Consumption-led Growth - Princeton Universityitskhoki/papers/growthCA_slides.pdf · Consumption-led...

Consumption-led Growth

Markus Brunnermeier Pierre-Olivier Gourinchas

[email protected] [email protected]

Oleg Itskhoki

[email protected]

Stanford UniversitySeptember 2017

1 / 23

Motivation

1 What is the relationship between openness and growth?

— trade openness

— financial openness

2 Is it possible to borrow like Argentina or Spainand grow like China?

(i) What is wrong with Spanish-style (consumption-led) growth?

(ii) What is special about Chinese-style (export-led) growth?

• A model of endogenous convergence growth

— to open the blackbox of productivity evolution under differenteconomy openness regimes

— a neoclassical (DRS) environment with endogenous innovationdecisions by entrepreneurs

— emphasis on the feedback from international borrowing intothe pace and composition (T vs NT) of converegence

1 / 23

Motivation

— trade openness

1 / 23

Motivation

— trade openness

1 / 23

Empirical Motivation

Figure: CA imbalances in the Euro Zone2 / 23

Empirical Motivation

Figure: Sectoral reallocation in the Euro Zone

2 / 23

Main Insights• Openness has two effects:

(i) change in the relative size of the market

(ii) increase in both foreign competition and in domesticcost of production (unit labor costs)

• With balanced trade, it’s a wash: trade openness does notaffect the pace and direction of productivity growth

• Trade deficits unambiguously favor the non-tradable sectorand tend to reduce the pace of innovation

— a reduced-form relationship between NX and sectoral growth

— furthermore, NX/Y is a sufficient statistic

• Sudden stops in financial flows are followed by both recessionsand fast tradable productivity growth take off

— due to structural productivity imbalance, without sticky wages

— wage flexibility essential for a sharp productivity rebound

• Laissez-faire productivity growth is in general suboptimal— capital controls may improve upon market allocation

3 / 23

• Laissez-faire productivity growth is in general suboptimal— capital controls may improve upon market allocation 3 / 23

Literature

• Learning-by-doing and dutch disease

— Corden and Neary (1982), Krugman (1987), Young (1991)...

— Export-led growth: Rajan and Subramanian (2005)

• Trade and growth:

— Ventura (1997), Acemoglu and Ventura (2002)

— Technology transfer: Parente and Prescott (2002)

— Empirics: Frankel and Romer (1999)

• Transition growth after financial liberalization

— Aioke, Benigno and Kiyotaki (2009)

• Growth and trade with Frechet distribution:

— Kortum (1997), EK (2001, 2002), Klette and Kortum (2004)

4 / 23

MODEL SETUP

5 / 23

Model Setup

• Real small open economy in continuous time

— exogenous world interest rate r∗ in terms of world good

• Two sectors:

— tradable (exportable) and non-tradable (non-exportable)

• Rest of the world (ROW) in steady state:

W ∗ = A∗T = A∗N = A∗ and P∗F = P∗N = P∗ = 1

• We study convergence growth trajectories starting from

AT (0),AN(0) < A∗

5 / 23

Households

• Representative household:

max{C(t),L(t)}

∫ ∞0

e−ϑtU(t)dt, U = 11−σC

1−σ − 11+ϕL

s.t. B = r∗B+NX , NX = WL + Π− PC

• Results in labor supply:

Cσt Lϕt =

Pt≡ wt

• Aggregate GDP and absorbtion:

GDP = WL + Π and Y = PC ⇒ GDP = Y + NX

• Special cases: σ → 1 and ϕ→∞ (L = L)

6 / 23

Demand• Two sectors:

Y = PC = γPTCT + (1− γ)PNCN

C = CγTC

1−γN and CT =

ρ−1ρ

F + (1−κ)1ρC

ρ−1ρ

] ρρ−1

, ρ > 1

• Aggregators of individual varieties:

∫ ΛT

CH(i)ρ−1ρ di

] ρρ−1

and CN =

1− γ

∫ ΛN

CN(i)ρ−1ρ di

] ρρ−1

• Demand:

CH(i) = (1− κ)

(PH(i)

)−ρY

PTand CN(i) =

(PN(i)

