Trade and Labor Market Dynamics
Lorenzo Caliendo
Yale University, NBER
Maximiliano Dvorkin
St Louis Fed
Fernando Parro
Federal Reserve Board
March, 2016
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
1 / 24
Introduction
Aggregate trade shocks can have di¤erent disaggregate e¤ects (across
locations, sectors, locations-sectors) depending on
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degree of exposure to foreign trade
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indirect linkages through internal trade, sectoral trade
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labor reallocation process
We develop a model of trade and labor market dynamics that
explicitly recognizes the role of labor mobility frictions, goods mobility
frictions, I-O linkages, geographic factors, and international trade
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
1 / 24
This paper
Models with large # of unknown fundamentals: productivity, mobility
frictions, trade frictions, and more...
Propose a new method to solve dynamic discrete choice models
I
Solve the model and perform large scale counterfactuals without
estimating level of fundamentals
I
By expressing the equilibrium conditions of the model in relative time
di¤erences
Study how China’s import competition impacted U.S. labor markets
I
I
38 countries, 50 U.S. regions, and 22 sectors version of the model
Employment and welfare e¤ects across more than 1000 labor markets
F
F
Employment: approx. 0.8 MM manuf. jobs lost, reallocation to services
Welfare: aggregate gains; very heterogeneous e¤ects across labor
markets; transition costs re‡ect the importance of dynamics
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
2 / 24
Literature
Substantial progress in recent quantitative trade models, including Eaton
and Kortum (2002) and its extensions: multiple sectors Caliendo and Parro
(2015), spatial economics Caliendo et al. (2015), and other extensions
Monte (2015), Tombe et al. (2015), Fajgelbaum et.al. (2015), much more
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One limitation is their stylized treatment of the labor market (static
models, labor moves costessly or does not move)
We build on advances that underscore the importance of trade and labor
market dynamics: Artuç and McLaren (2010), Artuç Chaudhuri and
McLaren (2010), Dix-Carneiro (2014)
Relates to dynamic discrete choice models in IO, labor, macro literature Hotz
and Miller (1993), Berry (1994), Kennan and Walker (2011), Dvorkin (2014)
Relates to recent research on the labor market e¤ects of trade
I
Because of direct import exposure: Autor, Dorn and Hanson (2013),
and sectoral linkages: Acemoglu, Autor, Dorn and Hanson (2015),
other channels Handley and Limao (2015) Pierce and Schott (2015)
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
3 / 24
Road map
Model
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Households’dynamic problem
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Production structure
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Equilibrium
Solution method
Application: calibration and results
Conclusion
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
4 / 24
Model
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
5 / 24
Households’problem
N locations (index n and i) and each has J sectors (index j and k)
The value of a household in market nj at time t given by
n h
i
o
nj
ik
nj ,ik
ik
vnj
=
u
(
c
)
+
max
βE
v
τ
+
ν
e
,
t
t
t +1
t
fi ,k giN=,J1,k =0
s.t. u (ctnj )
I
I
I
log(b n )
i f j = 0,
nj
n
log(wt /Pt ) otherwise,
β 2 (0, 1) discount factor
τ nj ,ik additive, time invariant migration costs to ik from nj
eik
t are stochastic i.i.d idiosyncratic taste shocks
F
F
e
Type-I Extreme Value distribution with zero mean
ν > 0 is the dispersion of taste shocks
Unemployed obtain home production b n
Employed households supply a unit of labor inelastically
I
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Receive the competitive market wage w nj
t
k
Consume ctnj = ∏Jk =1 (ctnj ,k )α , where P nt is the local price index
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
6 / 24
Households’problem - Dynamic discrete choice
Using properties of Type-I Extreme Value distributions one obtains:
The expected (expectation over e) lifetime utility of a worker at nj
h
i
J
ik
nj ,ik 1/ν
Vtnj = u (ctnj ) + ν log ∑N
exp
βV
τ
i =1 ∑ k =0
t +1
Fraction of workers that reallocate from market nj to ik
,ik
µnj
t
=
exp βVtik+1
τ nj ,ik
J
mh
∑N
m =1 ∑h =0 exp βVt +1
1/ν
τ nj ,mh
1/ν
.
Evolution of the distribution of labor across markets
ik ,nj ik
N
J
Lnj
Lt
t +1 = ∑ i =1 ∑ k =0 µ t
Frechet and Multiplicative costs
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
7 / 24
Production - Static sub-problem
Notice that at each t, labor supply across markets is fully determined
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We can then solve for wages such that labor markets clear, using a very
rich static spatial structure (CPRHS 2015)
In each nj there is a continuum of intermediate good producers with
technology as in Eaton and Kortum (2002)
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Perfect competition, CRS technology, idiosyncratic productivity
z nj Fréchet(1, θ j ), deterministic sectoral regional TFP Anj
h
n
qtnj (z nj ) = z nj Anj [ltnj ]ξ [htnj ]1
ξn
iγnj
J
∏ [ Mt
nj ,nk γnj ,nk
]
k =1
Each n, j produces a …nal good (for …nal consumption and materials)
I
CES (elasticity η) aggregator of sector j goods from the lowest cost
supplier in the world subject to κ nj ,ij
1 “iceberg” bilateral trade cost
Intermediate goods
Final goods
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
8 / 24
Production - Static sub-problem - Equilibrium conditions
Sectoral price index,
Ptnj (wt ) = Γnj
h
∑
N
i =1
Aij [xtij (wt )κ nj ,ij ]
θj
i
1/θ j
Let Xtij (wt ) be total expenditure. Expenditure shares given by
j
,ij
π nj
(wt ) =
t
[xtij (wt )κ nj ,ij ] θ Aij
,
mj
nj ,mj ] θ j Amj
∑N
m =1 [xt (wt )κ
where xtij (wt ) is the unit cost of an input bundle
Labor Market clearing
Lnj
t =
where γnj (1
γnj (1
ξn )
wtnj
∑i =1 πijt ,nj (wt )Xtij (wt ),
N
ξ n ) labor share
Input bundle
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
9 / 24
Sequential and temporary equilibrium
N ,J
State of the economy = distribution of labor Lt = fLnj
t gn =1,j =0
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Let Θ
fAnj g, fκ nj ,ij g, fτ nj ,ik g, H nj , fbn g
N ,J ,J ,N
n =1,j =0,i =1,k =0
De…nition
Given (Lt , Θ) , a temporary equilibrium is a vector of wt (Lt , Θ) that
satis…es the equilibrium conditions of the static sub-problem
De…nition
Given (L0 , Θ) , a sequential competitive equilibrium of the model is a
sequence of fLt , µt , Vt , wt (Lt , Θ)gt∞=0 that solves HH dynamic problem
and the temporary equilibrium at each t
,ik N ,J ,J ,N
With µt = fµnj
gn =1,j =0,i =1,k =0 , and Vt = fVtnj gNn =,J1,j =0
t
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
10 / 24
Solution Method
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
11 / 24
Solving the model
Solving for an equilibrium of the model requires information on Θ
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Large # of unknowns N + 2NJ + N 2 J + N 2 J 2
Productivity, endowments of local structures, labor mobility costs,
home production, and trade costs
As we increase the dimension of the problem— adding countries,
regions, or sectors— the number of parameters grows geometrically
We solve this problem by computing the equilibrium dynamics of the
model in time di¤erences
Why is this progress?
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As in DEK (2008), Caliendo and Parro (2015), by conditioning on
observables one can solve the model without knowing the levels of Θ
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We apply this idea to a dynamic economy
Condition on last period migration ‡ows, trade ‡ows, and production
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Solve for the value function in time di¤erences
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
12 / 24
Equilibrium conditions
Expected lifetime utility
N
nj
J
Vtnj = log( wPtn ) + ν log ∑ ∑ exp βVtik+1
t
τ nj ,ik
1/ν
i =1 k =0
Transition matrix (migration ‡ows)
,ik
µnj
t
=
exp βVtik+1
N
J
∑ ∑
m =1 h =0
Caliendo, Dvorkin, and Parro (2015)
