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Optimal Development Policies
with Financial Frictions
Oleg Itskhoki Benjamin MollPrinceton Princeton
Ecole PolytechniqueJune 2015
1 / 35
Questions
1 Normative:
• Is there a role for governments to accelerate economicdevelopment by intervening in product and factor markets?
• Taxes? Subsidies? If so, which ones?
2 Positive:
• Most emerging economies pursue active development andindustrial policies
• Under which circumstances may such policies be justified?
2 / 35
Historical accounts of development policies
Uniform Targeted
Roughperiod
Suppressedwages
Limitedcompetition
Subsidiesto sectors
Subsidiesto firms
Japan 1950-70√ √ √
Korea 1960-80√ √ √ √
Taiwan 1960-80√ √ √ √
Malaysia 1960-90√ √ √ √
Singapore 1960-90√ √ √
Thailand 1960-90√ √ √ √
China 1980-?√ √ √
Detailed discussion of sources in Appendix of future draft. E.g. for China:
Lin (1992, 2012, 2013), Stiglitz-Yusuf (2001), Schuman (2010), Zhu (2012), Qi (2014)
• Example of wage suppression: South Korea• official upper limit on real wage growth:
nominal wage growth < 80% (inflation + productivity growth)
• Park Chung Hee: 1965 “year to work”
, 1966 “year of harder work”
• not in table: exchange rate policies3 / 35
Historical accounts of development policies
Uniform Targeted
Roughperiod
Suppressedwages
Limitedcompetition
Subsidiesto sectors
Subsidiesto firms
Japan 1950-70√ √ √
Korea 1960-80√ √ √ √
Taiwan 1960-80√ √ √ √
Malaysia 1960-90√ √ √ √
Singapore 1960-90√ √ √
Thailand 1960-90√ √ √ √
China 1980-?√ √ √
Detailed discussion of sources in Appendix of future draft. E.g. for China:
Lin (1992, 2012, 2013), Stiglitz-Yusuf (2001), Schuman (2010), Zhu (2012), Qi (2014)
• Example of wage suppression: South Korea• official upper limit on real wage growth:
nominal wage growth < 80% (inflation + productivity growth)
• Park Chung Hee: 1965 “year to work”, 1966 “year of harder work”
• not in table: exchange rate policies3 / 35
Questions
• All these policies are “crazy” from neoclassical perspective
• This paper: some of them may be justified under particularcircumstances
4 / 35
What We Do
• Optimal Ramsey policy in a standard growth model withfinancial frictions
1 one-sector economy: uniform policies
2 multi-sector economy: targeted policies
• Environment similar to a wide class of development models
— financial frictions ⇒ capital misallocation ⇒ low productivity
• but more tractable ⇒ Ramsey problem feasible: Gt(a, z)→ at
• Features:
— Collateral constraint: firm’s scale limited by net worth
— Financial wealth affects economy-wide labor productivity
— Pecuniary externality: high wages hurt profits and wealthaccumulation
5 / 35
Main Findings
1 Optimal uniform policy in one-sector model
— 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
— Rationale: dynamic externality akin to learning-by-doing, butoperating via misallocation of resources
2 Optimal targeted and exchange rate policies in multi-sectormodel
— favor comparative advantage sectors and speed up transition
— compress wages in tradable sectors if undercapitalized...
