GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 347

Dynamic effects of anticipated and temporary tax
changes in a R&D-based growth model

Kizuku Takao

September 2014

GCOE Secretariat
Graduate School of Economics
OSAKA UNIVERSITY
1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, JapanDynamic eﬀects of anticipated and temporary tax
changes in a R&D-based growth model∗
Kizuku Takao†
Osaka University
This version: August, 2014

Abstract
Tax changes are often announced before their implementation and are not permanent, but rather only temporary. Accordingly, R&D ﬁrms will optimally adjust theirinvestment decisions to ﬁt tax schedule changes. This study analyzes how changes invarious tax rates relevant to corporate activities aﬀect growth and welfare, considering their methods of implementation. For this purpose, we consider adjustment costs
involved in the investment process and allow ﬁrms to make a forward looking investment decision in a R&D-based endogenous growth model. Calibrating the model with
U.S. data, we ﬁnd that a dividend tax cut reduces the level of welfare irrespectiveof implementation method. On the other hand, a capital gains tax cut and a rise in
the R&D tax credit rate enhance the level of welfare irrespective of implementation.
However, the announcement of these tax changes prior to implementation reduces
their eﬀectiveness.
Keywords: Fiscal policy, R&D, Economic growth
JEL classiﬁcation: E62, O32, O41∗

I would like to express my sincere gratitude to Koichi Futagami, Been-Lon Chen, and Ching-Chong
Lai for the beneﬁcial discussions and suggestions. I would also like to thank Juin-Jen Chang, Takeo Hori,
Tatsuro Iwaisako, Yukihiro Nishimura, Katsunori Yamada, Hirokazu Ishise, and the participants at the 6th
Conference of Macroeconomics for Young Professionals in Osaka, the 2012 Spring Annual Meeting of theJapanese Economic Association in University of Hokkaido, and IEAS seminar in Academia Sinica, 2014
Australian Meeting of the Econometric Society in Hobart, and PET 14 in University of Washington. This
paper was written while visiting the Institute of Economics, Academia Sinica. The ﬁnancial support from
Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation (Japan Society
for the Promotion of Science) is gratefully acknowledged. All remaining errors are mine.
†
Institute of Social Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047,
Japan. E-mail address: takao@iser.osaka-u.ac.jp1

1

Introduction

Technological progress achieved through R&D activities is a major source of economic
growth. Firms decide upon the scope of their investment in R&D, considering the costs
and beneﬁts of these R&D activities, whose values are dependent upon the applicablestatutory tax rate. As Hall and Van Reenen (2000) point out, ﬁscal incentives for R&D
investments diﬀer across countries and change over time. The purpose of this study is toprovide the clear policy implications arising from tax changes relevant to R&D activities
in the context of a R&D-based endogenous growth model.
The novel feature of our study is its focus on growth and welfare not only of unanticipated tax changes, which have permanent implementation periods, but also of anticipated
and temporary tax changes. Accordingly, we consider an environment where technological progress is driven by in-house R&D by long-lived value-maximizing ﬁrms, and theseﬁrms make forward-looking investment decisions regarding in-house R&D activities. In
the real world, tax changes are usually announced before their implementation and are
not permanent but rather only temporary. In such a situation, ﬁrms and households havean opportunity to adjust their intertemporal behavior to ﬁt the tax schedule. For better
understanding of taxation policy eﬃcacy, it is important to consider what diﬀerences arise
depending on how tax changes are implemented.
The present analysis is based on a recent endogenous growth model developed by
Peretto (2007, 2011). Speciﬁcally, the model considers an economy where long-lived valuemaximizing ﬁrms continuously improve upon the quality of their speciﬁc product throughin-house R&D, while simultaneously new ﬁrms also enter the market. The model economy
contains two types of investment opportunities, i.e., in-house R&D (quality improving)
and the creation of a new ﬁrm (product proliferation). The model has the advantage ofeliminating the well-known undesirable scale eﬀect [Jones (1995)], while keeping the policy eﬀect property, which is supported by a growing body of recent empirical literature.1
1