τ nj ,ik
exp βVtmh
+1
Trade and Labor
() Markets Dynamics
1/ν
τ nj ,mh
1/ν
March, 2016
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Equilibrium conditions
Transition matrix (migration ‡ows) at t =
µnj1,ik
=
exp βV0ik
N
J
∑ ∑
m =1 h =0
Caliendo, Dvorkin, and Parro (2015)
1, Data
τ nj ,ik
exp βV0mh
1/ν
τ nj ,mh
Trade and Labor
() Markets Dynamics
1/ν
March, 2016
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Equilibrium conditions
Transition matrix (migration ‡ows) at t =
µnj1,ik
=
1, Data
exp βV0ik
N
J
∑ ∑
m =1 h =0
τ nj ,ik
exp βV0mh
1/ν
τ nj ,mh
1/ν
Transition matrix (migration ‡ows) at t = 0, Model
,ik
µnj
0
=
exp βV1ik
N
J
∑ ∑
m =1 h =0
Caliendo, Dvorkin, and Parro (2015)
τ nj ,ik
exp βV1mh
1/ν
τ nj ,mh
Trade and Labor
() Markets Dynamics
1/ν
March, 2016
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Equilibrium conditions
Transition matrix (migration ‡ows) at t =
µnj1,ik
=
1, Data
exp βV0ik
N
J
∑ ∑
m =1 h =0
τ nj ,ik
exp βV0mh
1/ν
τ nj ,mh
1/ν
Transition matrix (migration ‡ows) at t = 0, Model
,ik
µnj
0
=
exp βV1ik
N
J
∑ ∑
m =1 h =0
τ nj ,ik
exp βV1mh
1/ν
τ nj ,mh
1/ν
Take the time di¤erence
,ik
µnj
0
µnj1,ik
=
Caliendo, Dvorkin, and Parro (2015)
J
∑N
m =1 ∑ h =0
exp ( βV 1ik τ nj ,ik )
1/ν
exp ( βV 0ik τ nj ,ik )
1/ν
exp ( βV 1mh τ nj ,mh )
∑N
m 0 =1
∑Jh 0 =0
exp (
0 0
βV 0m h
Trade and Labor
() Markets Dynamics
1/ν
τ nj ,m
0 h 0 1/ν
)
March, 2016
9 / 24
Equilibrium conditions
Take the time di¤erence
,ik
µnj
0
nj ,ik
µ 1
=
Caliendo, Dvorkin, and Parro (2015)
J
∑N
m =1 ∑ h =0
exp ( βV 1ik τ nj ,ik )
1/ν
exp (
1/ν
βV 0ik
τ nj ,ik
exp (
∑N
m 0 =1
∑Jh 0 =0
)
βV 1mh
exp (
τ nj ,mh )
0 0
βV 0m h
Trade and Labor
() Markets Dynamics
1/ν
τ nj ,m
0 h 0 1/ν
)
March, 2016
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Equilibrium conditions
Take the time di¤erence
,ik
µnj
0
nj ,ik
µ 1
=
J
∑N
m =1 ∑ h =0
exp ( βV 1ik τ nj ,ik )
1/ν
exp (
1/ν
βV 0ik
τ nj ,ik
exp (
∑N
m 0 =1
∑Jh 0 =0
)
βV 1mh
exp (
τ nj ,mh )
0 0
βV 0m h
1/ν
τ nj ,m
0 h 0 1/ν
)
Simplify
,ik
µnj
0
µnj1,ik
exp V1ik
=
Caliendo, Dvorkin, and Parro (2015)
J
∑N
m =1 ∑ h =0
V0ik
β/ν
exp ( βV 1mh τ nj ,mh )
∑N
m 0 =1
∑Jh 0 =0
exp (
0 0
βV 0m h
Trade and Labor
() Markets Dynamics
1/ν
τ nj ,m
0 h 0 1/ν
)
March, 2016
10 / 24
Equilibrium conditions
Take the time di¤erence
,ik
µnj
0
nj ,ik
µ 1
=
J
∑N
m =1 ∑ h =0
exp ( βV 1ik τ nj ,ik )
1/ν
exp (
1/ν
βV 0ik
τ nj ,ik
exp (
∑N
m 0 =1
∑Jh 0 =0
)
τ nj ,mh )
βV 1mh
exp (
1/ν
0 0
βV 0m h
τ nj ,m
0 h 0 1/ν
)
Simplify
,ik
µnj
0
µnj1,ik
exp V1ik
=
J
∑N
m =1 ∑ h =0
V0ik
β/ν
exp ( βV 1mh τ nj ,mh )
∑N
m 0 =1
∑Jh 0 =0
exp (
1/ν
0 0
βV 0m h
τ nj ,m
0 h 0 1/ν
)
Use µnj1,mh once again
,ik
µnj
=
0
µnj1,ik exp V1ik
N
J
nj ,mh
∑ ∑ µ 1 exp V1mh
m =1 h =0
Caliendo, Dvorkin, and Parro (2015)
V0ik
β/ν
V0mh
Trade and Labor
() Markets Dynamics
β/ν
March, 2016
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Equilibrium conditions
Expected lifetime utility
N
nj
J
Vtnj = log( wPtn ) + ν log ∑ ∑ exp βVtik+1
t
τ nj ,ik
1/ν
i =1 k =0
Transition matrix
,ik
µnj
t
=
exp βVtik+1
N
J
∑ ∑
m =1 h =0
Caliendo, Dvorkin, and Parro (2015)
τ nj ,ik
exp βVtmh
+1
Trade and Labor
() Markets Dynamics
1/ν
τ nj ,mh
1/ν
March, 2016
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Equilibrium conditions - Time di¤erences
Expected lifetime utility
N
w nj /w nj
Vtnj+1
J
,ik
Vtnj = log( Ptn+1 /Ptn ) + ν log ∑ ∑ µnj
exp Vtik+2
t
t
t +1
Vtik+1
i =1 k =0
β/ν
Transition matrix
,ik
µnj
t +1
,ik
µnj
t
=
exp Vtik+2
N
Vtik+1
J
nj ,mh
exp Vtmh
∑ ∑ µt
+2
m =1 h =0
where
w tnj+1 /w tnj
P tn+1 /P tn
β/ν
Vtmh
+1
β/ν
is the solution to the temporary equilibrium in time
di¤erences
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
10 / 24
Temporary equilibrium conditions
How to solve for the temporary equilibrium in time di¤erences?