)−ρY

Price indexes

7 / 23

C = CγTC

1−γN and CT =

ρ−1ρ

F + (1−κ)1ρC

ρ−1ρ

] ρρ−1

, ρ > 1

∫ ΛT

CH(i)ρ−1ρ di

] ρρ−1

and CN =

1− γ

∫ ΛN

CN(i)ρ−1ρ di

] ρρ−1

• Demand:

CH(i) = (1− κ)

(PH(i)

)−ρY

PTand CN(i) =

(PN(i)

)−ρY

Price indexes

7 / 23

C = CγTC

1−γN and CT =

ρ−1ρ

F + (1−κ)1ρC

ρ−1ρ

] ρρ−1

, ρ > 1

∫ ΛT

CH(i)ρ−1ρ di

] ρρ−1

and CN =

1− γ

∫ ΛN

CN(i)ρ−1ρ di

] ρρ−1

• Demand:

CH(i) = (1− κ)

(PH(i)

)−ρY

PTand CN(i) =

(PN(i)

)−ρY

Price indexes

7 / 23

Exports and Imports• Tradable expenditure:

γPTCT = γPFCF +

∫ ΛT

0PH(i)CH(i)di

• Aggregate imports:

X ∗ = γPFCF = γκ

)1−ρY , PF = τP∗F = τ

• Aggregate exports:

X = γP∗HC∗H = γκ(τPH)1−ρY ∗

• Net exports:

NX = X − X ∗ = γκτ1−ρ[P1−ρH Y ∗ − Pρ−1

= γκτ1−ρ[Sρ−1Y ∗ − 1

κτ1−ρ+(1−κ)Sρ−1Y], S = P−1

8 / 23

Exports and Imports• Tradable expenditure:

γPTCT = γPFCF +

∫ ΛT

0PH(i)CH(i)di

• Aggregate imports:

X ∗ = γPFCF = γκ

)1−ρY , PF = τP∗F = τ

• Aggregate exports:

X = γP∗HC∗H = γκ(τPH)1−ρY ∗

• Net exports:

NX = X − X ∗ = γκτ1−ρ[P1−ρH Y ∗ − Pρ−1

= γκτ1−ρ[Sρ−1Y ∗ − 1

κτ1−ρ+(1−κ)Sρ−1Y], S = P−1

8 / 23

Technology and Revenues• Technology:

YJ(i) = AJ(i)LJ(i), i ∈ [0,ΛJ ], J ∈ {T ,N}

• Marginal cost pricing if technology is rival (same in J = N):

PH(i) =W

AT (i)⇒ PH =

AT, AT =

∫ ΛT

0 AT (i)ρ−1di] 1ρ−1

• Revenues:

RN(i) = PN(i)CN(i) =

(PN(i)

)1−ρRN ,

RT (i) = PH(i)CH(i) + P∗H(i)C ∗H(i) =

(PH(i)

)1−ρRT

RN = Y and RT = (1− κ)

)1−ρY + κ(τPH)1−ρY ∗

9 / 23

Technology and Revenues• Technology:

YJ(i) = AJ(i)LJ(i), i ∈ [0,ΛJ ], J ∈ {T ,N}

• Marginal cost pricing if technology is rival (same in J = N):

PH(i) =W

AT (i)⇒ PH =

AT, AT =

∫ ΛT

0 AT (i)ρ−1di] 1ρ−1

• Revenues:

RN(i) = PN(i)CN(i) =

(PN(i)

)1−ρRN ,

RT (i) = PH(i)CH(i) + P∗H(i)C ∗H(i) =

(PH(i)

)1−ρRT

RN = Y and RT = (1− κ)

)1−ρY + κ(τPH)1−ρY ∗

9 / 23

Technology Draws

• An entrepreneur has n� 1 possible ideas (projects):

ZJ(`)(`)iid∼ Frechet(z , θ), ` = 1..n, θ > ρ− 1

• A fraction γ of ideas are tradable, J(`) = T

• An entrepreneur can adopt only one project

• The technology is privately owned for one period, then rival

• Period profits:

ΠT (`) =1

ρ− 1

ZT (`)

)1−ρRT

Aρ−1T

ZT (`)ρ−1

ΠN(`) =1

ρ− 1

)1−ρRN

Aρ−1N

ZN(`)ρ−1

10 / 23

Technology Draws

• Period profits:

ΠT (`) =1

ρ− 1

ZT (`)

