Working Paper Series

Congressional Budget O¢ ce Washington, DC

The Impact of Progressive Dividend Taxation on

Investment Decisions

Maria I. Marika Santoro

Congressional Budget O¢ ce

Washington, DC

E-mail: marika.santoro@cbo.gov

Chao D. Wei

George Washington University

Washington, DC

E-mail: cdwei@gwu.edu

April 2008

2008-03

Working papers in this series are preliminary and are circulated to stimulate discussion and critical comment. These papers are not subject to

CBOís formal review and editing processes. The analysis and conclusions expressed in them are those of the authors and should not be

interpreted as those of the Congressional Budget O¢ ce. References in

publications should be cleared with the authors. Papers in this series

can be obtained at www.cbo.gov/publications/.

1
The Impact of Progressive Dividend

Taxation on Investment Decisions1

Abstract

In this paper, we study the distortionary impact of progressive dividend

taxation on dynamic investment decisions under the "new view" of dividend

taxation. We use a stochastic general equilibrium model to examine the

qualitative and quantitative importance of the distortion. We Önd that the

theoretical irrelevance of dividend taxation advocated by the new view does

not hold when dividends are taxed progressively in an economy with uncertainty. In such an economy, dividend taxation introduces a wedge between

the marginal cost and beneÖt of investment. The distortion is caused by

endogenous variations in the marginal tax rates over the business cycle, and

is absent if dividend taxes are proportional. We Önd that the magnitude of

distortion critically depends upon the progressivity of the tax system. We

calibrate our model to quantify the importance of the distortion for an income tax system as progressive as the one in the United States. We Önd that

the progressivity of such a tax system is too small for the distortion caused

by dividend taxation to be quantitatively important for investment decisions.

1The authors would like to thank Douglas Hamilton, Mark Huggett, William Randolph,

Roberto Samaniego, Harry Watson, and the participants of the Macroeconomics Seminars

at Georgetown University and at George Washington University for helpful comments and

suggestions.

2
1 Introduction

In the United States, tax codes are generally progressive. Traditionally all

the dividends received by an individual were included in the gross income and

were taxed as ordinary income with a progressive schedule (Section 1(h) of

the Code). The Jobs and Growth Tax Relief Reconciliation Act (JGTRRA),

enacted in 2003, reduced dividend tax rates until 2011 and converted the

taxation of dividends from a progressive to a proportional schedule for most

Ölers.2 There has been research on the importance of the dividend tax cut on

the corporate behavior in a proportional dividend tax environment.3 However, one question remains unanswered: Does the progressivity of dividend

taxes per se matter for dynamic corporate investment decisions?

In this paper we examine both the theoretical and quantitative importance of progressive dividend taxation on corporate investment decisions. We

introduce progressive dividend taxation into a general equilibrium model with

aggregate uncertainty. We Önd that progressive dividend taxation matters

for dynamic investment decisions at the theoretical level.

Two of our modelís features are behind the theoretical relevance of dividend taxation. First, given the progressivity of the tax schedule, the Örm

takes into account how its investment decisions a§ect not only the total

tax burden, but also the marginal tax rate on dividends that shareholders

bear. Second, in the presence of uncertainty, the marginal dividend tax rate

becomes a stochastic variable, so the Örm in the model makes investment decisions under stochastic taxation. Progressivity introduces a wedge between

the e§ect of dividend taxes on the marginal cost and marginal beneÖt of

investment because of the time-varying nature of the taxable income, thus

creating distortions in dynamic investment decisions. This wedge is absent

in a proportional dividend tax environment.

We then proceed to evaluate the quantitative importance of progressive

dividend taxation using the model. We parameterize our tax schedule to

capture the progressivity of the U.S. income tax code, and Önd that the

quantitative importance of dividend taxation crucially depends upon the

progressivity of the tax code. In the model, progressivity is indexed by the

derivative of the marginal tax rate with respect to the taxable income. We

2Under JGTRRA, dividends paid to most individuals by corporations are taxed at the

same áat rate (15%; for most income brackets) until 2011. That rate also applies to capital

gains until 2011 (Section 302 of JGTRRA).