Price index
Ptnj (wt )
=Γ
nj
h
∑
N
i =1
A
ij
j
[xtij (wt )κ nj ,ij ] θ
i
1/θ j
,
Trade shares
j
,ij
π nj
(wt ) =
t
Caliendo, Dvorkin, and Parro (2015)
[xtij (wt )κ nj ,ij ] θ Aij
,
mj
nj ,mj ] θ j Amj
∑N
m =1 [xt (wt )κ
Trade and Labor
() Markets Dynamics
March, 2016
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Temporary equilibrium - Time di¤erences
How to solve for the temporary equilibrium in time di¤erences?
Price index
P̂tnj+1 (w
^ t +1 )
=
h
∑
N
i =1
j
,ij ij
π nj
[x̂t +1 (w
^t +1 )] θ
t
i
1/θ j
,
Trade shares
,ij
π nj
^ t +1 )
t +1 (w
=
,ij ij
π nj
[x̂t +1 (w
^t +1 )]
t
nj ,mj
∑N
m =1 π t
θj
[x̂tmj
^t +1 )]
+1 (w
θj
,
Where P̂tnj+1 = Ptnj+1 /Ptnj , x̂tij+1 = xtij+1 /xtij , w
^t +1 = wt +1 /wt
Same “hat trick” applies to all equilibrium conditions
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
11 / 24
Solving the model
Proposition
Given L0 , µ 1 , π 0 , VA0 , GO0 , (ν, θ, β), solving the equilibrium in time
di¤erences does not require the level of Θ, and solves
nj ,ik
J
[Ytik+2 ] β ,
Ytnj+1 = (ŵtnj+1 /P̂tn+1 )1/ν ∑N
i =1 ∑ k =0 µ t
,ik
µnj
t +1 =
,ik
µnj
[Ytik+2 ] β
t
nj ,mh
J
∑N
m =1 ∑ h =0 µ t
β
[Ytmh
+2 ]
,
ik ,nj ik
N
J
Lnj
Lt ,
t +1 = ∑ i =1 ∑ k =0 µ t
where ŵtnj+1 /P̂tn+1 solves the temporary equilibrium given L̂t +1 , where
Ytik+1 exp(Vtik+1 Vtik )1/ν .
Example
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
12 / 24
Solving for counterfactuals
Want to study the e¤ects of changes in fundamentals Θ̂ = Θ0 /Θ
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Recall that
Θ
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fAnj g, fκ nj ,ij g, fτ nj ,ik g, H nj , fbn g
N ,J ,J ,N
n =1,j =0,i =1,k =0
TFP, trade costs, labor migration costs, endowments of local
structures, home production
We can use our solution method to study the e¤ects of changes in Θ
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One by one or jointly
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Changes across time and space
Proposition
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
13 / 24
Appplication: The Rise of China
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
14 / 24
The rise of China
U.S. imports from China almost doubled from 2000 to 2007
I
At the same time, manufacturing employment fell while employment in
other sectors, such as construction and services, grew
Several studies document that an important part of the employment
loss in manufactures was a consequence of China’s trade expansion
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e.g., Pierce and Schott (2012); Autor, Dorn, and Hanson (2013),
Acemoglu, Autor, Dorn, and Hanson (2014)
We use our model, and apply our method, to quantify and understand
the e¤ects of the rise of China’s trade expansion, “China shock”
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Initial period is the year 2000
We calculate the sectoral, regional, and aggregate employment and
welfare e¤ects of the China shock
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
15 / 24
Identifying the China shock
Follow Autor, Dorn, and Hanson (2013)
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We estimate
∆MUSA,j = a1 + a2 ∆Mother ,j + uj ,
where j is a NAICS sector, ∆MUSA,j and ∆Mother ,j are changes in U.S.