— ... but whether this results in depreciated real exchange rate isinstrument-dependent
6 / 35
One-Sector Economy
1 Workers: representative household with wealth (bonds) b
max{c(·),`(·)}
∫ ∞0
e−ρtu(c(t), `(t)
)dt,
s.t. c(t) + b(t) ≤ w(t)`(t) + r(t)b(t)
2 Entrepreneurs: heterogeneous in wealth a and productivity z
max{ce(·)}
E0
∫ ∞0
e−δt log ce(t)dt
s.t. a(t) = πt(a(t), z(t)
)+ r(t)a(t)− ce(t)
πt(a, z) = maxn≥0, 0≤k≤λa
{A(t)(zk)αn1−α − w(t)n − r(t)k
}• Collateral constraint: k ≤ λa, λ ≥ 1
• Idiosyncratic productivity: z ∼ iidPareto(η)
7 / 35
One-Sector Economy
1 Workers: representative household with wealth (bonds) b
max{c(·),`(·)}
∫ ∞0
e−ρtu(c(t), `(t)
)dt,
s.t. c(t) + b(t) ≤ w(t)`(t) + r(t)b(t)
2 Entrepreneurs: heterogeneous in wealth a and productivity z
max{ce(·)}
E0
∫ ∞0
e−δt log ce(t)dt
s.t. a(t) = πt(a(t), z(t)
)+ r(t)a(t)− ce(t)
πt(a, z) = maxn≥0, 0≤k≤λa
{A(t)(zk)αn1−α − w(t)n − r(t)k
}• Collateral constraint: k ≤ λa, λ ≥ 1
• Idiosyncratic productivity: z ∼ iidPareto(η)
7 / 35
Policy functions
• Profit maximization:
kt(a, z) = λa · 1{z≥z(t)},
nt(a, z) =
(1− αw(t)
A
)1/α
zkt(a, z),
πt(a, z) =
[z
z(t)− 1
]r(t)kt(a, z),
where
αA1/α
(1− αw(t)
) 1−αα
z(t) = r(t)
• Wealth accumulation:
a = πt(a, z) +(r(t)− δ
)a
8 / 35
Aggregation
• Output:
y = A
(η
η − 1z
)α· κα`1−α
• Capital demand:
κ = λxz−η,
where aggregate wealth x(t) ≡∫adGt(a, z) evolves:
x = Π +(r − δ
)x ,
• Lemma: National income accounts
w` = (1− α)y , rκ = αη − 1
ηy , Π =
α
ηy .
9 / 35
Aggregation
• Output:
y = A
(η
η − 1z
)α· κα`1−α
• Capital demand:
κ = λxz−η,
where aggregate wealth x(t) ≡∫adGt(a, z) evolves:
x = Π +(r − δ
)x ,
• Lemma: National income accounts
w` = (1− α)y , rκ = αη − 1
ηy , Π =
α
ηy .
9 / 35
General equilibrium
1 Small open economy: r(t) ≡ r∗
and κ(t) is perfectly elastically supplied
• Lemma:
y = y(x , `) = Θxγ`1−γ , γ =α/η
(1− α) + α/η
and zη ∝ (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 zη = λx/κ
10 / 35
General equilibrium
1 Small open economy: r(t) ≡ r∗
and κ(t) is perfectly elastically supplied
• Lemma:
y = y(x , `) = Θxγ`1−γ , γ =α/η
(1− α) + α/η
and zη ∝ (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 zη = λx/κ
10 / 35
Excess Return of Entrepreneurs• Key to understanding all policy interventions: entrepreneurs
earn higher return than workers
• not only individually
R(z) = r
(1 + λ
[z
z− 1
]+)≥ r
• but also on average
ER(z) = r +α
η
y
x> r
• Could generate Pareto improvement with
• transfer from workers to all entrepreneurs at t = 0+ reverse transfer at later date
• essentially allows planner to sidestep friction
• perhaps not feasible, e.g. for political economy reasons
• Next: explore alternative policies
11 / 35
Excess Return of Entrepreneurs• Key to understanding all policy interventions: entrepreneurs
earn higher return than workers
• not only individually
R(z) = r
(1 + λ
[z
z− 1
]+)≥ r
• but also on average
ER(z) = r +α
η
y
x> r
• Could generate Pareto improvement with
• transfer from workers to all entrepreneurs at t = 0+ reverse transfer at later date
• essentially allows planner to sidestep friction
• perhaps not feasible, e.g. for political economy reasons
• Next: explore alternative policies
11 / 35
Optimal Ramsey Policiesin a Small Open Economy
• Start with three policy instruments:
1 τ`(t): labor supply tax
2 τb(t): worker savings tax
3 T (t): lump-sum tax on workers; GBC: τ`w`+ τbb = T
Lemma (Primal Approach)
Any aggregate allocation {c , `, b, x}t≥0 satisfying
c + b = (1− α)y(x , `) + r∗b
x = αη y(x , `) + (r∗ − δ)x
can be supported as a competitive equilibrium under appropriatelychosen policies {τ`, τb}t≥0.