The ﬁrst generation R&D-based endogenous growth model [e.g. Romer(1990) and Grossman andHelpman (1991)] predicts that the equilibrium growth rate is increasing in the labor endowment. However,Jones (1995a) refutes this assertion using time-series data covering the post-war period. Then, the following
two prominent model types are developed. The former type is referred to as the semi-endogenous growth
type [e.g. Jones (1995b) and Segerstrom (1998)]. They resolve the undesirable scale eﬀect property by2Increases in the scale of the aggregate economy are perfectly fragmented by endogenous
product proliferation. Aggregate growth is driven by quality growth arising from ﬁrm’s
in-house R&D activities. The intensity of in-house R&D is dependent on the demand forintermediate goods at the individual ﬁrm level, not the aggregate level.2
However, in the model of Peretto (2007, 2011), a ﬁrm’s investment decision regarding
in-house R&D turns out to be a static problem. This occurs because the model assumes
that the production function of in-house R&D is linear. This implies that the current
intensity of in-house R&D reﬂects only on current market conditions and tax rates, notfuture variables. As a result, if anticipated and temporary tax changes are incorporated
into the model’s setting, the dynamic response of ﬁrm’s investment decisions could not be
considered, and thus the actual impact of such tax shocks could not be captured.
To overcome this problem, we incorporate a framework of the adjustment costs ofinvestment as used in the literature of investment theory.3 More speciﬁcally, we assume thatﬁrms require the convex adjustment costs associated with in-house R&D investments. This
speciﬁcation is indeed more realistic. Some empirical literature points out the existence ofhigh adjustment costs for R&D investments [e.g., Bernstein and Nadiri (1989), Himmelberg
and Petersen (1994), and Brown and Petersen (2011)]. In the presence of adjustment costs,
ﬁrms’ investment decisions regarding in-house R&D are a forward-looking problem. The
dynamic system of an economy is also characterized by the (tax-adjusted) shadow valueof in-house R&D, which determines the intensity of in-house R&D.4 The shadow value

assuming the diminishing returns in R&D production technologies. This speciﬁcation yields the result thatthe steady state growth rate is only pinned down to population growth rate. By contrast, the latter typeis referred as the fully-endogenous type [e.g. Peretto (1998), Howitt (1999) and Futagami and Ohkusa(2003)]. They assume that both vertical innovation and horizontal innovation occur. This speciﬁcation
yields the conclusion that the steady-state growth rate is also dependent on the other parameters andpolicy variables. A recent growing body of empirical literature [e.g. Laincz and Peretto (2006), Ha andHowitt (2007), and Ang and Madsen (2011)] report that the latter type performs well, rather than theformer type.
2
This prediction is consistent with many empirical studies [e.g. Cohen and Klepper (1996), Adams and
Jaﬀe (1996), and Pagano and Schivardi (2003)].
3
See, for example, Hayashi (1982), Abel (1982), and Abel and Blanchard (1983)
4
In Peretto (2007), the dynamic system of the economy is characterized by only one state variable (thenumber of ﬁrms per capita). In Peretto (2011), it is characterized by one state variable (the number ofﬁrms per capita) and one jump variable (consumption ratio). On the other hand, the dynamic system of
the model used in our analysis is characterized by not only the number of ﬁrms per capita and consumption
ratio but also one additional jump variable (shadow value of innovation).

3

summarizes all informations relevant to in-house R&D investment decisions. The ﬂexibility
provided by the shadow value is very useful in analyzing how investment decisions regarding
in-house R&D dynamically react to both anticipated and temporary tax changes.
Using this modiﬁed model, we study the policy implications of (1) a dividend tax cut,(2) a corporate tax cut, (3) a capital gains tax cut, and (4) a rise in the R&D tax credit
rate, taking into account diﬀerences arising depending on tax change implementation methods. Calibrating the model with U.S. data, we obtain the following main results. First, a
dividend tax cut reduces the level of welfare irrespective of implementation method. After the tax cut is implemented, it is detrimental to in-house R&D and aggregate growth.
However, the anticipation of a dividend tax cut stimulates in-house R&D and aggregate
growth during the announcement phase. Although the overall welfare eﬀect remains negative, pre-announcement of the tax cut mitigates the resultant welfare losses. Second, thepolicy eﬀect of a corporate tax cut depends upon whether or not in-house R&D expenditures are tax deductible. If in-house R&D expenditures are not deductible, a corporate
tax cut leads to higher economic growth and welfare gains irrespective of implementation.
However, if they are fully (or partially) deductible, the policy eﬀect mirrors that observed
for the dividend tax cut. On the other hand, a capital gains tax cut and a rise in the R&D
tax credit rate improve the level of welfare irrespective of implementation method. After implementation, they stimulate in-house R&D and aggregate growth. However, theseanticipated tax changes are detrimental to in-house R&D and aggregate growth during
the announcement phase. Therefore, although the overall welfare eﬀect remains positive,
pre-announcement of these tax changes worsens their eﬀectiveness.
Our results have implications regarding the following important channels. First, tax
changes have a direct but diﬀerent eﬀect on both after-tax gross cash ﬂow and ﬁrms’ costof in-house R&D. For example, during the announcement phase, the anticipated dividend
tax cut increases future after-tax gross cash ﬂow, whereas it does not change the cost of inhouse R&D. As a result, ﬁrms dynamically adjust the timing of in-house R&D investments
in reaction to the tax schedule. Second, tax changes also aﬀect incentives to create a newﬁrm and thus impinge on endogenous ﬁrm entry. This determines the scale of production
at the individual-ﬁrm level given an aggregate market size, which in turn aﬀects incentives
4

for ﬁrms to engage in R&D in-house. In addition, households can dynamically adjust thetiming of consumption (saving), resulting in a general equilibrium eﬀect.
Peretto (2007, 2011) examined the policy eﬀect of tax changes relevant to corporate
R&D activities. In particular, Peretto (2007, 2011) mainly focuses on the policy eﬀect of adividend tax cut such as the U.S.’s Jobs Growth and Taxpayer Relief Reconciliation Act of2003. Speciﬁcally, Peretto (2007) analyzes the revenue-neutral tax changes in an environment where the dividend tax rate is endogenously determined to balance the government’s
budget constraint and shows that lowering the corporate tax rate and capital gains tax
rate or increasing the R&D tax credit rate can lead to higher economic growth and improve welfare levels. Peretto (2011) analyzes the case where the government can ﬁnancethe outlay required by tax changes via debt, and quantitatively shows that a dividend tax
cut leads to the slowdown of in-house R&D and aggregate growth, and thus leads to substantial welfare losses. The diﬀerences between our study and that of Peretto (2011) are
as follows. First, Peretto (2007, 2011) focuses only on unanticipated and permanent tax
changes. On the other hand, we also consider anticipated and temporary tax changes inan environment where ﬁrms dynamically react to these tax changes. Second, we examine
the eﬀectiveness of alternative policy instruments rather than the dividend tax cut in anenvironment where the government ﬁnances with debt as just in Peretto (2011).
Our study is also related to the following previous studies. Zeng and Zhang (2002) and
Peretto (2003) also study the eﬀects of tax changes on the basis of a non-scale R&D-based
growth model. However, both these studies analyze only unanticipated and permanent
tax changes and do not consider transitional dynamics and welfare implications. Summers(1981) and Abel (1982) analyze how anticipated and temporary tax changes aﬀect ﬁrms’
forward-looking investment decisions by using the framework of adjustment costs for investment. However, their analysis are based on the partial equilibrium approach. As a result,they can not consider the impacts on aggregate growth and welfare. Strulik and Trimborn(2010) study the eﬀects of anticipated and temporary tax changes in a general equilibrium
setting. Their model is based on the neoclassical growth model with endogenous corporateﬁnance, making the steady-state growth rate exogenous in this setting.
The remainder of this paper is as follows. Section 2 describes the model. Section 3
5characterizes the dynamic system and the steady-state equilibrium of the market economy.
Section 4 quantitatively analyzes the transitional adjustment of macroeconomic variables
to tax changes and welfare consequences, calibrating the model with U.S. data. Section 5analyzes the sensitivity of the numerical analysis. Finally, Section 6 concludes the study.

2

The model

In this section, we establish our model, which is based on that of Peretto (2011). Timeis continuous. The economy is closed and consists of a ﬁnal goods sector, an intermediate
goods sector, households, and government. Perfect competition prevails in the ﬁnal goods
sector, while monopolistic competition prevails in the intermediate goods sector. Both thelabor and asset markets are competitive. All ﬁscal variables either change only at discrete
events or remain static. Thus, we can treat them parametrically and omit the time indext.

2.1

Final goods sector

The price of ﬁnal goods is set to be the numeraire. Final goods are consumed by households
and used as only one factor of production and investment by the intermediate goods sector.
The ﬁnal goods, Yt is produced by the following production function:
∫ Nt
Yt =

)1−θ
(
di, 0 < α, θ < 1,
Xitθ Zitα Z̄t1−α Lit(1)0where Nt is the variety of intermediate goods (the number of intermediate goods ﬁrms),
Xit is the input of intermediate goods i ∈ [0, Nt ] (produced by ﬁrm i), and Lit is the
input of labor that uses intermediate goods i. The productivity of Lit depends not only
on the quality of intermediate good i, Zit , but also on the average quality level across∫N
all intermediate goods, Z̄t ≡ 0 t N1t Zjt dj. Therefore, we obtain the following optimal
conditions:
(
Xit =

θ
Pit

1
) 1−θ

(

)
Zitα Z̄t1−α Lit ,

6

(2)

(
Lit =

1−θ
Wt

) θ1

(
) 1−θ
Xit Zitα Z̄t1−α θ ,(3)where Pit and Wt represent the price of intermediate good i and the labor wage rate,
respectively.

2.2

Intermediate goods sector

Firm i exclusively produces its diﬀerentiated good at quality, Zit . Each ﬁrm’s monopoly ispermanently protected by perfect patent protection. Producing one unit of intermediate
goods requires one unit of ﬁnal goods. Firms improve the quality of their speciﬁc productthrough their in-house R&D. In contrast to Peretto (2007, 2011), however, we assume thatgiven increases in ﬁrm-speciﬁc quality level, Rit ≥ 0, involve adjustment costs associatedwith innovation, following à la Hayashi (1982) speciﬁcation. Speciﬁcally, the law of motion
pertaining to ﬁrm-speciﬁc quality isŻit = Rit ,(4)

and the amount of R&D expenditure is given byΦ(Rit , Zit ) = Rit +h Rit2
,
2 Zit

(5)

where h > 0 reﬂects the extent of adjustment costs associated with in-house R&D and thecase of h = 0 corresponds to the speciﬁcation of Peretto (2007, 2011).5
At each point in time, ﬁxed operating costs, ϕZ̄t (ϕ > 0), are imposed. Accordingly,
the gross cash ﬂow is Fit = (Pit − 1)Xit − ϕZ̄t , where the ﬁrst term represents revenue
minus variable production costs and the second term represents ﬁxed operating costs. Let
σ represent the rate of R&D tax credits (the fraction of R&D expenditure that ﬁrms areallowed to deduct from their corporate taxable amount).6 The total amount of corporate
tax is τΠ [Fit − σΦ(Rit , Zit )], where τΠ represents the corporate tax rate. The gross cash
5This functional form is based on Turnovsky (2000).
Although σ is assumed to be zero for simpliﬁcation in Peretto (2011), we follow the speciﬁcation of
Peretto (2007) so that we can consider the eﬀects of the tax credit policy for R&D investment as well.
6

7

ﬂow must therefore be distributed as follows:
Fit = τΠ [Fit − σΦ(Rit , Zit )] + Eit dit + Jit ,where Eit is the number of equities, dit is the pre-tax dividends on a per-share basis, and Jit
is the retained earnings. A ﬁrm’s ﬁnancial constraint is written by Jit + Ėit vit = Φ(Rit , Zit ),where Ėit and vit represent the number of newly issued equities and the equity price on a
per-share basis, respectively. Since we do not consider here the case where in-house R&D
is ﬁnanced by a bond issue, the above identity indicates that in-house R&D investments
must be ﬁnanced by retaining earnings, newly issued equities, or both.7 Along the lines of
Peretto (2011), we focus only on the scenario where the marginal source of in-house R&D
is limited only to retaining earnings. The scenario is called “New view” in the corporateﬁnance literature. In this scenario, Φ(Rit , Zit ) = Jit because Ėit = 0.
Let Vit ≡ Eit vit and Dit ≡ Eit dit . Without loss of generality, Eit is normalized to one.
Dividends is given by
Dit = (1 − τΠ )Fit − (1 − στΠ )Φ(Rit , Zit ).

(6)

The return on equity can be rewritten by
rt = (1 − τD )

V̇it
Dit
+ (1 − τV ) .
Vit
Vit

(7)

where τD is the dividend tax rate and τV is the capital gains tax rate.
Integrating (7) yields the value of ﬁrm i as follows:
(∫ s

∫ ∞
Vit =

exp
t

t

1
rv dv
−
1 − τV)(1 − τD1 − τV)[(1 − τΠ )Fis − (1 − στΠ )Φ(Ris , Zis )] ds.

Throughout this exercise, we consider a symmetric equilibrium by assuming that any new
ﬁrm starts with the same technology level as incumbents so that the subscript i can be
dropped. In the equilibrium, Zt = Z̄t holds. Each ﬁrm maximizes its value, subject to7

See Turnovsky (1990) for a detailed discussion.

8

(2) and (4), given Z̄. To solve the inter-temporal maximization problem, we deﬁne thefollowing current-value Hamiltonian asH≡

1 − τD[(1 − τΠ )Ft − (1 − στΠ )Φ(Rt , Zt )] + qt [Rt ] ,1 − τV

where the co-state variable, qt , represents a shadow value for in-house R&D. We obtainthe following optimal conditions:1
Pt = ,
θ[](1 − τD )(1 − στΠ )
Rt
1+h
,
qt =
(1 − τV )
Zt

(8)
(9)

∂Ft 1
h
rt = (1 − τD )(1 − τΠ )+ (1 − τD )(1 − στΠ )∂Zt qt2(
The transversality condition is lims→∞ exp

1
− 1−τ
V

∫s
t

(

Rt
Zt

)2

1
q̇t
+ (1 − τV ) .
qt
qt

(10)

)
rv dv Zs qs = 0. From (4) and (9),the quality growth rate is given by
 



1
1
(1
−
τ
)
V



 ≡ [q̃t − 1] ,

q
−
1
t
Żt
h
= h (1 − τD )(1 − στΠ )
ẑt ≡
Zt 



0, if q̃t ≤ 1.

if q̃t > 1,
(11)(8) represents the pricing rule with constant mark-up. (9) indicates that ﬁrms invest
in-house R&D up to the point where the shadow value of in-house R&D (RHS) equals
the actual cost of in-house R&D (LHS). Since in-house R&D is funded only by retaining earnings, the outlay of one dollar for in-house R&D decreases dividend payments forD )(1−στΠ ). Thus, reductions in the dividend tax rate and corporate tax
shareholders by (1−τ(1−τV)

rate increase the cost of in-house R&D, whereas reductions in the capital gains tax rate
and a higher R&D tax credit rate lowers the cost of in-house R&D.8 (10) represents the
no-arbitrage condition between the return on equity and that on in-house R&D. Hereafter,V)
we call q̃t ≡ (1−τ(1−τ
qt as modiﬁed q along the lines of Hayashi (1982). If there are noD )(1−στΠ )8If σ = 0, a decrease in the corporate tax does not change the cost of in-house R&D.

9

adjustment costs (h = 0), modiﬁed q always pins down to one.9 By contrast, in our setting,modiﬁed q is endogenously determined and has a transitional process in equilibrium. (11)shows that the rate of quality growth is an increasing function of modiﬁed q. Since modiﬁed q is derived from ﬁrms’ intertemporal optimization problem, all informations relevant
to in-house R&D decisions are summarized by modiﬁed q.
Developing new products requires βZt (β > 1). New entry ﬁrms are ﬁnanced by issuingequity. Free-entry conditions yields
Vt = βZt ⇔ Ṅt > 0.

(12)

From (6) and (12), the return on equity, (7), can be rewritten by[]Ft
Φ(Rt , Zt )Żt
rt = (1 − τD ) (1 − τΠ )− (1 − στΠ )+ (1 − τV ) .
βZt
βZt
Zt

2.3

(13)

Households

The model’s economy has identical households. Each individual household member is
identically endowed with one unit of time and provides labor supply elastically. The
population grows at a constant rate, λ > 0. Without loss of generality, the population size
at time 0 is normalized to one. Hence, the number of population at time t is given by eλt .
Households maximize the following utility function:
∫ ∞
Ut =

[
]
e−(ρ−λ)(s−t) log Cs e−λs + ζ log (1 − ls ) ds,t

where Ct is the aggregate consumption, lt is the fraction of time allocated to work per
capita, ζ > 0 is the measure of preference for leisure, and ρ (> λ) is the rate of the time
preference. The household budget constraint is given by][Ṅt Vt = Nt (1 − τD )Dt − τV V̇t + (1 − τL )Wt lt eλt − (1 + τC )Ct − Tt ,9

See Peretto (2007, 2011).

10

where τL is the labor income tax rate, τC is the consumption tax rate, and Tt is the lumpsum tax. Solving the inter-temporal optimization problem yields the following optimal
conditions:Ċt= rt − ρ + λ,Ct
lt = 1 −(1 + τC )ζCt.
(1 − τL )Wt eλt

(14)
(15)

The transversality condition is lims→∞ e−(ρ−λ)(s−t) as µs = 0, where µt represents the shadow
value of holdings assets.

2.4

Government

Government spending is given by Gt = gYt (0 < g < 1), where the share of the government
spending to outputs is assumed to be exogenously given. Along the lines of Peretto (2007,2011), it is assumed that government spending does not aﬀect a household’s utility or
the eﬃciency of production activities. This allows the eﬀects of distortionary taxes to beisolated from the eﬀects of government expenditure. The government’s budget constraint
is given by
Gt = τL Wt eλt lt + τC Ct + τΠ Nt [Ft − σΦ(Zt , Rt )] + τD Nt Dt + τV Nt V̇t + Tt .
Since the Ricardian equivalence holds, the same equilibrium dynamics occurs as in theeconomy with public debt.

3

Market equilibrium

3.1

Equilibrium dynamics

In this section, we derive the dynamic system of market equilibrium. The market equilibrium condition of ﬁnal goods is given by
Yt = Gt + Ct + Nt [Xt + ϕZt + Φ(Zt , Rt )] + βZt Ṅt .

11

(16)

Deﬁne the number of ﬁrms per capita as nt ≡ Nt /eλt and the ratio of the aggregate
consumption to outputs as ct ≡ Ct /Yt . With full proof presented in Appendix 1, the labor
supply per capita is given byl(ct ) =1,
1 + ΓctΓ≡(1 + τC )ζ
> 0.
(1 − τL )(1 − θ)(17)

The reduced-form aggregate production function of ﬁnal goods is given by2θ

Yt = Ωl(ct )eλt Zt , Ω ≡ θ 1−θ .

(18)

For simplifying the notation, we hereafter deﬁneS≡(1 − τV )1 − στΠand η ≡.
(1 − τD )(1 − στΠ )1 − τΠIn Appendix 2, we provide proof for the following simultaneous diﬀerential equation, whichconstitutes the economy’s dynamical system (in the case where q̃t > 1):[][] Ωl(ct )nt(Sqt )2 − 1
2
− ϕ+
+ βλ
,
ṅt = 1 − θ − g − ct
β
2h
β
[
]
Sqt − 1ċt = ct [1 + Γct ] rt − ρ −,h1αθ(1 − θ) Ωl(ct ) (Sqt − 1)2q̇t =r t qt −−,1 − τV
Sη
nt
2Sh

(19)
(20)
(21)

where the interest rate (return on equity) is given by[](Sqt )2 − 1(1 − τV )Ωl(ct )
Sqt − 1−ϕ−ηrt =θ(1 − θ)+ (1 − τV )
.
βSη
nt
2h
h

(22)

See Appendix 3 for proof of the dynamic system in the case where q̃t ≤ 1.

3.2

Steady-state equilibrium

Let yt ≡ Yt /(lt eλt ), which represents the output per worker. From (18), the growth rate ofoutput per worker is given by ŷt ≡ ẏt /yt = ẑt = (q̃t − 1)/h. In what follows, we characterize
12the steady-state equilibrium, {n∗ , c∗ , q̃ ∗ (≡ Sq ∗ ), l∗ , r∗ , ŷ ∗ }. From (20), ċt = 0 and c∗ > 0
implies (if q̃ ∗ > 1)r∗ = ρ +q̃ ∗ − 1.
h(23)From (21), q̇t = 0 and q̃ ∗ > 1 impliesr∗ = (1 − τV )αθ(1 − θ) Ωl(c∗ ) 1(q̃ ∗ − 1)2 1
+
(1
−
τ
)
.
V
η
n∗ q̃ ∗
2h
q̃ ∗

(24)

This equation represents the no-arbitrage condition between the return on in-house R&D
and that on equity in the steady-state equilibrium. Other things being equal, a dividend
tax cut has no direct impact on the return from in-house R&D. A dividend tax cut boosts
a ﬁrm’s after-tax gross cash ﬂow and thus enhances the beneﬁt derived from quality growththrough in-house R&D. But the tax cut also increases the cost of in-house R&D, as previously discussed. As described in public ﬁnance literature [e.g. Summers (1981) and
Hassett and Hubbard (2002)], the eﬀects of the dividend tax cut cancel each other out. On
the other hand, a corporate tax cut, a capital gains tax cut, and an increase in the R&D
tax credit rate directly enhance the return on in-house R&D. From (23) and (24), we candetermine that eliminating r∗ yields (if q̃ ∗ > 1)ηΩl(c∗ )=∗nαθ(1 − θ)

{

[
]
}
1
q̃ ∗ − 1 ∗ (q̃ ∗ − 1)2
ρ+
q̃ −
.
1 − τVh2h(25)

Substituting (23) and (25) in (22), we ﬁnd that q̃ ∗ is derived by solving f (q̃) = 0 withrespect to q̃ where




q̃
−
1
(q̃ − 1)2q̃ 2 − 1
1



ρ +
 (Sαβ − q̃) ++α
1 − τV
h
2h
2h




q̃ − 1 αϕf (q̃) ≡−Sαβ+, if q̃ > 1,


h
η



 ρ

αϕ



(Sαβ − q̃) +, if q̃ ≤ 1.
1 − τVη

13(26)

If Sαβ ≤ 1 − (1−τηρV )αϕ < 1, f (1) ≤ 0 and f ′ (q̃) < 0. In such a case, no steady-state
equilibrium exists with a positive quality growth rate. If 1 − (1−τηρV )αϕ < Sαβ, f (1) > 0. In
such a case, f (q̃) is depicted, as shown in Figure 1. Figure 1 shows that if 1 − (1−τηρV )αϕ <Sαβ, then q̃ ∗ is uniquely determined at the point where q̃ ∗ is higher than 1. In what
follows, we focus on the case where 1 − (1−τηρV )αϕ < Sαβ. In such a case, there exists a
unique steady-state equilibrium with a positive rate of quality growth. See Appendix 4 forproof.
f (q̃)

f (1)

0

f (1)

1

q̃ ∗

q̃

0

1

q̃ ∗

q̃

Figure 1: The steady-state equilibrium: the left (right) ﬁgure represents the case where f (q̃) isinverted U-shapes (monotonically decreasing in q̃) for q̃ > 1.

Since the Jacobian matrix derived from the linear approximation of (19)-(21) in theneighborhood of the steady-state equilibrium is complicated, we cannot analytically examine the dynamic system’s local stability. However, our numerical simulations conﬁrm thatthe unique steady state is locally saddle-point stable in the benchmark setting and in thesubsequent sensitivity analysis, as shown below.10

10Since the dynamic system has one state variable (nt ) and two jump variables (ct and qt ), it musthave two positive characteristic roots and one negative characteristic root to assure that the unique steadystate is saddle-point stable. Our numerical simulation reports that the value of three characteristic rootcorresponding to the dynamic system are −0.4129, 0.2240, and 0.1478 in the benchmark parameter setting.

14

From (19) and (25), ṅt = 0 and n∗ > 0 implies[][] αθ(1 − θ)q̃ ∗2 − 12
c = 1−θ −g −ϕ++ βλ ,φ(q̃ ∗ )
2h
∗

where

[
]
η
q̃ ∗ − 1 ∗(q̃ ∗ − 1)2q̃ − η
.
φ(q̃ ) ≡ρ+
1 − τVh
2h∗

Rewriting (25) yieldsn∗ =αθ(1 − θ)Ωl(c∗ ).
φ(q̃ ∗ )The mechanism that eliminates the scale eﬀect on the steady-state growth rate of output
is consistent with the case where adjustment costs are absent [Peretto (2007, 2011)]. In
the steady-state equilibrium, modiﬁed q is independent of the scale factor for the economy,l(c∗ ) [see (26)]. Increases in the economy’s scale factor lead to higher aggregate demandfor intermediate goods at the individual ﬁrm level. This larger scale of production at theindividual ﬁrm level allows in-house R&D expenditures to be spread over a greater numberof units of goods, thus having a direct positive eﬀect on incentives for a ﬁrm to engage in
R&D in-house. This eﬀect is called the cost-spreading eﬀect. However, higher aggregate
demand for intermediate goods also attracts new ﬁrms to enter the market as ﬁrm values
rise. Thus, the per-ﬁrm market share of intermediate goods demand shrinks. This reduces
the scale of production at the individual ﬁrm level, which in turn lowers incentives to
conduct in-house R&D activities. This eﬀect is called the market share eﬀect. In thesteady-state equilibrium, the market share eﬀect derived from higher aggregate demandfor intermediate goods perfectly cancels out the cost-spreading eﬀect [see discussion in
Peretto (2007)].11

11Furthermore, we conﬁrm that the comparative statics of the parameters in the steady-state equilibrium
obtain similar results to those in Peretto (2007, 2011). Increases in α, β, and ϕ enhance the steady-state
growth rate of outputs, respectively. Increases in α allow each ﬁrm to more intensely internalize positive
returns derived from its own in-house R&D activities. Increases in β and ϕ make it more diﬃcult forpotential new ﬁrms to enter the market, thus reallocating resources from product proliferation to quality
improving. An increase in h reduce the steady-state growth rate of output because it directly increases
the cost of in-house R&D. On the other hand, the eﬀect of ρ upon the steady-state growth rate of outputs
is ambiguous.

15

3.3

Steady-state eﬀect of tax changes

The manner in which a permanent change of tax variables aﬀects quality growth in thesteady-state equilibrium is also consistent with Peretto (2007, 2011). We summarize thoseﬁndings as follows:
Quality growth in the steady-state equilibrium is increasing in the rates of dividend tax andcorporate tax (if σ ≥ 1) and R&D tax credit rate. On the other hand, it is decreasing in
the rate of the corporate tax (if σ = 0). Increases in the corporate tax rate (if σ ∈ (0, 1))
and capital gains tax rate have ambiguous eﬀects upon the steady-state quality growth rate.
Proofs can be found in Appendix 5. A dividend tax cut has no direct impact on aﬁrms’ incentive to pursue in-house R&D, as previously discussed. On the other hand, adividend tax cut directly enhances the returns on equity. Given the aggregate market
demand for intermediate goods, the number of ﬁrms per capita increases. The resulting
product proliferation lowers incentives to conduct in-house R&D through the market shareeﬀect. Thus, a dividend tax cut unambiguously has an unambiguously negative eﬀect on
quality growth.12
On the other hand, a higher R&D tax credit rate has an unambiguously positive eﬀect
on quality growth. It reduces the cost of conducting in-house R&D, which dominates theother eﬀect so that it functions like a direct subsidy for in-house R&D.
Both a corporate tax cut (if σ ∈ (0, 1)) and a capital gains tax cut have ambiguous
eﬀects on quality growth. These tax cuts directly enhance both the returns on in-house
R&D and on equity. However, if σ = 0, it is shown that a corporate tax cut unambiguously
enhances quality growth in the steady state. Furthermore, if α and β are suﬃciently low,a capital gains tax cut enhances quality growth in the steady state.

12

If σ = 1, a corporate tax cut also has the same qualitative eﬀect as a dividend tax cut. When in-house
R&D expenditures are fully deductible against corporate tax, no qualitative diﬀerence exists between thedividend tax and corporate tax.

16

4

Numerical analysis

4.1

Data and methodology

Since analytically examining the transitional adjustment of aggregate economy in response
to various tax changes is complicated, we calibrate the model with U.S. data by using
relaxation algorithm method developed by Trimborn, Koch, and Steger (2008).13
As the benchmark, we use the value of all tax variables, following the methodology in
Peretto (2011).14 The values of θ and ρ are set to 0.30 and 0.04, respectively, which areconventional values in the macroeconomic literature. The value of λ is set to 0.01, whichis consistent with the average annual population growth rate in the U.S. economy. The
parameter choice associated with adjustment costs, h, is less clear. According to Schubert
and Turnovsky (2011), the parameter of adjustment costs for physical capital investment isgenerally assumed to fall within 10-15 in the literature [e.g., Ortigueira and Santos (1997)
and Auerbach and Kotlikoﬀ (1987)]. Bernstein and Nadiri (1989) and Himmelberg andPetersen (1994) report the extent to which adjustment costs associated with R&D investment equals or surpasses than that associated with physical capital investment. Therefore
h = 12.0 is employed as the benchmark. The parameter associated with entry costs, β, isalso less clear. Following Peretto (2011), we employ β = 6.55 as the benchmark.15 The
values of α and ϕ are set to 0.141 and 0.266, respectively, so that the consumption ratio
and growth rate of output in the steady state are 0.69 and 0.02, respectively. ζ is set to1.459 so that the fraction of time devoted to labor supply is 0.33.
Table 1 summarizes the benchmark parameter values. Table 2 reports the values ofkey endogenous variables in the steady-state equilibrium, {n∗ , c∗ , q̃ ∗ , l∗ , r∗ , ŷ ∗ }, which arecharacterized under the benchmark parameter setting.
13

Trimborn, Koch, and Steger (2008) details the relaxation algorithm. They also provide MATLAB programs for the relaxation algorithm, which are downloadable for free at http://www.wiwi.unisiegen.de/vwli/forschung/relaxation/matlab applications.html?lang=de. Using this method, Strulik andTrimborn (2010) examine how both anticipated and temporary tax reforms aﬀect the aggregate economy
within the framework of the neoclassical (exogenous) growth model.
14
R&D costs are in fact fully deductible against corporate tax liability in the U.S. tax code. However,setting σ = 0 allows us to clearly see the fundamental distinction between corporate and dividend taxes. If
R&D costs are assumed to be fully deductible (σ = 1.0), then a corporate tax cut has the same qualitativeeﬀects upon the economy as a dividend tax cut.
15
See Peretto (2011) for a detailed explanation of this estimation.

17

Table 1: Benchmark parameter setting
Parameter

Benchmark Value

g
τD
σ
τΠ
τV
τC
τL
α
1−θ
h
ϕ
β
ζ
ρ
λ

0.143
0.35
0.0
0.335
0.20
0.05
0.256
0.141
0.7
12.0
0.266
6.55
1.459
0.04
0.01

Description
Government expenditure share
Dividend tax rate
R&D tax credit rate
Corporate tax rate
Capital gains tax rate
Consumption tax rate
Labor income tax rate
Appropriable quality
Labor share
The extent of adjustment costs
The extent of ﬁxed operating costs
The extent of entry costs
Preference for leisureTime discount rate
Population growth rate

Table 2: Steady-state equilibrium values (benchmark)
n∗

c∗

q̃ ∗

l∗

r∗

ŷ ∗

0.0256

0.69

1.24

0.33

0.06

0.02

In what follows, we investigate the speciﬁc transitional adjustments in key macro variables and welfare induced by the following speciﬁc tax changes: (a) a 10% point reductionin the dividend tax rate, (b) a 10% point reduction in the corporate tax rate, (c) a 10%
point reduction in the capital gains tax rate, and (d) a 20% point rise in the R&D tax
credit rate. In addition, we consider the following three diﬀerent implementation scenarios: (1) an unanticipated and permanent tax change, (2) an anticipated and permanent
tax change, and (3) an unanticipated and temporary tax change. In every scenario, theeconomy initially (at t = 0) remains in the steady-state equilibrium before the tax change.
In implementation scenario (1), each tax change suddenly comes into eﬀect at t = 5 andlasts forever from that point forward. In implementation scenario (2), all economic agents
expect at t = 0 that each tax change will be implemented at t = 5 and last forever fromthat point on. In implementation scenario (3), each tax change comes into eﬀect unexpect-18

edly at t = 0 and but reverts to its initial level after t = 10. This reversion is expected by
all economic agents at t = 0.
Figures 2-5 show the transitional path of key macro variables in response to each tax
change within the diﬀerent implementation scenarios as given above. Speciﬁcally, eachpanel of these ﬁgures represents the transitional path of: (1) the number of ﬁrms per
capita (nt ), (2) the consumption ratio (ct ), (3) modiﬁed q (q̃t ), (4) hours worked per capita(lt ), (5) the interest rate (rt ), (6) the growth rate of outputs per workers (ŷt ), (7) the ratio
of after-tax dividend payments to ﬁrm value, and (8) the ratio of distortionary tax revenue
to outputs. The horizontal axes in each panel measures years. In the vertical axes, rt andