ECON280D
Lecture 4: Dynamics
Cecile Gaubert
U.C. Berkeley
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Migrations
I
So far, static models of the crosssection
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Some questions are inherently dynamic:
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How long/costly is it for the economy to reach a new steady state after a
shock ? Total welfare impact, including transition
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What are the frictions to migrations, and spatial reallocation ?
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Does the spatial organization of economic activity matter for
growth
?
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This lecture: papers and modeling tools that tackle spatial questions in a
dynamic context
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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First, a detour
Artuc, Chaudhuri, MacLaren, AER 2010
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Trade Shocks and Labor Adjustment: A Structural Empirical Approach
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Key question: what are the welfare gains from opening to trade when there
are costs/frictions to the reallocation of workers between sectors ?
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How long does it take for factors to reallocate
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What are the welfare gains/losses accounting for transitional dynamics
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What is their distribution across groups ; are gains equalized?
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Strategy: write down a tractable dynamic model with simple estimating
equations
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Note  this paper has no cities/regions. It studies frictions to reallocation
between sectors.
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But the framework can be directly adapted to tackle spatial questions,
modeling regions instead of sectors and frictions to moving between regions.
See e.g. Caliendo, Dvorkin and Parro (2017) and Problem Set.
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Preliminary observations
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The data shows a high level of gross flows of workers between sectors, an
order of magnitude higher than net flows
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Changes taking place two ways: people are moving in to declining sectors
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Idiosyncratic motives for changing sector, beyond arbitraging wage
differences
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Model will capture these gross flows
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Gross flows between sectors
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Gross and Net flows
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Model: labor supply
Artuc, Chaudhuri, MacLaren, AER 2010
I
N sectors
i
∈
1
...
N
in the economy
Timing:
1.
Each worker
ω
starts a period
t
in some sector
i
2.
Earns wage
w
i
t
3.
Then decides whether to stay or move.
I
Each period, observes his vector of iid benefits of being in each sector
j
∈
1
..
N
,
ε
(
ω
)
t
=
{
ε
(
ω
)
j
t
}
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Observing these shocks, a worker can decide to stay and collect
ε
(
ω
)
i
t
...
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... or move to another sector
j
, get benefit
ε
(
ω
)
j
t
, and start next period in
sector
j
4.
When moving: incurs a moving cost
C
ij
of moving from
i
to
j
, with
C
ii
= 0.
So overall cost of moving can be thought of as
C
ij
+
ε
(
ω
)
j
t

ε
(
ω
)
i
t
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Model: labor supply
Artuc, Chaudhuri, MacLaren, AER 2010
I
At time
t
,
L
i
t
workers in sector
i
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Discount rate
β
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State of the economy at time
t s
t
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Rational expectations
ECON280D. Spring 2019. C. Gaubert
Lecture 4

Dynamics
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Utility
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Utility of a worker in period
t
and sector
i
:
U
i
t
=
w
i
t
+
max
j
∈
1
..
N
{
ε
j
t

C
ij
+
β
E
t
(
V
j
t
+1
)
}
I
where
V
j
t
+1
=
E