gravity without apology: the science of elasticities...
TRANSCRIPT
Gravity without Apology: The Science ofElasticities, Distance, and Trade
Celine Carrere
Geneva and CEPR
Monika Mrazova
Geneva and CEPR
J. Peter Neary
Oxford, CEPR and CESifo
Royal Economic Society Annual ConferenceUniversity of Warwick
April 15, 2019
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 1 / 80
Introduction
Introduction: Gravity and International Trade
Gravity: The value of trade declines with distance
One of the great successes of modern economics
Gravity in trade is both fact and theory– Like evolution: Gould (1981)
Though this is not widely known by economists outside trade
And “anti-gravity” continues to have popular appeal
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 2 / 80
Introduction
Gravity in the News05/03/2019, 18+12Financial Times (UK) | Tuesday, April 19, 2016 | Front Page | 1
Page 1 of 1http://digital.olivesoftware.com/Olive/APA/FinancialTimesUK/Pri…sue_date=Tuesday%2C%20April%2019%2C%202016§ion=Front%20Page
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 3 / 80
Introduction
Anti-Gravity
“Today, we stand on the verge of an unprecedented ability to liberate global tradefor the benefit of our whole planet with technological advances dissolving away thebarriers of time and distance. It is potentially the beginning of what I might call ‘postgeography trading world’ where we are much less restricted in having to find partnerswho are physically close to us.”
– Liam Fox, UK Minister for International Trade, Sept. 2016
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 4 / 80
Introduction
This Lecture
Review the evidence for gravity
Introduce some simple ways of understanding CES gravity
Note some problems with CES
Sketch some alternatives
Background: Brexit ...
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 5 / 80
Introduction
Brexit: Not Just Economics
“I don’t think we’ll be poorer out [of the EU], but if you told memy family would have to eat grass I’d still have voted to leave.”
– anon.; quoted by Robert Shrimsley, Financial Times, Dec. 14, 2018
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 6 / 80
Introduction
What they told us ...
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 7 / 80
Introduction
What they didn’t tell us ...
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 8 / 80
Introduction
Sincere, Strongly-Held Views – On Both Sides
“I don’t think we’ll be poorer out, but if you told me my familywould have to eat grass I’d still have voted to leave.”
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 9 / 80
Introduction
Here: Focus on the Economics
“I don’t think we’ll be poorer out, but if you told me my familywould have to eat grass I’d still have voted to leave.”
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 10 / 80
Introduction
Economics of Brexit
Many studies of the trade effects of Brexit
Predominantly using the gravity model
Dhingra et al. (2017), Sampson (2017)Brakman, Garretsen, and Kohl (2018)Mayer, Vicard, and Zignago (2019)
I ignore work on other economic aspects of Brexit
Davies and Studnicka (2018): Stock-market responseMcGrattan and Waddle (2018): Impact on foreign investmentAlabrese, Becker, Fetzer, and Novy (2019): Determinants of votingO’Rourke (2019): Historical context
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 11 / 80
Introduction
Economics of Brexit: Professional Consensus
Professional consensus: Three Iron Laws of the Economics of Brexit
Focusing on trade in goods ...... ignoring transitional problems ...
... and macro policy responses
1 The only good Brexit is a dead Brexit
2 The harder the Brexit the higher the economic costs
3 Even a hard Brexit will not have “very” large costs
2% of GDP if soft, 6+% of GDP if hard
Compare: UK spent 7.26% of GDP on NHS in 2016/17
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 12 / 80
Introduction
Background
Carrere, C., M. Mrazova, and J. P. Neary (2019): “Subconvex Gravity,” inpreparation.
Mrazova, M., and J. P. Neary (2017): “Not so Demanding: Demand Structureand Firm Behavior,” American Economic Review, 107(12), 3835–3874.
Mrazova, M., and J. P. Neary (2019): “Selection Effects with HeterogeneousFirms,” Journal of the European Economic Association, forthcoming.
Mrazova, M., and J. P. Neary (2019): “IO for Export(s),” Working Paper No.868, Department of Economics, University of Oxford.
