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TECHNICAL APPENDIX
Appendix A.1 – District-level Industry Output and First
Stage Regressions with Bartik IVs
Figure A.1.1: Distribution of
qjr /Mjr
−ϵj
for NAICS 3-digit industries, Lorenz curve and Gini
Figure A.1.2: Predicted district-level tariffs by NAICS-3 industries
1
Figure A.1.3: Number of NAICS 3-digit industries with predicted district-level tariffs
Table A.1.1: Average tariffs and NTMs by NAICS-3 industry
NAICS-3 Industry
No. & Label
311 - Foods
312 - Beverages
313 - Textiles
314 - Text. Prods.
315 - Apparel
316 - Leather
321 - Wood
322 - Paper
324 - Petroleum
325 - Chemicals
326 - Plastic
327 - Non-metal
331 - Prim. Metal
332 - Fab. Metal
333 - Machinery
334 - Computers
335 - Elec. Eq.
336 - Transp.
337 - Furniture
339 - Miscellaneous
Total (Average)
Tariffs
No. of lines Average
1,061
0.056
78
0.017
695
0.078
225
0.044
588
0.092
301
0.080
177
0.011
242
0.005
43
0.010
1,768
0.026
242
0.023
310
0.038
584
0.022
441
0.024
879
0.011
719
0.017
303
0.016
236
0.013
55
0.004
507
0.023
9,454
(0.035)
Core NTMs
No. of lines Average
966
0.411
74
0.094
606
0.181
211
0.234
584
0.353
196
0.109
143
0.172
139
0.000
19
0.000
1,553
0.051
175
0.005
292
0.001
449
0.000
389
0.031
819
0.041
535
0.061
278
0.163
229
0.161
54
0.055
499
0.029
8,210
(0.131)
Predicted
τjr
1.225
0.546
0.477
0.276
0.294
0.042
1.357
0.479
0.295
0.401
0.948
0.850
0.240
0.812
0.232
0.291
0.164
0.207
0.898
0.354
(0.519)
No. of CDs
with τjr > 0
190
147
77
128
111
112
131
132
53
113
152
179
100
169
151
119
150
113
172
185
(134)
Notes: Averages weighted by the number of tariffs and NTM lines in columns (3) & (5). Simple average over 433 CDs in
columns (6) & (7).
2
3
qj2 /Mj2
−ϵj
Region 2
Mid-Atlantic
-2.425
(2.550)
4.383
(1.000)
6.957
(2.640)
2.696
(3.260)
-8.479
(2.630)
1.612
(2.440)
-9.468
(2.540)
-1.917
(1.360)
12.6
(1.940)
-2.165
(0.460)
9,454
0.454
qj3 /Mj3
−ϵj
Region 3
E-N Central
-1.913
(1.990)
6.953
(1.860)
12.03
(4.630)
2.804
(3.770)
-12.30
(4.540)
2.338
(4.230)
-15.91
(4.840)
0.713
(0.400)
11.72
(1.740)
-1.654
(0.340)
9,454
0.587
Endogenous Variables:
qj4 /Mj4
qj5 /Mj5
−ϵj
−ϵj
Region 4
Region 5
W-N Central S Atlantic
-5.815
-1.61
(3.360)
(1.960)
14.47
0.663
(2.200)
(0.160)
21.93
9.779
(5.640)
(3.120)
6.338
2.386
(5.150)
(2.350)
-21.00
-4.367
(4.730)
(1.250)
4.221
0.92
(4.650)
(1.250)
-31.53
-17.07
(5.810)
(4.090)
-2.746
-0.831
(1.000)
(0.740)
37.65
17.81
(3.030)
(3.510)
-14.47
-2.532
(1.640)
(0.690)
9,454
9,454
0.547
0.769
statistics in Table 2.
2SLS results are robust to using, instead, instrumenting each endogenous variable
qj7 /Mj7
−ϵj
Region 7
W-S Central
-3.149
(4.280)
5.075
(1.730)
12.85
(4.600)
3.256
(4.140)
-11.29
(3.990)
2.164
(3.710)
-13.52
(3.820)
0.0162
(0.010)
5.019
(0.890)
3.508
(0.890)
9,454
0.529
qj9 /Mj9
−ϵj
Region 9
Pacific
-2.052
(3.160)
4.824
(1.760)
8.411
(3.840)
2.985
(4.120)
-6.915
(2.840)
1.291
(2.520)
-12.53
(4.160)
-1.846
(2.010)
17.81
(3.980)
-7.923
(2.600)
9,454
0.443
qjr /Mjr
using the nine share ratios zjd /zjr d = 1, . . . , 9. (iii) See notes and weak-instrument
−ϵj
qjr /Mjr
, Region = 1, . . . , 9 constructed as in (19).
−ϵj
qj6 /Mj6
−ϵj
Region 6
E-S Central
-0.86
(1.020)
-6.719
(1.090)
12.26
(4.140)
2.183
(2.550)
-6.22
(1.860)
1.18
(1.750)
-13.50
(3.810)
2.278
(1.100)
7.793
(1.170)
6.016
(1.070)
9,454
0.508
Note: (i) t-values in parentheses. Errors clustered at HS 2-digits. (ii) Nine Bartik-like IVs for each endogenous variable
N
R2
Constant
BIV Region = 9
BIV Region = 8
BIV Region = 7
BIV Region = 6
BIV Region = 5
BIV Region = 4
BIV Region = 3
BIV Region = 2
BIV Region = 1
qj1 /Mj1
−ϵj
Region 1
New England
-1.616
(2.240)
5.338
(1.710)
5.683
(2.880)
2.361
(3.950)
-5.958
(2.620)
1.099
(2.310)
-10.30
(4.030)
-1.519
(1.570)
14.83
(3.380)
-6.288
(1.930)
9,454
0.516
Table A.1.2: First Stage Regressions for Small Country results in Tables 2 and 3.
Using Bartik IVs (BIV) constructed as in (19).
Table A.1.3: First Stage Regressions for Large Country results in Tables 2 and 3.
Using Bartik IVs (BIV) constructed as in (19)
.
BIV Region = 1
BIV Region = 2
BIV Region = 3
BIV Region = 4
BIV Region = 5
BIV Region = 6
BIV Region = 7
BIV Region = 8
BIV Region = 9
Constant
N
R2
qj4 /Mj4
−δj
Region 4
W-N Central
-8.445
(4.42)
16.91
(3.89)
20.11
(5.96)
6.421
(5.08)
0.856
(0.17)
-0.879
(0.74)
-25.94
(5.55)
-5.066
(3.22)
32.21
(4.30)
-30.65
(3.52)
8,735
0.529
Endogenous Variables:
qj5 /Mj5
qj7 /Mj7
−δj
−δj
Region 5
Region 7
S. Atlantic W-S Central
-2.345
-3.933
(2.97)
(3.79)
3.4
5.977
(1.28)
(2.70)
6.834
9.929
(3.72)
(5.40)
2.142
2.890
(2.98)
(4.31)
2.95
-0.716
(1.02)
(0.22)
-0.768
-0.216
(1.15)
(0.28)
-12.39
-9.811
(4.64)
(3.88)
-2.016
-1.387
(2.92)
(1.49)
14.30
5.29
(4.35)
(1.34)
-9.054
-5.922
(2.46)
(1.20)
8,735
8,735
0.776
0.521
µj θjg .
Qg /Mj
−δj
-0.239
(1.47)
0.402
(1.81)
0.116
(0.31)
-0.142
(1.32)
0.709
(0.85)
-0.236
(1.17)
0.293
(1.21)
0.0787
(0.82)
-0.501
(0.89)
-0.677
(1.08)
8735
0.537
Notes: (i) t-values in parentheses; errors clustered at HS 2-digits. (ii) Nine Bartik-like IVs for each endogenous variable
qjr /Mjr
−δj
, r = 1, . . . , 9 constructed as in (19). 2SLS results are robust to using the nine share ratios
instruments for each endogenous variable
2.
qjr /Mjr
−δj
zjd
zjr
d = 1, . . . , 9, as
. (iii) Additional notes and weak-instrument statistics are reported in Table
4
Table A.1.4: 2SLS estimates for models (16) and (27). with Political Coalitions
Dependent Variable: Applied Tariff+ Ad-valorem NTMs 2002
Small Country
Qgr
Qr
Large Country
β1 : Competitive State, Competitive District
Eq. (16)
0
0.09
Eq. (27)
0
β2 : Competitive State, Safe (DEM) District
0
0.09
0
β3 : Competitive State, Safe (REP) District
0.350
(0.035)
0
0.09
0.12
0.322
(0.056)
0
0.27
0
β6 : Safe (DEM) State, Safe (REP) District
0.261
(0.041)
0
0.15
0
β7 : Safe (REP) State, Competitive District
0
0.05
0
β8 : Safe (REP) State, Safe (DEM) District
0.151
(0.056)
0.252
(0.035)
0.12
0
0.06
0.439
(0.035)
2.690
(0.281)
β4 : Safe (DEM) State, Competitive District
β5 : Safe (DEM) State, Safe (DEM) District
β9 : Safe (REP) State, Safe (REP) District
β X : µj θjg .
α:
Qj /Mj
−ϵj
α:
Qj /Mj
−δj
Qg /Mj
−δj
−1
−
1
∗
1+ϵX
j
+ µj θjg .
Dg /Mj
−δj
−1
N
First Stage Statistics
Anderson-Rubin χ2 (10 df)
Anderson-Rubin p-value
Kleibergen-Paap weak IV
8210
7675
1099
(0.00)
539.2
676.4
(0.00)
2566
Notes: (1) Standard errors (in parentheses) clustered at 2-digit HS. (2) α is constrained to equal −1 required by (16) and
(27). (3) Equations (16) and (27) require dropping the constant term in the regressions. (4) Qgr /Qr is the share of the output
of export industry COMPUTER (3-digit NAICS=334) for each coalition r. Larger shares (in blue) suggest export-oriented
coalitions. (6) In the large country case: (i) unconstrained estimates of β1 , β2 , β4 , β5 , β6 , β7 and β8 are negative and
constrained to zero to disallow import subsidies or export taxes. (ii) µj is assumed to equal 1 (equal bargaining strength) for
all j. (iii) θjg is calculated as in 26.
5
Appendix A.2 – Comparison with Grossman–Helpman
Predictions
Expression (12) in Proposition 3 may be used to draw a comparison with GH, beyond those
performed earlier, about district tariff preferences in equations (3) and (5). Consider the
GH model in which all sectors are organized as lobbies, and αK denotes the fraction of the
population that owns specific factors and whose interests lobbies represent. In our model,
this fraction is αK = nK /n. While Grossman and Helpman (1994) unitary government
dispenses with legislatures and districts we can compare Proposition 2 in GH as the GH
counterpart to equation (12) in our model. Proposition 2 in GH is:
(1 − αK )
τj
=
1 + τj
a + αK
Qj /Mj
−ϵj
(1)
.
q /M
Eliminating districts in (12) is achieved by reducing the coefficients on the jr−ϵj j terms to
a constant. Forcing the welfare weight on each owner of specific factors to be invariant across
K
regions r “folds” the model in this manner. Suppose ΓK
for all j and r. Then, noting
jr = Γ
K K
K
Γ n = γ (aggregate welfare weight to owners of specific capital), (12) can be written as:
R
X ΓK nK 1
τj
=
1 + τj
γ K + γ L αK
r=1
qjr /Mj
−ϵj
−
Qj /Mj
−ϵj
=
Qj /Mj
γK
1
−1
.
γ K + γ L αK
−ϵj
The first equality uses αK = nK /n, while the second equality uses
γ
eK as the share γ
eK = γ K /(γ K + γ L ) yields
(e
γ K − αK )
τj
=
1 + τj
αK
Qj /Mj
−ϵj
.
P
r qjr
= Qj . Defining
(2)
In the GH model, equation (1), τj approaches zero as a → ∞, i.e., the government becomes singularly welfare-minded. In our model, folded to simulate a unitary government,
τj approaches zero as γ
eK → αK . This is the same situation noted above where the mobile
factor (L) and specific factors (K) owners get exactly the same welfare weights (αK is the
proportion of the population with specific factor ownership). If owners of capital and owners
of labor are treated equally, the classic free trade result is obtained.
The unitary government chooses positive tariffs in the GH model if a is finite. In the
folded version of our model, with no role for legislative bargaining, the reason for positive
tariffs is that γ̃ K > αK . However, the reason why specific factors get a larger representation
than their numbers is left unexplained since legislative bargaining is folded. The GH model
builds a lobbying structure to provide an explanation.
6
A closer parallel with the GH model is possible by letting the weight on specific capital
K
owners be sector-varying before folding, or ΓK
jr = Γj for all r. From (12),
R
K
X
ΓK
τj
1
j nj
=
K
L
1 + τj
γ + γ αjK
r=1
qjr /Mj
−ϵj
−
Qj /Mj
−ϵj
(e
γjK − αjK )
=
αjK
Qj /Mj
−ϵj
.
Using αjK = nK
j /n, the fraction of specific factor owners that are employed in sector j, yields
K
K
L
the first equality. Defining γ̃jK = ΓK
j nj /(γ + γ ), the share of aggregate welfare given to
specific factors in sector j, yields the second equality. In this way, sector j interests are
represented by the continuous variable (γ̃jK − αjK )/αjK – akin to the binary existence-oflobbying-organization variable in the GH model – bringing our version closer to GH. The
mechanism determining the national tariff in our model as a function of legislative bargaining
is, however, different from GH.
7
Appendix B – Technical Appendix
1
Model with importing sectors
1.1
General framework
Notation. The following notation is used throughout this section:
• The economy consists of J sectors, with j = 0, 1, ..., J, and R regions, with r = 1, ..., R.
There are two types of economic agents: m = L, owners of a non-specific factor (often
defined as a mobile factor of production); m = K, and owners of sector-specific factors
of production (often defined as sector-specific capital).
• Non-sector specific factor: Mobile across sectors, but immobile across regions.
– Lr : units of nonspecific factors in region r.
– nLr : number of type-L individuals in r.
– nLr = (nL0r , nL1r , nL2r , . . . , nLJr ): vector of mobile factors across sectors in district r.
P
– nL = r nLr : total number of owners of the mobile factor in the economy.
• Owners of specific factors: Immobile across sectors and regions.
– Kr : number of owners of the specific factor of production in region r.
K
– nK
jr : number of type-K individuals producing in sector j in r; njr ≥ 0 (not all
regions are active in sector j).
K
K
K
– nK
r = (n1r , n2r , . . . , nJr ): distribution of the specific factor across sectors (vector);
the distribution of endowments may differ across regions r.
P
K
– nK
r =
i∈J nir : number of type-K individuals in r.
P
– nK = r nK
r : total number of specific factor owners in the economy.
• Total population in region r is nr = nLr + nK
r , and total population in the economy is
P
P
n = nL + nK , where nL = r nLr , nK = r nK
r .
• Welfare weights: District and national weights may differ.
– Λm
jr : weight district r places on a type-m agent in sector j;
– Γm
jr : weight placed at the national level on a type-m agent in sector j and district
r.
• Prices:1 Domestic prices are denoted by p0 = 1, p = (p1 , ..., pJ ), and world prices by
p = (p1 , ..., pJ ).
1
Initially, we develop a framework that does not include terms-of-trade effects (we assume that world
prices are taken as exogenously given). We later extend this framework and include terms-of-trade effects.
8
• Tariffs: Specific tariffs are denoted by tj , so that pj = pj + tj , and ad-valorem tariffs
by τj , so that pj = (1 + τj )pj .