and other adv. countries, imports from China from 2000 to 2007
Obtain predicted changes in U.S. imports with this speci…cation
Use the model to solve for the change in China’s 12 manufacturing
12
industries TFP ÂChina,j j =1 such that model’s imports match
predicted imports from China from 2000 to 2007
I
We feed in to our model
n
ÂChina,j
to study the e¤ects of the shock
o12
j =1
by quarter from 2000 to 2007
Figure: shock and predicted imports
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
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Taking the model to the data (quarterly)
Model with 50 U.S. states, 22 sectors + unempl. and 38 countries
I
More than 1000 labor markets
Need data for L0 , µ
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1 , π 0 , VA0 , GO0
L0 : PUMS of the U.S. Census for the year 2000
µ 1 : Use CPS to compute intersectoral mobility and ACS to compute
Table
interstate mobility Details
π 0 : CFS and WIOD year 2000
VA0 and GO0 : BEA VA shares and U.S. IO, WIOD for other countries
Need values for parameters (ν, θ, β)
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θ : We use Caliendo and Parro (2015)
β = 0.99 Implies approximately a 4% annual interest rate
υ = 5.34 (implied elasticity of 0.2) Using ACM’s data and
speci…cation, adapted to our model Estimation
Need to deal with trade de…cits. Do so similar to CPRHS
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
Imbalances
March, 2016
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Employment e¤ects
Manufacturing - No China Shock
Manufacturing - China Shock
16.00
15.50
15.00
Employment share (%)
14.50
0
10
20
30
40
Time (quarters)
50
15
W & Retail - No China Shock
W & Retail - China Shock
14.9
14.8
14.7
0
10
20
30
40
Time (quarters)
50
Employment share (%)
16.50
63.00
62.50
62.00
61.50
Services - No China Shock
Services - China Shock
61.00
60.50
Employment share (%)
Employment share (%)
Figure: The Evolution of Employment Shares
0
10
20
30
40
Time (quarters)
50
7.65
Construction - No China Shock
Construction - China Shock
7.60
7.55
7.50
7.45
0
10
20
30
40
Time (quarters)
50
Chinese competition reduced the share of manufacturing employment
by 0.5% in the long run, 0.8 million employment loss
I
Proposition
About 50% of the change not explained by a secular trend
Validation
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
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Manufacturing employment e¤ects
Sectors most exposed to Chinese import competition contribute more
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1/2 of the decline in manuf. employment originated in the Computer &
Electronics and Furniture sectors Sectoral contributions
F
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1/4 of the total decline comes from the Metal and Textiles sectors
Food, Beverage and Tobacco, gained employment
F
Less exposed to China, bene…ted from cheaper intermediate goods,
other sectors, like Services, demanded more of them (I-O linkages)
Unequal regional e¤ects
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Spatial distribution
Regions with a larger concentration of sectors that are more exposed to
China lose more jobs Regional contributions
F
California, the region with largest share of employment in Computer &
Electronics, contributed to about 12% of the decline
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
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Welfare e¤ects across labor markets
Figure: Welfare changes across labor markets
80
70
60
Density
50
40
30
20
10
0
0.3
0.4
Note: Largest and smallest 5 percentile are excluded
0.5
0.6
0.7
0.8
0.9
1
Percentage change
Very heterogeneous response to the same aggregate shock
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welfare
Most labor markets gain as a consequence of cheaper imports from
China
Unequal regional e¤ects welfare reg
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
20 / 24
Transition cost to the steady state
Figure: Transition cost to the steady state across labor markets
80
70
60
Density
50
40
30
20
10
0
-8
-6
-4
Note: Largest and smallest 5 percentile are excluded
-2
0
2
4
6
8
10
12
Percentage change
Adjustment costs re‡ect the importance of labor market dynamics
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With free labor mobility AC=0
Heterogeneity shaped by trade and migration frictions as well as
geographic factors.
AC
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
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0
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
United Kingdom
Turkey
Taiwan
Sweden
Spain
Slovenia
Slovakia
Russia
Romania
Rest of the World
Portugal
Poland
Netherlands
Mexico
Lithuania
Korea
Japan
Italy
Ireland
Indonesia
India
Hungary
Greece
Germany
France
Finland
Estonia
Denmark
Czech Republic
Cyprus
Canada
Bulgaria
Brazil
Belgium
Austria
Australia
Percentage change
Welfare e¤ects across countries
Figure: Welfare e¤ects across countries
0.9
1
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
March, 2016
22 / 24
Conclusion
Develop a dynamic and spatial model to quantify the disaggregate
e¤ects of aggregate shocks
Show how to perform counterfactual analysis in a very rich spatial
model without having to estimate a large set of unobservables
Dynamics and realistic structure matters for capturing very
heterogenous e¤ects at the disaggregate level
Our model can be applied to answer a broader set of questions:
changes in productivity or trade costs in any location in the world,
commercial policies, and more...
Where we go from here:
1- Migration crisis in Europe.
2- Human capital accumulation
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
23 / 24
This is the END
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
24 / 24
Results with Fréchet and Multiplicative Costs
Expected lifetime utility
Vtn,j
=u
ctn,j
+
∑
N
i =1
∑
J
k =0
,k
βVti+
1
τ
n,j ;i ,k
1/ν
ν
,
Measure of workers that reallocate (Choice equation)
;i ,k
µn,j
=
t
,k
n,j ;i ,k
βVti+
1τ
∑N
m =1
∑Jh =0
βVtm,h
+1
1/ν
τ n,j ;m,h
1/ν
.
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
25 / 24
State B
State A
Information in CPS and ACS
Ind 1
Ind 2
...
Ind J
Total
Ind 1
Ind 2
...
Ind J
Total
Ind 1
x
x
...
x
y
y
State A
Ind 2 . . .
x
...
x
...
...
...
x
y
...
y
...
