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A
Theoptimalexportpolicyunderinequality aversion
ConsiderasmallopeneconomywithanidenticalstructureastheonedescribedinSection2,except
fortwofeatures. The…rstfeatureis s thatconsumersarestandardrationalagents,that is,theyare
notlossaverse.Hence,I=I=0,andthesumofland-owners’indirectutilitycanbeexpressedas
V
L
(p)=(p)+[CS(p)+GR(p)];
whilethesumofworkers’indirectutilityisgivenby
V
l
(p)=(1 )[1+CS(p)+GR(p)]:
Thesecondfeatureisthatthegovernmentisassumedtobeaversetoinequality. Thesimplestway
tocapturegovernment’sinequalityaversionisbyde…ningsocialwelfareas
G(p)=h(V
L
(p))+h(V
l
(p))
wherefunctionh()istwice continuously di¤erentiablewithh
0
()> 0;h
00
()<0. Functionh() ) is
meant tocapturethe ideathat, coeterisparibus, amore equitable distributionof resources across
workersandland-ownersiswelfareenhancing.
Government’sobjectiveistheoneof…ndingpricep,andhencetax/subsidyt= s=p p,which
maximizessocialwelfare.FromtheFOCweobtain
dG
dp
=(p
p)x
0
(p)[h
0
l
(1 )+h
0
L
] (1 )y(p)(h
0
l
h
0
L
)=0;
where
h
0
l
dh
dV
l
;h
0
L
dh
dV
L
:
Afterafewalgebraicstepswecan…nallyexpresstheoptimaltax/subsidyas
=
t
p t
=
(1 )(h0
l
h0
L
)
(1 )h0
l
+h0
L
z(p)
e(p)
;
(14)
wherez(p)y(p)=x(p),e(p)x
0
(p)p=x(p).
Theoptimalpolicy istheonewhichoptimally trades o¤theusualmarginallosscausedby the
deviationfromfreetradewiththemarginalgainassociatedwithamoreequitablesociety. Inpar-
ticular,theoptimalpolicyis atax x ifandonly y if h
0
l
> h
0
L
, thatis, ifthemarginalcontributionof
workers’utilitytosocialwelfareisstrictlyhigherthantheoneofland-owners,whileitisasubsidyin
theoppositecase.Onlywhenh0
L
=h0
l
(whichhappenswhenworkersandland-ownersreachthesame
levelofwelfare),theoptimalpolicyisfreetrade.
Moreover,andcruciallyforourpurpose,itispossibletoprovethattheoptimalexporttax(sub-
sidy),givenbyexpression(14),isanincreasing(decreasing)functionofinternationalfoodpricep
.
41
41
De…nethe"non-standard"partoftheformulafortheoptimalexportpolicyin(14)as
H
(1 )
h
0
l
h
0
L
(1 )h
0
l
+h
0
L
;
It is possible to provethat dH=dp
<0to theextent that h
00
l
;h
00
L
<0(that is, to theextentthatthegovernment is
inequalityaverse). Therestoftheprooffollowsfromthepreviousliteratureontradepolicy(GrossmanandHelpman,
1994,FreundandOzden,2008).
30
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The intuitionfor this s result t is straightforward: : an n increase e in n p is s bene…cialtoland-owners and
harmfulto workers. . A A government whichis inequality averse raises the export tax (or lowers the
exportsubsidy)toattenuatethewelfarelossofworkers.
Ontheotherhand,andasshowninSection3,asimultaneousimpositionofexporttaxesacrossa
continuumofidenticalexportingcountriesraisestheinternationalpriceoffood(whileexportsubsidies
lowerit). Onceitisproventhatacomplementarityexistsbetweenexporttaxesandfoodprices s -as
theformer respondpositivelyto o the latter r andviceversa-, , amultiplier e¤ect t necessarily y follows (a
formalproofofthisstatementisisomorphictothatofProposition6inCooperandJohn,1988). As
aresult, thetheoretical…ndingsofthis s papercontinuetoholdandtodeliver the samehypotheses
whichhavebeentestedintheempiricalanalysis.
B
Proofs
Proof of Proposition1. . TheproofofProposition1follows,mutatismutandis,fromFreund
andOzden(2008)andisthusomitted.
ProofofProposition2.Forp
2(
p;
p
c
),thepolicyruleofeachcountryiscapturedbyexpression
t=p
p. However,whileeachcountrytakes s p
asgiven(beingtoosmalltoa¤ectit),itsvalueis
a¤ectedbythetax policy implementedby thewholeset of exporters. . Worldprice e p is implicitly
de…nedby(8),whiletheuntaxedworldpricep
ft
isimplicitlyde…nedbythelaissezfaire equilibrium
intheworldmarket,m
p
ft
=x
p
ft
.Wecanthende…netheworldpriceasanincreasingfunction
oftheexporttax andof the freetradeworldprice, p
t;p
ft
,where p
ft
parameterizestheworld
pricefunctionandcapturesanyshockthata¤ectsfunctionsm()orx()otherthanchangesint.
Theequilibriumtaxisthenimplicitlyde…nedby
t=p
t;p
ft
p:
Wenowwant toshowthat the total derivative of t withrespect to o p
ft
is greater thanits partial
derivative. Itis
@t
@p
ft
=
@p
@p
ft
;
(15)
while
dt
dp
ft
=
@p
@p
ft
+
dp
dt
dt
dp
ft
;
fromwhichweobtain
dt
dp
ft
=
1
dp
dt
@p
@p
ft
:
Usingexpression(15)andthe fact that dp=dt2(0;1)(whichisproveninfootnote17),itfollows
immediately
dt
dp
ft
=
@t
@p
ft
;
wherethemultiplierisgivenby

1
dp
dt
>1:
31
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Theproofforthemultipliere¤ectofsubsidieswhenp 2
p
c;p
followsimmediatelyonceitisrealized
thatt= s. . Forp 2
p
;
p
,t(p)=0implyingthatp
0;p
ft
=p
ft
. Thepair(p
ft
;t)=
p
ft
;0
describestheequilibriumintheworldfoodmarketandnomultipliere¤ectexists: dp
=dp
ft
=1.
Proof of Proposition 3. . (i) ) Worldprice p
is de…nedimplicitly y by y (9), while e the untaxed
worldpricep
ft
isimplicitlyde…nedbythelaissezfaire equilibriumintheworldmarket,m
p
ft
=
P
n
i=1
x
p
ft
. As s inthe smallcountry case, , itis s usefulto o de…netheworldprice as s afunctionof
bothexport taxes andof the untaxedworldprice, , p
t;p
ft
, where t   ft
1
;::;t
i
;::;t
n
g, andp
ft
parameterizestheworldpricefunction,thuscapturingallexogenousforcesa¤ectingimportdemand
andexportsupplyotherthanexporttaxes.
De…ne(a)
p
ft
asthevalueofthefreetradeworldpricesuchthatthedomesticpriceresultingfrom
themaximizationof(11)byallcountriesisequaltop:
p
ft
:p
^
t;
p
ft
^
t= p;
(16)
(b)
p
c
ft
as the value of the free trade worldprice suchthat the domestic price resulting g from the
maximizationof(10)byallcountriesisequaltop:42
p
c
ft
:p
t;
p
c
ft
t= p:
(17)
Itcanbeshownthat
p
ft
<
p
c
ft
.Thisresultsfromexploitingthefollowingthreefactsinexpressions
(16)and(17):(1)
tisstrictlyhigherthan
^
t;(2)thedomesticpriceincountryiisadecreasingfunction
oft
i
;(3)theequilibriumworldpricep
isincreasinginp
ft
.
43
Facts(1)and(2)implyalowerdomestic
priceassociatedtotax
t.Hence,inorderforbothdomesticpricestobeexactlyequalto
pasin(16)
and(17),fact(3)implies
p
ft
<
p
c
ft
.
Wecannowdistinguishamongthreeregions.Region1:Ifthefundamentalsoftheworldeconomy
aresuchthatp
ft
6
p
ft
(andhigherthanp
ft
),lossaversiondoesnotmatter,theequilibriumpolicy
istheinteriorsolution(
^
t)resultingfromthemaximizationof(11)(seefootnote20),andhencefact
(3)appliedto(16)impliesthatthedomesticpriceis strictlylowerthanthreshold
p. Region2: If
insteadp
ft
>
p
c
ft
,thedomesticpriceisabovetheupperthresholdandlossaversionmatters. Inthis
case,theequilibriumpolicyistheinterior solution(
t)resultingfromthemaximizationof(10).The
reasonisthat,foranyp
ft
>
p
c
ft
,fact(3)appliedto(17)impliesp
t;p
ft
t>p.Region3:When
42
To simplify y the notation we onlywrite
^
t and
t instead of
^
t
p
ft
and
t
p
ft
. Both, , however, depend d on the
exogenous p
ft
.
43
Fact (1) canbeproven as follows. . Tax
^
t is the onefor which W
0
i
^
t
=0. Moreover, , for any t>
^
t(t<
^
t), it is
W0
i
^
t
<0(W0
i
^
t
>0). Tax
t is instead the onesuch that W0
i
t
+H0
i
t
=0. Given n that, where it is de…ned,
H
0
i
()>0,itmustbeW
0
i
t
<0,whichonlyoccursfortaxvaluesstrictlyhigherthan
^
t. ToproveFact(2),…rstnotice
thatdp
i
=dt
i
=dp
=dt
i
1. Then,itsu¢ ¢ cesto o provethat dp
=dt
i
belongsto (0;1)8i=1;:::;n. De…ne