3For example, Chettty and Saez (2005, 2007) and Gourio and Miao (2006).

3
Önd that the income tax code of the United States is not progressive enough

for dividend taxation to be quantitatively important for marginal investment

decisions.

These Öndings are important not only for policy makers, but also for

academic economists.

There has been much research on the impact of dividend taxation on

corporate investment decisions. However, virtually all of that literature has

conÖned itself to the analysis of áat-rate taxes. There are two prevalent

competing views of how áat dividend taxes a§ect decisions by Örms. Under

the ìtraditionalî view, the marginal source of investment Önance is new

equity and the return to investment is used to pay dividends. Thus, dividend

tax reductions lower the pre-tax return that Örms are required to earn; hence

dividend tax reductions raise investment. Under the ìnewî view, Örms use

internal funds and do not issue new equity. Because these future taxes are

capitalized into share values, shareholders are indi§erent between policies

that retain earnings for investment or that use earnings to pay dividends.

Thus, dividend taxes have no impact on a Örmís marginal incentive to invest4.

Our model is constructed under the premise of the new view. However,

our results contrast with the new view in that the progressivity of dividend

taxation is theoretically relevant for dynamic investment decisions.

Our work relates to an expanding literature on progressive taxation in heterogeneous agent models, including Erosa and Koreshkova (2007) and Consea

and Krueger (2006). We choose to work in a representative-agent environment because of our focus on the dynamic impact of progressive taxation.

A progressive tax system has both distributional and dynamic implications.

By distributional implications, we mean that heterogeneous agents may be

in di§erent tax brackets at any given point in time and, as a result, may

make di§erent decisions. The distributional implications are present even

when agents are locked in their respective tax brackets forever. The dynamic

implications, however, capture how an agentís intertemporal investment decisions are altered because of the di§erent marginal tax rates that individual

might be facing over time. The focus of our paper is on the latter. We

examine this issue in a representative-agent model to isolate the dynamic

implications from distributional issues.

4The traditional view is examined by Poterba and Summers (1983, 1985). Auerbach

(2002) and Hasset and Hubbard (2002) have a comprehensive survey of the literature on

the new view.

4
Our paper also relates to the literature on the clientele e§ect, as postulated by Miller and Modigliani (1961). The clientele e§ect implies that

shareholders in high-income tax brackets may choose to reduce holding of

shares that pay high dividends. In our model, the representative household

holds one unit of shares for all periods. As a result, it cannot reduce its

tax burden by selling its shares. We share the main theme of this literature,

namely, that dividend taxation a§ects investor behavior. However, this literature focuses on the change in shareholding, which might allow individuals

to minimize their dividend tax burden. In our model, we do not analyze this

type of shareholding behavior.

The organization of the paper is as follows. Section 2 describes a representativeagent dynamic stochastic general equilibrium model. Section 3 presents results and discusses intuition. Section 4 concludes.

2 The Model

There are a large number of identical and inÖnitely-lived Örms and households. There is a single consumption-investment good. The householdsí

personal income is subject to progressive taxation. The economy grows at a

constant trend g on the balanced growth path.

2.1 Households

Each household maximizes a lifetime utility function:

max

at+1;ft+1;ct

E0

X1

t=0



t

(Ct  bCt1)

1


1  


(1)

subject to the following budget constraint:

Ct + at+1Vt + ft+1V

f

t = at(Vt + Dt) + ft(V

f

t + D

f

t

) + WtLt  T(St) + t: (2)

Here  is the subjective discount factor and Ctis real consumption at

time t. The coe¢ cient 
 measures the curvature of the representative agentís

utility function with respect to its argument Ct  bCt1: When b > 0; the

utility function allows for habit persistence based on the householdís own

consumption in the previous period.