Ind J
x
x
...
x
y
y
Ind 1
y
x
x
...
x
y
State B
Ind 2 . . .
y
x
x
...
x
y
Ind J
...
...
...
...
...
y
x
x
...
x
y
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
26 / 24
Model - Intermediate goods
Representative …rms in each region n and sector j produce a
continuum of intermediate goods with idiosyncratic productivities z nj
I
I
Drawn independently across goods, sectors, and regions from a Fréchet
distribution with shape parameter θ j
Productivity of all …rms is also determined by a deterministic
productivity level Anj
The production function of a variety with z nj and Anj is given by
h
n
qtnj (z nj ) = z nj Anj [ltnj ]ξ [htnj ]1
with ∑Jk =1 γnj ,nk = 1
Caliendo, Dvorkin, and Parro (2015)
ξn
iγnj
J
∏ [Mtnj ,nk ]γ
nj ,nk
,
k =1
γnj
Trade and Labor
() Markets Dynamics
March, 2016
27 / 24
Model - Intermediate good prices
The cost of the input bundle needed to produce varieties in (nj ) is
xtnj
=B
nj
rtnj
ξn
wtnj
nj
1 ξn γ
J
∏ [Ptnk ]γ
nj ,nk
k =1
The unit cost of a good of a variety with draw z nj in (nj ) is
xtnj nj
[A ]
z nj
γnj
and so its price under competition is given by
(
)
κ nj ,ij xtij
nj j
pt (z ) = min
,
ij
i
z ij [Aij ]γ
with κ nj ,ij
Back
1 are “iceberg” bilateral trade cost
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
28 / 24
Model - Final goods
The production of …nal goods is given by
Qtnj
=
Z
RN
++
nj
[q̃tnj (z j )]1 1/η φj (z j )dz j
η nj /(η nj 1 )
,
where z j = (z 1j , z 2j , ...z Nj ) denotes the vector of productivity draws
for a given variety received by the di¤erent n
The resulting price index in sector j and region n, given our
distributional assumptions, is given by
Ptnj = $
where $ is a constant
h
∑
j
j ij
N
[x ij κ nj ,ij ] θ [Aij ]θ γ
i =1 t
i
1/θ j
,
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
29 / 24
Data - Quarterly gross ‡ows
Current Population Survey (CPS) monthly frequency
I
I
I
Information on intersectoral mobility
Source of o¢ cial labor market statistics
We match individuals surveyed three months apart and compute their
employment (industry) or unemployment status
F
Our 3-month match rate is close to 90%
American Community Survey (ACS) to compute interstate mobility
I
I
I
I
Table
Representative sample (0.5 percent) of the U.S. population for 2000
Mandatory and is a complement to the decennial Census
Information on current state and industry (or unemployment) and state
they lived during previous year
Limitation: no information on workers past employment status or
industry
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
30 / 24
Data - Quarterly gross ‡ows
Table: U.S. interstate and intersectoral labor mobility
Probability
Changing j in same n
Changing n but not j
Changing j and n
Staying in same j and n
p25
3.74%
0.04%
0.03%
91.1%
p50
5.77%
0.42%
0.04%
93.6%
p75
8.19%
0.73%
0.06%
95.2%
Note: Quarterly transitions. Data sources: ACS and CPS
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
31 / 24
Identifying the China shock
Predicted change in U.S. imports from China
Estimated change in measured TFP (quarterly, percent)
0.0
Furniture Mtg
1
Transport Mtg
1.0
Computer, Elect
10
Machinery
2.0
Metal
100
NonMetallic
3.0
Plastics, Rubber
1000
Chemicals
4.0
Petroleum, Coal
10000
Wood, Paper
5.0
Textiles
100000
Food, Bev, Tob
Prediceted change in U.S. imports (millions, log sclae)
Figure: Predicted change in imports vs. model-based Chinese TFP change
Change in measured TFP in China
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
32 / 24
Identifying the China shock
1.2
10000
1.15
1000
1.1
100
1.05
1
10
Estimated China change in TFP (Quarterly)
100000
0.95
Predicted change in U.S. imports from China
Furniture Mfg
Transport Mfg
Computer, Elect
Machinery
Metal
Nonmetallic
Plastics, Rubber
Chemicals
Petroleum, Coal
Wood, Paper
Textiles
1
Food, Bev, Tob
Predicted change in U.S. imports (millions, log scale) Figure: Predicted change in imports vs. model-based Chinese TFP change
Change in TFP in China
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
33 / 24
Manufacturing Employment E¤ects
Figure: Sectoral contribution to the change in manuf. employment
30
Percentage change
25
20
15
10
5
0
Furniture Mfg.
Transport Mfg.
Computer, Elect.
Machinery
Metal
Nonmetallic
Plastics, Rubber
Chemicals
Petroleum, Coal
Wood, Paper
Textiles
Food, Bev., Tob.