Preferences. Following the literature on trade protection, we assume preferences are repP
resented by a quasi-linear utility function: um = x0 + i∈J um
i (xi ). Good 0, the numeraire,
is sold at price p0 = 1. Goods xj , the imported goods, are sold domestically at prices pj . In
general, preferences for the imported goods j may differ across types m = L, K.2
Demand for goods. Consider the utility maximization problem for a representative conP
m
m
um
sumer of type m in region r, with income zrm : max{xm
r = zr −
i pi xir +
jr ,j=1,...,J}
P m m
m
m
m
m′ m
i ui (xir ). From the FOCs, −pj + u (xjr ) = 0 ⇒ djr ≡ djr (pj ), where djr is the demand
m
for good j of a representative consumer of type m in region r. Then, nm
r djr is the demand for
P
m
good j of all consumers of type m in region r, and Djm = r nm
r djr is the aggregate demand
for good j for all individuals of type m. Consumers of type m are identical across regions
P
m
m m
r, so the demand for good j for all individuals of type m is Djm = ( r nm
r ) dj = n dj .
P
P
Finally, aggregate demand for good j is Dj = m Djm = m nm dm
j .
Consumer surplus. Consumer surplus for a type-m individual from the consumption of
m m
m
m
m m
good j is defined by ϕm
j (pj ) = vj (dj ) − pj dj , where vj (pj ) ≡ uj [dj (pj )]. Summing
P m
over all goods gives the surplus i ϕi . Therefore, consumer surplus for type-m individP m
P m m
m m
m
m
m
uals in region r is ϕm
r (p) = nr
i ϕi = nr ϕ , and aggregate
i [vi (di ) − pi di ] = nr
P
P
P
m
m m
m
consumer surplus for type-m individuals is Φm = r ϕm
r =
i ϕi = n ϕ . Note
r nr
m
m
m
that ∂Φm /∂pj = −nm dm
j = −Dj . The indirect utility can be expressed as vr (p, zr ) =
P
P
m
m
zrm + i [vim (pi ) − pi dm
i ] = zr +
i ϕi (pi ). When individuals have identical preferences,
P
Φm = nm ϕ = nm i ϕi .
Production. The production of good 0 only requires the mobile non-specific factor of production and uses a linear technology represented by q0r = w0r nL0r , where w0r > 0. The wage
received by workers in sector {0r} is w0r . Good j is produced domestically using a CRS proL
L
K
duction function qjr = Fjr (nK
jr , njr ) = fjr (njr ), where njr is sector-region specific (immobile
across sectors and regions). We omit, to simplify notation, nK
jr from the production function
from now onwards.
Profits. Profits in sector-region {jr} are πjr ≡ pj fjr (nLjr ) − wjr nLjr , and the demand for
′
the mobile factor in sector-region jr is defined by pj fjr
(nLjr ) = wjr , which defines nL,D
≡
jr
L,D
L,D
L
njr (pj , wjr ). The profit function becomes πjr (pj , wjr ) ≡ pj fjr (njr ) − wjr njr . The production of good j in region r (using the envelope theorem) is given by ∂πjr (pj , wjr )/∂pj =
P
qjr (pj , wjr ). Aggregate production of good j is Qj = r qjr . Workers employed in sector {jr}
receive wjr , j = 0, 1, ..., J. Since workers are perfectly mobile across sectors, w0r = wjr = wr
in equilibrium.
2
The analysis performed in the text assumes that agents have identical preferences.
9
Imports and tariff revenue Imports of good j are Mj = Dj − Qj . Let pj denote the
P
internationally given price of good j. Revenue generated from tariff collection is T = i ti Mi ,
where ti = pi − pi . Note that
∂T
tj
′
= Mj + tj Mj = Mj 1 + ϵj , where ϵj ≡ Mj′ pj /Mj .
∂tj
pj
Total utility. The total utility of the mobile factor in sector-region {jr} is
L
Wjr
= wjr nLjr + nLjr
T
ΦL
T
+ nLjr ϕLr = wjr nLjr + nLjr + nLjr L .
n
n
n
An increase in the tariff on good j affects the utility of the mobile factor as follows:
L
nLjr ∂T
nLjr ∂ΦL
nLjr
DjL
∂Wjr
′
L
=
+ L
=
(Mj + tj Mj ) − njr L .
∂pj
n ∂pj
n ∂pj
n
n
The total utility of specific factor owners in sector-region {jr} is
K
Wjr
= πjr + nK
jr
T
ΦK
+ nK
jr K .
n
n
Note that
K
∂Wjr
nK
DjK
jr
′
K
= qjr +
(Mj + tj Mj ) − njr K .
∂pj
n
n
Region r’s welfare. The welfare of mobile factors in region r is ΩLr =
ΩLr
X
=
ΛLjr wjr nLjr
P
+
i
i
ΛLir nLir
T+
n
P
i
P
i
ΛLir WirL , or
ΛLir nLir L
ΦL
T
L
Φ = λr w r + + L ,
nL
n
n
P
P
where λLr = Ji=0 ΛLir nLir , and ΦL = nL i ϕLi . The welfare of specific factor owners in region
P K K
r is given by ΩK
r =
i Λir Wir , or
ΩK
r
=
X
P
ΛK
ir πir
+
K K
i Λir nijr
n
i
where λK
r =
K K
i Λir nir .
P
Ωr =
λL
r
K K
i Λijr nir
nK
P
T+
Φ
K
=
X
K
ΛK
ir nir
i
πir
nK
ir
+
K
For region r, welfare is given by Ωr = ΩL
r + Ωr =
ΦL
T
wr + + L
n
n
+
X
K
ΛK
ir nir
i
10
πir
nK
ir
+
λK
r
λK
r
T
ΦK
+ K
n
n
T
ΦK
+ K
n
n
,
m
m
m Λir Wir ,
P P
i
or
When preferences are identical,
Ωr = λ L
r wr +
X
K
ΛK
ir nir
i
K
where λr = λL
r + λr , and and Φ = nϕ = n
πir
nK
ir
Ω =
wr
X
r
L
ΓL
ir nir
+γ
L
i
+ λr
T
+ϕ ,
n
P
i ϕi .
Aggregate welfare. National total welfare is Ω =
X
T
ΦL
+ L
n
n
+
m
m
m Γir Wir ,
P P P
r
i
XX
r
K
ΓK
ir nir
i
πir
nK
ir
or
+γ
K
T
ΦK
+ K
n
n
,
m
m
where γ m = r i Γm
ir nir . Note that the weights used at the national level, Γjr , may not coincide
with those considered at the district level, ΛK
jr . When preferences are identical
P P
Ω =
X
wr
X
r
L
ΓL
ir nir
r
i
where γ = γ L + γ K , and Φ = nϕ = n
1.2
+
XX
P
K
ΓK
ir nir
i
πir
nK
ir
+γ
Φ
T
+
n
n
,
i ϕi .
Tariffs
District specific tariffs. Consider the case of specific tariffs with no terms-of-trade effects, i.e.
pj = pj + tj , where pj is taken as exogenously given, so that ∂pj /∂tj = 1. The tariff vector that
maximizes the total welfare of region r, Ωr , is determined by the following FOCs:
#
"
DjL
∂Ωr
′
L 1
K
M j + t j Mj − L + Λ K
≡ λr
jr njr
∂pj
n
n
qjr
nK
jr
!
"
+
λK
r
DjK
1
Mj + tj Mj′ − K
n
n
#
= 0,
for j = 1, ..., J, where Djm = nm dm
j . Isolating tjr gives
tjr
n
=− ′
Mj
!