Maggi, G., M. Mrazova, and J. P. Neary (2018): “Choked by Red Tape? The
Political Economy of Wasteful Trade Barriers,” CEPR Discussion Paper No. 12985.
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 13 / 80
Introduction
Outline
1 Gravity as Fact
2 Gravity as Theory
3 Gravity Anomalies
4 Subconvex Gravity
5 Conclusion
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 14 / 80
Gravity as Fact
Outline
1 Gravity as Fact
2 Gravity as Theory
3 Gravity Anomalies
4 Subconvex Gravity
5 Conclusion
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 15 / 80
Gravity as Fact
The Gravity Equation: A Universal Tendency
Overwhelming professional consensus that distance matters for trade
Head and Mayer (2014): review of 159 papers
Average preferred estimate of distance elasticity: −1.1
S.D. 0.41; median −1.14
Not just geographical distance matters:
Common language, legal system, colonial origins, FTA membership,etc.
Results below for distance elasticity of 2017 UK exports in line withthe literature:
−0.752 (0.098): OLS, simple regression, n = 181−1.441 (0.029): OLS, full controls, n = 23, 251−0.977 (0.021): PPML, full controls, n = 42, 230
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 16 / 80
Gravity as Fact
Gravity: Not Just for Trade in Goods
Distance also matters (though less so on average) for:
Services trade: Kimura and Lee (2006)
FDI: Kleinert and Toubal (2010), Keller and Yeaple (2013)
Equities: Portes and Rey (2005)
eBay: Lendle, Olarreaga, Schropp, and Vezina (2016)
Google: Cowgill and Dorobantu (2012)
And the distance coefficient for goods trade has not fallen over time
“The Mystery of the Missing Globalization”!
But: Not a mystery
Distance is relative
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 17 / 80
Gravity as Fact
Data Sources, etc.
Survey:
Head and Mayer (2014)
Data: CEPII
http://www.cepii.fr/CEPII/en/bdd_modele/presentation.
asp?id=8
UK trade policy: UK Trade Policy Observatory
http://blogs.sussex.ac.uk/uktpo/
EU trade agreements
http://ec.europa.eu/trade/policy/countries-and-regions/
negotiations-and-agreements/
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 18 / 80
Gravity as Fact
UK Exports and Importer GDP, 2017
slope = 1.06R² = 0.826
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0
UK
Exp
orts
(log
US$
)
Importer GDP (logUS$)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 19 / 80
Gravity as Fact
UK Exports/Importer GDP and Distance, 2017
slope= -0.75R² = 0.246
‐16
‐15
‐14
‐13
‐12
‐11
‐10
‐9
5.7 6.7 7.7 8.7 9.7
UK
Exp
orts
/Im
port
er G
DP
(log)
Distance (log km)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 20 / 80
Gravity as Fact
Gravity Weighted by Exports, UK, 2017
slope= -0.75R² = 0.246
‐16
‐15
‐14
‐13
‐12
‐11
‐10
‐9
5.7 6.7 7.7 8.7 9.7
UK
Exp
orts
/Im
port
er G
DP
(log)
Distance (log km)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 21 / 80
Gravity as Fact
Trade Agreements, UK, 2017
‐16
‐15
‐14
‐13
‐12
‐11
‐10
‐9
5.7 6.7 7.7 8.7 9.7
UK
Exp
orts
/Im
port
er G
DP
(log)
Distance (log km)
EU
EU‐FTA
Non‐EU
Best Fit
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 22 / 80
Gravity as Fact
Trade Agreements and ex-Colonies, UK, 2017
‐16
‐15
‐14
‐13
‐12
‐11
‐10
‐9
5.7 6.7 7.7 8.7 9.7
UK
Exp
orts
/Im
port
er G
DP
(log)
Distance (log km)
EU
EU‐FTA
Non‐EU
Ex‐Colony
Best Fit
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 23 / 80
Gravity as Theory
Outline
1 Gravity as Fact
2 Gravity as TheoryStructural GravityComparative Statics for Structural GravityAn Application: Brexit
3 Gravity Anomalies
4 Subconvex Gravity
5 Conclusion
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 24 / 80
Gravity as Theory
Gravity as Theory
“[I] have explained the phenomena of the heavens and of our seaby the power of gravity, but have not yet assigned the cause ofthis power.”
– Isaac Newton (1713)
“The intent of this paper is to provide a theoretical explanationfor the gravity equation applied to commodities.”
– Jim Anderson (1979)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 25 / 80
Gravity as Theory Structural Gravity
Foundations of the Gravity Model
A variety of different supply sides, all with CES preferences
The gravity equation has been shown to be consistent with:
Armington (1969) model of pure exchange
Anderson (1979), Anderson and van Wincoop (2003)
Models of monopolistic competition such as Krugman (1980)
Bergstrand (1985) and Helpman (1987)
Heterogeneous-firms model of Melitz (2003)
Chaney (2008)
Multi-country Ricardian model
Eaton and Kortum (2002)
Synthesis: Arkolakis, Costinot, and Rodrıguez-Clare (2012)
All yield the same “structural gravity” model
Here: I focus on the simplest Armington-based version
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 26 / 80
Gravity as Theory Structural Gravity
Start with CES Demands
n countries, each endowed with a unique good
Common CES preferences: Each country consumes all goods:
xjk = βj
(pjkPk
)−σ EkPk
⇒ Vjk = βj
(pjkPk
)1−σEk
Vjk = pjkxjk: Value of exports from j to k
βj : Taste parameter for country j good
pjk: Delivered price of j’s export in kpjk = pjtjk: Equals home price times an “iceberg” trade cost
Pk: Importer price index:
Pk =
(∑h
βhp1−σhk
) 11−σ
σ: Elasticity of substitution
Ek: Country k’s expenditure on all goods
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 27 / 80
Gravity as Theory Structural Gravity
From CES Demands to Structural Gravity
Total sales by country j sum to GDP in equilibrium:∑k
Vjk = Yj
Forward
Substitute into this from CES demands:
Yj =∑k
Vjk = (βjpj)1−σ
∑k
(tjkPk
)1−σEk
Use this to eliminate (βjpj)1−σ from Vjk and Pk
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 28 / 80
Gravity as Theory Structural Gravity
Structural Gravity
Structural gravity:[Anderson (1979), Anderson and van Wincoop (2003)]
Vjk =
(tjk
ΠjPk
)1−σ
︸ ︷︷ ︸(1)
YjEkYW︸ ︷︷ ︸(2)
(2): Frictionless trade: YW is world income
(1): Trade costs relative to outward and inward “multilateral resistance”:
(Πj)1−σ
=∑h
(tjhPh
)1−σEhYW
(Pk)1−σ
=∑h
(thkΠh
)1−σYhYW
Πj : Index of outward trade costs
Pk: In equilibrium, price index is also an index of inward trade costs
Dual to one anotherSect3 Sect4
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 29 / 80
Gravity as Theory Structural Gravity
Uses of Structural Gravity
Estimation
Usually in log-linear form with importer and exporter fixed effects:
log Vjk = Fj + Fk + β log tjk + ujk, tjk = δjk exp(γ′Djk)
Compare
Simulation
Policy analysis, e.g. Brexit
Theoretical Analysis
Not possible in levels
What about comparative statics for local changes?