-5
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
34 / 24
Sectoral concentration across regions
Computers an Electronics (shares)
Wood and Paper (shares)
NI
NI
229
261
AL
OR
NE
EN
2222
2213
222
EI
SE
122
2222
TT
OI
2227
IL
222
AO
2273
2224
122
2294
LZ
NE
323
OK
LR
2224
2211
SE
NV
2617
AL
666
122
NA
LZ
427
NE
267
AL
SA
LK
2222
2252
2222
2622
2666
VL
KY
2666
261
AV
261
OK
LR
2691
161
EE
EE
2
2667
TN
166
NA
6
2619
LL
AL
SA
666
669
6
TX
1121
661
II
22223
169
662
169
IN
EO
261
LL
TX
IL
161
261
NJ
AL
OI
166
KS
2667
AT
266
IL
AO
2662
2611
NY
2611
2621
TT
AV
161
RI
262
2622
AY
EL
169
2626
761
NE
EE
EI
AI
2224
124
2221
162
2627
122
TN
LK
EN
2616
2666
EE
2214
2232
EE
NE
2611
IE
222
VL
KY
EO
122
124
IN
121
KS
222
1
VT
ET
NJ
AL
IL
NE
2212
OR
2212
2224
2221
NV
RI
AT
322
2217
AY
2222
NY
2
1
227
2225
225
AI
IE
EL
2212
VT
ET
1122
AL
AL
EE
123
LL
ES
LL
II
2219
322
2626
2211
LL
ES
LL
161
266
266
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
35 / 24
0
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
Percentage change
Manufacturing employment e¤ects
Figure: Regional contribution to the change in manuf. employment
14
12
10
8
6
4
2
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
36 / 24
Regional welfare e¤ects
NI
6665
AL
EE
6665
OR
NE
EN
6695
6642
6662
EI
6665
SE
6625
6654
6646
6649
TT
OI
665
IL
6669
AO
6692
6652
6655
NJ
666
6646
2662
6662
666
AV
666
666
6645
TN
LZ
NE
6655
OK
LR
6699
6669
6665
NA
6666
6652
LK
6699
EE
EE
VL
KY
EO
AL
6664
IN
666
KS
6646
AT
6659
IL
NE
NV
6644
NY
6699
2662
AL
RI
6625
AY
6666
6664
666
AI
IE
EL
6652
VT
ET
LL
AL
SA
6666
664
6695
TX
6652
II
6669
LL
ES
LL
6665
6665
6659
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
37 / 24
Sectoral and regional welfare e¤ects
Sectoral e¤ects very di¤erent in the long run than in the short run
I
Services and Construction gain the most
F
I
Sectoral e¤ects
Reasons: no direct exposure, bene…t from cheaper intermediate inputs,
increased in‡ow of workers from manufacturing
Welfare gains are more uniform in the long run
F
Workers reallocate from depressed industries
U.S. regions fare better in the short and the long run
I
Regions bene…t directly from cheaper intermediate goods from China
F
I
Regional e¤ects
and indirectly from the e¤ect of imports on the cost of inputs
purchased from other U.S. regions
The regional welfare distribution is more uniform in the long run
F
workers reallocate from regions with lower real income
Worst o¤ individual labor markets
I
F
Wood and Paper in Nevada, Transport and Equip. in Louisiana, and
Wholesale and Retail in Alaska
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
38 / 24
Solving the model
Proposition
Given L0 , µ 1 , π 0 , VA0 , GO0 , (ν, θ, β), and Θ̂ = fΘ̂t gt∞=1 , solving the
equilibrium in time di¤erences does not require Θ, and solves
nj ,ik
J
[Ytik+2 ] β ,
Ytnj+1 = (w̃tnj+1 /P̃tn+1 )1/ν ∑N
i =1 ∑ k =0 µ t
,ik
µnj
t +1
=
,ik
µnj
[Ytik+2 ] β
t
nj ,mh
J
∑N
m =1 ∑ h =0 µ t
β
[Ytmh
+2 ]
,
ik ,nj ik
N
J
Lnj
Lt ,
t +1 = ∑ i =1 ∑ k =0 µ t
where w̃tnj+1 /P̃tn+1 solves the temporary equilibrium at L̃t +1 given Θ̂t +1 ,
and Ytik+1 exp(Vtik+1 Vtik )1/ν
Back
Back
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Trade and Labor
() Markets Dynamics
March, 2016
39 / 24
How to perform counterfactuals?
Solve the model conditioning on observed data at an initial period
I
Value added, Trade shares, Gross production, all consistent with
observed labor allocation across labor market at t = 0
I
Use the labor mobility matrix µ 1 . For this, we we need to specify
agents expectations at t = 1 about future policies
Assumption: Policy changes are unanticipated at t =
I
I
I
1
Allows us to condition on observed data and solve for the sequential
equilibrium with no policy changes
Let fVt gt∞=0 be the equilibrium sequence of values with constant
,J
policies, where Vt = fVti ,k gN
i =1,k =1 .