5
In the budget constraint, at represents shares of the representative Örm

held from period t  1 to t. Vt and Dt are the value per share and preincome-tax dividends per share, respectively. The vector ft represents the

vector of other Önancial assets held at period t and chosen at t1; including

private bonds and other assets. The vectors V

f

t and D

f

t are corresponding

vectors of asset prices and current-period real payouts; Wt represents the

real wage, and Ltis the labor supply at time t. Each household faces a

(normalized) time constraint 1: Given that leisure does not enter the utility

function, agents allocate their entire time endowment to productive work. t

is a lump sum transfer of all the tax revenues from the government.5 The

tax function T () represents the income tax based on taxable income, St,

which is a combination of dividends and labor income. According to the tax

function, labor income and dividends are taxed jointly and progressively:6

St = Dtat + WtLt: (3)

The householdís Örst-order condition with respect to the real equity holding is given by

Vt = Et



t+1

t

[(1   t+1)Dt+1 + Vt+1]



;  t+1 =

@Tt+1

@St+1

: (4)

Here tis the Lagrange multiplier of the budget constraint (2), and  t

denotes the marginal tax rate at time t. The Örst order condition demonstrates that the value of the Örm is the present discounted value of after-tax

dividends.

2.2 Production

Output Ytis produced using the Cobb-Douglas production technology:

Yt = ZtK

t L

(1)

t

: (5)

where K is the capital stock, and the logarithm of the stochastic productivity

level, Zt; follows a Örst-order autoregressive process given by:

zt = zt1 + t: (6)

5We assume that the government rebates all the tax revenues to the household as a

lump sum. By doing this, we abstract from the income e§ect of the taxation system, and

focus on the distortionary aspect of progressive taxation.

6

In equilibrium, the representative household holds zero real bonds. As a result, in the

model interest payment is not included in taxable income.

6
We assume convex capital adjustment costs in the capital accumulation process, similar to Jermann (1998) and Boldrin, Christiano, and Fisher

(2001):

Kt+1 = (1  )Kt +  

It

Kt



Kt; (7)

where  is the depreciation rate and  () is a positive, concave function.

Concavity of the function  () captures the idea that changing the capital

stock rapidly is more costly than changing it slowly, and the adjustment cost

of investment is less when the capital stock is large.

We assume that the representative Örm does not issue new shares and

Önances its capital stock solely through retained earnings. The dividends to

shareholders are then equal to:

Dt = Yt  WtLt  It; (8)

where It represents investment.

The representative Örm maximizes the present value of a stream of aftertax dividends:

max

It

E0

X1

t=0





t t

0

[(1   t)Dt]



; (9)

subject to equation (7).

The Örst-order condition with respect to investment is:

1   t  Dtat

@

2Tt

@S2

t

0



It

Kt

 = E0



t+1

t



1   t+1  Dt+1at+1

@

2Tt+1

@S2

t+1  

Yt+1

Kt+1

+

(1  ) +  

It+1

Kt+1 

 

0



It+1

Kt+1 

It+1

Kt+1

0



It+1

Kt+1 

3

5

9

=

;

: (10)

The left-hand side represents the shadow price of the installed capital in

terms of the consumption good, or the marginal q. There are two factors that

make investment cheaper in terms of the consumption good. First, a positive

marginal tax rate means that, by investing the marginal unit of the good,

the representative household avoids paying dividend taxes at  t: This e§ect

is present even when dividend tax is proportional. Second, by investing the

marginal unit of the good, the representative household avoids paying taxes

7
at a higher marginal income tax rate, which would have been in e§ect with

a larger dividend distribution. This e§ect, captured by Dtat

@

2Tt

@S2

t

; reáects the

progressivity of the income tax system, and disappears in a proportional dividend tax environment. Investment provides an additional beneÖt in avoiding

dividend taxes. As a result, the marginal q is lower.

The right-hand side of equation (10), which is the marginal beneÖt of

investing an extra unit of the good, is a§ected by dividend taxes as well.

The marginal gain from investment is subject to the marginal income tax

rate  t+1: At the same time, the marginal increase in dividends may move

the household to a higher marginal tax rate, which is captured by the term

Dt+1at+1

@

2Tt+1

@S2

t+1

: In our model with aggregate uncertainty, the Örm makes

investment decisions under stochastic dividend taxation.

There is a wedge between the e§ect of progressive dividend taxes on the

marginal cost and beneÖt of investment due to the time-varying nature of

the combination term, 1 t  Dt

@

2Tt

@S2

t

@St

@Dt

: This term is time-varying because

dividend taxes are progressive and depend upon the time-varying taxable

income.