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 30 / 80
Gravity as Theory Comparative Statics for Structural Gravity
Comparative Statics for Structural Gravity
Allen, Arkolakis, and Takahashi (2019)
Eaton, Kortum, and Sotelo (2013)
Baqaee and Farhi (2017)
Jones (1965)
Diewert and Woodland (1977), Jones and Scheinkman (1977)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 31 / 80
Gravity as Theory Comparative Statics for Structural Gravity
The Structure of Simple Structural Gravity Models
Comparative Statics:
Define GDP and expenditure shares:
λjk =VjkYj
θjk =VjkEk
Back
Express changes in terms of these:[x ≡ d log x]
Yj =∑k
Vjk ⇒ Yj =∑k
λjkVjk
Pk =
(∑h
p1−σhk
) 11−σ
⇒ Pk =∑j
θjkpjk
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 32 / 80
Gravity as Theory Comparative Statics for Structural Gravity
Gravity at the Margin
Demands at the margin:
xjk = −σpjk + (σ − 1)Pk + Ek
Own and cross-price derivatives:
∂ log xjk∂ log pjk
= −{σ(1− θjk) + θjk}∂ log xjk∂ log pjh
∣∣∣∣h 6=j
= (σ − 1)θjh
Gross substitutes: − ∂ log xjk∂ log pjk
>∂ log xjk∂ log pjh
> 0
Add:
Trade costs: pjk = pjtjk ⇒ pjk = pj + tjk
Balanced trade: Ej = κjYj ⇒ Ej = Yj
Supply side:
{Yj = pjQjwj = pj
}⇒ Yj = wj = pj
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 33 / 80
Gravity as Theory An Application: Brexit
An Application: Brexit
Specialize to 3 countries: A, B, and E
A and E large
Take pA as numeraire
Equilibrium: Market-clearing conditions for outputs of B and E ...
... determine equilibrium wages: wB = pB and wE = pE
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 34 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
wB
wE
Illustrate equilibrium in {pE , pB}, i.e., {wE , wB} space
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 35 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
wB
wE
S
Initial equilibrium at S.
Goods-market-equilibrium locus for good B?
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 36 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
ESB
EDB
wB
wE
S
Goods-market-equilibrium locus for good B:
Higher wB , i.e. pB , leads to excess supply, lower to excess demand
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 37 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
ESB
EDB
EDBESB S
wB
wE
Goods-market-equilibrium locus for good B:
Higher wB , i.e. pB , leads to excess supply, lower to excess demandConversely for wE , though effect is weaker
Gross substitutes in each market, and so in all
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 38 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
ESB
EDB
EDBESB
wB
wE
S
Goods-market-equilibrium locus for good B:
Higher wB , i.e. pB , leads to excess supply, lower to excess demandConversely for wE , though effect is weaker
Gross substitutes in each market, and so in all
Uniformly higher wB and wE leads to excess supply
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 39 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
YB
ESB
EDB
wB
wE
Goods-market-equilibrium locus for good B:
Higher wB , i.e. pB , leads to excess supply, lower to excess demandConversely for wE , though effect is weaker
Gross substitutes in each market, and so in all
Uniformly higher wB and wE leads to excess supplySo market-clearing locus is upward-sloping as shown
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 40 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
YE
YB
wB
wE
Similarly for good E
Close to vertical if B is small
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 41 / 80
Gravity as Theory An Application: Brexit
Goods-Market Equilibrium
YE
YB
wB
wE
Intersection of the two determines equilibrium wages wB and wE
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 42 / 80
Gravity as Theory An Application: Brexit
Trade Cost Scenarios
Decompose trade costs: [Maggi, Mrazova, and Neary (2018)]
tjk = δjkτjk
{δjk : “natural”τjk : policy-induced
Possible scenarios:
Scenario δBE τBE δBA τBA
Status quo low low high high
“Cake and Eat” low low high low
“Global Britain” low high high low
(1) All assumed to be bilaterally symmetric.
(2) Revenue from policy costs ignored.