 (p
;t)
n
X
i=1
x(p
t
i
) m(p
)
astheimplicit functionof theworldpricew.r.t. theexporttaxes. Usingtheimplicitfunctiontheorem,weobtain
dp
dt
i
dt
i
dp
=
dx
dp
n
dx
dp
dm
dp
8i=1;:::;n:
whichbelongsto (0;1=n)asdm=dp <0. Hence,itis dp
i
=dt
i
<0:Fact(3)istruebyde…nitionofp andp
ft
.
32
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p
ft
2
p
ft
;
p
c
ft
, loss s aversionmatters but the interior solution n (
t) is such h that t the domesticprice
wouldbelowerthan p(again,thisisanimplicationoffact(3)appliedto(17)). Thesolutiontothe
maximizationof(10)isthenacorner solutionsuchthatthedomesticpriceisexactlyequalto p:
t
i
=t:p
t;:::;t;p
ft
t=p 8i=1;:::;nand8p
ft
2
p
ft
;
p
c
ft
:
(ii) Theproofofthissecondstatementproceedsthroughthesamelogicalstepsasabove. . First,
valuesp
c
ft
;p
ft
arede…nedasthevaluesofthefreetradeworldpricesuchthatthedomesticpriceis
equaltop
whenlossaversion(of producers) matters anddoesnot matter,respectively. . Thenitis
shownthatp
c
ft
<p
ft
,andthat,alongtheinterval
p
c
ft
;p
ft
,theexportpolicyisoneofcompensating
protectionism. Theonlydi¤erenceisthatthispolicyisnotnecessarilyasubsidybutmayalsobea
tax. Thereasonforthisisthefollowing: sincetheequilibriumexportpolicywhenlossaversiondoes
not matterisastrictlypositivetax(
^
t>0),whenp
ft
is"slightly"belowp
ft
,theequilibriumpolicy
(whichistheone thatkeeps the domesticpriceconstant at p=p
) is stillataxandsoitremains
untilp
ft
becomessu¢cientlylow. Inparticular,whenthefreetradeworldpriceislowerthanp
,the
onlywaytokeepthedomesticpriceatlevelp
istoreversethepolicytoanexportsubsidy.Formally,
wecandistinguishamongthefollowingthreepossibilitieswhenp
ft
2
p
c
ft
;p
ft
. Ifp
ft
isabovep
,a
strictlynegativesubsidys= t<0isneededinordertomakep
t;p
ft
t=p
. Ifp
ft
=p
,s=0
isneededinordertomakep
0;p
ft
0p
ft
=p
. Finally,ifp
ft
<p
,astrictlypositivesubsidy
s>0isneededinordertomakep
s;p
ft
+s=p
.
ProofofProposition4. (i)Thereactionfunctionofcountryi,t
i
(t
i
),isimplicitlygivenby
t
i
=p
t
i
;t
i
;p
ft
p:
(18)
wheret
i
ft
1
;::;t
i 1
;t
i+1
;::t
n
g.De…ne
J(t
i
;t
i
)p
t
i
;t
i
;p
ft
p t
i
:
Usingtheimplicitfunctiontheorem,foranyelementt
i
2t
i
weobtain
dt
i
dt
i
dJ
dt
i
dJ
dt
i
=
dp
dt
i
dp
dt
i
:
Giventhatdp
=dt
i
=dp
=dt
i
2(0;1=n)(wheren>2),itthenimmediatelyfollowsthatdt
i
=dt
i
2
(0;1).
(ii) Fromthereactionfunctionofcountryi(expression18) wenowwanttoshowthat thetotal
derivativeoft
i
withrespecttop
ft
isgreaterthanitspartialderivative.Itis
@t
i
@p
ft
=
@p
@p
ft
;
while
dt
i
dp
ft
=
@p
@p
ft
+
dp
dt
i
dt
i
dp
ft
+
X
j6=i
dp
dt
j
dt
j
dp
ft
:
33
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Ascountriessharesymmetricfundamentals,itisdt
i
=dp
ft
=dt
j
=dp
ft
anddp=dt
i
=dp=dt
j
. Hence,
fromthelasttwoequationsweobtain
dt
i
dp
ft
=
@t
i
@p
ft
8i=1;::;n:
where

1
1 n
dp
dt
i
>1;
asdp
=dt
i
2(0;1=n).
34
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35 
 
Figure 1: International food prices 1990‐2010 
 
 
 
Figure 2: International food prices and export restrictions 
 
 
70
90
110
130
150
170
190
210
230
250
deflated
nominal
0
5
10
15
20
25
30
35
40
110
130
150
170
190
210
230
250
N. of countries imposing an export   restriction
Price Index
price index (deflated)
Export restrictions
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36 
 
Figure 3: Export policy (small economy) 
 
 
 
Figure 4: Multiplier effect (small economies) 
 
37 
 
 
Figure 5: Multiplier effect (large economies) 
 
 
 
 
 
Table 1: International food prices before and after 2006 
  
Food  
Meat  
Dairy  
Cereals  
Oils  
Sugar  
  
Mean 
s.d. 
Mean 
s.d. 
Mean 
s.d. 
Mean 
s.d. 
Mean 
s.d. 
Mean 
s.d. 
  
  
  
  
  
  
  
  
  
  
  
  
1990‐2006 
107.6  12.6  112.3  13.0    99.5    18.0    103.5  15.7    97.5  20.2    139.5  38.7 
World Food crisis 2007‐ mid‐2008  177.5    32.4  132.7  13.6  223.8  41.4  199.5  52.4  202.0  54.2    154.8  18.8 
World Food crisis 2009‐2010 
183.3  29.4  148.7  14.7  182.7  41.4  193.9  34.8  190.3  46.2    298.0  74.6 
 