12 / 35
Optimal Ramsey Policiesin a Small Open Economy
• Start with three policy instruments:
1 τ`(t): labor supply tax
2 τb(t): worker savings tax
3 T (t): lump-sum tax on workers; GBC: τ`w`+ τbb = T
Lemma (Primal Approach)
Any aggregate allocation {c , `, b, x}t≥0 satisfying
c + b = (1− α)y(x , `) + r∗b
x = αη y(x , `) + (r∗ − δ)x
can be supported as a competitive equilibrium under appropriatelychosen policies {τ`, τb}t≥0.
12 / 35
Optimal Ramsey Policies
• Benchmark: zero weight on entrepreneurs
• Planner’s problem:
max{c,`,b,x}t≥0
∫ ∞0
e−ρtu(c , `)dt
subject to c + b = (1− α)y(x , `) + r∗b,
x =α
ηy(x , `) + (r∗ − δ)x ,
and denote by ν the co-state for x (shadow value of wealth)
• Isomorphic to learning-by-doing externality
13 / 35
Optimal Ramsey PoliciesCharacterization
• Inter-temporal margin undistorted:
ucuc
= ρ− r∗ ⇒ τb = 0
• Intra-temporal margin distorted:
−u`uc
=[1 + γ(ν − 1)
](1− α)
y
`⇒ τ` = γ − γ · ν
• Two confronting objectives:
1 Monopoly effect: increase wages by limiting labor supply
2 Dynamic productivity externality: accumulate x by subsidizinglabor supply to increase future labor productivity
• Which effect dominates and when?14 / 35
Optimal Ramsey PoliciesCharacterization
• ODE system in (x , ν) with a side-equation:
x = αη y(x , `) + (r∗ − δ)x ,
ν = δν − (1− γ + γν)αηy(x ,`)
x ,
− u`/uc = (1− γ + γν)(1− α) y(x ,`)` ,
τ` = γ − γ · ν
• Proposition: Assume δ > ρ = r∗. Then:
1 unique steady state (x , τ`), globally saddle-path stable
2 starting from x0 ≤ x , x and τ` increase to (x , τ`)
3 labor supply subsidized (τ` < 0) when x is low enough andtaxed in steady state: τ` = γ
γ+(1−γ)δ/ρ > 0
4 intertemporal margin not distorted, τb ≡ 0
15 / 35
Optimal Ramsey PoliciesCharacterization
• ODE system in (x , τ`) with a side-equation:
x = αη y(x , `) + (r∗ − δ)x ,
τ` = δ(τ` − γ) + γ(1− τ`)αηy(x ,`)
x ,
` = `(x , τ`; µ)
• Proposition: Assume δ > ρ = r∗. Then:
1 unique steady state (x , τ`), globally saddle-path stable
2 starting from x0 ≤ x , x and τ` increase to (x , τ`)
3 labor supply subsidized (τ` < 0) when x is low enough andtaxed in steady state: τ` = γ
γ+(1−γ)δ/ρ > 0
4 intertemporal margin not distorted, τb ≡ 0
15 / 35
Optimal Ramsey PoliciesPhase diagram
0.5 1 1.5
−0.04
−0.02
0
0.02
0.04
0.06
0.08
τℓ = 0
x = 0
Optimal Tra jectory
τℓ
x
16 / 35
Optimal Ramsey PoliciesTime path
0 20 40 60 80−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
Years
(a) Labor Tax, τℓ
Equilibrium
Planner
0 20 40 60 800
0.2
0.4
0.6
0.8
1
Years
(b) Entrepreneurial Wealth, x
Equilibrium
Planner
17 / 35
Deviations from laissez-faire
0 20 40 60 80−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
(a) Labor Supply, ℓ
Years0 20 40 60 80
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
(b) Entrepreneurial Wealth, x
Years
0 20 40 60 80−0.06
−0.05
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
(c) Wage, w , and Labor Productivity, y/ℓ
Years0 20 40 60 80
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
(d) Total Factor Productivity, Z
Years
0 20 40 60 80−0.1
−0.05
0
0.05
0.1
0.15
(e) Income, y
Years0 20 40 60 80
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
( f ) Worker Period Util ity, u(c, ℓ)
Years
17 / 35
Optimal Ramsey PoliciesDiscussion
• Many alternative implementations
• common feature: make workers work hard even though firmspay low wages
1 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
• Interpretation:
— Pro-business (or wage suppression, or pro-output) policies
— Policy reversal to pro-labor for developed countries
• Intuition: pecuniary externality
— High wage reduces profits and slows down wealth accumulation
18 / 35
Optimal Policy with Transfers
• Generalized planner’s problem:
max{c,`,b,x ,ςx}t≥0
∫ ∞0
e−ρtu(c , `)dt
subject to c + b = (1− α)y(x , `) + r∗b − ςxx ,
x =α
ηy(x , `) + (r∗ + ςx − δ)x ,
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?
