laffer strikes again: dynamic scoring of capital taxes · modelcalibrationfortheus description...

Laffer Strikes Again: Dynamic Scoring of CapitalTaxes

Holger Strulik and Timo TrimbornUniversity of Hannover

09.09.2011

Introduction

I Budgetary effects of tax cuts are on the policy agenda eversince

I We reinvestigate budgetary effects for corporate taxes in adynamic general equilibrium model

I We extend the standard neoclassical model by a corporatesector with taxes on

I corporate income (including depreciation allowances)I dividendsI capital gainsI private interest income

I We conduct dynamic scoring analytically and numerically (wecalculate the degree of self-financing of a tax cut)

I We calculate Laffer curves for net present value of taxrevenues

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IntroductionI Renowned Laffer-curve: there are always two tax rates that

yield the same level of revenueI Revenues from a particular tax start at the origin and end at

zero

0 10

max

τ

Rτ

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IntroductionI But we are interested in total tax revenues:→ general equilibrium model setup

I In addition: we investigate net present value of tax revenues(not steady state revenues)

0 10

max

τ

R

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IntroductionI With respect to total tax revenues the Laffer curve can exhibit

a different shapeI The revenue maximizing tax rates can also equal 0 (or 1)

0 10

max

τ

R

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IntroductionI Dynamic Scoring: Degree of self-financing of a (marginal) tax

cutI Depends on current tax legislation

0 t* 10

R*

max

τ

R

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Related literature

I Novales and Ruiz (2002), Agell Persson (2000), and Bruceand Turnovsky (1999) investigate tax revenues from capitaltaxation in endogenous growth models

I Mankiw and Weinzierl (2006) examine the extent to which atax cut pays for itself in a neoclassical growth model

I Trabandt and Uhlig (2009) calculate Laffer curves for capitaland labor taxes in a neoclassical growth model

I Both papers introduce a standard neoclassical firm, onlycapital income is taxed

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The model

I Neoclassical, continuous-time economyI A representative household maximizes utility from

consumption and leisureI Firms maximize their market valueI Firms face a finance decision (equity/debt)I Agency costs of debt ensure that firms choose an interior

equity/debt ratioI Government raises taxes and distributes the revenues as lump

sum transfers

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The model: households

I Households maximizemaxc,`

∫ ∞0

[ 11− σ

(c1−σ

(1− κ(1− σ)`1+ 1

φ

)σ− 1

)]e−ρtdt

withI c: consumptionI `: hours workedI ρ: time preference rateI φ: Frisch elasticity of labor supplyI 1/σ: elasticity of intertemporal substitution for consumptionI κ: weight for disutility of labor

I Trabandt and Uhlig (2009) show that this utility function iscompatible with a constant Frisch elasticity in a growingeconomy.

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The model: households

I With σ = 1 this simplifies to

maxc,`

∫ ∞0

[log(c)− κ`1+ 1

φ

]e−ρtdt

I The budget constraint isa = (1− τw)`w + (1− τp)ra− (1 + τs)c+ T

I First order conditions arec = c((1− τp)r − ρ)

`1φ = (1− τw)w

(1 + τs)κ(1 + 1

φ

)c

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The model: firms

I A representative firm maximizes its value VI Gross dividends D are taxed with τdI Households pay the tax rate τp on interest income and the tax

rate τc on the value gain of sharesI This yields the no-arbitrage condition

(1− τp)rV = (1− τc)V + (1− τd)D

I or

V (t) =∫ ∞t

(1− τd)D1− τc

e−∫ vt

1−τp1−τc

r(s)dsdv

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The model: firms (II)I We follow Sinn (1987) and assume that the share z of

investment is immediately tax deductable, while the rest isdeductable with economic rate δ

I With accounting profit Π, net investment I, tax on retainedprofit τr and new debt B we obtain

D = Π + B + S − I(1− zτr)− τr(Π−D)

I Firms pay the interest rate r on debt and agency-costs of debta(B/K)

I Neoclassical production functionI Labor augmenting technological progress with rate γI Accounting profits are

Π = F (K,AL)− wL− δK − rB − a(B/K)B − τrzI

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The model: maximization of firms