K K
L DL
K DK
Λjr njr qjr
Mj
λ
λ
j
j
r
r
λ r nK − λ r nL + λ r nK + n
jr
|{z}
| {z } |
{z
} (iii)
(i)
(3)
(ii)
K
where λr = λL
r + λr . Expression (i) in (3) captures the effect of tariff tj on domestic producers
of good j in region r. This effect would tend to rise tj . Expression (ii) captures the impact of the
tariff on consumer surplus. The effect is different for the different groups of individuals L and K.
This term tends to put downward pressure on tj . Finally, expression (iii) captures the impact of the
tariff on tariff revenue. Since domestic residents benefit from tariff revenue, this term would tend
to increase tj .
Note that expression (i) reflects the impact of the tariff on the returns to the specific factors,
in this case, owners of specific factors in sector j. Given that the model assumes the nonspecific
factor is perfectly mobile across sectors within region r (but not across regions), wr = wjr for all j
11
in region r. Changes in tariffs do not have an impact on the income of the mobile factor because
wr does not depend on tj .3
When agents have identical preferences i.e., DjL /nL = DjK /nK = Dj /n, expression (3) can
written as
!
K
ΛK
nK
n
jr njr qjr
j Qj
−
.
(4)
tjr = − ′
Mj
λ r nK
n nK
jr
j
K
Moreover, if ΛL
jr = Λjr = Λr ,
tjr
n
= − ′
Mj
nK
nK
jr qjr
j Qj
−
nr nK
n
nK
jr
j
!
.
K
K
K
Then, tjr > 0 if and only if (nK
jr /nr )(qjr /njr ) > (nj /n)(Qj /nj ), or qjr /nr > Qj /n.
National tariffs. The tariff that maximizes aggregate welfare satisfies
∂Ω
∂pj
K qjr
ΓK
jr njr K
njr
r
X
=
Mj′
+ tj γ
−
n
DjL
DjK
Mj
γ L + γK K − γ
n
n
n
L
!
,
where γ = γ L + γ K . Isolating tj gives
"
K
n X ΓK
jr njr qjr
tj = − ′
−
Mj r
γ nK
jr
γ L DjL γ K DjK
+
γ nL
γ nK
!
#
Mj
+
.
n
(5)
If preferences are identical across groups, then
n
tj = − ′
Mj
K
X ΓK
Qj
jr njr qjr
−
K
γ njr
n
r
!
.
(6)
Ad-valorem Tariffs Suppose, as before, that world prices are fixed (i.e., there are no termsof-trade effects), but tariffs are now ad-valorem. Specifically, pj = (1 + τj )pj . This means that
∂pj /∂τj = pj . Note that τj = (pj − pj )/pj , which means that τj /(1 + τj ) = (pj − pj )/pj . When
agents have identical preferences i.e., DjL /nL = DjK /nK = Dj /n. Then, the district-preferred and
national ad-valorem tariffs can be expressed, respectively as
τjr
n
=
1 + τjr
−ϵj Mj
"
#
K
ΛK
n
q
Q
jr jr jr
j
−
,
λ r nK
n
jr
"
#
K
X ΓK
n
τj
q
Q
n
jr jr jr
j
=
−
,
1 + τj
−ϵj Mj r
γ nK
n
jr
(7)
where ϵj ≡ Mj′ pj /Mj < 0.
Comparing district tariff preference with national tariffs. How does the vector of
preferred tariffs by district r differ from those effectively chosen at the national level? Evaluated at
3
If the mobile factor were completely immobile across sectors (also sector-specific), then changes in tariffs
would have a differential effect on wages across sectors as well.
12
the solution obtained when tariffs are set at τj , the difference between τjr and τj can be written as:
n
τjr − τj =
(−ϵj Mj )
"
K
K
X ΓK
ΛK
jℓ njℓ qjℓ
jr njr qjr
−
λ r nK
γ nK
jr
jℓ
!#
,
(8)
ℓ
where the subindex ℓ is used to sum over districts. This expression identifies three sources of
discrepancy between district r’s preferred tariff on good j, τjr , and the central tariff τj . The sign of
K
(τjr − τj ) depends on (i) the difference between the weights ΛK
jr and Γjr , (ii) the spatial distribution
4
of nK
jr , and (iii) the production levels of good qjr across all locations r. Even when each district r
places the same weights to each sector j and group m as those chosen at the central or national level,
expression (8) may still be different from zero if the allocation of production across jurisdictions
is not homogeneous, i.e., nK
jr differs across locations r. In other words, there will be districts that
win and districts that lose just because of a non-uniform allocation of activity across space, and the
legislative bargaining carried out at the national level.5
1.3
Tariffs and Lobbying
Suppose lobbying is organized at the national level and owners of the specific factors (sectors)
are in charge of deciding the level of political contributions. Moreover, lobbying is decided at the
sectoral level. Specifically, a subset of sectors O ⊂ J are organized and engaged in lobbying, and
the “central authority” chooses the tariff vector t ≡ {t1 , . . . , tJ } that maximizes (C + aΩ), where C
are campaign contributions, Ω aggregate welfare, and a captures the trade-off between welfare and
P
contribution dollars (as in GH). The latter is equivalent to maximizing U = i∈O WiK + aΩ w.r.t.
t, or
max U
= a
{t1 ,...,tJ }
XX
r
L
ΓL
r Wir + a
X X
K
ΓK
ir Wir +
r i∈J\O
i
XX
r
K
(1 + aΓK
ir )Wir .
i∈O
For organized sectors j ∈ O, the specific tariff becomes
tO
j
n
= −A ′
Mj
(
X
r
K
ΓK
nK
jr njr
jr
+
γ
aγ
!
"
qjr
γ L DjL
−
+
γ nL
nK
jr
nK
γK
j
+
γ
aγ
!
DjK
nK
#
1 Mj
+
A n
)
,
4
Note that if njr = 0, then since capital is essential in the production of good j, qjr = 0. However, to the
extent that qjr > 0, not only the spatial distribution of activity but also the scale, represented by qjr /nK
jr
becomes relevant in determining tariffs and explaining the difference between τjr and τj .
5
When preferences differ across groups, expression (8) becomes
"
!
#
K
K
K
X ΓK
ΛK
n
λL
γ L DjL
λr
γ K DjK
jr njr qjr
jℓ njℓ qjℓ
r
τjr − τj =
−
−
−
−
−
.
(−ϵj Mj )
λ r nK
γ nK
λr
γ
nL
λr
γ
nK
jr
jℓ
ℓ
The last two terms capture the impact of the tariff on consumption. The effects contribute positively or
negatively to the difference (τjr − τj ) depending on the relationship between the weights attached to each
m
m
m
m
m
group by region r. Suppose Γm
jr = Γ and Λjr = Λ. Then, λr /λr = nr /nr and γ /γ = n /n. If the
proportion of group m in district r is the same as the respective average proportion, then the last two terms
K
of the previous expression cancel out. Finally, if preferences are identical such that dL
j = dj , the last two
terms cancel out.
13
where A ≡ aγ/(aγ + nK
j ). For sectors that are not organized (i.e., j ∈ J\O), the tariff tj is the
same as before.
Comparing tariffs How do the (specific) tariffs change if a sector becomes organized and lobbies
for protection? We now compare the tariff tj derived earlier in (5) to tO
j . Specifically,
tO
j − tj
=
nK
j
"
n
Mj′
aγ + nK
j
DjK
Qj
Mj
− K −
K
n
n
nj
!
#
− tj .
As a → ∞, A → 1, and (tUj − tj ) → 0; this means that tariffs are exactly the same. If a = 0, then
the tariff for sector j becomes tUj = (n/Mj′ )[(DjK /nK ) − (Qj /nK
j ) − (Mj /n)]. Note that in this case,
m
the tariff does not depend on Γjr .
2
Model with importing and exporting sectors
Suppose now that there are two countries: country U S (or the domestic country), and country
RoW (the foreign country, or, the rest of the world). We will the symbol “∗” to denote variables
referring to RoW . We also incorporate into the present framework terms of trade (TOT) effects, so
that tariffs imposed by an individual country may affect equilibrium world prices.