19 / 35
Unlimited Transfers
0 20 40 60 80
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
Years
(a) Transfer , ςx
Equilibrium
Planner
0 20 40 60 800
0.2
0.4
0.6
0.8
1
Years
(b) Entrepreneurial Wealth, x
Equilibrium
Planner
20 / 35
Bounded Transfers
0 20 40 60 80−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
Years
(a) Labor Tax, τℓ
Equilibrium
Planner, No Transf.
Planner, Lim. Transf.
0 20 40 60 800
0.2
0.4
0.6
0.8
1
Years
(b) Entrepreneurial Wealth, x
Equilibrium
Planner, No Transf.
Planner, Lim. Transf.
21 / 35
Additional Tax Instruments
• Additional policy instruments, all affecting entrepreneurs andfinanced 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:
a = (1 + ςπ)π(a, z) + (r∗ + ςx)a− ce ,
π(a, z) = maxn≥0,
0≤k≤λa
{(1 + ςy )A(zk)αn1−α − (1− ςw )w`− (1− ςk)r∗k
}
22 / 35
Additional Tax Instruments
• Generalize output function
y(x , `) =
(1 + ςy1− ςk
)γ(η−1)Θxγ`1−γ
• Proposition:
(i) Profit subsidy ςπ, as well as ςy = −ςk = −ςw , has the sameeffect as a transfer from workers to entrepreneurs, anddominates other tax instruments.
(ii) When a transfer cannot be engineered, all available policyinstruments are used to speed up the accumulation ofentrepreneurial wealth.
• E.g.: ςk , ςw ∝ γ(ν − 1)
• Pro-business policy bias during early transition
23 / 35
Multi-Sector Economy: Targeted Policies
• Want framework for thinking about policies targeted toparticular sectors
• arguably most prevalent type of development policy
• Generalize framework to multiple sectors
• both tradable and non-tradable sectors
• In addition to sectoral policies, also explore implications forreal exchange rate
24 / 35
Multi-Sector Economy: Households• Households have preferences∫ ∞
0e−ρtu(c0, c1, ..., cN)dt
• goods 0, ..., k : tradable
• goods k + 1, ...,N: not tradable
• good 0 is numeraire ⇒ p0 = 1
• inelastically supply L units of labor, split across sectors
N∑i=0
`i = L
• Budget constraint
N∑i=0
(1 + τ ci )pici + b ≤ (r − τb)b +N∑i=0
(1− τ `i )wi`i + T
• As before, can extend to additional tax instruments
25 / 35
Multi-Sector Economy: Households• Households have preferences∫ ∞
0e−ρtu(c0, c1, ..., cN)dt
• goods 0, ..., k : tradable
• goods k + 1, ...,N: not tradable
• good 0 is numeraire ⇒ p0 = 1
• inelastically supply L units of labor, split across sectors
N∑i=0
`i = L
• Budget constraint
N∑i=0
(1 + τ ci )pici + b ≤ (r − τb)b +N∑i=0
(1− τ `i )wi`i + T
• As before, can extend to additional tax instruments25 / 35
Production
• Within each sector, everything as before
• Output in sector i :
yi (xi , `i ; pi ) = Θixγii `
1−γii p
γi (ηi−1)i , where
γi =αi/ηi
1− αi + αi/ηiand Θi =
r
αi
[ηiλiηi − 1
(αiAi
r
)ηi/αi]γi
• Wealth accumulation
xi =αi
ηipiyi (xi , `i ; pi ) + (r − δ)xi
26 / 35
Optimal Targeted Ramsey Policies
• Planner’s Problem:
max{xi ,`i}Ni=0,{pi}
Ni=k+1
∫ ∞0
e−ρtu(c0, ..., cN)dt s.t.
