Consumption-led Growth Markus Brunnermeier Pierre-Olivier Gourinchas [email protected] [email protected] Oleg Itskhoki [email protected] Stanford University September 2017 1 / 23
Apr 27, 2020
Consumption-led Growth
Markus Brunnermeier Pierre-Olivier Gourinchas
[email protected] [email protected]
Oleg Itskhoki
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
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
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
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
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
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
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
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
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
1+ϕ
s.t. B = r∗B+NX , NX = WL + Π− PC
• Results in labor supply:
Cσt Lϕt =
Wt
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
where
C = CγTC
1−γN and CT =
[κ
1ρC
ρ−1ρ
F + (1−κ)1ρC
ρ−1ρ
H
] ρρ−1
, ρ > 1
• Aggregators of individual varieties:
CH =
[1
γ
∫ ΛT
0
CH(i)ρ−1ρ di
] ρρ−1
and CN =
[1
1− γ
∫ ΛN
0
CN(i)ρ−1ρ di
] ρρ−1
• Demand:
CH(i) = (1− κ)
(PH(i)
PT
)−ρY
PTand CN(i) =
(PN(i)
PN
)−ρY
PN
Price indexes
7 / 23
Demand• Two sectors:
Y = PC = γPTCT + (1− γ)PNCN
where
C = CγTC
1−γN and CT =
[κ
1ρC
ρ−1ρ
F + (1−κ)1ρC
ρ−1ρ
H
] ρρ−1
, ρ > 1
• Aggregators of individual varieties:
CH =
[1
γ
∫ ΛT
0
CH(i)ρ−1ρ di
] ρρ−1
and CN =
[1
1− γ
∫ ΛN
0
CN(i)ρ−1ρ di
] ρρ−1
• Demand:
CH(i) = (1− κ)
(PH(i)
PT
)−ρY
PTand CN(i) =
(PN(i)
PN
)−ρY
PN
Price indexes
7 / 23
Demand• Two sectors:
Y = PC = γPTCT + (1− γ)PNCN
where
C = CγTC
1−γN and CT =
[κ
1ρC
ρ−1ρ
F + (1−κ)1ρC
ρ−1ρ
H
] ρρ−1
, ρ > 1
• Aggregators of individual varieties:
CH =
[1
γ
∫ ΛT
0
CH(i)ρ−1ρ di
] ρρ−1
and CN =
[1
1− γ
∫ ΛN
0
CN(i)ρ−1ρ di
] ρρ−1
• Demand:
CH(i) = (1− κ)
(PH(i)
PT
)−ρY
PTand CN(i) =
(PN(i)
PN
)−ρY
PN
Price indexes
7 / 23
Exports and Imports• Tradable expenditure:
γPTCT = γPFCF +
∫ ΛT
0PH(i)CH(i)di
• Aggregate imports:
X ∗ = γPFCF = γκ
(PF
PT
)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
T Y]
= γκτ1−ρ[Sρ−1Y ∗ − 1
κτ1−ρ+(1−κ)Sρ−1Y], S = P−1
H
8 / 23
Exports and Imports• Tradable expenditure:
γPTCT = γPFCF +
∫ ΛT
0PH(i)CH(i)di
• Aggregate imports:
X ∗ = γPFCF = γκ
(PF
PT
)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
T Y]
= γκτ1−ρ[Sρ−1Y ∗ − 1
κτ1−ρ+(1−κ)Sρ−1Y], S = P−1
H
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 =
W
AT, AT =
[1γ
∫ ΛT
0 AT (i)ρ−1di] 1ρ−1
• Revenues:
RN(i) = PN(i)CN(i) =
(PN(i)
PN
)1−ρRN ,
RT (i) = PH(i)CH(i) + P∗H(i)C ∗H(i) =
(PH(i)
PH
)1−ρRT
where
RN = Y and RT = (1− κ)
(PH
PT
)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 =
W
AT, AT =
[1γ
∫ ΛT
0 AT (i)ρ−1di] 1ρ−1
• Revenues:
RN(i) = PN(i)CN(i) =
(PN(i)
PN
)1−ρRN ,
RT (i) = PH(i)CH(i) + P∗H(i)C ∗H(i) =
(PH(i)
PH
)1−ρRT
where
RN = Y and RT = (1− κ)
(PH
PT
)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
(ρ
ρ− 1
W
ZT (`)
1
PH
)1−ρRT
= %RT
Aρ−1T
ZT (`)ρ−1
ΠN(`) =1
ρ
(ρ
ρ− 1
W
ZN(`)
1
PN
)1−ρRN
= %RN
Aρ−1N
ZN(`)ρ−1
10 / 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
(ρ
ρ− 1
W
ZT (`)
1
PH
)1−ρRT
= %RT
Aρ−1T
ZT (`)ρ−1
ΠN(`) =1
ρ
(ρ
ρ− 1
W
ZN(`)
1
PN
)1−ρRN
= %RN
Aρ−1N
ZN(`)ρ−1
10 / 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
(ρ
ρ− 1
W
ZT (`)
1
PH
)1−ρRT
= %RT
Aρ−1T
ZT (`)ρ−1
ΠN(`) =1
ρ
(ρ
ρ− 1
W
ZN(`)
1
PN
)1−ρRN
= %RN
Aρ−1N
ZN(`)ρ−1
10 / 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
(ρ
ρ− 1
W
ZT (`)
1
PH
)1−ρRT = %
RT
Aρ−1T
ZT (`)ρ−1
ΠN(`) =1
ρ
(ρ
ρ− 1
W
ZN(`)
1
PN
)1−ρRN = %
RN
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
RN.
(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
• 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 ≡(PH
PN
)ρ−1 RT
RN.
(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
• 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 ≡(AN
AT
)ρ−1 RT
RN.
(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
• 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 ≡(AN
AT
)ρ−1 RT
RN.
(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
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:
AT
AT=
δ
ρ− 1
[(A
AT
)ρ−1(πTγ
)ν− 1
]where A ≡ A∗
(λ
δ
) 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:
AT
AT=
δ
ρ− 1
[(A
AT
)ρ−1(πTγ
)ν− 1
]where A ≡ A∗
(λ
δ
) 1ρ−1
.
12 / 23
CLOSED ECONOMY
13 / 23
Closed Economy, κ ≡ 0• In closed economy RT = RN = Y , and therefore:
χ =
(PH
PN
)ρ−1
=
(AN
AT
)ρ−1
• The project choice is, thus:
πT (t)
1− πT (t)=
γ
1− γ
(AN(t)
AT (t)
)θ
• 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
δ.
(ii) Equilibrium allocation C = w1+ϕσ+ϕ , L = w
1−σσ+ϕ , w = A.
(iii) Efficiency: . . .
13 / 23
Closed Economy, κ ≡ 0• In closed economy RT = RN = Y , and therefore:
χ =
(PH
PN
)ρ−1
=
(AN
AT
)ρ−1
• The project choice is, thus:
πT (t)
1− πT (t)=
γ
1− γ
(AN(t)
AT (t)
)θ
• 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
δ.
(ii) Equilibrium allocation C = w1+ϕσ+ϕ , L = w
1−σσ+ϕ , w = A.
(iii) Efficiency: . . .
13 / 23
Closed Economy, κ ≡ 0• In closed economy RT = RN = Y , and therefore:
χ =
(PH
PN
)ρ−1
=
(AN
AT
)ρ−1
• The project choice is, thus:
πT (t)
1− πT (t)=
γ
1− γ
(AN(t)
AT (t)
)θ
• 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
δ.
(ii) Equilibrium allocation C = w1+ϕσ+ϕ , L = w
1−σσ+ϕ , w = A.
(iii) Efficiency: . . .
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:
RT
RN= (1− κ)
(PH
PT
)1−ρ
+ κ(τPH)1−ρY∗
Y= 1 +
NX
γY.
(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 ·(
1
τ2ρ−1
A∗
AT
) 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
• Consider open economy with κ > 0 and τ ≥ 1
• Lemma 3 (i) The relative revenue shifter is given by:
RT
RN= (1− κ)
(PH
PT
)1−ρ
+ κ(τPH)1−ρY∗
Y= 1 +
NX
γY.
(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 ·(
1
τ2ρ−1
A∗
AT
) 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
• Consider open economy with κ > 0 and τ ≥ 1
• Lemma 3 (i) The relative revenue shifter is given by:
RT
RN= (1− κ)
(PH
PT
)1−ρ
+ κ(τPH)1−ρY∗
Y= 1 +
NX
γY.
(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 ·(
1
τ2ρ−1
A∗
AT
) κγ1+(2−κ)(ρ−1)
• Laisser-faire productivity dynamics is suboptimal.The planner would choose πT (t) < γ for all t ≥ 0.