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 43 / 80
Gravity as Theory An Application: Brexit
“Cake and Eat”
YE
YB
wB
wE
Lower τBA raises demand for YB , tending to raise equilibrium wage wB
∂ logXB
∂ log τBA= −(σ − 1)(λBA(1− θBA)︸ ︷︷ ︸
+
−λBBθAB︸ ︷︷ ︸−
)
Details
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 44 / 80
Gravity as Theory An Application: Brexit
“Cake and Eat”
YE
YB
wB
wE
Lower τBA also lowers demand for YE , though not by much if B is small
∂ logXE
∂ log τBA= (σ − 1)(λEA θBA︸︷︷︸+λEB︸︷︷︸ θAB)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 45 / 80
Gravity as Theory An Application: Brexit
“Cake and Eat”
YE
YB
wB
wE
Net effect: Rise in wB , ambiguous change in wE
wB ↑ ⇔ wB > wA: Because A is bigger
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 46 / 80
Gravity as Theory An Application: Brexit
“Global Britain”: Symmetric Benchmark
YB
wB
wE
YE
Complete symmetry between A and E: No net effect
τBE ↑ exactly offsets the effect of τBA ↓
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 47 / 80
Gravity as Theory An Application: Brexit
“Global Britain”: Departures from Symmetry
Depth of integration
Single market is a deeper trade agreement: τBE
∣∣∣S< τBA
∣∣∣GB
Size
What matters is not absolute size, but size in initial UK trade
EU27 accounts for 40% of 2017 UK trade; but countries with EU tradeagreements add another 15%
Asymmetries between increases in low policy costs and decreases in highones
This matters for discrete changesCost of 10%-point increase in τBE is greater than the gain from a10%-point decrease in τBA
Distance a fixed cost
tjk = δjk + τjk ⇒ tjk = (1− ωjk)τjk, ωjk ≡δjktjk
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 48 / 80
Gravity as Theory An Application: Brexit
“Global Britain”: Reality Bites
YE
YB
wB
wE
Net effect: Higher trade costs with E dominate
More than offset the (only slightly) lower trade costs with A
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 49 / 80
Gravity Anomalies
Outline
1 Gravity as Fact
2 Gravity as Theory
3 Gravity Anomalies
4 Subconvex Gravity
5 Conclusion
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 50 / 80
Gravity Anomalies
Gravity Anomalies
Counter-factual implications of CES preferences:
1 Firm-level markups and pass-through
CES demands imply constant markups and 100% pass-through
But: Mounting firm-level empirical evidence to the contraryData Skip
2 Elasticities of import demand across markets
Evidence that they vary by market size and distance
Novy (2013)Details
3 Bilateral trade surpluses
CES gravity imposes very strong counter-factual restrictions
Davis and Weinstein (2002)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 51 / 80
Gravity Anomalies
Firm-Level Evidence Against CES
Inverse demand function:
p = p(x) p′ < 0
Two key demand parameters:
1 Slope/Elasticity:
ε(x) ≡ − p(x)xp′(x) > 0
2 Curvature/Convexity:
ρ(x) ≡ −xp′′(x)p′(x)
4
4
3
2
11
0-2 -1 0 1 2 3
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 52 / 80
Gravity Anomalies
CES Demands
In general, both ε and ρ vary withsales
Exception: CES/iso-elastic case:
p = βx−1/σ
⇒ ε = σ, ρ = σ+1σ > 1
⇒ ε = 1ρ−1 0.0
1.0
2.0
3.0
4.0
-2.0 -1.0 0.0 1.0 2.0 3.0
CES
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 53 / 80
Gravity Anomalies
CES Demands
In general, both ε and ρ vary withsales
Exception: CES/iso-elastic case:
p = βx−1/σ
⇒ ε = σ, ρ = σ+1σ > 1
⇒ ε = 1ρ−1 0.0
1.0
2.0
3.0
4.0
-2.0 -1.0 0.0 1.0 2.0 3.0
Cobb-Douglas
CES
Cobb-Douglas: ε = 1, ρ = 2
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 54 / 80
Gravity Anomalies
Sub- and Superconvexity
p(x) is subconvex at x0 IFF:
log p(x) is concave in log x
p(x) is less convex than a CESdemand function with the sameelasticity: ρ < ε+1
ε
ε is decreasing in sales:
εx = εx
[ρ− ε+1
ε
] 0.0
1.0
2.0
3.0
4.0
-2.0 -1.0 0.0 1.0 2.0 3.0
SC
Sub-Convex Super-Convex
A
C
B
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 55 / 80
Gravity Anomalies
Sub- and Superconvexity
p(x) is subconvex at x0 IFF:
log p(x) is concave in log x
p(x) is less convex than a CESdemand function with the sameelasticity: ρ < ε+1
ε
ε is decreasing in sales:
εx = εx
[ρ− ε+1
ε
] 0.0
1.0
2.0
3.0
4.0
-2.0 -1.0 0.0 1.0 2.0 3.0
SC
Sub-Convex Super-Convex
Subconvexity confirmed empirically, and theoretically plausible:
Introspection: “Marshall’s 2nd Law of Demand”
Dixit and Stiglitz (1977), Krugman (1979), etc.
