Thorough structural change occurs periodically across world economies. In a parsimonious overlapping generation setup with political economy, we present a novel result: structural change not only exacerbates the rise in inequality but it also strengthens preference for redistribution. Labor mobility frictions are instrumental in this mechanism.

1. Preference for redistribution during structural change with labor mobility frictions
Krzysztof Makarski (FAME|GRAPE and Warsaw School of Economics)
Joanna Tyrowicz (FAME|GRAPE, University of Regensburg, and IZA)
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2. Motivation

3. Motivation
Economies undergo deep structural change
• When we can “time” the beginning of the change, then data show
• gradual change in employment structure ...
2

4. Motivation
Economies undergo deep structural change
• When we can “time” the beginning of the change, then data show
• gradual change in employment structure ...
• ... and immediate, hump-shaped adjustment in wages
3

5. Motivation
Economies undergo deep structural change
• When we can “time” the beginning of the change, then data show
• gradual change in employment structure ...
• ... and immediate, hump-shaped adjustment in wages
• Theoretical models so far mostly assume perfect labor mobility, thus:
• immediate adjustment in wages
• effects for aggregate dynamics, but no for inequality
4

6. Motivation
Economies undergo deep structural change
• When we can “time” the beginning of the change, then data show
• gradual change in employment structure ...
• ... and immediate, hump-shaped adjustment in wages
• Theoretical models so far mostly assume perfect labor mobility, thus:
• immediate adjustment in wages
• effects for aggregate dynamics, but no for inequality
• Meanwhile, empirical research finds:
• substantial changes in inequality (Milanovic, 2013; Smyk & Tyrowicz, 2019)
• employment change due to demographics rather than worker flows Tyrowicz & van der Velde, 2018)
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7. Motivation
Economies undergo deep structural change
• When we can “time” the beginning of the change, then data show
• gradual change in employment structure ...
• ... and immediate, hump-shaped adjustment in wages
• Theoretical models so far mostly assume perfect labor mobility, thus:
• immediate adjustment in wages
• effects for aggregate dynamics, but no for inequality
• Meanwhile, empirical research finds:
• substantial changes in inequality (Milanovic, 2013; Smyk & Tyrowicz, 2019)
• employment change due to demographics rather than worker flows Tyrowicz & van der Velde, 2018)
Our approach: labor mobility frictions + OLG
• study the effects of structural change on inequality
• study the consequences for redistribution (median voter preferences)
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8. Preview of results
• Stylized model: structural change necessitates reallocation of labor from manufacturing to services.
• Overlapping generations
• Imperfect labor mobility slows down the reallocation process
• Wages in services are higher than in manufacturing
• The distance between the median and average wage increases
• Median voter prefers more redistribution
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9. Literature
• Empirical literature on structural and technological change
Barany and Siegel (2018), Yashiro et. al. (2020), Dauth et. al. (2021), Tyrowicz and van der Velde (2018)
• Literature on reallocation in an economy experiencing exogenous productivity shocks in GE economy
with perfect labor mobility
Hansen and Prescott (2002), Ngai and Pissarides (2007b), Duarte and Restuccia (2010), Buera and Kaboski (2012)
• Literature on labor market frictions
Mortensen and Pissarides (1998), Pissarides and Vallanti (2007), Miyamoto and Takahashi (2011)
• Political economy of redistribution starting with seminal paper by Meltzer and Richard (1981)
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10. The Model