The term t;t+1; deÖned as

t;t+1 =

1   t+1  Dt+1

@

2Tt+1

@S2

t+1

1   t  Dt

@

2Tt

@S2

t

; (11)

augments the stochastic discount factor and alters the marginal investment

decision. The farther t;t+1 is from 1; the larger the distortion of the progressive dividend tax. Under a proportional dividend tax regime, @

2Tt

@S2

t

is

equal to zero and  tis constant; as a result, t;t+1is equal to 1: Thus, under

a proportional tax schedule, dividend taxation has no impact on the Örmís

investment decisions. This is the essence of the new view. Furthermore, in

the steady state where marginal income tax rate is constant, dividend tax

has no impact on investment decisions. Thus, the steady state equilibrium

in our model is the same as in an economy with proportional dividend tax.7

7This result is particular to our model where labor is inelastic. When labor supply is

elastic, the steady state equilibria will be di§erent for economies with di§erent proportional

income tax rates.

8
2.3 Equilibrium

In equilibrium, all produced goods are either consumed or invested:

Yt = Ct + It: (12)

Labor is supplied inelastically at 1: Financial market equilibrium requires

that at equals 1 for all t; and that all other assets are in zero net supply.

In our model, the representative household cannot vary its labor supply or

shareholding to avoid income taxes. This allows us to isolate the impact of

progressive dividend taxation on dynamic investment decisions.

In equilibrium, what is not distributed as dividends and labor compensation is used for Örm investment. Therefore, the taxable income St

; which is a

combination of dividends and labor compensation, is equal to consumption

Ct.

3 Calibration and Model Results

The objective of the quantitative evaluation is to examine the implications of

progressive dividend taxation on investment and other aggregate variables.

We Örst present our benchmark calibration and then discuss the model results.

3.1 Calibration

3.1.1 Production

We set the quarterly trend growth rate, 1 + g; to 1:005;the capital depreciation rate  is 0:025; the constant labor share in a Cobb-Douglas production

function is 0:64: We assume that the capital adjustment cost function  ()

takes the following form:8





It

Kt



=

(g + )



1  



It

Kt

1

+

 (g + )

  1

: (13)

The capital supply becomes inelastic as  approaches inÖnity. We follow

Jermann (1998) in setting  to 4:3:

8The functional form implies that 



I

k



= g +  and 

0



I

K



= 1 when evaluated at

the steady state. As a result, incorporation of capital adjustment costs does not change

the steady state of the model.

9
3.1.2 Preferences

We set the trend-adjusted subjective time preference,  (1 + g)

1


, to 0:99:

We will Öx the risk-aversion parameter, 
; at 3 for our benchmark parameterization. We set b to 0:819; a value similar to that used in Constantinides

(1990)9.

3.1.3 Technology Shock Process

Estimates of the Solow residual, zt; typically yield a highly persistent AR(1)

process in levels. We calibrate the standard deviation of the shock innovation

to replicate U.S. postwar quarterly output growth volatility of 1%: We set

 to 0:97 in our benchmark case, as is standard in the real business cycle

models.

3.1.4 Calibration of Tax Function

The progressive tax schedule in the model is based on a relationship between

individual e§ective federal income tax rates and income for the U.S. tax

return estimated by Gouveia and Strauss (1994). The tax function is given

by:

T(St) = 0fSt  [S

1

t + 2

]

 1

1 g; 0

; 1 > 0: (14)

When 1is equal to 0; the tax system is close to proportional with a

tax rate of 0: Gouveia and Strauss (1994) use this parametric class of tax

functions to approximate the U.S. tax system prior to the tax reform in 2003.

They obtain values of 0 = 0:258 and 1 = 0:768: The parameter 2is not

unit free. We set 2to 0:3045 so that the average tax rates in the U.S.

economy and in the model are the same.10

The Örst-order derivative of the tax function with respect to taxable income is the marginal income tax rate  t

, which is given by

 t = 0f1  [S

1

t + 2

]

 1

1

1

S

11

t g: (15)

9We assume habit persistence in the householdís preferences to obtain hump-shaped

impulse responses of consumption to technology shocks, as is standard in the real business

cycle models. Our results on the quantitative relevance of progressive income taxes remain

robust when b = 0:

10This normalization amounts to choosing 2

in the model so that 

m odel

2 =

2



AHIm odel

AHIU . S . 1 9 9 0 1

, where AHI is the average household income (about $50 thousand

for the United States)

10
The second-order derivative of the tax function, which measures the progressivity of the tax system, is given by

@

2Tt

@S2

t

= 0(1 + 1) 2[S

1

t + 2

]

 1

1

2

S

12

t

: (16)

Given the estimates of 0; 1 and 2; the marginal tax rate and the secondorder derivative of the tax function in the steady state are respectively 17

percent and 0:02: Figure 1 plots the marginal tax rate and the second-order

derivative of the tax function as a function of taxable income.

3.2 The Theoretical and Quantitative Importance of

Progressive Taxation

We use Dynare to compute the nonlinear solutions to the model to take

into account possible second order e§ects of progressivity. The policy and

transition functions are contained in Table 1.

The coe¢ cients of the policy and transition functions, even those on the

second-order terms, are very similar under both proportional and progressive

dividend taxation. These results indicate that progressive taxation does not

have quantitative impact on dynamic investment decisions. The distortion

arising from progressive dividend taxation is very small.11

Figure 2 plots the impulse responses of consumption and investment in

response to a one-unit standard deviation in the technology shock with and

without progressive dividend taxes. The dynamic responses of consumption

and investment with and without taxes are very similar. They show a humpshaped impulse response of consumption observed in the data. Investment

increases in response to the positive technology shock but returns to a level

slightly higher than the steady state after about four quarters. Afterward,

investment reverts slowly to the steady state level because of the presence of

capital adjustment costs. Since taxable income Stis equal to consumption in

equilibrium, its dynamic response mimics that of consumption. As a result,

there are no visible di§erences in the impulse responses of taxable income

under progressive or proportional dividend taxation.

11We also augment the model with a áat capital gain tax and a áat corporate income

tax. The distortion from progressive dividend taxation remains quantitatively very small.

The results are available from the authors upon request.

11
As mentioned above,  determines the distortions in dynamic responses

of consumption and investment caused by progressive taxes. The term  is

a function of the Örst-and second-order derivatives of the tax function. We

thus plot the dynamic responses of the two components  t and t, where

t =

@

2Tt

@S2

t

. As shown in Figure 3, following a one-unit standard-deviation in

the technology shock, the largest absolute deviation of the marginal tax rate

is merely 0:05 percent above the steady state rate of 17 percent: Similarly, the

largest absolute deviation of tfrom its steady state value of 0:02 is merely

0:0003: Therefore, the changes in these two components are too small for the

distortionary term t;t+1 to deviate from 1.

The model is able to capture other salient features of real business cycle

models. The model replicates the relative volatility of consumption and

investment with respect to output observed in the data.

4C

4Y

4I

4Y

Model 0:50 2:55

Data 0:51 2:65

3.2.1 Intuition: Why is the Quantitative E§ect So Small?

Additional insight into why the quantitative e§ect is so small can be obtained

from a log-linear approximation of t;t+1; which summarizes the distortionary

e§ect of progressive dividend taxes on corporate investment decisions. The

log-linear approximation of Etlog t;t+1

can be represented as:12

Etlog t;t+1

 



1    D

(Et4St+1 + Et4Dt+1); (17)

where  =

@

2T

@S2









s:s:

There are three factors that determine the size of the distortion. The Örst

factor is the expected change in taxable income. For a given level of progressivity of the tax system indexed by , the larger the expected change of

taxable income St+1, the larger the possible di§erences between the marginal

12There is a third term on the right hand side of equation (17), 

'D

1D, where ' =

@

3T

@S3







s:s:

We ignore this term because ' is not only very small, but also has a negative

sign, which compensates the distortionary e§ect of progressive taxation.

12
tax rates facing the agent in periods t and t + 1: Similarly, given the same

progressivity of the tax system, a larger expected change in dividends also

implies a higher tax burden. The last element, 

1D; measures the amount

of distortion from expected changes in taxable income and dividends. The

term  represents the marginal change in the marginal tax rate due to the

marginal change in the taxable income: the higher ; the larger the distortion brought by the tax wedge on both sides of the investment equation. The

distortion is higher for a higher marginal tax rate : According to our benchmark calibration using the tax function estimated to match the U.S. income

code, 

1D takes the value of 0:0274 in the steady state. The distortionary

e§ect of progressive dividend taxation turns out to be too small to have any

impact on dynamic investment decisions.

We proceed to examine whether our results are robust under more progressive tax codes around the 1960s in the United States. Figure 4 compares

the plots of the marginal tax rates and the second-order derivatives of the tax

functions as a function of taxable income in 1957, 1967, and our benchmark

case.13 The tax system in 1957 is the most progressive of the three, with 

and  being respectively 33:37% and 0:0599 when evaluated at our modelís

steady state. Consequently, the term 

1D takes the value of 0:0918 in

the steady state, nearly four times higher than the corresponding value in

our benchmark model. Figures 5 and 6 plot the dynamic evolutions of consumption, investment,  t and t

in response to a positive technology shock.

Again, the plots of the Örst two variables are very similar to their áat-tax

counterparts. The marginal tax rate  t and the second-order derivative t

vary more in response to a one-unit standard deviation in the technology

shock, as compared with the benchmark case. However, even under such a

highly progressive tax system, the distortionary e§ect of progressive dividend

taxation is still too small to a§ect dynamic investment decisions.14

Even in heterogeneous-agent models where the expected growth rate of

taxable income and dividends may be higher than in our representativeagent model,15 our results still impose strong restrictions on the size of the

13The tax parameters 0

; 1; and 2for the e§ective tax functions in 1957 and 1967 are

estimated by Young (1990).

14We have carried out a heuristic experiment by Öxing  but varying . We Önd that we

need the value of  to be as high as 2 for progressive income taxes to have distinguishable

impact on investment decisions, an unrealistic value for the U.S. income tax code. The

results are available from the authors upon request.

15 In the representative-agent model, taxable income is much less volatile compared with

13
distortion in investment. In heterogeneous-agent models, the term t

1 tDtt

can be evaluated at di§erent levels of taxable income. However, given the

tax function in the model, the second-order derivative tranges from close

to 0 to 0:4 (the latter value occurs in the lowest income bracket). Moreover,

for the households that would most likely hold on to stocks (typically people

in the middle to top income tax brackets), the second order derivative of the

tax function is even smaller.

4 Conclusion

In this paper, we study the distortionary impact of progressive dividend

taxation on dynamic investment decisions. We use a stochastic general equilibrium model to examine the qualitative and quantitative importance of the

distortion. We Önd that, theoretically, progressive dividend taxation distorts

dynamic investment decisions by creating a wedge between the marginal cost

and beneÖt of investment. The wedge is introduced by the variations in the

marginal tax rate caused by dynamic evolutions of taxable income over the

business cycle. This type of distortion is not present if dividend taxes are

proportional.

We calibrate our model to quantify the importance of this distortion for an

income tax system that is as progressive as the system in the United States.

We Önd that the magnitude of distortion critically depends upon both the

marginal tax rate and the progressivity of the tax system, as measured by

the derivative of the marginal tax rate with respect to the taxable income.

We Önd the progressivity of the U.S. tax code too weak for the distortion

caused by progressive dividend taxation to be quantitatively important for

dynamic investment decisions.

Our model is constructed under the premise of the new view. We Önd

that the theoretical irrelevance of dividend taxation advocated by the new

view does not hold when dividends are taxed progressively. However, it is a

reasonable approximation to reality because of the weak progressivity of the

U.S. income tax system.

that of heterogeneous-agent models because of aggregation.

14
Table 1: Comparison of the Model Results

Ct It t  t t

(a) (b) (a) (b) (a) (b) (a) (a)

constant 2:5519 2:5519 1:0793 1:0793 1:8059 1:8054 0:17 0:02

Kbt 0:0052 0:0052 0:0311 0:0311 0:1040 0:1033 0:00 0:00

zbt1 0:9697 0:9694 2:5526 2:5528 20:1120 20:0462 0:02 0:01

Cbt1 0:6405 0:6419 0:6405 0:6419 4:889 4:8398 0:01 0:01

bt 0:01 0:01 0:0263 0:0263 0:2073 0:2067 0:00 0:00

Kb2

t 0:0001 0:0001 0:0002 0:0002 0:0060 0:006 0:00 0:00

zbt1Kbt 0:0026 0:0025 0:0378 0:0378 1:4323 1:4226 0:00 0:00

zb

2

t1 0:0399 0:0342 1:7483 1:7425 124:0330 123:3532 0:01 0:00

Cbt1Kbt 0:0033 0:0033 0:0033 0:0032 0:3956 0:3917 0:00 0:00

Cbt1zbt1 0:3530 0:3508 0:3530 0:3508 64:3132 63:6573 0:00 0:00

Cb2

t1 0:0606 0:0604 0:0606 0:0604 7:7041 7:5980 0:00 0:00

b

2

t 0:0000 0:0000 0:0002 0:0002 0:0132 0:0131 0:00 0:00

Kbt

bt 0:0000 0:0000 0:0004 0:0004 0:0148 0:0147 0:00 0:00

zbt1

bt 0:0008 0:0007 0:0360 0:0359 2:5574 2:5434 0:00 0:00

Cbt1

bt 0:0036 0:0036 0:0036 0:0036 0:6630 0:6563 0:00 0:00

Column (a) contains the coe¢ cients of policy and transition functions for

the benchmark model with progressive taxation (the second-order approximation). Column (b) contains the coe¢ cients for the case with proportional

taxation. For  t and t; the entries in column (b) (the áat-tax case) are all

zero. The b variables in the rows represent deviations from their respective

steady state values. The constant term is the sum of the steady state value

and the shift e§ect of the variance of future shocks.

15
Figure 1: The First and Second Derivative of the Tax Function

The vertical line represents the taxable income in the steady state.

16
Figure 2: Impulse Responses for Consumption and Investment

The impulse is a 1 percent positive productivity shock. The responses

are in percentage deviations from steady state values. The solid lines are the

impulse responses under our benchmark progressive income taxation, and

the dashed lines are those under áat taxes.

17
Figure 3: Responses of  and 

The responses are in absolute deviations from steady state values in response to a one-unit standard deviation in the productivity process z.

18
Figure 4: Comparison of the Tax Functions

The vertical line represents the taxable income in the steady state.

19
Figure 5: Impulse Responses: The Case of 1957

The impulse is a 1 percent positive productivity shock, the responses are

in percentage deviations from steady state values. The solid lines are the

impulse responses under our benchmark progressive income taxation, and

the dashed lines are those under áat taxes.

20
Figure 6: Responses of  and : The Case of 1957

The responses are in absolute deviations from steady state values in response to a one-unit standard deviation in z.

21
References

[1] Allen F., A. Bernardo and I. Welch, 2000, "A Theory of Dividends Based

on Tax Clienteles", Journal of Finance, vol. 55, no. 6, pp 2499-2536.

[2] Auerbach A. J., and L. Kotliko§, 1987, Dynamic Fiscal Policy, Cambridge, MA: Cambridge University Press.

[3] Auerbach A. J., 2002, "Taxation and Corporate Financial Policy", in

Handbook of Public Economics, vol 3, eds. by A. Auerbach and M. Feldstein, Amsterdam: Elsevier Science.

[4] Boldrin M., L. J. Christiano, and J. Fisher, 2001, "Habit Persistence,

Asset Returns and the Business Cycle", American Economic Review,

vol. 91, no. 1, pp. 149-166.

[5] Chetty R., and E. Saez, 2007, "An Agency Theory of Dividend Taxation", NBER Working Papers, no. 13538.

[6] Chetty R., and E. Saez, 2005, "Dividend Taxes and Corporate Behavior: Evidence from the 2003 Dividend Tax Cut", Quarterly Journal of

Economics, vol. 120, no. 3, pp 791-833.

[7] Consea J.C., and D. Krueger, 2006, "On the Optimal Progressivity of

the Tax Code", Journal of Monetary Economics, vol. 53, no. 7, 1425-

1450.

[8] Constantinides G.M., 1990, "Habit Formation: A Resolution of the Equity Premium Puzzle", Journal of Political Economy, vol. 98, no.2, pp

519-543.

[9] Cooley T. F., and G. D. Hansen, 1992, "Tax Distortions in a Neoclassical

Monetary Economy", Journal of Economic Theory, vol. 58, no. 2, 290-

316.

[10] Cooley T. F., and E. C. Prescott, 1995, îEconomic Growth and Business Cyclesî, in Frontiers of Business Cycle Research, T. F. Cooley ed.,

Princeton: Princeton University Press

[11] Erosa A., and T. Koreshkova, 2007, "Progressive Taxation in a Dynastic

Model of Human Capital", Journal of Monetary Economics, vol. 54, no.

3, pp 667-685.

22
[12] Feldstein M., 2006, "The E§ect of Taxes on E¢ ciency and Growth",

NBER Working Papers, no. 12201.

[13] Gourio F., and J. Miao, 2006, "Firm Heterogeneity and the Long-Run

E§ects of Dividend Tax Reform", Boston University Working Paper.

[14] Gouveia M. and R. Strauss, 1994, "E§ective Federal Individual Tax

Functions: An Exploratory Empirical Analysis", National Tax Journal,

vol. 47, no. 2, 317-339

[15] Graham J., and A. Kumar, 2006, "Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors", Journal of Finance,

vol. 61, no. 3, pp 1305-1336.

[16] Hassett K., and G. Hubbard, 2002, "Tax Policy and Business Investment", in Handbook of Public Economics, vol 3, eds. by A. Auerbach

and M. Feldstein, Amsterdam: Elsevier Science.

[17] Jermann U.,1998, "Asset Pricing in Production Economies", Journal of

Monetary Economics, vol. 41, no. 2, pp 257-275.

[18] Kotliko§ L., and D. Rapson, 2006, "Does it Pay, At the Margin, to Work

and Save? - Measuring E§ective Marginal Taxes on AmericansíLabor

Supply and Saving", NBER Working Papers, no. 12533.

[19] Li W., and P.-D. Sarte, 2004, "Progressive Taxation and Long-Run

Growth", American Economic Review, vol 94, no. 5, pp 1705-1716.

[20] Lucas R. E. Jr, 1990, "Supply-Side Economics: An Analytical Review",

Oxford Economic Papers, vol. 42, no. 2, pp. 293-316

[21] McGrattan E., and E. C. Prescott, 2005, "Taxes, Regulations, and the

Value of U.S. and U.K. Corporations", Review of Economic Studies, vol.

72, no. 3, pp 767-796.

[22] Miller M., and F. Modigliani, 1961, "Dividend Policy, Growth and the

Valuation of Shares", Journal of Business, vol.34, no. 4, pp. 411-433.

[23] Nishiyama S. and K. Smetters, 2002, "Consumption Taxes and Economic E¢ ciency in a Stochastic OLG Economy", Congressional Budget

O¢ ce Working Paper Series 2002-6.

23
[24] Nishiyama S., and K. Smetters, 2005, "Consumption Taxes and Economic E¢ ciency with Idiosyncratic Wage Shocks", Journal of Political

Economy, vol. 113, no. 5, pp. 1088-1115.

[25] Poterba J., and L. Summers, 1983, "Dividend Taxes, Corporate Investment, and ëQí", Journal of Public Economics, vol. 22, no. 1, pp135-167.

[26] Poterba J., and L. Summers, 1985, "The Economic E§ects of Dividend

Taxation", NBER Working Papers, no. 1353.

[27] Sarte P.-D., 1997, "Progressive Taxation and Income Inequality in Dynamic Competitive Equilibrium", Journal of Public Economics, vol. 66,

no. 1, pp 145-171.

[28] Summers L., 1981, "Taxation and Corporate Investment: A q-Theory

Approach, Brookings Papers on Economic Activity, no. 1:1981, pp 67-

127.

[29] Young H. P., 1990, "Progressive Taxation and Equal SacriÖce", American Economic Review, vol 80, no. 1, pp 253-266.

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