b = rb +N∑i=0
(1− αi )piyi (xi , `i , pi )−N∑i=0
pici
xi =αi
ηipiyi (xi , `i , pi ) + (r − δ)xi , i = 0, . . . ,N
ci = yi (xi , `i , pi ), i = k + 1, . . . ,N
L =∑N
i=0 `i
27 / 35
Optimal Targeted Ramsey Policies
• Optimal taxes
τb = 0,
τ ci =1
ηi − 1(1− νi ), i = k + 1, . . . ,N
τ `i = γi
(1− νi −
ηiαiτ ci
)=
{γi (1− νi ), i = 1, . . . , k ,
−τ ci , i = k + 1, . . . ,N
• Explore two special cases
1 all sectors are tradable: implications of comparative advantage
2 one tradable, one non-tradable sector: implications for RER
28 / 35
All Sectors are TradableComparative advantage and industrial policies
• International prices {p∗i }
• sectoral revenues: p∗i yi = Θ∗i xγii `
1−γii , Θ∗i = (p∗i )γiηi/αi Θi
• Comparative advantage:
— Long run (latent): Θ∗i
— Short run (actual): Θ∗i xγi
• Optimal policy: favors the (latent) comparative advantagesector and speeds up the transition
29 / 35
All Sectors are TradableComparative advantage and industrial policies
• International prices {p∗i }
• sectoral revenues: p∗i yi = Θ∗i xγii `
1−γii , Θ∗i = (p∗i )γiηi/αi Θi
• Comparative advantage:
— Long run (latent): Θ∗i
— Short run (actual): Θ∗i xγi
• Optimal policy: favors the (latent) comparative advantagesector and speeds up the transition
29 / 35
All Sectors are TradableComparative advantage and industrial policies
0 20 40 60 80
0.16
0.18
0.2
0.22
0.24
(a) Subsidy to Sector 1
Years0 20 40 60 80
0
0.5
1
1.5
2
2.5
(b) Sectoral Wealth, x i
Sector 1
Sector 2
Years
• Sector one has (latent) comparative advantage: p∗1Θ1 > p∗2Θ2
• Optimal policy speeds up the transition
• Potentially measurable sufficient statistic: γi · νi , where
νi − δνi = −(
1− αi +αi
ηiνi
)pi∂yi∂xi
29 / 35
Non-tradables and the RER• Consider economy with two sectors
• sector 0 produces tradable good, p0 = 1
• sector 1 produces non-tradable good
• For simplicity u(c0, c1) = CES(θ)
• What are implications of optimal policy for real exchange rate
RER = (p1−θ0 + p1−θ1 )1
1−θ
• Intuition: if want to subsidize tradables ⇒ compresseconomy-wide w ∝ p1 ⇒ RER depreciates• see e.g. Rodrik (2008)
• We find: robust policy recommendation = compress wagesin tradable sector if that sector is undercapitalized.