11. Assumptions
• Standard Blanchard-Yaari model with constant mortality rate, ρ, Nt = 1
• Two production sectors κ ∈ {m, s}
• New workers randomly assigned to sector with probability = shares in employment in t − 1
• Each new worker can change the sector after incurring idiosyncratic mobility cost ⇒ in equilibrium,
w̄s,t ≥ w̄m,t
• Older workers cannot change sectors, we denote employment in κ as Nκ,t
• Each new worker draws idiosyncratic productivity ω
• from monomodal distribution
• with ωmod < median ωmed < ω̄ = 1 (normalization)
• Assumption 1 max{wmod
s,t , wmod
m,t } < min{wmed
s,t , wmed
m,t }
similar approach Walker (2011); Sim & Oh (2017)
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12. Firms
• Both sectors are perfectly competitive with CRS technology Yκ,t = Aκ,t Lκ,t
• Thus, wages w̄κ,t = pκ,t Aκ,t , where pκ,t price of κ sector output
• pm,t normalized to 1
• Productivity Aκ,t evolves as follows Aκ,t = γκ,t Aκ,t−1
• with γm,t > γs,t (supported empirically)
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13. Consumers
• Preferences of consumer working in sector κ with productivity ω given by
X
t
(βρ)t
{ϑ(cκ
s,t (ω))
ε−1
ε + (1 − ϑ)(cκ
m,t (ω))
ε−1
ε }
ε
ε−1
where cκ
s,t denotes consumption of services and cκ
m,t manufacturing
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14. Consumers
• Preferences of consumer working in sector κ with productivity ω given by
X
t
(βρ)t
{ϑ(cκ
s,t (ω))
ε−1
ε + (1 − ϑ)(cκ
m,t (ω))
ε−1
ε }
ε
ε−1
where cκ
s,t denotes consumption of services and cκ
m,t manufacturing
• Budget constraint
ps,t cκ
s,t (ω) + cκ
m,t (ω) = (1 − τt )ωw̄κ,t − τ2
t Γωw̄κ,t + mt
where τ ≥ 0 tax rate, τ2
t Γωw̄κ,t nonlinear cost of taxation (Alesina & Giuliano, 2011), mt - lump sum
transfer
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15. Consumers
• Preferences of consumer working in sector κ with productivity ω given by
X
t
(βρ)t
{ϑ(cκ
s,t (ω))
ε−1
ε + (1 − ϑ)(cκ
m,t (ω))
ε−1
ε }
ε
ε−1
where cκ
s,t denotes consumption of services and cκ
m,t manufacturing
• Budget constraint
ps,t cκ
s,t (ω) + cκ
m,t (ω) = (1 − τt )ωw̄κ,t − τ2
t Γωw̄κ,t + mt
where τ ≥ 0 tax rate, τ2
t Γωw̄κ,t nonlinear cost of taxation (Alesina & Giuliano, 2011), mt - lump sum
transfer
• In equilibrium
cm,t
cs,t
= (ps,t )ε
(
1 − ϑ
ϑ
)ε
with γm,t > γs,t , for ε ∈ (0, 1), share of services increases with time
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16. Model closure
• The government redistributes, i.e. collects taxes to finance lump sum transfer
mt = τt
X
κ∈{m,s}
Nκ,t w̄κ,t
thus the government is described by a single variable τ
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17. Model closure
• The government redistributes, i.e. collects taxes to finance lump sum transfer
mt = τt
X
κ∈{m,s}
Nκ,t w̄κ,t
thus the government is described by a single variable τ
• Markets clear
• labor market Lκ,t = Nκ,t
R
ωdµ(ω)
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18. Model closure
• The government redistributes, i.e. collects taxes to finance lump sum transfer
mt = τt
X
κ∈{m,s}
Nκ,t w̄κ,t
thus the government is described by a single variable τ
• Markets clear
• labor market Lκ,t = Nκ,t
R
ωdµ(ω)
• and goods market cκ,t + τ2
t Γt Yκ,t = Yκ,t
where cκ,t = Nm,t
R
cm
κ,t (ω)dµ(ω) + Ns,t
R
cs
κ,t (ω)dµ(ω)
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19. Competitive equilibrium
Competitive equilibrium is an allocation {(cκ
s,t (ω), cκ
m,t (ω))ω∈Ω,κ∈{m,s}, Ym,t , Ys,t , Nm,t , Ns,t , Lm,t , Ls,t }∞
t=0,
prices {ps,t , w̄m,t , w̄s,t }∞
t=0 and idiosyncratic productivity distribution µ(ω) satisfying
• {(cκ
s,t (ω), cκ
m,t (ω))}∞
t=0 maximizes utility subject to the budget constraint
• wages in services relative to manufacturing are given by w̄s,t = w̄m,t + %̄t
• wages in each sector are given by the value of MPL: w̄κ,t = pκ,t Aκ,t
• government budget is balanced
• markets clear
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20. Results

21. Labor market
Proposition
Let ε ∈ (0, 1), Nm,t−1 ≥ Ñm,t−1 and γm,t > γs,t . Labor reallocates from manufacturing to services,
Nm,t < Nm,t−1. Labor mobility frictions slow down this reallocation, Nm,t − Nm,t−1 > Ñm,t − Nm,t−1.
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22. Labor market
Proposition
Let ε ∈ (0, 1), Nm,t−1 ≥ Ñm,t−1 and γm,t > γs,t . Labor reallocates from manufacturing to services,
Nm,t < Nm,t−1. Labor mobility frictions slow down this reallocation, Nm,t − Nm,t−1 > Ñm,t − Nm,t−1.
Sketch of the proof With perfect labor mobility
Nm,t
(1−Nm,t )
= (
As,t
Am,t
)1−ε
(1−ϑ
ϑ
)ε
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23. Labor market
Proposition
Let ε ∈ (0, 1), Nm,t−1 ≥ Ñm,t−1 and γm,t > γs,t . Labor reallocates from manufacturing to services,
Nm,t < Nm,t−1. Labor mobility frictions slow down this reallocation, Nm,t − Nm,t−1 > Ñm,t − Nm,t−1.
Sketch of the proof With perfect labor mobility
Nm,t
(1−Nm,t )
= (
As,t
Am,t
)1−ε
(1−ϑ
ϑ
)ε
=⇒ decline of As,t /Am,t lowers Nm,t ⇒ imperfect mobility slows down this process.
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24. Labor market
Proposition
Suppose the economy is going through structural change with imperfect labor mobility
ε ∈ (0, 1), Nm,t−1 > Ñm,t−1, γm,t > γs,t , then:
• wages in services are higher than in manufacturing w̄s,t > w̄m,t ,
• relative price of services is higher than with perfect labor mobility ps,t > p̃s,t = Am,t /As,t .
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25. Labor market
Proposition
Suppose the economy is going through structural change with imperfect labor mobility
ε ∈ (0, 1), Nm,t−1 > Ñm,t−1, γm,t > γs,t , then:
• wages in services are higher than in manufacturing w̄s,t > w̄m,t ,
• relative price of services is higher than with perfect labor mobility ps,t > p̃s,t = Am,t /As,t .
Sketch of the proof With perfect labor mobility p̃s,t = Am,t /As,t .
Mobility frictions slow down labor reallocation Nm,t < Ñm,t , thus production of services is lower which
raises price of services ps,t > p̃s,t = Am,t /As,t .
Since wages are perfectly competitive w̄s,t = ps,t As,t > Am,t = w̄m,t .
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26. Labor market
Proposition
Suppose the economy is going through structural change with imperfect labor mobility
ε ∈ (0, 1), Nm,t−1 > Ñm,t−1, γm,t > γs,t , then:
• wages in services are higher than in manufacturing w̄s,t > w̄m,t ,
• relative price of services is higher than with perfect labor mobility ps,t > p̃s,t = Am,t /As,t .
Sketch of the proof With perfect labor mobility p̃s,t = Am,t /As,t .
Mobility frictions slow down labor reallocation Nm,t < Ñm,t , thus production of services is lower which
raises price of services ps,t > p̃s,t = Am,t /As,t .
Since wages are perfectly competitive w̄s,t = ps,t As,t > Am,t = w̄m,t .
=⇒ wages in service sector remain higher than in manufacturing
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27. Implications for indirect utility over policy
• Individual welfare is fully characterized by consumption = income ⇒ infer indirect utility from budget
constraint
(1 − τt )ωκw̄κ,t − τ2
t Γωk w̄κ,t + mt
• substituting for mt from budget constrain we obtain indirect utility over policy τt
W (τt , ωκw̄κ,t ) = ωκw̄κ,t − τ2
t Γωκw̄κ,t
| {z }
distortion
+ τt (
X
κ
Nκ,t w̄κ,t − ωκw̄κ,t )
| {z }
redistribution
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28. Preference towards redistribution: tax rate
Proposition
In economy with no structural change or no labor mobility frictions, the tax rate selected in pure majority
voting equals
τ̃t =
ω̄ − ωmed
2Γωmed
> 0
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29. Preference towards redistribution: tax rate
Proposition
In economy with no structural change or no labor mobility frictions, the tax rate selected in pure majority
voting equals
τ̃t =
ω̄ − ωmed
2Γωmed
> 0
Sketch of the proof With single-peaked preferences, the pure majority voting selects median voter
preferred policy.
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30. Preference towards redistribution: tax rate
Proposition
In economy with no structural change or no labor mobility frictions, the tax rate selected in pure majority
voting equals
τ̃t =
ω̄ − ωmed
2Γωmed
> 0
Sketch of the proof With single-peaked preferences, the pure majority voting selects median voter
preferred policy.
=⇒ inequality (distance between average and median) determines the extent of redistribution (tax rate).
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31. Preference towards redistribution: tax rate
Lemma: Suppose Assumption 1 is satisfied w̄s,t 6= w̄m,t implies wmed
t < Nm,t wmed
m,t + Ns,t wmed
s,t
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32. Preference towards redistribution: tax rate
Lemma: Suppose Assumption 1 is satisfied w̄s,t 6= w̄m,t implies wmed
t < Nm,t wmed
m,t + Ns,t wmed
s,t
Proposition
Suppose Assumption 1 is satisfied. In an economy going through structural change with imperfect labor
mobility majority selected tax rate is higher, than in an economy with no structural change (or with perfect
labor mobility).
τt =
(w̄t − wmed
t )
2Γwmed
t
> τ̃t > 0
Sketch of the proof Follows from Lemma. With structural change w̄s,t > w̄m,t and average wage in an
economy is equal weighted average of wages in both sectors, but median is lower than the weighted
average median in sectors. Thus distance between median and average wage (inequality) increases, so does
the tax rate.
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33. Preference towards redistribution: tax rate
Lemma: Suppose Assumption 1 is satisfied w̄s,t 6= w̄m,t implies wmed
t < Nm,t wmed
m,t + Ns,t wmed
s,t
Proposition
Suppose Assumption 1 is satisfied. In an economy going through structural change with imperfect labor
mobility majority selected tax rate is higher, than in an economy with no structural change (or with perfect
labor mobility).
τt =
(w̄t − wmed
t )
2Γwmed
t
> τ̃t > 0
Sketch of the proof Follows from Lemma. With structural change w̄s,t > w̄m,t and average wage in an
economy is equal weighted average of wages in both sectors, but median is lower than the weighted
average median in sectors. Thus distance between median and average wage (inequality) increases, so does
the tax rate.
=⇒ inequality (distance between average and median) is higher with reallocation and labor mobility frictions
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34. Data supports our implications

35. Empirical observations
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36. Summary

37. Our contribution
Study structural change with labor frictions
• Main features: model that fits the empirical regularities
• Main implications: reallocation leads to more redistribution
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38. Our contribution
Study structural change with labor frictions
• Main features: model that fits the empirical regularities
• Main implications: reallocation leads to more redistribution
Limitations:
• GE setup is parsimonious, some channels are not operational
• Key mechanism: wmed
t < Nm,t wmed
m,t + Ns,t wmed
s,t
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39. Our contribution
Study structural change with labor frictions
• Main features: model that fits the empirical regularities
• Main implications: reallocation leads to more redistribution
Limitations:
• GE setup is parsimonious, some channels are not operational
• Key mechanism: wmed
t < Nm,t wmed
m,t + Ns,t wmed
s,t ⇒ are all reallocations made equal?
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40. Questions or suggestions?
Thank you!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
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