I Firms maximize their market value

V (t) =∫ ∞t

((1− τd)D1− τc

)e−∫ vt

1−τp1−τc

r(s)dsdv

with I = K

I First order condition is0 = f ′(k)− δ + a′(b)b2 −

[(1− τ2

r z)(1− τp)(1− τp)− (1− τc)(1− τr)

](a(b) + a′(b)b)

with b = B/K and capital in efficiency units k.I Hence, the financial structure of firms b = B/K just depends

on the stock of capital and various tax rates

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The model: government and general equilibrium

I Government revenues are transferred to households bylump-sum transfers

I good market equilibrium:Y = C + I + δK + a(b)B = F (K,AL)

I The dynamic system can be simplified tok/k = f(k, `)/k − a[b(k)]b(k)− c− δ − γc/c = (1− τp)r(k)− ρ− γ.and

`1φ = (1− τw)w

(1 + τs)κ(

1 + 1φ

)c

0 = f ′(k)− δ + a′(b)b2 −[

(1− τ2r z)(1− τp)

(1− τp)− (1− τc)(1− τr)

](a(b) + a′(b)b)

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Dynamic scoring of corporate taxes: theory

I Strulik (2003) has shown that dkdτr

< 0 and dbdτr

> 0 forreasonable parameter values

I Higher taxes on corporate income drive down incentives toinvest and firms finance less by equity and more by debt

I Thus we can conclude thatdY

dτr= dkα`1−α

dτr= αkα−1`1−α

dk

dτr+ (1− α)kα`−α d`

dτr< 0

I d`dτr

< 0 because for our calibration the substitution effectdominates the wealth effect

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Dynamic scoring of corporate taxes: theory (ii)

I We obtain for tax revenues from corporate taxes Rr:dRrdτr

= Π︸︷︷︸>0

+ τrΠ/kdk

dτr︸︷︷︸<0

+ τrkdΠ/kdτr︸︷︷︸

<0I Three effects:

I First term: static scoring effectI Second term: “size” effect of standard neoclassical growth

modelI Third term: firm finance effect

I Firms restructure towards higher debt:dΠ/Kdτr

= αdy

dτr︸︷︷︸<0

−r db

dτr︸︷︷︸>0

− da(b)bdτr︸︷︷︸>0

−zγk − τrzγdk

dτr︸︷︷︸<0

.

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Dynamic scoring of corporate taxes: overall effect

I Note that dRpdτw

, dRddτr, dRsdτr

, dRcdτrare negative because of the size

effectI The sign ofdRpdτr

= dτprAbk

dτr= τprAb

dk

dτr︸︷︷︸<0

+τprAkdb

dτr︸︷︷︸>0

≶ 0

is indeterminateI Summarizing dynamic scoring of the corporate tax rate, we

havedR

dτr= dRr

dτr︸︷︷︸≶0

+ dRwdτr︸︷︷︸<0

+ dRddτr︸︷︷︸<0

+ dRpdτr︸︷︷︸≶0

+ dRsdτr︸︷︷︸<0

+ dRcdτr︸︷︷︸<0

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Model calibration for the US

description notation value source

capital share α 0.38 Trabandt and Uhlig (2010)

inverse of IES σ 2 Traband and Uhlig (2010)

Frisch elasticity φ 1 Traband and Uhlig (2010)

labor income tax τw 0.28 Traband and Uhlig (2010)

consumption tax τs 0.05 Traband and Uhlig (2010)

gov. purchases/GDP G/Y 0.18 Traband and Uhlig (2010)

capital output ratio K/Y 2.38 Traband and Uhlig (2010)

labor supply `∗ 0.25 Traband and Uhlig (2010)

investment tax credit z 0.4 House and Shapiro (2008)

gross investment rate (I + δK)/Y 0.17 BEA(2009)

debt ratio b∗ 0.194 Gordon and Lee (2001,2007)

agency costs a(b) = a0ba1 a(b) = 7.6b4.6 Gordon and Lee (2001,2007)

capital income tax τp 0.25 IRS (2009)

corporate tax τr 0.35 IRS (2009)

dividend tax τd 0.25 IRS (2009)

capital gains tax τc 0.2 × 0.25 Poterba (2004)

weight of labor κ 3.14 implied

economic depreciation δ 0.056 implied

time preference ρ 0.039 implied

consumption/GDP C/Y 0.65 implied

revenue from labor tax/GDP Rw 0.174 implied

revenue from capital tax/GDP Rk 0.106 implied

revenue from cons. tax/GDP Rs 0.032 implied

gov. transfers/GDP T 0.083 implied

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Dynamic scoring: quantitative results

Tax Steady State Net Present Value

total primary total primary

τw (labor) 41.8 23.2 35.3 19.9τr (corporate) 89.4 43.6 71.3 42.3τp (interest) 47.6 6.6 15.7 7.3τc (capital gains) 445 1.3 219 15.3τd (dividends) 1.4 0 1.4 0z (depreciation) 233 20.7 121 12.0

aggregate capital tax 67.3 28.9 50.2 28.2

Self-financing degree of marginal tax cuts in percent (marginal increase in case of the investment tax creditz). The primary effect is the degree of self-financing through revenue of the tax that has been cut, i.e. throughRi when τi has been changed i = w, p, r, c, d. For z the primary effect is the degree of self-financingthrough Rr .

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Dynamic scoring: quantitative results

Part I: Steady-State

Tax σ = 1 φ = 1 σ = 2 φ = 1 σ = 1 φ = 3 σ = 2 φ = 3

τw 34.9 41.8 52.5 69.6τr 87.9 89.4 91.6 95.1τp 43.4 47.6 54.1 64.5τc 426 444 473 519τd 1.36 1.36 1.36 1.36z 222 233 249 274

aggregate capital tax 65.7 67.28 69.7 73.5Part II: Net Present Value

Tax σ = 1 φ = 1 σ = 2 φ = 1 σ = 1 φ = 3 σ = 2 φ = 3

τw 30.3 35.3 46.4 59.7τr 72.6 71.3 78.1 78τp 16.6 15.7 29.9 33.4τc 235 219 304 306τd 1.36 1.36 1.36 1.36z 128 121 165 168

aggregate capital tax 51.3 50.2 56.8 57.2

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Calculation of Laffer curves

I We calculate the impact of tax changes on steady stategovernment revenue (solid blue line)

I We calculate the impact of tax changes on net present valueof government revenue (dashed red line)

I Note that the latter curve depends on current tax rates, i.e.the curve shifts if the economy faces a different baseline taxrate

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Laffer curves for τw

0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

τw

R

Solid lines: steady-state Laffer curve; dashed lines: NPV Laffer curve.22 / 28

Laffer curves for τr

0.3 0.4 0.5 0.6 0.7 0.8 0.90.8

0.9

1

1.1

1.2

1.3

τr

R


Laffer curves for τp

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350.8

0.9

1

1.1

1.2

1.3

τp

R

Solid lines: steady-state Laffer curve; dashed lines: NPV Laffer curve.

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Laffer curves for τc

0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

4 ⋅ τc

R


Laffer curves for z

0 0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

1.2

1.3

z

R


Max. of Laffer curve and max. tax revenue

Part I: Steady-State

Tax σ = 1 φ = 1 σ = 2 φ = 1 σ = 1 φ = 3 σ = 2 φ = 3

Tax max. Rev. Tax max. Rev. Tax max. Rev. Tax max. Rev.

τw 59 22 57 17 48 9 41 4τr 53 1.1 52 0.9 49 0.6 21 0.4τc 0 1.1 0 1.2 0 1.3 0 1.4z 100 1.5 100 1.7 100 1.9 100 2.3

Part II: Net Present Value

Tax σ = 1 φ = 1 σ = 2 φ = 1 σ = 1 φ = 3 σ = 2 φ = 3

Tax max. Rev. Tax max. Rev. Tax max. Rev. Tax max. Rev.

τw 64 28 64 26 52 13 47 8τr 75 6.9 80 9.2 71 4.4 76 5.9τc 0 0.35 0 0.32 0 0.57 0 0.61z 94 0.17 92 0.13 100 0.66 100 0.76

Tax denotes the tax rate in percent at which revenue is maximized. Max. Rev. is the size of extra revenuecollected at the maximum and expressed in percent of status quo revenue.

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Conclusion

I Our results at the aggregate level are broadly consistent withthe literature

I Laffer curves for capital taxes and depreciation allowances arevery flat

I Corporate taxes can be drastically reduced with little effect ontotal tax revenues

I The revenue maximizing tax rate on capital gains is zero

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laffer strikes again: dynamic scoring of capital taxes · modelcalibrationfortheus description...

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