-linearities appear for values close to 1. (p.75=0.626)
More of a plateau than a genuine increase.
Notes: Speciﬁcation is the same as Table 1 Column 4, but including the square of ˆθ

Results
Results by occupation
Share of workers with same title
Point estimates and 90% CI
Weak relation - signiﬁcant only in some occupations
No clear pattern for correlation
Notes: Speciﬁcation is the same as Table 1 Column 4 estimated within each occupation with 50+
workers in the sample

Results
Results by occupation
Literacy skills
Negative correlation for high/medium skill occupations
No or positive corrrelation for low skill occupations
Notes: Speciﬁcation is the same as Table 1 Column 4 estimated within each occupation with 50+
workers in the sample

Results
Alternative proxy for the probability of finding a partner
(1) (2) (3) (4)
Share region -0.0387*** -0.0296*** -0.0321*** -0.0298***
(0.008) (0.010) (0.010) (0.010)
Literacy skills -0.0030*** -0.0056*** -0.0049*** -0.0050***
(0.000) (0.000) (0.000) (0.000)
Occupation FE Y Y Y
Individual Y Y
Job Y
N obs. 29,238 29,238 29,238 29,238
R2
0.009 0.044 0.050 0.053
Notes: all regressions include country fixed effects. Robust standard errors presented in
parenthesis. Individual includes controls for age, gender, education level, marital status.
Jobs includes additional controls for industry (4 codes), size of the firm, and whether it is a
public worker. ***, **, * denote significance at the 1%, 5% and 10% level.

Summmary
Summary
We presented a model where workers choose and exchange tasks
gains of excange comes from specialization → can potentially explain
dispersion in tasks.
We tested the model using PIAAC and SES data
Use a measure based on Walesiak’s Indexs to capture specialization
We also proxy for the probability of ﬁnding a suitable partner and the
skill level
Results were mostly against the predictions of the model

Summmary
Next steps
What went wrong?
Model construction
Shortcoming: Model assummes workers exchange in vacuum
Possible solution: Introduce an employer who can extract rents (and
whose bargaining power depends on how substitutable a worker is)
Measuring specialization
Shortcoming: Is Walesiak index a good measure of specialization?
Possible solution: Simulate workers whose decisions follow the model
structure and apply index to the simulated data.
Other proxies
Shortcoming: Literacy and other skills could also proxy for innate
ability (α in our model)
Possible solution: look at other measures of friction.

Summmary
Thank you for you attentionl
Lucas van der Velde
Contact: lvandervelde@grape.org.pl
lvelde@sgh.waw.pl

Task specialization and market size

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