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 56 / 80
Gravity Anomalies
From Demand Functions to Demand Manifolds
Represent demand functions in {ε, ρ} space by their Demand Manifold
Definition: A curve in {ε, ρ} space corresponding to the demandfunction p(x)
Existence: A smooth manifold corresponds to every demand function
Except for CES: Manifold is a point
Invariance: ε(x, φ) and ρ(x, φ) ⇒ ρ(ε)?
Necessary and sufficient condition in Mrazova-Neary (2017)Holds for most widely-used demand functions
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 57 / 80
Gravity Anomalies
Manifolds for Some Common Demand Functions
0.00
1.00
2.00
3.00
4.00
-2.00 -1.00 0.00 1.00 2.00 3.00
Linear
CARA
LES
SC
Translog/AI
All manifold-invariant
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 58 / 80
Gravity Anomalies
Evidence Rejects CES
Mrazova and Neary (2017) show that ε and ρ can be inferred fromestimates of pass-through and markups (as in de Loecker et al. (2016))
CES lies outside the implied confidence regions
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 59 / 80
Subconvex Gravity
Outline
1 Gravity as Fact
2 Gravity as Theory
3 Gravity Anomalies
4 Subconvex Gravity
5 Conclusion
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 60 / 80
Subconvex Gravity
Beyond Gravity Anomalies: Subconvex Gravity
Assume additively separable demands:
u′(xjk) = λkpjk ⇒ xjk = f (λkpjtjk)
→ Vjk = −(σjk − 1)pj − σjkλk − (σjk − 1) tjk
Subconvexity: σjk ≡ σ (xjk), decreasing in xjk
To estimate this, we use quantile regression:
Order data by Vjk
Estimate for each quantile q: Recall CES
log Vq,jk = Fq,j + Fq,k + βq log tjk + uq,jk
Estimation and bootstrapped confidence intervals:
Baltagi and Egger (2016), Machado and Santos Silva (2019)
CMN (Geneva and Oxford) Gravity without Apology RES: April 15, 2019 61 / 80
Subconvex Gravity
Quantile Regression: Estimated Distance Coefficient
‐1.60
‐1.55
‐1.50
‐1.45
‐1.40
‐1.35
‐1.30
0.0 0.2 0.4 0.6 0.8 1.0
Distance Co
effic
ient
Quantiles
Quantile
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Subconvex Gravity
Quantile Regression Results: Compared to OLS
‐1.60
‐1.55
‐1.50
‐1.45
‐1.40
‐1.35
‐1.30
0.0 0.2 0.4 0.6 0.8 1.0
Distance Co
effic
ient
Quantiles
Quantile
OLS
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Subconvex Gravity
Quantile Regression Results: Tests
Significance Tests for Differences Between
Quantile and OLS Estimates of Distance Coefficient
βOLS βQ10 βQ20 βQ30 βQ40 βQ50 βQ60 βQ70 βQ80 βQ90
βQ10 * 0βQ20 n.s. n.s. 0βQ30 n.s. n.s. n.s. 0βQ40 n.s. * n.s. n.s. 0βQ50 n.s. * n.s. n.s. n.s. 0βQ60 n.s. * * n.s. n.s. n.s. 0βQ70 n.s. * * * n.s. n.s. n.s. 0βQ80 n.s. * * * * n.s. n.s. n.s. 0βQ90 * * * * * * * n.s. n.s. 0
* Significantly different at 5% leveln.s. Not significant
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Subconvex Gravity
Subconvex Gravity: Evidence and Implications
Persuasive Evidence for Subconvexity
Distance coefficient significantly decreasing (in absolute value) in trade
Replication needed ...
Implications for the Trade Balances Puzzle?
Bilateral balances now depend on distance
Provisional evidence confirming this
Implications for Brexit?
