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
Empirical motivation 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
Theoretical motivation 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
This paper 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
Setup and Mechanism 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
Setup and Mechanism 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
Literature 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
Two Period Model Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Entrepreneurs Entrepreneurial ability θ ∼ F ( θ ), known at t = 0 and constant over t Investment technology k 1 ǫθ k 1 → ���� ���� investment at t =0 capital output at t =1 � η, η − 1 � Idiosyncratic productivity ǫ ∼ Γ , η > 0 ⇒ E ǫ = 1 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Entrepreneurs Entrepreneurs maximize � U E = log C 0 ( θ ) + β log C 1 ( θ, ǫ ) h ( ǫ ) d ǫ ǫ subject to C 0 ( θ ) + k 1 ( θ ) = (1 − τ 0 ) k 0 [ θ r 0 + (1 − δ )] + b 1 ( θ ) C 1 ( θ, ǫ ) + ˆ b 1 ( θ, ǫ ) = (1 − τ 1 ) k 1 ( θ ) [ θǫ r 1 + (1 − δ )] Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Loan contract Banks can only observe entrepreneurs’ type θ and capital output ǫθ k 1 Incentive compatibility � log C 0 ( θ ) + β log C 1 ( θ, ǫ ) h ( ǫ ) d ǫ ≥ ǫ � � � ǫ ˆ � � �� k k 1 ( θ ) − ˆ max log C 0 ( θ ) + ρ k + β log C 1 h ( ǫ ) d ǫ θ, k 1 ( θ ) ˆ k ǫ Banks break even � ˆ b 1 ( θ, ǫ ) h ( ǫ ) d ǫ = (1 + r f ) b 1 ( θ ) ǫ Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Workers and representative firm Workers U W = log ( w 0 + T 0 ) + β log ( w 1 + T 1 ) � �� � � �� � c 0 c 1 Representative firm w t = F N ( K t , N t ) and r t = F K ( K t , N t ) � ¯ θ where K t = θ θ k t ( θ ) d F ( θ ) and N t = 1. Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Government Chooses taxes ( τ 0 , τ 1 ), transfers ( T 0 , T 1 ) and debt/savings ( B 1 ) to max γ U W + (1 − γ ) U E � �� � =0 subject to � � � ¯ θ G + B 1 + T 0 = τ 0 k 0 r 0 θ d F ( θ ) + (1 − δ ) θ � ¯ θ G + T 1 = τ 1 k 1 ( θ ) [ θ r 1 + (1 − δ )] d F ( θ ) + B 1 (1 + r f ) θ Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Results Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Financial wedge Result 1 Suppose δ = 1. Then the equilibrium entrepreneurial allocation depends on preference and technology parameters initial wealth - τ 0 matters prices summarized by � � x = (1 − τ 1 ) r 1 B 1 = H − 1 1 + r f (1 − τ 0 ) r 0 k 0 Note that: τ 1 does not matter x is the gap between interest rates generated by financial frictions (if no financial frictions then (1 − τ 1 ) r 1 = 1 + r f ) Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Optimal τ 1 Result 2 Suppose δ = 1. Then the optimal tax rate in period 1 is τ 1 → 1. Intuition: the optimal choice of k 1 ( θ ) does not depend on τ 1 the governement can improve the welfare of workers by increasing τ 1 , without distorting the investment choice of entrepreneurs artifact of the two-period model Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Optimal τ 0 with no financial frictions Result 3 Suppose ρ = 0 (no financial frictions). Then the optimal tax rate in period 0 is τ 0 → 1. Intuition: in the equilibrium only the entrepreneur with the highest θ invests � � (1 − τ 1 ) θ r 1 + 1 − δ = 1 + r f ⇒ K 1 does not depend on τ 0 market clearing � ¯ θ β (1 − τ 0 ) k 0 ( θ r 0 + 1 − δ ) K 1 = B 1 + d F ( θ ) 1 + β θ Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Effect of government policy on the financial wedge Result 4 Suppose δ = 1. Then x = (1 − τ 1 ) r 1 B 1 is strictly increasing in (1 − τ 0 ) r 0 k 0 . 1+ r f Moreover, ∃ ¯ x < ∞ such that lim x = ¯ x B 1 ( 1 − τ 0 ) r 0 k 0 →∞ Intuition: high B 1 worsens the wedge high τ 0 worsens the wedge there is an upper bound to how ‘bad’ financial frictions can be if τ 0 → 1 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Effect of capital taxes B 1 = 0 and ρ = 1 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Capital taxes and welfare B 1 = 0 and ρ = 1 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Capital taxes and government debt 2.1 2.05 2 Welfare 1.95 1.9 B 1 =0 B 1 >0 1.85 B 1 <0 1.8 0 0.2 0.4 0.6 0.8 1 τ 0 ρ = 1 and τ 1 = 0 . 9 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Capital taxes and government spending 2.2 2 1.8 Welfare 1.6 G=0 G=0.5 1.4 G=1 1.2 1 0 0.2 0.4 0.6 0.8 1 τ 0 B 1 = 0, ρ = 1 and τ 1 = 0 . 9 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
Future work 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
Capital taxes and financial frictions 2.3 2.25 2.2 2.15 2.1 Welfare 2.05 2 1.95 1.9 ρ =1 ρ =0.5 1.85 ρ =0.1 1.8 0 0.2 0.4 0.6 0.8 1 τ 0 B 1 = 0 and τ 1 = 0 . 9 Corina Boar, Matthew Knowles Entrepreneurship, Agency Frictions and Redistributive Capital Taxation
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