Smith suggested that the size of the market determines the extent of specialization. Is this the case of workers? Using a modified version of the Walesiak index (1999) to measure specialization, I explore whether workers in areas with more workers on the same occupation are more likely to specialize.
1. Task specialization and size of the market
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
Task specialization and size of the market
2. Task specialization and size of the market
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?
van der Velde Warsaw School of Economics
Task specialization and size of the market
3. Task specialization and size of the market
Introduction
Motivation
Previous analysis
Literature on the task content of job
ā Workersā exposure to automation varies by tasks they perform
(Autor et al, 2003; Autor et al, 2006, Acemoglu and Autor, 2011)
ā ā Wage inequality within occupations
Social skills
ā Social skills help to explain wage diļ¬erences ā role of exchange?
(Deming, 2017)
Our intended contribution
Explain diļ¬erences in tasks performed by workers within occupation
Heterogeneity analysis
van der Velde Warsaw School of Economics
Task specialization and size of the market
4. Task specialization and size of the market
Introduction
A token model of trade of tasks
Each occupation i has a production function that combines R tasks
Yi = (
r in Ri
Ī²r TĻ
r dr)1/Ļ
Workers produces tasks according to their ability Ī±j,r and the time spent
on that task lj,r
Tr = Ī±j,r ā lj,r
Time constraint: r in Ri
lj,r dr = L
van der Velde Warsaw School of Economics
Task specialization and size of the market
5. Task specialization and size of the market
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-oļ¬ is the amount produced Yi
van der Velde Warsaw School of Economics
Task specialization and size of the market
6. Task specialization and size of the market
Introduction
A token model of trade of tasks
Trade scenario
Expected pay-oļ¬ in occupation i for a worker j is given by
E(Yi,j ) = (1 ā Īøi ) ā (Yi,j ((1 ā cj )L)) + Īøi E(Ļj,k Yi,jk ((1 ā cj )L, (1 ā ck )L)))
where
cj L represents the time spent ļ¬nding a partner
Īøi is the probability of ļ¬nding a partner.
Ļj,k is the share of total output that corresponds to worker j.
Ļ =
Yi,j ((1ācj )L)
Yi,j ((1ācj )L)+Yi,k ((1āck )L)
van der Velde Warsaw School of Economics
Task specialization and size of the market
7. Task specialization and size of the market
Introduction
The workersā problem formalized
A worker engages in trade only if
E(solo) ā¤ E(trade)
Solving
E(solo) ā¤E(trade)
Yi,j (L) ā¤(1 ā Īøi )Yi,j ((1 ā cj )L) + Īøi E(Ļj,k Yi,jk ((1 ā cj )L, (1 ā ck )L))
Yi,j (L) ā¤(1 ā Īøi )Yi,j ((1 ā cj )L) + Īøi E(
Yi,j ((1 ā cj )L)
Yi,j ((1 ā cj )L) + Yi,k ((1 ā cj )L)
Yi,jk ((1 ā cj )L, (1 ā c
Yi,j (L) ā¤(1 ā Īøi )(1 ā cj )Yi,j (L) + Īøi (1 ā cj )Yi,j (L)E(
Yi,jk ((1 ā cj )L, (1 ā ck )L)
Yi,j ((1 ā cj )L) + Yi,k ((1 ā ck )L)
)
1 ā¤(1 ā Īøi )(1 ā cj ) + Īøi (1 ā cj )E(
Yi,jk ((1 ā cj )L, (1 ā ck )L)
Yi,j ((1 ā cj )L) + Yi,k ((1 ā ck )L)
)
Let b denote the gains of exchange
Yi,jk ((1ācj )L,(1āck )L)
Yi,j ((1ācj )L)+Yi,k ((1āck )L)
van der Velde Warsaw School of Economics
Task specialization and size of the market
8. Task specialization and size of the market
Introduction
The workersā problem formalized
Upon rearrangement, a worker will exchange tasks if
Īøi (1 ā cj )(E(bi,j ) ā 1) ā cj ā„ 0
Workers will trade tasks if
cj is low
Īøi is high
E(bi,j ) is high
van der Velde Warsaw School of Economics
Task specialization and size of the market
9. Task specialization and size of the market
Introduction
Towards an empirical speciļ¬cation
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 ā= low cj
2. the density of workers in an occupation in an area ā Īøj
3. the returns to specialization ā E(bi,j )
van der Velde Warsaw School of Economics
Task specialization and size of the market
10. Task specialization and size of the market
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 deļ¬ned using 2-digits ISCO08 codes.
van der Velde Warsaw School of Economics
Task specialization and size of the market
11. Task specialization and size of the market
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
van der Velde Warsaw School of Economics
Task specialization and size of the market
12. Task specialization and size of the market
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 ā information loss.
Build on Walesiakās (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.
van der Velde Warsaw School of Economics
Task specialization and size of the market
13. Task specialization and size of the market
Introduction
Walesiakās Index
distj,k =
1
2
ā(1ā
N
t=1(1(lt.j = lt,k ) ā 1) + J
h=1
N
t=1 sgn(lt,j ā lt,h)sgn(lt,k ā lt,h)
( J
h=1
N
t=1 sgn(lt.j ā lt,k ))2 ā ( J
h=1
N
t=1 sgn(lt.j ā lt,k ))2
)
Elements
N
t=1(1(lt.j = lt,k ) ā 1) sums the diļ¬erence between two workers
J
h=1
N
t=1 sgn(lt.j ā lt,h)sgn(lt,k ā lt,h)
whether workers j, k deviate in the same direction against all workers
( J
h=1
N
t=1 sgn(lt.j ā lt,k ))2 ā ( J
h=1
N
t=1 sgn(lt.j ā lt,k ))2
geometric average of diļ¬erences between j,k and all others
van der Velde Warsaw School of Economics
Task specialization and size of the market
14. Task specialization and size of the market
Introduction
Model operationalization: RHS variables
Remember our condition for exchange in tasks
Īøi (1 ā cj )(E(bi,j ) ā 1) ā cj ā„ 0
We operationalize these variables as follows
1. ĖĪø is proxied by the average share of workers with the same ISCO
code as respondent across ļ¬rms. (Source: EUSES)
2. 1 ā cj is proxied by workersā literacy skills (higher literacy, easier to
communicate). (Source: PIAAC)
3. E(bi,j ) is controlled for using workersā and jobā characteristics.
van der Velde Warsaw School of Economics
Task specialization and size of the market
15. Task specialization and size of the market
Results
Main speciļ¬cation
We estimate the following regression
distj,i,c = Ī²0 + Ī²1
ĖĪøi,c + Ī²2
Ė(1 ā c)j + X Ī² + Ī³i + Ī³c + j
where
disti,j,c is the measure of specialization (based on Walesiak index)
ĖĪøi,c is a measure of the probability to ļ¬nd a trading partner
(1 ā c)j measures costs of ļ¬nding a partner
X Ī² worker characteristics
Ī³i , Ī³c Occupation and country ļ¬xed eļ¬ects
van der Velde Warsaw School of Economics
Task specialization and size of the market
16. Task specialization and size of the market
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 ļ¬xed eļ¬ects. 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 ļ¬rm, and whether it is a public worker. ***, **, * denote signiļ¬cance at
the 1%, 5% and 10% level.
van der Velde Warsaw School of Economics
Task specialization and size of the market
17. Task specialization and size of the market
Results
Non-linear eļ¬ects
Is the relation between specialization and ĖĪøi,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: Speciļ¬cation is the same as Table 1 Column 4, but including the square of ĖĪø
van der Velde Warsaw School of Economics
Task specialization and size of the market
18. Task specialization and size of the market
Results
Results by occupation
Share of workers with same title
Point estimates and 90% CI
Weak relation - signiļ¬cant only in some occupations
No clear pattern for correlation
Notes: Speciļ¬cation is the same as Table 1 Column 4 estimated within each occupation with 50+
workers in the sample
van der Velde Warsaw School of Economics
Task specialization and size of the market
19. Task specialization and size of the market
Results
Results by occupation
Literacy skills
Negative correlation for high/medium skill occupations
No or positive corrrelation for low skill occupations
Notes: Speciļ¬cation is the same as Table 1 Column 4 estimated within each occupation with 50+
workers in the sample
van der Velde Warsaw School of Economics
Task specialization and size of the market
20. Task specialization and size of the market
Results
Alternative proxy for the probability of ļ¬nding 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 ļ¬xed eļ¬ects. 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 ļ¬rm, and whether it is a
public worker. ***, **, * denote signiļ¬cance at the 1%, 5% and 10% level.
van der Velde Warsaw School of Economics
Task specialization and size of the market
21. Task specialization and size of the market
Summmary
Summary
We presented a model where workers choose and exchange tasks
gains of excange comes from specialization ā can potentially explain
dispersion in tasks.
We tested the model using PIAAC and SES data
Use a measure based on Walesiakās Indexs to capture specialization
We also proxy for the probability of ļ¬nding a suitable partner and the
skill level
Results were mostly against the predictions of the model
van der Velde Warsaw School of Economics
Task specialization and size of the market
22. Task specialization and size of the market
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 (Ī± in our model)
Possible solution: look at other measures of friction.
van der Velde Warsaw School of Economics
Task specialization and size of the market
23. Task specialization and size of the market
Summmary
Thank you for you attentionl
Lucas van der Velde
Contact: lvandervelde@grape.org.pl
lvelde@sgh.waw.pl
van der Velde Warsaw School of Economics
Task specialization and size of the market