The consumption-real exchange rate anomaly withextensive margins
Masashige Hamano
University Luxembourg

November 2011

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Structure of the presentation

Introduction
The static model (analytical explanation)
The dynamic model (quantitative analysis)
Conclusion.

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Introduction: Perfect risk sharing condition with complete
asset markets
Under the assumption of complete asset markets, one countries’
consumption should rise when its price decreases relative to othercountries (real exchange rate depreciation):With the standard CRRA preference:
U=C1 γ
1 γQ

P=PCCQPWe haveγ

In log deviations,Masashige Hamano (Institute)P = γ (CThe BS puzzle with extensive margins

C )
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But this is not observed in reality, known as theBackus-Smith puzzle (Kollmann (1995), Backus and Smith(1993))
Table: BS correlation

Country
U.S. ROW Country
Austria-0.11 0.05
Italy
Belgium/Luxembourg -0.16 0.50
JapanCanada-0.52 -0.31 Netherlands
Denmark-0.14 -0.10 Portugal
Finland-0.30 -0.49 Spain
France-0.20 0.43
SwedenGermany-0.51 -0.27 U.K.
Greece-0.45 -0.35 U.S.
Ireland-0.39 0.72
MedianSource: Corsetti et al. (2008a)
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U.S.
-0.28
0.05
-0.45
-0.61
-0.63
-0.56
-0.51
N/A
-0.42

ROW
-0.52
0.25
-0.20
-0.77
-0.64
-0.40
-0.21
-0.71
-0.27

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What we observe is zero or even negative correlation between relative
consumption and real exchange rate (Medium is -0.27 )Put another way, a country consumes more relative to ROW when theprice of its consumption basket becomes expensive, namely when thereal exchange rate appreciates.

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How can these zero or even negative correlations arise?

No complete asset markets which tightly link relative consumption
and real exchange rate.
However, under incomplete assets markets, the standard international
macroeconomic model with di¤erentiated traded goods fails toreproduce a realistic BS correlation: real exchange rate depreciates
along with the terms of trade depreciation following a positive
productivity shock.

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Benigno and Thoenissen (2008) and Corsetti et al. (2008a)

Under incomplete asset markets and with non-traded sector, zero oreven negative correlation may arise through theHarrod-Balassa-Samuelson e¤ect (Benigno and Thoenissen (2008)).
Also under incomplete markets, zero or even negative correlation mayarise when a strong income e¤ect takes place due to a low elasticity
of substitution between local and imported goods (Corsetti et al.
(2008a), henceforth CDL).

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Contribution of the paper

The paper explores how extensive margins (the number of varieties)
and market incompleteness might contribute to the resolution of thepuzzle.
Consumers take care of not only price of goods but also the variety ofgoods they consume.
What really matters for international risk sharing is the“welfare-based” real exchange rate ‡uctuations including those inextensive margins.
Fundamentally, the BS puzzle cannot be tested fully because we
systematically fails to observe ‡uctuations in extensive margins withstandard “empirical-based” price indices (Broda and Weinstein(2004,2006,2010)).

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Intuition of the paper

Under incomplete markets, when a country is hit by a positive
productivity shock, it produces more in terms of extensive margins
relative to ROW.
Labor demand which comes from these new entrants/varieties furtherpushes up wage rate in the country.
It follows that the “empirical-based” real exchange rate appreciates.
The higher the love for variety or the substitution e¤ect between local
and imported goods is, the stronger the real exchange rate
appreciation. A realistic BS correlation may arise when the elasticity
of substitution between local and imported goods is high (elasticityoptimism).

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Intuition of the paper

Following a positive productivity shock, zR " ) NR " and wR ".
In welfare-based, Q " and C

Masashige Hamano (Institute)C ".

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Intuition of the paper

Following a positive productivity shock, zR " ) NR " and wR ".
In welfare-based, Q " and C C ".
e # and C
e Ce ".
In empirical-based, Q

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The static model

A two country general equilibrium model based on monopolisticcompetition.
The number of …rms in each country (product varieties or extensivemargins) is determined endogenously through free entry condition asin Krugman (1980).
No international lending and borrowing (the balanced trade or
extremely incomplete markets).

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The terms of trade with extensive margins

TOT =

1
1 + 2α (ω|{zCDL termzR1)}2α (ω 1)ψNR .
1 + 2α (ω 1)|{z}Variety e¤ect

where TOT pf ph , α (> 1/2): home bias in consumption, ω(> 0): elasticity of substitution between local and imported goods, ψ(> 0): love for variety.
From the …rst CDL term, the terms of trade can appreciate when
ω < 1 1/2α while depreciate when 1 1/2α < ω.
But with love for variety ψ (> 0), the second term is also at work. A
positive extensive margins NR > 0 makes them appreciated.
The appreciation is higher the higher the elasticity of substitution ωor love for variety ψ.
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Calibration with and without love for variety

3
Without love (ψ =0)With love (ψ =0.2)
2Elasticity

10-1-2-3012345

ωFigure 1: Terms of trade (α = 0.72)

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The BS correlation in “welfare-based”

From the balanced trade condition, we can get
Q=2α 1(C2αω 1C ).

This is exactly the same expression as in CDL. The coe¢ cient can be
negative only when ω < 1/2α.
But in "welfare-basis" the above real exchange rate Q andconsumption C C include unobservable ‡uctuations in extensivemargins NR .

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The "empirical-based" measure

Fluctuations in the welfare-based real exchange rate and relative
consumption can be decomposed into those empirically observablee and Ce Ce ) and extensive margins NR as follows:parts (Qe + ψ (2αQ=Q

whereAndC

Masashige Hamano (Institute)e = (2αQe
C =C

1 ) NR ,1) TOT.

e + ψ (2αCThe BS puzzle with extensive margins

1 ) NR .

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The BS correlation in “empirical-based”

Using the above relations, we havee = 2α 1 CeQ
2αω1|{zCDL termeC}

ψ|2α (2α 1) (ω2αω{z 1Variety e¤ect1)

NR .
}Unobservable positive extensive margins NR > 0 can bring thee <0empirical-based real exchange rate into an appreciation Qe Ce > 0 . This is more so when thewhile consumption rise C
elasticity of substitution is ω or love for variety ψ is high.

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Calibration with and without love for variety

0.8
Without love (ψ =0)With love (ψ =0.2)

0.6
0.4

Elasticity

0.2
0-0.2
-0.4
-0.6
-0.8
01234

5

ω

Figure 2: BS correlation (α = 0.72)

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Quantitative analysis

Introducing full dynamics based on Ghironi and Melitz (2005). But
for simplicity …rms are homogenous.
For more realistic speci…cation, …rms are required to pay sunk costs interms of capital goods as well as labor.
Labor supply is assume to be endogenous.
A part of consumption risk is insured by non-contingent bonds. Thus
…nancial markets are incomplete but not totally.

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Impulse response function
Without variety variations
0.6
Real exchange rate
Terms of trade
Relative consumption

%

0.4
0.2
0-0.2

01020

30

010

2030

40
50
60
quarters
With variety variations

7080

90

100

70

80

90

100

0.6

%

0.4
0.2
0-0.2

4050
quarters

60

Figure 3: IRF under Incomplete markets.
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11

Incomplete markets

Incomplete markets
0.8

0.8

0.6

0.6
BS correlation

BS correlation

0.4

0.4

0.2

0.2
0-0.2

0-0.4

-0.2

-0.4

-0.6

12

3

4

5

6

7

-0.8
00.1

0.2

0.3

0.4

0.5

ω

ψ

Figure 4: BS correlation and theelasticity of substitution.

Figure 5: BS correlation and thelove for variety.

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Conclusion

This paper investigates how the interaction of extensive margins andmarket incompleteness may contribute to the resolution of the BSpuzzle.
International risk sharing is fundamentally for welfare-based realexchange rate and consumption.
A realistic BS correlation is reproduced when the elasticity ofsubstitution between local and imported goods is high.
The model predicts that in welfare-based, a positive BS correlation
tends to remain.

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