Notation. From the perspective of the domestic country U S, the economy can be described
as follows. There are three types of goods: a numeraire good 0, or sector 0, importable goods:
i = 1, ..., ⟨j⟩, ..., J, or sector M (exportable sector for RoW or M ∗ ), and exportable goods: g =
1, ..., ⟨s⟩, ..., G, or sector X (importable sector for RoW , or X ∗ ). Factors of production are allocated
0
M
X
0
M
X
across sectors as follows: nL = nL + nL + nL , nL = nL + nL + nL , and n = nL + nK , where
P P KX
P
P
P
P
P
P
P
0
0
KM
KX =
LX
KM =
LM
LX =
LM =
nL = r nL
r ,n
r
g ngr .
r
i nir , n
r
g ngr , n
r
i nir , n
Moreover, since there are only two “countries” (U S and RoW ), the set of importable goods for U S
is equal to the set of exportable goods for RoW , and the set of exportable goods for U S is equal
to the set of importable goods for RoW . Additionally, the market clearing conditions are given by
M ∗ − D M ∗ , and D X − QX = QX ∗ − D X ∗ .
DjM − QM
s
s
s
s
j = Qj
j
Ad-valorem tariffs. Suppose that countries set ad-valorem tariffs on importable goods, but they
cannot use export subsidies. Specifically, country U S sets tariffs on importable goods from RoW ,
∗
τjM , and country RoW sets tariffs on importable goods from country U S, τsX . The domestic price
M
of good j in country U S (pM
j ) and the foreign country RoW (pj ) are, respectively,
M M
pM
j = (1 + τj )pj ,
X
pX
s = ps ,
X∗
ps
∗
pM
= pM
j
j ,
X∗
= (1 + τs )pX
s .
(9)
(10)
X
where pM
j is the international (world) price of good j, and ps is the international (world) price of
M
M
M
M
M
M
M
good s.6 Note that τj = (pM
j −pj )/pj , and (1+τj ) = pj /pj , so that τj /(1+τj ) = (pj −pj )/pj .
This is the wedge between domestic and world price as a proportion of the domestic price pM
j .
Since good j is imported by country U S, then country U S chooses τjM ≥ 0. For the foreign country
RoW , τjM ∗ = 0, i.e., RoW does not subsidize exports of good j.
6
14
Given the tariffs, the equilibrium prices are determined by the following equations (from the
perspective of country U S):
∗ M
Mj (pM
j ) = Xj (pj ),
Xs (pX
s )
=
market for importable goods,
(11)
market for exportable goods.
(12)
∗
Ms∗ (pX
s ),
∗
∗
M M
M
X
X
It follows from (9) and (11) that pM
j (τj ) and pj (τj ). Similarly, from (10) and (12), ps (τs )
∗
∗
X
and pX
s (τs ).
Comparative static analysis: Domestic country U S. Consider good j imported by country U S. Differentiating the system of equations (9) and (11) with respect to τjM gives
∂pM
j
∂τjM
=
′ M
pM
j Mj (pj )
M
′ M
Xj∗ ′ (pM
j ) − (1 + τj )Mj (pj )
< 0,
∂pM
j
=
∂τjM
∗′ M
pM
j Xj (pj )
M
′ M
Xj∗ ′ (pM
j ) − (1 + τj )Mj (pj )
> 0.
We define elasticities as
ϵM
j =
∂Mj pM
j
,
M
∂pM
j
j
∗
ϵX
=
j
∂Xj∗ pM
j
∗,
X
∂pM
j
j
M
M
∂pM
j τj
j
∂τjM
ϵpτ M =
,
pM
j
M
M
∂pM
j τj
j
∂τjM pM
j
ϵpτ M =
.
Rewriting the comparative static results in terms of elasticities:
∂pM
j
∂τjM
=
pM
j
ϵM
j
∗
M
(1 + τjM ) (ϵX
j − ϵj )
,
∂pM
j
∂τjM
=
pM
j
ϵX
j
∗
∗
M
(ϵX
j − ϵj )
,
or
pM
j
τjM
ϵ
=
τjM
ϵM
j
X∗
(1 + τjM ) (ϵj
− ϵM
j )
,
pM
j
τjM
ϵ
=
pM
∗
ϵX
j
τjM
X∗
(1 + τjM ) (ϵj
⇒
− ϵM
j )
ϵτ jM
j
pM
j
τjM
=
ϵ
ϵM
j
ϵX
j
∗
.
Note that
M
∂pM
j /∂τj
M
∂pM
j /∂τj
=
Mj′
Xj∗ ′
ϵM
1
j
=
∗,
M
X
(1 + τj ) ϵj
and
pM
j
M
∂pM
j /∂τj
=1−
ϵM
j
ϵX
j
∗
.
Comparative statics: Foreign country RoW . Differentiating the system of equations (10)
∗
and (12) with respect to τsX gives
∗
∗
∗′ X
′ X
∂pX
pX
∂pX
pX
s
s Ms (ps )
s
s Xs (ps )
=
<
0,
=
> 0.
∗
∗
∗
∗
∗′ X
∗′ X∗
X
X∗
∂τsX
∂τsX
Xs ′ (pX
Xs ′ (pX
s ) − (1 + τs )Ms (ps )
s ) − (1 + τs )Ms (ps )
Using elasticities,
∗
∗
2
∂pX
pX
ϵM
(pX
ϵM
s
s
s
s )
s
=
=
,
M∗)
X ∗ (ϵX − ϵM ∗ )
∂τsX ∗
(1 + τsX ∗ ) (ϵX
−
ϵ
p
s
s
s
s
s
15
∗
∂pX
ϵX
s
s
X
=
p
∗ ,
s
∂τsX ∗
(ϵX
−
ϵM
s
s )
or
∗
pX
ϵτ sX ∗ =
s
∗
τsX
ϵM
s
∗ ,
(1 + τsX ∗ ) (ϵX
−
ϵM
s
s )
pX
∗
∗
ϵτ sX =
s
ϵX
τsX
s
∗ ,
(1 + τsX ∗ ) (ϵX
−
ϵM
s
s )
∗
M is elasticity
where ϵX
s is the elasticity of exports of good s from the domestic country U S, and ϵs
of imports of good s by the foreign country RoW .
P
Tariff revenue. Using ad-valorem tariffs, the tariff revenue is given by T = i τiM pM
i Mi . Note
that T ≥ 0, since export subsidies are not allowed in our model. Differentiating T with respect to
τjM :
τjM
∂pM
∂T
∂T ∂pM
dT
j
j
M
=
+
=
p
M
+
M
δ
,
j
j
j
j
M
M
M
M
M
dτj
∂τj
∂pj ∂τj
(1 + τj )
∂τjM
where δj = ϵM
j
1+ϵX
j
ϵX
j
∗
∗
< 0. Note that in the absence of TOT effects, δj = ϵM
j .
Total welfare. The aggregate welfare (in both countries) includes the welfare of both owners of
0
M
the mobile factor and owners of the specific factors across all sectors: Ω = ΩL + ΩK = ΩL + ΩL +
X
M
X
ΩL + ΩK + ΩK , where7
!
L0
X
ΩL =
L0
X
Γr n0r w0r +
r
X X
r
Υ=
X
LM
Γir nir wr +
X
KM
M (pM )
πir
i
M
nK
ir
KM
Γir nir
i
M
ϕM
i (pi ) +
X
g
i
LX
LX
Γgr ngr wr
+ γ L Υ,
g
i
"
ΩK =
LM
!
+
X
KX
KX
Γgr ngr
g
X (pX )
πgr
g
X
nK
gr
!#
+ γ K Υ,
T
X
,
ϕX
g (pg ) +
n
!
γL =
X
L0
Γr nL
0r +
r
X
LM
LM
Γir nir +
X
LX
LX
Γgr ngr
,
g
i
!
