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Entrepreneurship, Agency Frictions and Redistributive Capital Taxation Corina Boar Matthew Knowles University of Rochester December 10, 2015 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Corina Boar Matthew Knowles
University of Rochester
December 10, 2015
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
How should entrepreneurial wealth be taxed? Business owners account for 40-50% of total wealth and produce half of total output Among the top 5% of the wealth distribution, 70% are business owners Entrepreneurs face idiosyncratic risk associated with business ownership This risk cannot be completely diversified because of financial frictions How should wealth from family businesses be taxed? Family owned businesses account for 30% of GDP and 27% of workforce
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Chamley-Judd type of models imply that: Taxing capital at 100% in t = 0 is optimal, unless rulled out If bounds are imposed, it may still be optimal to tax capital at the upper bound until private net worth falls to zero This can be avoided if the government cannot save (reasonable?) Even in this case, the capital tax rate can rise to 100% if IES < 1 and there is no government spending ... but would investment be misallocated if wealth were owned by the state?
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Examines the optimal Ramsey capital tax when the efficiency cost of confiscating private wealth is taken into account: Entrepreneurs’ ability to invest is constrained by their own wealth - financial frictions If the government takes their wealth away, there will be less investment and it will be more inefficiently allocated
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Entrepreneurs invest capital and hand-to-mouth workers supply labor to a representative firm Entrepreneurs fund investment via contracts with risk-neutral banks Banks cannot observe how entrepreneurs divide resources between consumption and investment - moral hazard The optimal loan contract requires entrepreneurs to have some ’skin in the game’ The government taxes entrepreneurial wealth and makes lump sum transfers to workers
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Equity-efficiency trade-off capital taxes are desirable for redistribution to workers limit the amount of external financing that entrepreneurs can obtain ⇒ reduce investment and output capital has an endogenously higher return when held by a productive entrepreneur than when held by the government Efficiency-efficiency trade-off (overlapping generations) capital taxes are desirable so that businesses are not passed along to children with low entrepreneurial ability (efficiency gain) hurt the business of the parent entrepreneur by reducing his ’skin in the game’ (efficiency loss)
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Optimal capital taxation Judd (1985), Chamley (1986), Judd (1999), Chari and Kehoe (1999), ColemanII (2000), Abel(2007), Conesa et al. (2009), Straub and Werning (2014) Financial frictions Bernanke and Gertler (1989), Cagetti and De Nardi (2006, 2009), Kiyotaki and Moore (2012), Buera and Moll (2015) Optimal capital taxation + Financial frictions Shourideh (2014), Itskhoki and Moll (2015), Biljanovska (2015)
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Entrepreneurial ability θ ∼ F (θ), known at t = 0 and constant over t Investment technology k1
→ ǫθk1
Idiosyncratic productivity ǫ ∼ Γ
, η > 0 ⇒ Eǫ = 1
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Entrepreneurs maximize UE = log C0 (θ) + β
log C1 (θ, ǫ) h (ǫ) dǫ subject to C0 (θ) + k1 (θ) = (1 − τ0) k0 [θr0 + (1 − δ)] + b1 (θ) C1 (θ, ǫ) + ˆ b1 (θ, ǫ) = (1 − τ1) k1 (θ) [θǫr1 + (1 − δ)]
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Banks can only observe entrepreneurs’ type θ and capital output ǫθk1 Incentive compatibility log C0 (θ) + β
log C1 (θ, ǫ) h (ǫ) dǫ ≥ max
ˆ k
log
k
log C1
ǫˆ k k1 (θ)
Banks break even
ˆ b1 (θ, ǫ) h (ǫ) dǫ = (1 + rf ) b1 (θ)
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Workers UW = log (w0 + T0)
+β log (w1 + T1)
Representative firm wt = FN (Kt, Nt) and rt = FK (Kt, Nt) where Kt = ¯
θ θ θkt (θ) dF (θ) and Nt = 1.
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Chooses taxes (τ0, τ1), transfers (T0, T1) and debt/savings (B1) to max γUW + (1 − γ)
=0
UE subject to G + B1 + T0 = τ0k0
¯
θ θ
θdF (θ) + (1 − δ)
= τ1 ¯
θ θ
k1 (θ) [θr1 + (1 − δ)] dF (θ) + B1 (1 + rf )
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Result 1 Suppose δ = 1. Then the equilibrium entrepreneurial allocation depends on preference and technology parameters initial wealth - τ0 matters prices summarized by x = (1 − τ1) r1 1 + rf = H−1
(1 − τ0) r0k0
τ1 does not matter x is the gap between interest rates generated by financial frictions (if no financial frictions then (1 − τ1) r1 = 1 + rf )
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Result 2 Suppose δ = 1. Then the optimal tax rate in period 1 is τ1 → 1. Intuition: the optimal choice of k1 (θ) does not depend on τ1 the governement can improve the welfare of workers by increasing τ1, without distorting the investment choice of entrepreneurs artifact of the two-period model
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Result 3 Suppose ρ = 0 (no financial frictions). Then the optimal tax rate in period 0 is τ0 → 1. Intuition: in the equilibrium only the entrepreneur with the highest θ invests (1 − τ1)
market clearing K1 = B1 + ¯
θ θ
β (1 − τ0) k0 (θr0 + 1 − δ) 1 + β dF (θ)
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Result 4 Suppose δ = 1. Then x = (1−τ1)r1
1+rf
is strictly increasing in
B1 (1−τ0)r0k0 .
Moreover, ∃¯ x < ∞ such that lim
B1
(1−τ0)r0k0 →∞
x = ¯ x Intuition: high B1 worsens the wedge high τ0 worsens the wedge there is an upper bound to how ‘bad’ financial frictions can be if τ0 → 1
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
B1 = 0 and ρ = 1
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
B1 = 0 and ρ = 1
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
0.2 0.4 0.6 0.8 1 1.8 1.85 1.9 1.95 2 2.05 2.1 τ0 Welfare B1=0 B1>0 B1<0
ρ = 1 and τ1 = 0.9
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
0.2 0.4 0.6 0.8 1 1 1.2 1.4 1.6 1.8 2 2.2 τ0 Welfare G=0 G=0.5 G=1
B1 = 0, ρ = 1 and τ1 = 0.9
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Infinite horizon problem
long-run optimal capital tax misallocation of capital
Overlapping generations
role of intergenerational persistence of entrepreneurial ability bequest taxation
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
0.2 0.4 0.6 0.8 1 1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 τ0 Welfare ρ=1 ρ=0.5 ρ=0.1
B1 = 0 and τ1 = 0.9
Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation