Optimal Development Policies
with Financial Frictions
Oleg Itskhoki
Benjamin Moll
Princeton
Princeton
CUNY
March 2015
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Questions
1
Normative:
• Is there a role for governments to accelerate economic
development by intervening in product and factor markets?
• Taxes? Subsidies? If so, which ones?
2
Positive:
• Most emerging economies pursue active development and
industrial policies
• Under which circumstances such policies may be justified?
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What We Do
• Optimal Ramsey policy in a standard growth model with
financial frictions
• Environment similar to a wide class of development models
— financial frictions ⇒ capital misallocation ⇒ low productivity
• but more tractable ⇒ Ramsey problem feasible: Gt (a, z) → āt
• Features:
— Collateral constraint: firm’s scale limited by net worth
— Financial wealth affects economy-wide labor productivity
— Pecuniary externality: high wages hurt profits and wealth
accumulation (bad idea to equalize MPL when MPK are not)
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Main Findings
1
Robust optimal policy intervention:
— pro-business (pro-output) policies for developing countries,
during early transition when entrepreneurs are undercapitalized
— pro-labor policy for developed countries, close to steady state
2
Rationale: dynamic externality akin to learning-by-doing, but
operating via misallocation of resources
3
Extension with nontradables and real exchange rate:
— policies may induce real devaluation, joint with capital
outflows and FDI inflows
4
Multisector extension with comparative advantage:
— optimal industrial policies favor the comparative advantage
sectors and speed up the transition
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Empirical Relevance
• Input price suppression policies in developing Asia
(Lin, 2012, 2013; Kim and Leipziger, 1997)
• Industrial revolution in the 19th century Britain
(Ventura and Voth, 2013)
• Real exchange rate devaluation policy, financial repression
(Rodrik, 2008)
• Support to comparative advantage industries, export
promotion and import substitution
(Harrison and Rodriguez-Clare, 2010; Lin, 2012)
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Model Setup
1
Workers: representative household with wealth (bonds) b
Z ∞
e −ρt u c(t), `(t) dt,
max
{c(·),`(·)}
s.t.
0
c(t) + ḃ(t) ≤ w (t)`(t) + r (t)b(t)
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Model Setup
1
Workers: representative household with wealth (bonds) b
Z ∞
e −ρt u c(t), `(t) dt,
max
{c(·),`(·)}
s.t.
2
0
c(t) + ḃ(t) ≤ w (t)`(t) + r (t)b(t)
Entrepreneurs: heterogeneous in wealth a and productivity z
Z ∞
max E0
e −δt log ce (t)dt
{ce (·)}
0
s.t. ȧ(t) = πt a(t), z(t) + r (t)a(t) − ce (t)
πt (a, z) =
max
A(t)(zk)α n1−α − w (t)n − r (t)k
n≥0, 0≤k≤λa
• Collateral constraint: k ≤ λa, λ ≥ 1
• Idiosyncratic productivity: z ∼ iidPareto(η)
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Policy functions
• Profit maximization:
kt (a, z) = λa · 1{z≥z(t)} ,
1/α
1−α
zkt (a, z),
nt (a, z) =
A
w (t)
z
πt (a, z) =
− 1 r (t)kt (a, z),
z(t)
where
1/α
αA
1−α
w (t)
1−α
α
z(t) = r (t)
• Wealth accumulation:
ȧ = πt (a, z) + r (t) − δ a
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Aggregation
• Output:
y =A
η
z
η−1
α
· κα `1−α
• Capital demand:
κ = λxz −η ,
R
where aggregate wealth x(t) ≡ adGt (a, z) evolves:
ẋ = Π + r − δ x,
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Aggregation
• Output:
y =A
η
z
η−1
α
· κα `1−α
• Capital demand:
κ = λxz −η ,
R
where aggregate wealth x(t) ≡ adGt (a, z) evolves:
ẋ = Π + r − δ x,
• Lemma: National income accounts
w ` = (1 − α)y ,
rκ = α
η−1
y,
η
Π=
α
y.