With subconvexity, elasticities are higher in smaller markets
Implications for estimated effects of Brexit unlikely to be major
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Conclusion
Outline
1 Gravity as Fact
2 Gravity as Theory
3 Gravity Anomalies
4 Subconvex Gravity
5 Conclusion
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Conclusion
Conclusion
Gravity as Fact
Overwhelming evidence that trade tends to fall with distance
Gravity as Theory
A simple general equilibrium systemNew analytic tools for understanding it
Gravity Anomalies
Constant Elasticity of Trade not the whole story
Subconvex gravity a promising direction
Unlikely to change the Three Iron Laws of the Economics of Brexit
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Conclusion
What They Should Have Told Us ...
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Conclusion
Thanks and Acknowledgements*
Thank you for listening. Comments welcome!
* Some of the research on which this lecture draws received funding from the EuropeanResearch Council under the European Union’s Seventh Framework Programme(FP7/2007-2013), ERC grant agreement no. 295669.
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Supplementary Material Details: Effects of Shocks to Goods-Market-Equilibrium
Details: Goods-Market Equilibrium
Equilibrium in market for YB: Back to text
XB = εBB pB + εBE pE + εBtE tBE + εBtA tBA = 0
where the elasticities of excess demand for YB are:
εBB : −(σ − 1)λBB(1− θBB)− λBE{σ(1− θBE) + θBE} − λBA{σ(1− θBA) + θBA}εBE : (σ − 1)λBBθEB + λBE{(σ − 1)θEE + 1}+ (σ − 1)λBAθEA
εBtE : −(σ − 1){λBE(1− θBE)− λBBθEB}εBtA : −(σ − 1){λBA(1− θBA)− λBBθAB}
Similarly in the market for YE :
XE = εEB pB + εEE pE + εEtE tBE = 0
εEB : (σ − 1)λBBθEB + λBE{(σ − 1)θEE + 1}+ (σ − 1)λBAθEA
εEE : −(σ − 1)λBB(1− θBB)− λBE{σ(1− θBE) + θBE} − λBA{σ(1− θBA) + θBA}εEtE : −(σ − 1){λBE(1− θBE)− λBBθEB}εEtA : 0
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Supplementary Material Gravity Anomalies 1: Micro Evidence
Gravity Anomalies 1: Micro Evidence
Back to text
CES demands imply constant markups and 100% pass-through:
p
c=
σ
σ − 1and
d log p
d log c= 1
But: Mounting empirical evidence to the contrary
Mark-ups differ a lot across firms, even in narrowly-defined industries.
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Supplementary Material Gravity Anomalies 1: Micro Evidence
Empirical Evidence on Markups I
PRICES, MARKUPS, AND TRADE REFORM 493
FIGURE 4.—Distribution of marginal costs and markups in 1989 and 1997. Sample only in-cludes firm–product pairs present in 1989 and 1997. Outliers above and below the 3rd and 97thpercentiles are trimmed.
higher markups. The results indicate that firms offset the beneficial cost reduc-tions from improved access to imported inputs by raising markups. The overalleffect, taking into account the average declines in input and output tariffs be-tween 1989 and 1997, is that markups, on average, increased by 12.6 percent.This increase offsets almost half of the average decline in marginal costs, andas a result, the overall effect of the trade reform on prices is moderated.52
Although tempting, it is misleading to draw conclusions about the pro-competitive effects of the trade reform from the markup regressions in Col-umn 3 of Table IX. The reason is that one needs to control for the impacts of
52These results are robust to controlling India’s de-licensing policy reform; see Table A.I in theSupplemental Material.
From: de Loecker, Goldberg, Khandelwal and Pavcnik (2016)
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Supplementary Material Gravity Anomalies 1: Micro Evidence
Empirical Evidence on Markups II
From: Lamorgese, Linarello and Warzynski (2014)
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Supplementary Material Gravity Anomalies 2: Cross-Market Heterogeneity
Gravity Anomalies 2: Cross-Market Heterogeneity
Back to text
CES-based models predict the same elasticity of import demand in allmarkets.
Macro elasticity, not micro elasticity facing firms
By contrast, Novy (2013) finds that elasticities are systematically lower inlarger and closer markets.
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