Optimal Development Policies with Financial ... - Semantic Scholar
Optimal Development Policies with Financial Frictions
Oleg Itskhoki
Benjamin Moll
Princeton
Princeton
Boston University April 2014 1 / 27
Question
• Is there a role for governments to accelerate economic
development by intervening in product and factor markets? • Taxes? Subsidies? If so, which ones?
2 / 27
What We Do • Optimal Ramsey policy in 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
3 / 27
What We Do • Optimal Ramsey policy in 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 • 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
3 / 27
Main Findings 1
Optimal policy intervention: — pro-business policies for developing countries, i.e. during early transition when entrepreneurs are undercapitalized — pro-labor policy for developed countries, close to steady state — policies reminiscent of developing Asia
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 4 / 27
Empirical Relevance
• Input price suppression policies in developing Asia (Lin, 2012,
2013; Kim and Leipziger, 1997) • Industrial revolution in Britain (Ventura and Voth, 2013) • Real exchange rate devaluation (Rodrik, 2008) • Support to comparative advantage industries (Harrison and
Rodriguez-Clare, 2010; Lin, 2012)
5 / 27
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) + b(t) ≤ w (t)`(t) + r (t)b(t)
6 / 27
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) + b(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. a(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) 6 / 27
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:
a˙ = πt (a, z) + r (t) − δ a 7 / 27
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: x˙ = Π + r − δ x,
8 / 27
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: x˙ = Π + r − δ x,
• Lemma: National income accounts
w ` = (1 − α)y ,
rκ = α
η−1 y, η
Π=
α y. η 8 / 27
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
9 / 27
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 9 / 27
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
11 / 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
Lemma (Primal Approach) Any aggregate allocation {c, `, b, x}t≥0 satisfying c + b˙ = (1 − α)y (x, `) + r ∗ b − ςx x, x˙ = αη y (x, `) + (r ∗ + ςx − δ)x can be supported as a competitive equilibrium under appropriately chosen policies {τ` , τb , ςx }t≥0 . 11 / 27
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 + b˙ = (1 − α)y (x, `) + r ∗ b, α x˙ = 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
12 / 27
Optimal Policies without Transfers Characterization
• Inter-temporal margin undistorted:
u˙ c = 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? 13 / 27
Optimal Policies without Transfers Characterization
• ODE system in (x, ν) with a side-equation:
x˙ = αη y (x, `) + (r ∗ − δ)x, ν˙ = δν − (1 − γ + γν) αη y (x,`) x , u` /uc = (1 − γ + γν)(1 − α) y (x,`) ` , τ` = γ − γ · ν
14 / 27
Optimal Policies without Transfers Characterization
• ODE system in (x, τ` ) with a side-equation:
x˙ = αη y (x, `) + (r ∗ − δ)x, τ˙` = δ(τ` − γ) + γ(1 − τ` ) αη y (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 and γ taxed in steady state: τ¯` = γ+(1−γ)δ/ρ >0
4
intertemporal margin not distorted, τb ≡ 0 14 / 27
Optimal Policies without Transfers Phase diagram 0.08 x˙ = 0 0.06
0.04 Opt im al Tr a je c t or y
τℓ
0.02
0
−0.02
−0.04 τ˙ ℓ = 0 0.5
x
1
1.5 15 / 27
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
16 / 27
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
16 / 27
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), 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 + b˙ = (1 − α)y (x, `) + r ∗ b − ςx x, α x˙ = 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? 18 / 27
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
20
40 Ye ar s
60
80
0
0
20
40 Ye ar s
60
80
19 / 27
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
3
Closed economy
4
Economy with a non-tradable sector — real exchange rate implications
5
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:
a˙ = (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
22 / 27
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 ∝ (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 − 1 b b˙ = (1 − α) + α y (x, κ, `) − c − ςx x, η κ α η−1x x˙ = +α y (x, κ, `) + (ςx − δ)x, η η κ κ=x +b
24 / 27
Closed Economy • Planner’s problem:
Z max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
κ˙ = y (x, κ, `) − c − δx, α η−1x x˙ = +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) 24 / 27
Closed Economy • Planner’s problem:
Z max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
κ˙ = y (x, κ, `) − c − δx, α η−1x x˙ = +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) 24 / 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
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
26 / 27
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 26 / 27
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 ν˙ − δν = − 1 − α + ν η ∂x 27 / 27
Oleg Itskhoki
Benjamin Moll
Princeton
Princeton
Boston University April 2014 1 / 27
Question
• Is there a role for governments to accelerate economic
development by intervening in product and factor markets? • Taxes? Subsidies? If so, which ones?
2 / 27
What We Do • Optimal Ramsey policy in 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
3 / 27
What We Do • Optimal Ramsey policy in 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 • 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
3 / 27
Main Findings 1
Optimal policy intervention: — pro-business policies for developing countries, i.e. during early transition when entrepreneurs are undercapitalized — pro-labor policy for developed countries, close to steady state — policies reminiscent of developing Asia
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 4 / 27
Empirical Relevance
• Input price suppression policies in developing Asia (Lin, 2012,
2013; Kim and Leipziger, 1997) • Industrial revolution in Britain (Ventura and Voth, 2013) • Real exchange rate devaluation (Rodrik, 2008) • Support to comparative advantage industries (Harrison and
Rodriguez-Clare, 2010; Lin, 2012)
5 / 27
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) + b(t) ≤ w (t)`(t) + r (t)b(t)
6 / 27
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) + b(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. a(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) 6 / 27
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:
a˙ = πt (a, z) + r (t) − δ a 7 / 27
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: x˙ = Π + r − δ x,
8 / 27
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: x˙ = Π + r − δ x,
• Lemma: National income accounts
w ` = (1 − α)y ,
rκ = α
η−1 y, η
Π=
α y. η 8 / 27
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
9 / 27
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 9 / 27
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
11 / 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
Lemma (Primal Approach) Any aggregate allocation {c, `, b, x}t≥0 satisfying c + b˙ = (1 − α)y (x, `) + r ∗ b − ςx x, x˙ = αη y (x, `) + (r ∗ + ςx − δ)x can be supported as a competitive equilibrium under appropriately chosen policies {τ` , τb , ςx }t≥0 . 11 / 27
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 + b˙ = (1 − α)y (x, `) + r ∗ b, α x˙ = 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
12 / 27
Optimal Policies without Transfers Characterization
• Inter-temporal margin undistorted:
u˙ c = 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? 13 / 27
Optimal Policies without Transfers Characterization
• ODE system in (x, ν) with a side-equation:
x˙ = αη y (x, `) + (r ∗ − δ)x, ν˙ = δν − (1 − γ + γν) αη y (x,`) x , u` /uc = (1 − γ + γν)(1 − α) y (x,`) ` , τ` = γ − γ · ν
14 / 27
Optimal Policies without Transfers Characterization
• ODE system in (x, τ` ) with a side-equation:
x˙ = αη y (x, `) + (r ∗ − δ)x, τ˙` = δ(τ` − γ) + γ(1 − τ` ) αη y (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 and γ taxed in steady state: τ¯` = γ+(1−γ)δ/ρ >0
4
intertemporal margin not distorted, τb ≡ 0 14 / 27
Optimal Policies without Transfers Phase diagram 0.08 x˙ = 0 0.06
0.04 Opt im al Tr a je c t or y
τℓ
0.02
0
−0.02
−0.04 τ˙ ℓ = 0 0.5
x
1
1.5 15 / 27
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
16 / 27
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
16 / 27
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), 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 + b˙ = (1 − α)y (x, `) + r ∗ b − ςx x, α x˙ = 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? 18 / 27
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
20
40 Ye ar s
60
80
0
0
20
40 Ye ar s
60
80
19 / 27
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
3
Closed economy
4
Economy with a non-tradable sector — real exchange rate implications
5
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:
a˙ = (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
22 / 27
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 ∝ (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 − 1 b b˙ = (1 − α) + α y (x, κ, `) − c − ςx x, η κ α η−1x x˙ = +α y (x, κ, `) + (ςx − δ)x, η η κ κ=x +b
24 / 27
Closed Economy • Planner’s problem:
Z max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
κ˙ = y (x, κ, `) − c − δx, α η−1x x˙ = +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) 24 / 27
Closed Economy • Planner’s problem:
Z max
{c,`,κ,b,x,ςx }t≥0
subject to
∞
e −ρt u(c, `)dt
0
κ˙ = y (x, κ, `) − c − δx, α η−1x x˙ = +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) 24 / 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
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
26 / 27
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 26 / 27
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 ν˙ − δν = − 1 − α + ν η ∂x 27 / 27