The assumption implies that the initial observed labor mobility matrix
µ 1 is the outcome of forward looking behavior under fVt gt∞=0 .
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
40 / 24
Solving the model (example)
Figure: Equilibrium Value Functions in Time Di¤erences
1.6
1.4
Ynj
t
1.2
1
0.8
0.6
0.4
0
10
20
30
40
50
60
70
80
90
100
110
Time (quarters)
Proposition
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
41 / 24
Taking the model to the data (quarterly)
υ = 5.34 (implied elasticity of 0.2) Using ACM’s data and
speci…cation, adapted to our model
I
I
Data: migration ‡ows and real wages for 26 years between 1975-2000,
using March CPS
We deal with two issues: functional forms, and timing
Estimating equation
,ik
,nj
log µnj
/µnj
=C+
t
t
I
I
I
β
,ik
nj ,nj
log wtik+1 /wtnj+1 + β log µnj
t +1 /µt +1 + v t +1 ,
υ
We transform migration ‡ows from …ve-month to quarterly frequency
GMM estimation, past ‡ows and wages used as instruments
ACM estimate υ = 1.88 (annual), υ = 2.89 (…ve-month frequency)
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
42 / 24
Model validation
Compare reduced-form evidence with model’s predictions
I
I
First run second-stage regression in ADH with our level of aggregation
Then, run same regression with model generated data
Table: Reduced-form regression results
∆Lm
it
∆IPWuit
Obs
R2
∆ūit
data
(1)
model
(2)
data
(3)
model
(4)
-1.718
(0.194)
-1.124
(0.368)
0.461
(0.138)
0.873
(0.252)
49
0.51
50
0.16
49
0.13
50
0.20
Results are largely aligned with those in ADH
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
43 / 24
Adjustment costs
We follow Dix-Carneiro (2014)’s measure of adjustment cost
The steady-state change in the value function due changes in
nj
nj
fundamentals is given by VSS
(Θ̂) VSS
Therefore, the transition cost for market nj to the new long-run
equilibrium, AC nj (Θ̂), is given by
0
AC nj (Θ̂) = log @
nj
VSS
(Θ̂)
1
1 β
∑t∞=0 β
t
Vtnj+1 (Θ̂)
nj
VSS
Vtnj+1
1
A,
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
44 / 24
Imbalances
Assume that in each region there is a mass of one of Rentiers
I
I
I
Owners of local structures, obtain rents ∑Jk =1 rtik H ik
Send all their local rents to a global portfolio
n
Receive a constant share ιi from the global portfolio, with ∑N
n =1 ι = 1
Imbalances in region i given by
J
∑ rtik H ik
ιi χt ,
k =1
J
ik ik
where χt = ∑N
i =1 ∑k =1 rt H are the total revenues in the global
portfolio
Rentier uses her income to purchase local goods
I
Same preferences as workers
Back
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
45 / 24
Welfare e¤ects from changes in fundamentals
Let Wtnj (Θ̂) be the welfare e¤ect of change in Θ̂ = Θ0 /Θ
∞
nj
Wtnj (Θ̂) = ∑ βs log (µ̂njĉs,nj )ν ,
s =t
I
I
s
Note that this is a consumption equivalent measure of welfare
,nj )ν is the change in the option value of migration
(µ̂nj
s
In our model, ĉtnj = ŵtnj /P̂tn is shaped by several mechanisms,
ĉtnj =
I
I
ŵ tnj
k
J
∏k =1 (ŵ tnk )α
∏Jk =1
ŵ tnk
P̂ tnk
αk
,
First component re‡ects the unequal e¤ects within a region
Second component is common to all HH residing in region n, given by
!
J
L̂nk
nk ,nk
t
n
k
γnk /θ k
ξ log nk .
∑ α log(π̂t )
Ĥ
k =1
Caliendo, Dvorkin, and Parro (2015)
Trade and Labor
() Markets Dynamics
March, 2016
46 / 24
Welfare e¤ects from changes in fundamentals
Let Wtnj (Θ̂) be the welfare e¤ect of change in Θ̂ = Θ0 /Θ
∞
nj
Wtnj (Θ̂) = ∑ βs log (µ̂njĉs,nj )ν ,
s =t
I
I
s
Note that this is a consumption equivalent measure of welfare
,nj )ν is the change in the option value of migration
(µ̂nj
s
In a one sector model with no materials and structures, ĉtn = ŵtn /P̂tn
Wtn (Θ̂) =
∞
∑
s =t
βs log
1/θ
(π̂ n,n
s )
,
ν
(µ̂n,n
s )
Similar to a ACM (2010) + ACR (2012)
back
Caliendo, Dvorkin, and Parro (2015)
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() Markets Dynamics
March, 2016
47 / 24