γ
K
=
X X
r
M KM
ΓK
ir nir
+
X
X KX
ΓK
gr ngr
.
M
X
g
i
0
L
K
Suppose that ΓrL = ΓL,M
= ΓL,X
sr = Γr , and Γjr
jr
P
K
and γ K = r ΓK
r nr .
2.1
K
L
= ΓK
sr = Γr for all j, s. Then, γ =
P
r
L
ΓL
r nr ,
Nash Bargaining
Tariffs are the outcome of the following Nash Bargaining game between the domestic country
∗
U S and the RoW : choose the vectors of tariffs {τ M , τ X } that maximize
US σ
RoW (1−σ)
ΩRoW − Ω
,
N = ΩU S − Ω
7
We assume identical preferences for the two types of agents.
16
taking the tariffs of the other country
as given. Equivalently, the
tariffs are the solution to the
US
RoW
U
S
problem: max{τ M ,τ X ∗ } N = σLog Ω − Ω
+ (1 − σ)Log ΩRoW − Ω
, where τ M =
∗
∗
∗
∗
(τ1M , ..., τjM , ..., τJM ), and τ X = (τ1X , ..., τsX , ..., τGX ). The FOCs with respect to each τjM (chosen
∗
by the domestic country) and τsX (chosen by the foreign country) are given by:8
τjM
τsX
∗
:
:
US
dΩU S
dΩRoW
(1 − σ)
+
= 0,
RoW
dτjM
dτjM
ΩRoW − Ω
(13)
US
(1 − σ)
dΩU S
dΩRoW
+
= 0.
RoW
dτsX ∗
dτsX ∗
ΩRoW − Ω
(14)
σ
ΩU S − Ω
σ
ΩU S − Ω
Intuition from a two-good model. Suppose that country U S produces one importable good
j and one exportable good s (this means that the foreign country exports the good j and imports
the good s). Rearranging (13) and (14) gives
dΩRoW /dτjM
dΩU S /dτjM
=
dΩU S /dτsX ∗
dΩRoW /dτsX ∗
⇒
"
#
dΩRoW /dτjM dΩU S
dΩU S
−
= 0.
dΩRoW /dτsX ∗ dτsX ∗
dτjM
(15)
Consider the following interpretation of expression (15). Suppose that the agreement between
countries U and RoW is such that when a country U S raises the tariff on exports from country
RoW , RoW is “entitled” to increase the tariff on exports from U such that the utility in RoW is
unchanged (similarly if RoW is the country raising the tariff). In other words,
dΩRoW /dτjM
∗
dΩRoW /dτsX
∗
=
dτsX
dτjM
,
because RoW increases its tariff so that ΩRoW remains constant. In this case, the expression
between [·] in (15) would represent the increase in the tariff by country RoW in response to an
increase in the tariff by country U S “authorized” by the agreement in place. Now, this increase
∗
∗
in τsX would negatively affect country U S’s (net) welfare because a higher τsX lowers the price
received by exporters from U S.9
General case. Now, assume country U S (RoW ) imports (exports) J goods and exports (imports)
G goods. The analysis below focuses on the determination of tariffs from the perspective of the
domestic country U S. From (13):
dΩU S
dτjM
RoW
(1 − σ)/ ΩRoW − Ω
RoW
dΩ
+
= 0.
US
dτjM
σ/ ΩU S − Ω
(16)
We want to derive an expression for [·] in (16) above. Summing (14) over all goods exported
(imported) by country U S (RoW ):
X dΩU S
σ
8
9
ΩU S − Ω
US
X∗
g
dτg
+
X dΩRoW
(1 − σ)
ΩRoW − Ω
RoW
g
dτgX ∗
= 0.
Remember that countries only choose import tariffs, i.e., countries cannot subsidy exports.
We say “net” because the lower price would benefit consumers of the exportable good s in U S.
17
(17)
Isolating [·] from the previous expression gives
RoW
P
∗
(1 − σ)/ ΩRoW − Ω
dΩU S /dτgX
= −P g
.
RoW /dτ X ∗
US
g
g dΩ
σ/ ΩU S − Ω
(18)
Substituting (18) into (16) and rearranging, we obtain
#
"
X dΩU S
dΩRoW /dτjM
dΩU S
P
−
= 0.
∗
RoW /dτ X
dτgX ∗
dτjM
g
g dΩ
g
(19)
where
dΩU S
∂ΩU S ∂pM
∂ΩU S
j
=
+
,
dτjM
∂pM
∂τjM
∂τjM
j
and
dΩU S
∂ΩU S ∂pX
s
=
.
∗
X∗
dτsX
∂τ
∂pX
s
s
(20)
∗
∗
Note that in the previous expression ∂ΩU S ∂τsX = 0, since the impact of τsX on the welfare of
M =
country U S only takes place through the TOT effects, and for ad-valorem tariffs, ∂pM
j /∂τj
∂pM
M j
pM
j + τj ∂τ M .
j
Interpretation of the term between [·] in (19). When country U S increases τjM , it affects
RoW /dτ M . The
RoW because τjM has a negative impact on pM
j . This effect is captured by dΩ
j
M
increase in τj “triggers” a response by country RoW , which reacts by raising potentially all tariffs
∗
in tX .10 This increase ultimately affects producers and consumers of the exportable goods in
∗
country U S (because τsX negatively affects pX
s ).
M = 0 and
Suppose country U S is “small” relative to RoW . In this case, ∂pM
j /∂τj
dΩU S /dτjM = ∂ΩU S /∂τjM , which is the same expression we obtained earlier when only importable
M
RoW /dτ M = 0, so there is no interaction
goods are considered. However, if ∂pM
j /∂τj = 0, then dΩ
j
between U S and RoW .
2.2
Effect of changes in prices and tariffs on welfare
Impact of a change in pX
s . What is the impact on the welfare of U S of a change in the
international price of exports (due to a change in tariffs by the foreign country RoW )? A change
X
in pX
s (a decrease in ps when country RoW imposes a higher import tariff on good s) affects both
producers and consumers of good s in U S. Producers of good s are active in different regions r in
the domestic country. Therefore, the impact of a change in pX
s is spread across all (active) regions
in country U S affecting welfare in U as follows:
X X X
∂ΩU S
K
=
ΓK
sr nsr
X
∂ps
r
10
Note that this is a simultaneous decision.
18
X
qsr
X
nK
sr
−
γ X
D .
n s
∗
However, country RoW chooses a vector of tariffs τ X that affect all prices received by domestic
producers of exportable goods, pX
g . The impact of such change on the domestic country U S is
X ∂ΩU S
∂pX
g
g
XX
=
r
KX
X
qgr
KX
Γgr ngr
!
−
X
nK
gr
g
γX X
Dg .
n g
Impact of change in pM
j . The direct impact of changes in domestic prices on the domestic
country’s welfare (the first term of (20)) is given by
X M M
∂ΩU S
K
ΓK
=
jr njr
∂pM
j
r
!
M
qjr
+
M
nK
jr
γ M M ′
(τ p Mj − Dj ).
n j j
Direct impact of a change in τjM . A change in τjM also affects ΩU S by affecting tariff revenue
T directly and through its impact on the equilibrium world price pM
j :
∂ΩU S
γ
=
M
n
∂τj
2.3
pM
j
τjM
+
∂pj
!
Mj .
∂τjM
Solution - Ad-valorem tariffs
Suppose the weights placed on fixed factors producing importable (exportable) goods is the same
M
K M , ΓK X = ΓK X . Substituting the previous expressions
across sectors j (g). Specifically, ΓK
sr
r
jr = Γr
into (19), gives
"
X
KM
Γr
M
qjr
KM
nr
!
KM
nr
r
+
τjM
1 + τjM
γDjM
γMj δj
−
n
n
#
∂pM
j
∂τjM
=−
X dΩU S
γpM
j Mj
F
− µM
∗ .
j
n
dtX
g
g
Isolating τjM /(1 + τjM ) gives
τjM
1 + τjM
where γ L =
P
r
0
" M M
!#
M
K
q
1 X ΓK
n
n
jr
r
r
r
= −
M
δj r
γ
Mjr
nK
r
" X X
!#
X
K
X
q
n
n
1 X ΓK
gr
r
r
r
F
µM
θjg
−
j
X
δj r
γ
M
nK
jr
r
g
"
!#
X
QM
DgX
1 ϵM
j
j
MF
+
+
+ µj
θjg
,
δj ϵX ∗
Mj
Mj
g
M
M
L
L
L
ΓL
r n0r + Γr nr
X
X
L
+ ΓL
r nr
, γK =
P
r
M
ΓK
nK
r
r
M
X
K
+ ΓK
r nr
(21)
X
, γ = γ L +γ K ,
DjM = QM
j + Mj , Mjr = Mj (nr /n), and
∗
δj =
ϵM
j
(1 + ϵX
j )
ϵX
j
∗
< 0, θjg =
X
∂pX
g /∂τg
∗
M
∂pM
j /∂τj
< 0,
19
F
µM
j
dΩRoW /dτjM
P
=−
> 0.
RoW /dτ X ∗
g
g dΩ
Expression θjg
Dg
Mj
X
pg Dg
D
can be rewritten as θjg Mgj = θejg pM
where
M
j
j
∗
θejg =
3
ϵM
M ) X g M∗
(pM
/p
(ϵ
j
j
g −ϵg )
∗
∗
X
X
(pg /pg ) ϵX
j
∗
X
(ϵj −ϵM
j )
< 0.
Baron and Ferejohn (BF) legislative bargaining framework
This section develops a simplified version of the BF legislative bargaining framework used in the
text. We illustrate the outcome of the bargaining process using a three-district example. We later
discuss how the main results would apply more generally.11
3.1
A three-district BF model
We begin by deriving the tariff vector region r would choose if it could choose the national tariff
unconditionally, i.e., if r is chosen as the agenda setter and can implement its preferred tariff. We
next obtain the tariff that region r would choose conditional on attracting region r′ and form a
majority coalition.
Unconditional preferred tariff
Suppose that region r can choose its preferred tariff unconditionally, i.e., without considering
the impact of the tariffs on other regions in the federation.12 This tariff is obtained by maximizing
P L L L P K K K
K
Ωr = Ω L
r + Ωr =
i Λri nri ωri with respect to tr = {t1r , ..., tjr , ..., tJr }, which gives
i Λri nri ωri +
tjr
"
#
λK
Qj (tjr )
n
jr qjr (tjr )
−
,
=
−Mj′ (tjr ) λr nK
n
jr
(22)
K K
where λK
jr = Λjr njr is the aggregate welfare weight placed on special interests in district r, and
P P m m
L
λr = Λ L
0r n0r +
m
j Λjr njr is the aggregate welfare weight on the district r’s population, and
13
m ∈ {L, K}.
The solution vector, denoted by tr , is the vector of tariffs that district r would
choose if it had the ability to impose its own preferences over the other districts. Note that the
term [−Qj (tjr )/n] in (22) is the sum of per capita tariff revenue (Mj (tjr )/n) and the loss in consumer
surplus due to the tariff [−Dj (tjr )/n]. Also, all the endogenous terms are evaluated at pj = p̄j + tjr
so they depend on tjr since p̄j is given in this case.
11
See Celik et al (2013). To simplify the exposition, we consider only importing sectors and no terms-oftrade effects.
12
We still assume that the region is part of a federation of regions, which means that tariff revenue is
uniformly distributed across all residents, and aggregate market clearing conditions hold.
13
The subscript ℓ is the index used to sum over regions.
20
Equation (22) can also be rewritten in terms of ad-valorem tariffs τjr = tjr /pj as
"
#
λK
τjr
Qj (τjr )
n
jr qjr (τjr )
,
=
−
(1 + τjr )
−ϵj (τjr )Mj (τjr ) λr nK
n
jr
(23)
where τjr /(1 + τjr ) = tjr /pj , since pj = pj + tjr , and ϵj (τjr ) = Mj′ (τjr )[pj /Mj (τjr )]. The solution is
essentially the same as the district’s preferred tariff derived in the text.
Conditional preferred tariff
Consider a one-period BF bargaining model with three districts, each one with the same number
of residents nr = n/3. District r is randomly selected to be the agenda setter and proposes a vector
of tariffs. District r’s proposal is implemented if at least one other district (a majority, in the
three-district case), district r′ , joins to form a majority coalition.
The agenda setter, district r, solves the following problem:
1. Choose the vector of (specific) tariffs tr = {t1r , . . . , tjr , . . . , tJr } that maximizes district r’s
welfare Ωr (tr ) subject to Ωr′ (t)r ≥ Ωr′ (t) for all r′ ̸= r (the two other districts), where t is
the vector of existing (status-quo) tariffs.
2. Choose to form a coalition with the district that gives r the highest utility level.
The first stage of this problem can be described as follows. The agenda setter, district r,
maximizes the Lagrangian Lr = Ωr (tr ) + ρr′ [Ωr′ (tr ) − Ωr′ (t̄)] with respecth to tr , wherei ρr′ ≥ 0
∂Ω /∂t
denotes the Lagrange multiplier for each r′ ̸= r. Specifically, ρr′ = Max − ∂Ω r′ /∂tjj , 0 . At an
r
interior solution, when the constraint is binding, the numerator and denominator have opposite
signs: conceding a higher tj to satisfy r′ lowers r’s welfare. The size of ρr′ depends on the rate
of this trade-off at the constrained maximum. The solution to this problem gives the vector of
specific tariffs that district r would propose to district r′ , and district r′ would accept. For each
′
j = 1, . . . , J, the solution tariff, denoted by trjr , is given by
′
trjr =
K
r′
K
ΛK
jr njr [qjr (tjr )/njr ]
K
r′
K
ρr′ ΛK
r′ j nr′ j [(qjr′ (tjr )/njr′ ]
+
n
′
P
P
P P m m−
′
r
m nm + ρ ′ Λ ′ nL +
−Mj (tjr ) ΛL nL +
Λ
′
r
r
0
0r 0r
m
j jr jr
m
j Λjr′ njr′
r0
′
Qj (trjr )
n
. (24)
The latter expression can be rewritten as:
r′
tjr =
=
"
#
′
K
r′
K
r′
K
λr (λK
Qj (trjr )
n
jr /λr )[qjr (tjr )/njr ] + ρr′ λr′ (λr′ j /λr′ )[qjr′ (tjr )/nr′ j ]
−
,
′
λr + ρr′ λr′
n
−Mj′ (trjr )
"
#
′
r′
r′
λK
λK
Qj (trjr )
n
jr qjr (tjr )
r′ j qr′ j (tjr )
αr
+ (1 − αr )
−
,
(25)
′
λ r nK
λr′ nK
n
−Mj′ (trjr )
jr
r′ j
m m
m
m m
L L
where λm
jr = Λjr njr , λjr′ = Λjr′ njr′ , λr = Λ0r n0r +
and αr = λr +ρλr ′ λ ′ .
r
r
21
m m
i Λir nir ,
P P
m
λr′ = Λr′ 0 nL
r′ 0 +
m m
i Λr′ i nr′ i ,
P P
m
′
′
′
r /(1 + τ r ) = tr /p as follows:
Expression (25) can be rewritten in terms of ad-valorem tariffs τjr
jr
jr j
′
r
τjr
′
r
1 + τjr
3.2
=
"
#
′
r′
r′
λK
λK
Qj (trjr )
n
jr qjr (tjr )
jr′ qjr′ (tjr )
αr
.