 
38 
 
 
Table 2: Export restrictions by product 
hscode 
Product Name 
N Exp. 
Restrictions  
% of trade 
covered by exp 
restrictions 
0203 
Meat of swine, fresh, chilled or frozen 
0.001 
1509 
Olive oil and its fractions, whether or not refined 
0.001 
1507 
Soya‐bean oil and its fractions 
0.023 
1207 
Other oil seeds and oleaginous fruits 
0.0 
1508 
Ground‐nut oil and its fractions 
0.0 
1514 
Rape, colza or mustard oil and fractions  
0.1 
1201 
Soya beans, whether or not broken 
0.5 
1512 
Sunflower‐seed, safflower or cotton‐seed oil and fats 
0.6 
0204 
Meat of sheep or goats, fresh, chilled or frozen 
0.6 
1504 
Fats and oils and their fractions 
0.8 
0405 
Butter and other fats and oils derived from milk 
0.9 
1007 
Grain sorghum 
1.0 
1701 
Cane or beet sugar and chemically pure sucrose 
1.2 
0207 
Meat and edible offal, of the poultry of heading 0 
1.6 
1208 
Flours and meals of oil seeds or oleaginous fruits 
2.3 
0201 
Meat of bovine animals, fresh or chilled 
3.8 
0901 
Coffee, whether or not roasted or decaffeinated 
4.0 
0703 
Onions, shallots, garlic, leeks and others 
9.3 
1001 
Wheat and meslin 
14.1 
1005 
Maize (corn) 
16.0 
1003 
Barley 
22.4 
1006 
Rice 
13 
34.6 
1511 
Palm oil and its fractions, whether or not refined 
46.7 
1801 
Cocoa beans, whole or broken, raw or roasted 
50.1 
  
Total 
85 
  
 
 
Table 3: Shares of export restrictions by type of measure 
  
Food                
(all sectors) 
Staple Food 
Export tax 
20 
24 
Export prohibition 
42 
48 
Quotas or licensing 
10 
10 
Other 
28 
24 
 
39 
 
Table 4: Determinants of export restrictions 
 
All food 
products 
All food 
products 
All food 
products 
All food 
products 
All food 
products 
All food 
products 
Staple 
products 
Staple 
products 
Staple 
products 
  
Logit 
LPM 
LPM 
Logit 
LPM 
LPM 
Logit 
Logit 
Logit 
  
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
(9) 
  
  
  
  
  
  
  
  
  
  
log Int. Prices
t‐1
 
0.001* 
0.001* 
0.001* 
0.0004* 
0.001* 
0.001* 
0.038* 
0.011 
0.034** 
  
[0.000] 
[0.000] 
[0.000] 
[0.000] 
[0.000] 
[0.000] 
[0.020] 
[0.009] 
[0.017] 
  
  
  
  
  
  
  
  
  
  
log quarterly Exports 
0.001** 
0.002** 
0.001 
0.001** 
0.002** 
0.001 
0.001** 
0.001** 
0.001** 
  
[0.000] 
[0.001] 
[0.001] 
[0.000] 
[0.001] 
[0.001] 
[0.001] 
[0.000] 
[0.001] 
  
  
  
  
  
  
  
  
  
  
Share Aggregate Value 
0.056* 
0.147 
  
0.055* 
0.147 
  
0.077** 
0.067** 
0.073** 
  
[0.033] 
[0.091] 
  
[0.033] 
[0.091] 
  
[0.037] 
[0.034] 
[0.036] 
  
  
  
  
  
  
  
  
  
  
log Global Export Restrictions
t‐1
  
  
  
  
0.019** 
0.084** 
0.084** 
  
0.041** 
  
  
  
  
  
[0.009] 
[0.039] 
[0.039] 
  
[0.019] 
  
  
  
  
  
  
  
  
  
  
  
log Global Tariff Reductions
t‐1 
 
  
  
0.002 
0.004 
0.004 
  
‐0.005* 
‐0.003 
  
  
  
  
[0.001] 
[0.003] 
[0.003] 
  
[0.003] 
[0.002] 
  
  
  
  
  
  
  
  
  
  
Time (monthly) FE 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Product FE 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Country FE 
  
  
Yes 
  
  
Yes 
  
  
  
Observations 
43186 
63548 
63548 
43186 
63548 
63548 
7716 
7716 
7716 
R‐squared 
  
0.022 
0.14 
  
0.024 
0.142 
  
  
  
 
 
Note: Standard errors clustered at country level.  *** p<0.01, ** p<0.05, * p<0.1. 
 
 
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