• instead implications for RER are instrument-dependent• if can differentially tax T and NT labor, RER appreciates
• conjecture: if instead cannot differentially subsidize T and NT⇒ RER depreciates (i.e. intuition correct)
30 / 35
Non-tradables and the RER• Consider economy with two sectors
• sector 0 produces tradable good, p0 = 1
• sector 1 produces non-tradable good
• For simplicity u(c0, c1) = CES(θ)
• What are implications of optimal policy for real exchange rate
RER = (p1−θ0 + p1−θ1 )1
1−θ
• Intuition: if want to subsidize tradables ⇒ compresseconomy-wide w ∝ p1 ⇒ RER depreciates• see e.g. Rodrik (2008)
• We find: robust policy recommendation = compress wagesin tradable sector if that sector is undercapitalized.
• instead implications for RER are instrument-dependent• if can differentially tax T and NT labor, RER appreciates
• conjecture: if instead cannot differentially subsidize T and NT⇒ RER depreciates (i.e. intuition correct)
30 / 35
Non-tradables and the RER
0 10 20 301
2
3
4
5
6
7
8
Years
(a) Sectoral Wealth, x i
Tradables
Nontradables
0 10 20 30−0.3
−0.2
−0.1
0
0.1
0.2
(b) Cons Tax on NT Sector
Years0 10 20 30
−0.4
−0.2
0
0.2
0.4
0.6
(c) Labor Tax on NT Sector
Years
0 10 20 300.45
0.5
0.55
0.6
0.65
0.7
0.75
(d) Emp Share in T Sector
Years0 10 20 30
1
1.5
2
2.5
3
Years
(e) Sectoral Wage
Tradables
Nontradables
0 10 20 301
1.2
1.4
1.6
1.8
2
( f ) Producer Price RER
Years31 / 35
Non-tradables and the RER
• Planner subsidizes NT demand (thereby increasing NTproducer price) and taxes NT labor supply
• Intuition: try to mimic transfer (equivalent to output subsidy+ taxes on both labor and capital)
• Conjecture: if planner cannot differentially subsidize sectors⇒ RER depreciates
32 / 35
Other Extensions
1 Positive Pareto weight on entrepreneurs
τ` = γ [1− ν − ω/x ]
2 Closed economy
3 Persistent productivity shocks
33 / 35
Closed Economy• Planner’s problem:
max{c,`,κ,b,x ,ςx}t≥0
∫ ∞0
e−ρtu(c, `)dt
subject to b =
[(1− α) + α
η − 1
η
b
κ
]y(x , κ, `)− c − ςxx ,
x =
[α
η+ α
η − 1
η
x
κ
]y(x , κ, `) + (ςx − δ)x ,
κ = x + b
• We study three cases:1 Unlimited transfers and x , κ ≥ 0 only
— No distortions (τb = τ` = 0) and x : αη
yx= δ
2 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)
34 / 35
Closed Economy
• Planner’s problem:
max{c,`,κ,b,x ,ςx}t≥0
∫ ∞0
e−ρtu(c , `)dt
subject to κ = y(x , κ, `)− c − δx ,
x =
[α
η+ α
η − 1
η
x
κ
]y(x , κ, `) + (ςx − δ)x
• We study three cases:
1 Unlimited transfers and x , κ ≥ 0 only
— No distortions (τb = τ` = 0) and x : αη
yx= δ
2 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)
34 / 35
Closed Economy
• Planner’s problem:
max{c,`,κ,b,x ,ςx}t≥0
∫ ∞0
e−ρtu(c , `)dt
subject to κ = y(x , κ, `)− c − δx ,
x =
[α
η+ α
η − 1
η
x
κ
]y(x , κ, `) + (ςx − δ)x
• We study three cases:
1 Unlimited transfers and x , κ ≥ 0 only— No distortions (τb = τ` = 0) and x : α
ηyx= δ
2 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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Conclusion
• Optimal Ramsey policy in standard growth model withfinancial frictions
• Main Lesson from one-sector model: pro-business policiesaccelerate economic development and are welfare-improving
— during initial transitions, and not in steady states
— when business sector is undercapitalized
• Main Lesson from multi-sector model:
— favor comparative advantage sectors and speed up transition
— implications for RER are instrument-dependent
• Although stylized, model points towards a measurablesufficient statistic: γi · νi , where
νi − δνi = −(
1− αi +αi
ηiνi
)pi∂yi∂xi
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