14 / 23
OPEN ECONOMY IIFINANCIAL OPENNESS
15 / 23
Financial Openness
• With open current account:
πT1− πT
=γ
1− γχ
θρ−1 =
(AN
AT
)θ [1 +
NX
γY
] 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
• With open current account:
πT1− πT
=γ
1− γχ
θρ−1 =
(AN
AT
)θ [1 +
NX
γY
] 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
• With open current account:
πT1− πT
=γ
1− γχ
θρ−1 =
(AN
AT
)θ [1 +
NX
γY
] 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
• With open current account:
πT1− πT
=γ
1− γχ
θρ−1 =
(AN
AT
)θ [1 +
NX
γY
] 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
Convergence Path
0 50 100 150 200 250 300
0
0.3
0.7
1
Figure: Productivity convergence in closed and open economies16 / 23
Impact of Openness
0 50 100 150
-1
-0.5
0
0.5
0 50 100 150
0
0.2
0.4
0.6
0.8
• Two effects of openness:
1 Relative size of the market: Y /Y ∗
2 Competition: PT/PH < 1
1 +NX
γY=
(PH
PT
)1−ρ·
[(1− κ) + κ
(τ
PH
)1−ρ
=X/X∗︷ ︸︸ ︷P1−ρH Y ∗
Pρ−1T Y
]17 / 23
Endogenous Innovation Rate
• Endogenous participation of entrepreneurs if EΠ ≥ φW :
λ = Φ
(EΠ
W
)and
EΠ
W=%RN/W
Aρ−1N
Emax{χZρ−1
T , Zρ−1N
}
• Lemma 5EΠ
W= %
(A∗
A· AAθ
)ρ−1 γχ
θρ−1 + 1− γ
γ(AN
AT
)θ+ 1− γ
ρ−1θ
C
w,
where χ =(ANAT
)ρ−1[1 + NX
γY
]and C
w = w1−σσ+ϕ[1 + NX
Y
] −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
Endogenous Innovation Rate
• Endogenous participation of entrepreneurs if EΠ ≥ φW :
λ = Φ
(EΠ
W
)and
EΠ
W=%RN/W
Aρ−1N
Emax{χZρ−1
T , Zρ−1N
}
• Lemma 5EΠ
W= %
(A∗
A· AAθ
)ρ−1 γχ
θρ−1 + 1− γ
γ(AN
AT
)θ+ 1− γ
ρ−1θ
C
w,
where χ =(ANAT
)ρ−1[1 + NX
γY
]and C
w = w1−σσ+ϕ[1 + NX
Y
] −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
Endogenous Innovation Rate
• Endogenous participation of entrepreneurs if EΠ ≥ φW :
λ = Φ
(EΠ
W
)and
EΠ
W=%RN/W
Aρ−1N
Emax{χZρ−1
T , Zρ−1N
}
• Lemma 5EΠ
W= %
(A∗
A· AAθ
)ρ−1 γχ
θρ−1 + 1− γ
γ(AN
AT
)θ+ 1− γ
ρ−1θ
C
w,
where χ =(ANAT
)ρ−1[1 + NX
γY
]and C
w = w1−σσ+ϕ[1 + NX
Y
] −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
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)
]
= g0
[−(ρ− 1) (1 + µ) log
AT (t)
AN(t)+µ
γ
NX (t)
Y (0)
],
with g0 ≡ δρ−1
(λδA∗
A0
)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)
]
= g0
[−(ρ− 1) (1 + µ) log
AT (t)
AN(t)+µ
γ
NX (t)
Y (0)
],
with g0 ≡ δρ−1
(λδA∗
A0
)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)
(A∗
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:
PH =
[1
γ
∫ ΛT
0
PH(i)1−ρdi
] 11−ρ
and PN =
[1
1− γ
∫ ΛN
0
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:
PH =W
AT, PN =
W
ANand PF = τ
• Real wage rate:
w =W
P= A
[1− κ+ κ
(WτAT
)ρ−1] γρ−1
, A ≡ AγTA1−γN
24 / 23
Solution for NXback to slides
• Equilibrium system:
C = w1+ϕσ+ϕ
[1 +
NX
Y
]− ϕσ+ϕ
where w = A
(W
τAT
)κγand
NX
Y=
γκ(WτAT
)ρ−κγ[τ1−2ρA
∗ 1+ϕσ+ϕ
C
A
AT−(
W
τAT
)(1−κγ)+(2−κ)(ρ−1)]
25 / 23