)1−ρRT

Aρ−1T

ZT (`)ρ−1

ΠN(`) =1

ρ− 1

)1−ρRN

Aρ−1N

ZN(`)ρ−1

10 / 23

Technology Draws

• Period profits:

ΠT (`) =1

ρ− 1

ZT (`)

)1−ρRT

Aρ−1T

ZT (`)ρ−1

ΠN(`) =1

ρ− 1

)1−ρRN

Aρ−1N

ZN(`)ρ−1

10 / 23

Technology Draws

• Period profits:

ΠT (`) =1

ρ− 1

ZT (`)

)1−ρRT = %

Aρ−1T

ZT (`)ρ−1

ΠN(`) =1

ρ− 1

)1−ρRN = %

Aρ−1N

ZN(`)ρ−1

10 / 23

Technology Adoption

• Project choice:ˆ = arg max

`=1..nΠJ(`)(`)

and we define (ZT , ZN , Z ) and (ΠT , ΠN , Π)

• Lemma 1 (i) The probability to adopt a tradable project:

πT ≡ P{ΠT ≥ ΠN} =γ · χ

θρ−1

γ · χθρ−1 + 1− γ

, χ ≡ ()ρ−1 RT

(ii) The productivity conditional on adoption:

E{Z ρ−1T

∣∣ ΠT ≥ ΠN

(πTγ

)ν−1

A∗ρ−1,

where A∗ ≡ EZ = (nz)1/θΓ(ν)1ρ−1 and ν ≡ 1− ρ−1

θ ∈ (0, 1).

11 / 23

Technology Adoption

`=1..nΠJ(`)(`)

θρ−1

γ · χθρ−1 + 1− γ

, χ ≡(PH

)ρ−1 RT

E{Z ρ−1T

∣∣ ΠT ≥ ΠN

(πTγ

)ν−1

A∗ρ−1,

θ ∈ (0, 1).

11 / 23

Technology Adoption

`=1..nΠJ(`)(`)

θρ−1

γ · χθρ−1 + 1− γ

, χ ≡(AN

)ρ−1 RT

E{Z ρ−1T

∣∣ ΠT ≥ ΠN

(πTγ

)ν−1

A∗ρ−1,

θ ∈ (0, 1).

11 / 23

Technology Adoption

`=1..nΠJ(`)(`)

θρ−1

γ · χθρ−1 + 1− γ

, χ ≡(AN

)ρ−1 RT

E{Z ρ−1T

∣∣ ΠT ≥ ΠN

(πTγ

)ν−1

A∗ρ−1,

θ ∈ (0, 1).

11 / 23

Productivity Dynamics

• λ is the innovation rate and δ is the rate at whichtechnologies become obsolete:

ΛT = λπT − δΛT

• Assume λ is country-specific and λ ≤ δ

• Lemma 2 The sectoral productivity dynamics is given by:

ρ− 1

)ρ−1(πTγ

)ν− 1

]where A ≡ A∗

) 1ρ−1

12 / 23

Productivity Dynamics

• λ is the innovation rate and δ is the rate at whichtechnologies become obsolete:

ΛT = λπT − δΛT

• Assume λ is country-specific and λ ≤ δ

• Lemma 2 The sectoral productivity dynamics is given by:

ρ− 1

)ρ−1(πTγ

)ν− 1

]where A ≡ A∗

) 1ρ−1

12 / 23

CLOSED ECONOMY

13 / 23

Closed Economy, κ ≡ 0• In closed economy RT = RN = Y , and therefore:

)ρ−1

• The project choice is, thus:

πT (t)

1− πT (t)=

1− γ

(AN(t)

AT (t)

• Proposition 1 (i) Starting from AT (0) = AN(0), equilibriumproject choice in the closed economy is πT (t) ≡ γ,

AT (t) =[e−δtAT (0)ρ−1 +

(1−e−δt

)Aρ−1

] 1ρ−1

and ΛT = γλ

(ii) Equilibrium allocation C = w1+ϕσ+ϕ , L = w

1−σσ+ϕ , w = A.

(iii) Efficiency: . . .

13 / 23

)ρ−1

πT (t)

1− πT (t)=

1− γ

(AN(t)

AT (t)

AT (t) =[e−δtAT (0)ρ−1 +

(1−e−δt

)Aρ−1

] 1ρ−1

and ΛT = γλ

1−σσ+ϕ , w = A.

13 / 23

)ρ−1

πT (t)

1− πT (t)=

1− γ

(AN(t)

AT (t)

AT (t) =[e−δtAT (0)ρ−1 +

(1−e−δt

)Aρ−1

] 1ρ−1

and ΛT = γλ

1−σσ+ϕ , w = A.

13 / 23

OPEN ECONOMY IBALANCED TRADE

14 / 23

Balanced Trade

• Consider open economy with κ > 0 and τ ≥ 1

• Lemma 3 (i) The relative revenue shifter is given by:

RN= (1− κ)

)1−ρ

+ κ(τPH)1−ρY∗

Y= 1 +

(ii) Under balanced trade, χ = (AN/AT )ρ−1, and henceπT (t) and (AT (t),AN(t)) follow the same path as in autarky.

• Equilibrium allocation is nonetheless different from autarkic.For σ = 1:

w = C = A ·(

τ2ρ−1

) κγ1+(2−κ)(ρ−1)

• Laisser-faire productivity dynamics is suboptimal.The planner would choose πT (t) < γ for all t ≥ 0.

14 / 23

Balanced Trade

RN= (1− κ)

)1−ρ

Y= 1 +

w = C = A ·(

τ2ρ−1

) κγ1+(2−κ)(ρ−1)

14 / 23

Balanced Trade

RN= (1− κ)

)1−ρ

Y= 1 +

w = C = A ·(

τ2ρ−1

) κγ1+(2−κ)(ρ−1)

14 / 23

OPEN ECONOMY IIFINANCIAL OPENNESS

15 / 23

Financial Openness

• With open current account:

πT1− πT

1− γχ

θρ−1 =

)θ [1 +

] θρ−1

• Lemma 4 NX (t)<0 and AT (t)≥AN(t) ⇒ AT (t)< AN(t).

• Proposition 5 In st.st. with NX =−r∗B > 0: AT > A > AN .

• Proposition 6 Starting from AT (0) = AN(0) < A, there existtwo cutoffs 0 < t1 < t2 <∞:

• NX (t) < 0 for t ∈ [0, t1) and NX (t) > 0 for t > t1, and

• AT (t) < AN(t) for t ∈ (0, t2) and AT (t) > AN(t) for t > t2.

At t = t2, AT (t) = AN(t) = A(t) < Aa(t).

15 / 23

Financial Openness

πT1− πT

1− γχ

θρ−1 =

)θ [1 +

] θρ−1

15 / 23

Financial Openness

πT1− πT

1− γχ

θρ−1 =

)θ [1 +

] θρ−1

15 / 23

Financial Openness

πT1− πT

1− γχ

θρ−1 =

)θ [1 +

] θρ−1

15 / 23

Convergence Path

0 50 100 150 200 250 300

Figure: Productivity convergence in closed and open economies16 / 23

Impact of Openness

0 50 100 150

• Two effects of openness:

1 Relative size of the market: Y /Y ∗

2 Competition: PT/PH < 1

)1−ρ·

[(1− κ) + κ

)1−ρ

=X/X∗︷︸︸︷P1−ρH Y ∗

Pρ−1T Y

]17 / 23

Endogenous Innovation Rate

• Endogenous participation of entrepreneurs if EΠ ≥ φW :

λ = Φ

W=%RN/W

Aρ−1N

Emax{χZρ−1

T , Zρ−1N

• Lemma 5EΠ

A· AAθ

)ρ−1 γχ

θρ−1 + 1− γ

)θ+ 1− γ

ρ−1θ

where χ =(ANAT

)ρ−1[1 + NX

]and C

w = w1−σσ+ϕ[1 + NX

] −ϕσ+ϕ .

• Proposition 8 (i) λ is increasing in A∗/A and in A/Aθ ≥ 1 .

(ii) λ increases with trade openness iff σ < 1 and ϕ <∞.

(iii) When σ = 1, λ increases with NX when AN ≥ AT .

18 / 23

λ = Φ

W=%RN/W

Aρ−1N

Emax{χZρ−1

T , Zρ−1N

• Lemma 5EΠ

A· AAθ

)ρ−1 γχ

θρ−1 + 1− γ

)θ+ 1− γ

ρ−1θ

where χ =(ANAT

)ρ−1[1 + NX

]and C

w = w1−σσ+ϕ[1 + NX

] −ϕσ+ϕ .

18 / 23

λ = Φ

W=%RN/W

Aρ−1N

Emax{χZρ−1

T , Zρ−1N

• Lemma 5EΠ

A· AAθ

)ρ−1 γχ

θρ−1 + 1− γ

)θ+ 1− γ

ρ−1θ

where χ =(ANAT

)ρ−1[1 + NX

]and C

w = w1−σσ+ϕ[1 + NX

] −ϕσ+ϕ .

18 / 23

Empirical Implications• Reduced-form relationship between NX and sectoral growth:

AT (t)

AT (t)− AN(t)

AN(t)= g0

[−(ρ− 1) log

AT (t)

AN(t)+ν(πT (t)− γ)

γ(1− γ)

[−(ρ− 1) (1 + µ) log

AT (t)

AN(t)+µ

NX (t)

with g0 ≡ δρ−1

(λδA∗

)ρ−1, which is also the base growth rate

— holds whether NX 6= 0 are market outcomes or policy-induced

— i.e., applies equally for NX < 0 in Spain and NX > 0 in China

• NX/Y is a sufficient statistic for the feedback effect fromequilibrium allocation to sectoral productivity growth

• Preliminary evidence of this effect in the KLEMS data

— CA/Y interacted with sector i tradability predicts sector iproductivity growth rate in the panel of country-sectors

19 / 23

Empirical Implications• Reduced-form relationship between NX and sectoral growth:

AT (t)

AT (t)− AN(t)

AN(t)= g0

[−(ρ− 1) log

AT (t)

AN(t)+ν(πT (t)− γ)

γ(1− γ)

[−(ρ− 1) (1 + µ) log

AT (t)

AN(t)+µ

NX (t)

with g0 ≡ δρ−1

(λδA∗

)ρ−1, which is also the base growth rate

— holds whether NX 6= 0 are market outcomes or policy-induced

— i.e., applies equally for NX < 0 in Spain and NX > 0 in China

• NX/Y is a sufficient statistic for the feedback effect fromequilibrium allocation to sectoral productivity growth

• Preliminary evidence of this effect in the KLEMS data

— CA/Y interacted with sector i tradability predicts sector iproductivity growth rate in the panel of country-sectors

19 / 23

Unit Labor Costs• Two ULC measures: w/A and W /AT

— move together holding τ constant

• Autarky (assume σ = 1):

wa(t) = C a(t) = A(t)

• Balanced trade:

wb(t) = Cb(t) = A(t)

AT (t)

) κγ1+(2−κ)(ρ−1)

> A(t)

• Open financial account:

wb(0) < w(0) < C (0)

• ULC increase on impact and gradually fall alongthe convergence path

20 / 23

APPLICATIONS

21 / 23

Application

1 Rollover crisis

• Sudden stop in capital flows during transition triggers areversal in trade deficits and a recession in non-tradable sector

• Rapid take off in tradable productivity growth, provided labormarket can flexibly adjust by a sharp decline in wages

2 Misallocation and growth policy

3 Physical capital and financial frictions

21 / 23

Rollover Crisis

Figure: Rollover crisis

22 / 23

CONCLUSION

23 / 23

APPENDIX

24 / 23

Price Indexesback to slides

• Average sectoral prices:

∫ ΛT

PH(i)1−ρdi

] 11−ρ

and PN =

1− γ

∫ ΛN

PN(i)1−ρdi

] 11−ρ

• Aggregate price indexes:

P = PγTP1−γN where PT =

[κP1−ρ

F + (1− κ)P1−ρH

] 11−ρ

• Equilibrium sectoral prices:

AT, PN =

ANand PF = τ

• Real wage rate:

[1− κ+ κ

(WτAT

)ρ−1] γρ−1

, A ≡ AγTA1−γN

24 / 23

Solution for NXback to slides

• Equilibrium system:

C = w1+ϕσ+ϕ

]− ϕσ+ϕ

where w = A

)κγand

γκ(WτAT

)ρ−κγ[τ1−2ρA

∗ 1+ϕσ+ϕ

AT−(

)(1−κγ)+(2−κ)(ρ−1)]

25 / 23

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