η
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General equilibrium
1
Small open economy:
r (t) ≡ r ∗
and κ(t) is perfectly elastically supplied
• Lemma:
y = y (x, `) = Θx γ `1−γ ,
γ=
α/η
(1 − α) + α/η
and z η ∝ (x/`)1−γ
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General equilibrium
1
Small open economy:
r (t) ≡ r ∗
and κ(t) is perfectly elastically supplied
• Lemma:
y = y (x, `) = Θx γ `1−γ ,
α/η
(1 − α) + α/η
γ=
and z η ∝ (x/`)1−γ
2
Closed economy:
κ(t) = b(t) + x(t)
and r (t) equilibrates capital market
• Lemma:
y = y (x, κ, `) = Θc xκη−1
α/η
`1−α
and z η = λx/κ
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Decentralized Equilibrium
• Proposition: Decentralized equilibrium is inefficient
• Simple deviations from decentralized equilibrium result in
strict Pareto improvement
1
Wealth transfer from workers to all entrepreneurs:
— Higher return for entrepreneurs:
+ z
R(z) = r 1 + λ
−1
≥r
z
αy
ER(z) = r +
>r
ηx
2
Coordinated labor supply adjustment by workers
10 / 27
Optimal Ramsey Policies
in a Small Open Economy
• Start with
1 τ` (t):
2 τb (t):
3 ςx (t):
three policy instruments:
labor supply tax
worker savings tax
asset subsidy to entrepreneurs
— an effective transfer between workers and entrepreneurs
— s ≤ ςx x ≤ S
4
T: lump-sum tax on workers; GBC: τ` w ` + τb b = ςx x + T
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Optimal Ramsey Policies
in a Small Open Economy
• Start with
1 τ` (t):
2 τb (t):
3 ςx (t):
three policy instruments:
labor supply tax
worker savings tax
asset subsidy to entrepreneurs
— an effective transfer between workers and entrepreneurs
— s ≤ ςx x ≤ S
4
T: lump-sum tax on workers; GBC: τ` w ` + τb b = ςx x + T
Lemma (Primal Approach)
Any aggregate allocation {c, `, b, x}t≥0 satisfying
c + ḃ = (1 − α)y (x, `) + r ∗ b − ςx x,
ẋ = αη y (x, `) + (r ∗ + ςx − δ)x
can be supported as a competitive equilibrium under appropriately
chosen policies {τ` , τb , ςx }t≥0 .
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Optimal Policies without Transfers
• Benchmark: zero weight on entrepreneurs
• Planner’s problem:
Z
max
{c,`,b,x}t≥0
subject to
∞
e −ρt u(c, `)dt
0
c + ḃ = (1 − α)y (x, `) + r ∗ b,
α
ẋ = y (x, `) + (r ∗ − δ)x,
η
and denote by ν the co-state for x (shadow value of wealth)
• Isomorphic to learning-by-doing externality
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Optimal Policies without Transfers
Characterization
• Inter-temporal margin undistorted:
u̇c
= ρ − r∗
uc
⇒
τb = 0
• Intra-temporal margin distorted:
−
u`
y
= 1 − τ` (1 − α) ,
uc
`
τ` = γ − γ · ν
• Two confronting objectives:
1
Monopoly effect: increase wages by limiting labor supply
2
Dynamic productivity externality: accumulate x by subsidizing
labor supply to increase future labor productivity
• Which effect dominates and when?
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Optimal Policies without Transfers
Characterization
• ODE system in (x, ν) with a side-equation:
ẋ = αη y (x, `) + (r ∗ − δ)x,
ν̇ = δν − (1 − γ + γν) αη y (x,`)
x ,
− u` /uc = (1 − γ + γν)(1 − α) y (x,`)
` ,
τ` = γ − γ · ν
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Optimal Policies without Transfers
Characterization
• ODE system in (x, τ` ) with a side-equation:
ẋ = αη y (x, `) + (r ∗ − δ)x,
τ̇` = δ(τ` − γ) + γ(1 − τ` ) αη y (x,`)
x ,
` = `(x, τ` ; µ̄)
• Proposition: Assume δ > ρ = r ∗ . Then:
1
unique steady state (x̄, τ̄` ), globally saddle-path stable
2
starting from x0 ≤ x̄, x and τ` increase to (x̄, τ̄` )
3
labor supply subsidized (τ` < 0) when x is low enough and
γ
taxed in steady state: τ̄` = γ+(1−γ)δ/ρ
>0
4
intertemporal margin not distorted, τb ≡ 0
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Optimal Policies without Transfers
Phase diagram
0.08
ẋ = 0
0.06
0.04
Opt im al Tr a je c t or y
τℓ
0.02
0
−0.02
−0.04
τ̇ ℓ = 0
0.5
x
1
1.5
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Optimal Policies without Transfers
Time path
( a) Labor Tax, τ ℓ
( b) Ent r e pr e ne ur ial We alt h, x
0.15
1
0.1
0.8
0.05
0
0.6
−0.05
0.4
−0.1
−0.15
0.2
−0.2
−0.25
0
Equilibrium
Planner
20
40
Ye ar s
60
Equilibrium
Planner
80
0
0
20
40
Ye ar s
60
80
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Deviations from laissez-faire
( b) Ent r e pr e ne ur ial We alt h, x
( a) Labor Supply, ℓ
0.25
0.08
0.2
0.06
0.04
0.15
0.02
0.1
0
0.05
−0.02
0
−0.04
−0.05
−0.1
0
−0.06
20
40
Ye ar s
60
80
−0.08
0
( c ) Wage , w , and Labor Pr oduc t ivity, y /ℓ
0.02
20
40
Ye ar s
60
80
( d) Tot al Fac t or Pr oduc t ivity, Z
0.02
0.01
0.01
0
0
−0.01
−0.02
−0.01
−0.03
−0.02
−0.04
−0.03
−0.05
−0.06
0
20
40
Ye ar s
60
80
−0.04
0
( e ) Inc ome , y
20
40
Ye ar s
60
80
( f ) Wor ke r Pe r iod Ut ility, u ( c, ℓ)
0.15
0.15
0.1
0.1
0.05
0.05
0
−0.05
0
−0.1
−0.05
−0.15
−0.1
0
20
40
Ye ar s
60
80
−0.2
0
20
40
Ye ar s
60
80
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Optimal Policies without Transfers
Discussion
• Implementation:
Subsidy to labor supply or demand
2 Non-market implementation: e.g., forced labor
3 Non-tax market regulation: e.g., via bargaining power of labor
1
• Interpretation:
— Pro-business (or wage suppression, or pro-output) policies
— Policy reversal to pro-labor for developed countries
— Reinterpretation of New Deal policies (cf. Cole and Ohanian)
• Intuition:
pecuniary externality
— High wage reduces profits and slows down wealth
accumulation
— How general?
17 / 27
Optimal Policy with Transfers
• Generalized planner’s problem:
Z
max
{c,`,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
c + ḃ = (1 − α)y (x, `) + r ∗ b − ςx x,
α
ẋ = y (x, `) + (r ∗ + ςx − δ)x,
η
s ≤ ςx (t) x(t) ≤ S
• Three cases:
1
s = S = 0: just studied
2
S = −s = +∞ (unlimited transfers)
3
0 < S, −s < ∞ (bounded transfers)
• Why bounded transfers?
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Unlimited Transfers
( a) Tr ans fe r , ς x
( b) Ent r e pr e ne ur ial We alt h, x
1
Equilibrium
Planner
0.03
0.8
0.02
0.01
0.6
0
0.4
−0.01
−0.02
0.2
Equilibrium
Planner
−0.03
0
0
20
40
Ye ar s
60
80
0
20
40
Ye ar s
60
80
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Bounded Transfers
( a) Lab or Tax, τ ℓ
( b) Ent r e pr e ne ur ial We alt h, x
0.15
1
0.1
0.8
0.05
0
0.6
−0.05
0.4
−0.1
−0.15
Equilibrium
Planner, No Transf.
Planner, Lim. Transf.
−0.2
−0.25
0
20
40
Ye ar s
60
80
0.2
0
0
Equilibrium
Planner, No Transf.
Planner, Lim. Transf.
20
40
Ye ar s
60
80
20 / 27
Extensions
1
Positive Pareto weight on entrepreneurs
τ` = γ [1 − ν − ω/x]
2
Additional tax instruments
— including capital (credit) subsidy
— joint use of all available instruments: ςk , ςw ∝ γ(ν − 1)
3
Closed economy
4
Persistent productivity shocks
5
Economy with a non-tradable sector
— real exchange rate implications
6
Multisector economy with comparative advantage
— optimal sectoral industrial policies
21 / 27
Additional Tax Instruments
• Additional policy instruments, all affecting entrepreneurs and
financed by a lump-sum tax on workers
1
ςπ (t): profit subsidy
2
ςy (t): revenue subsidy
3
ςw (t): wage bill subsidy
4
ςk (t): capital (credit) subsidy
• Budget set of entrepreneurs:
ȧ = (1 + ςπ )π(a, z) + (r ∗ + ςx )a − ce ,
n
o
π(a, z) = max (1 + ςy )A(zk)α n1−α − (1 − ςw )w ` − (1 − ςk )r ∗ k
n≥0,
0≤k≤λa
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Additional Tax Instruments
• Generalize output function
y (x, `) =
1 + ςy
1 − ςk
γ(η−1)
Θx γ `1−γ
• Proposition:
(i) Profit subsidy ςπ , as well as ςy = −ςk = −ςw , has the same
effect as a transfer from workers to entrepreneurs, and
dominates other tax instruments.
(ii) When a transfer cannot be engineered, all available policy
instruments are used to speed up the accumulation of
entrepreneurial wealth.
• E.g.: ςk , ςw ∝ γ(ν − 1)
• Pro-business policy bias during early transition
23 / 27
Closed Economy
• Planner’s problem:
Z
max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
η−1b
ḃ = (1 − α) + α
y (x, κ, `) − c − ςx x,
η κ
α
η−1x
ẋ =
+α
y (x, κ, `) + (ςx − δ)x,
η
η κ
κ=x +b
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Closed Economy
• Planner’s problem:
Z
max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
κ̇ = y (x, κ, `) − c − δx,
α
η−1x
ẋ =
+α
y (x, κ, `) + (ςx − δ)x
η
η κ
• We study three cases:
1 Unlimited transfers and x, κ ≥ 0 only
2
Unlimited transfers and x ≤ κ
3
Bounded transfers (limiting case s = S = 0)
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Closed Economy
• Planner’s problem:
Z
max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
κ̇ = y (x, κ, `) − c − δx,
α
η−1x
ẋ =
+α
y (x, κ, `) + (ςx − δ)x
η
η κ
• We study three cases:
1 Unlimited transfers and x, κ ≥ 0 only
— No distortions (τb = τ` = 0) and x :
2
αy
η x
=δ
Unlimited transfers and x ≤ κ
— No labor supply distortion (τ` = 0); subsidized savings: τb ≥ 0
3
Bounded transfers (limiting case s = S = 0)
— Both labor supply and savings are distorted: τ` , τb ∝ (1 − ν)
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Non-tradables and RER
• Modified setup:
— flow utility U(c, cN ), inelastic labor supply
— frictionless non-tradable production: yN = `N = 1 − `
• Same setup subject to reinterpretation: UN /Uc = (1 + τN )w
— Tax on non-tradables instead of labor subsidy
— Early transition: tax non-tradables ⇒ appreciated RER
25 / 27
Non-tradables and RER
• Modified setup:
— flow utility U(c, cN ), inelastic labor supply
— frictionless non-tradable production: yN = `N = 1 − `
• Same setup subject to reinterpretation: UN /Uc = (1 + τN )w
— Tax on non-tradables instead of labor subsidy
— Early transition: tax non-tradables ⇒ appreciated RER
• If no such instrument, then distort intertemporal margin
— Early transition: subsidize savings (τb < 0)
— Increases labor supply and reduces demand for non-tradables
— Real devaluation. . .
— Implementation: forced savings via reserve accumulation under
capital controls (China)
25 / 27
Multisector economy
Comparative advantage and industrial policies
• N sectors: yi = Θi xiγ `1−γ
i
• Allocation of labor: L =
PN
i=1 `i
• International prices {pi∗ }
• Comparative advantage:
— Long run (latent): pi∗ Θi
— Short run (actual): pi∗ Θi xiγ
26 / 27
Multisector economy
Comparative advantage and industrial policies
• N sectors: yi = Θi xiγ `1−γ
i
• Allocation of labor: L =
PN
i=1 `i
• International prices {pi∗ }
• Comparative advantage:
— Long run (latent): pi∗ Θi
— Short run (actual): pi∗ Θi xiγ
• Optimal policy: favors the (latent) comparative advantage
sector and speeds up the transition
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Multisector economy
Comparative advantage and industrial policies
( a) Subs idy t o Se c t or 1
( b) Se c t or al We alt h, x i
2.5
0.24
2
Se c t or 1
0.22
1.5
0.2
1
Se c t or 2
0.18
0.5
0.16
0
20
40
Ye ar s
60
80
0
0
20
40
Ye ar s
60
80
• Sector one has (latent) comparative advantage: p1∗ Θ1 > p2∗ Θ2
• Optimal policy speeds up the transition
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Conclusion
• Optimal Ramsey policy in standard growth model with
financial frictions
• Main Lesson: pro-business policies accelerate economic
development and are welfare-improving
— during initial transitions, and not in steady states
— when business sector is undercapitalized
• The model is tractable and can be extended to think about
exchange rate and industrial policies
• Although stylized, the model points towards a measurable
sufficient statistic: γ · ν, where
α
∂y
ν̇ − δν = − 1 − α + ν
η
∂x
27 / 27