+ (1 − αr )
−
′
′
λr nK
λr ′ n K
n
−ϵj (trjr )Mj (trjr )
jr
jr′
(26)
An Example
P
Suppose the utility of a representative consumer in region r is given by u = c0 + i (ψi ci − c2i /2),
with ψi > pi (for all pi considered here).14 This means that di ≡ di (pi ) = ψi − pi , and Di = ndi .
P
P
Then, consumer surplus is therefore given by ϕ = i (ψi − pi )2 /2 = i d2i /2. On the production
side, each unit of the sector-specific factor produces σri units of good i in region r. This means that
P
qri = σri nK
ri , denotes production of good i in region r, and Qi =
r qri aggregate production of
good i. Note that production is completely inelastic in this case. Finally, let ti = pi − pi , (specific
tariffs) and Mi = Di − Qi . Note that in this case Mi′ = Di′ = −n, so that ϵi = Mi′ (pi /Mi ) =
P L L L P K K K
K
−n(pi /Mi ). Total welfare in region r is Ωr = ΩL
r + Ωr =
i Λri nri ωri +
i Λri nri ωri , where
L
ωri
= 1+
X d2
i
2
}
{zi
|
+
indirect utility
K
ωri
= pri σri +
per cap tariff revenue
X d2
i
i
|
1X
(pi − pi )(Di − Qi ),
n
i
|
{z
}
{z
indirect utility
2
}
+
1X
(pi − pi )(Di − Qi ) .
n
i
|
{z
}
per cap tariff revenue
The unconditional preferred tariff is, in this case,
tjr =
X
nK
λK
jr
ℓj
σjr −
σℓj
,
λr
n
ℓ
K K
where λK
jr = Λjr njr is the aggregate welfare weight placed on special interests in district r, and
P P m m
L
λr = Λ L
0r n0r +
m
j Λjr njr is the aggregate welfare weight on the district r’s population, and
m ∈ {L, K}. The conditional preferred tariff is given by
′
trjr = αr
X
λK
λK
nℓj K
jr
r′ j
σjr + (1 − αr )
σr ′ j −
σℓj
.
λr
λr′
n
(27)
ℓ
Note that (27) can therefore be expressed as
′
trjr = αr tjr + (1 − αr )tjr′ .
14
We adopt some of the same assumptions as in Celik et al (2013).
22
(28)
′
′
r = t /p̄ can also be written as τ r = α τ + (1 − α )τ ′ ,
Equivalently, the ad-valorem tariff τjr
jr j
r jr
r jr
jr
since in this case p̄j is given. Alternatively,
′
r
τjr
1+
r′
τjr
= αr
1 + τjr
r′
1 + τjr
!
τjr
+ (1 − αr )
1 + τjr
1 + τjr′
r′
1 + τjr
!
τjr′
.
1 + τjr′
(29)
Note that
!
!
1 + τjr′
1 + τjr
+ (1 − αr )
= 1,
r′
r′
1 + τjr
1 + τjr
{z
} |
{z
}
αr
|
α
er
(30)
(1−e
αr )
which means that
′
r
τjr
1+
3.3
r′
τjr
=α
er
τjr′
τjr
+ (1 − α
er )
.
1 + τjr
1 + τjr′
(31)
Extension: More than three regions
The form of the solution in equation (26) generalizes to the case where r > 3. The characterization of the solution, however, gets more complicated as the number of districts R increases. This
is because both the number of goods J and their regional distribution matter as well.
Consider an economy with R districts (with R assumed to be an odd number), one of which,
district r, is the agenda setter. District r seeks to form a minimum winning coalition of (R + 1)/2
members by proposing a tariff vector to the other districts. We denote by Cr the set of minimum
winning coalitions that would allow district r to achieve a majority.15
In the first step, for each coalition Cr ∈ Cr , the agenda setter r computes the vector of tariffs
C
r
tr r that would satisfy districts in the coalition. In other words, the tariff vector tC
r would offer
those in the coalition a utility that is as large as what they can get in the status quo. The solution
to this first step problem is an extension of (26).
Cr
r
Specifically, under the assumptions considered in Section 3.2, it follows that tC
r and also τr
can be expressed as a convex combination of the preferred tariffs of the districts in the coalition:
Cr
τjr
=
X
αι τjι ,
for each Cr ∈ Cr ,
(32)
ι∈Cr
P
where τjι is the preferred tariff of region ι for good j, 0 ≤ αι ≤ 1 and ι∈Cr αι = 1.
In the second step, the agenda-setter representing r can always remain in the status quo, or
choose a coalition Cr that gives r the highest utility, conditional on r getting a utility level greater
than the status quo. To the extent that the agenda setter is able to form a coalition that gives all
members in the coalition a utility that is at least as high as the status quo, the solution tariff would
The agenda setter needs (R − 1)/2 additional districts in order to form a majority. The set of Cr would
(R−1)!
Γ[R]
therefore contain {[(R−1)/2]!}
2 = Γ[(1+R)/2]2 different coalitions, where Γ[x] = (x − 1)!.
15
23
look like (32).
24
Appendix C – Congressional District Data
Employment Data
Source: Bureau of Labor Statistics. File names: 2002_qtrly_by_industry
Data Source: BLS Employment Data
S
1. Employment by State S and industry IN D (EIN
D ).
S
2. Employment by State S for all the manufacturing sector (EM
AN U F ).
C
3. Employment by County C and industry IN D (EIN D ): there are non-disclosed observations
at this level; however, these values represent a small proportion of total observations (less
than 17% of the data).
4. Despite data being reported at the state level, there are a number of non-disclosed observations. In some instances, we use data available at the county level to impute the aggregate
as follows:
Employmenti
,
(a) Output per worker: Āi = RealSectoralOutput
i
A
ind
(b) Re-scaled output per worker: Ai = n P
.
Ā
ind∈I
ind
GDP Data
Source: Bureau of Economic Analysis (BEA). Files names: SAGDP2N and CAGDP2
Data Source: BEA Output Data
S
1. GDP by State S and industry IN D, for all industries (YIN
D ): these data are dissaggregated
S
S
S
S
S + Y S ; and Y S
for most industries, except for Y311−312 = Y311 + Y312 ; Y313−314 = Y313
314
315−316 =
S
S
Y315 + Y316 .
S , Y S , Y S , Y S , Y S , Y S , as follows:
We impute Y311
312
313
314
315
316
(a) Estimate weights using employment data calculated above:
S
S
S
S
N312
N313
N314
N311
S
S
S
S
ϕS311 = N S +N
S ; ϕ312 = N S +N S ; ϕ313 = N S +N S ; ϕ314 = N S +N S ; ϕ315 =
S
N315
S +N S
N315
316
311
312
; and ϕS316 =
311
S
N316
S
S
N315 +N316
312
313
314
313
314
S , Y S , Y S , Y S , Y S and Y S as:
(b) Calculate Y311
312
313
314
315
316
S = ϕS ∗Y S
S = ϕS ∗Y S
S
S
S
S
S
S
Y311
;
Y
;
311
311−312
312
312
311−312 Y313 = ϕ313 ∗Y313−314 ; Y314 = ϕ314 ∗Y313−314 ;
S = ϕS ∗ Y S
S
S
S
Y315
315
315−316 ; and Y316 = ϕ316 ∗ Y315−316
C ): In contrast to state level data, county GDP
2. GDP by county C and industry IND (YIN
D
data are only available at the aggregated level of total manufacturing (and also durables, and
C
non-durables). We construct YIN
D as follows:
C
C
C
N31
N32
N33
C
C
Calculate employment weights: ϕC
31 = N C +N C +N C ; ϕ32 = N C +N C +N C ; ϕ33 = N C +N C +N C ,
31
32
33
31
32
33
31
32
33
C = ϕC ∗Y C
C
C
C
C
C
C
and impute Y31
31
M anuf ; Y32 = ϕ32 ∗YM anuf ; Y33 = ϕ33 ∗YM anuf . We proceed similarly
C .
to construct each YIN
D
25
@FedFRASER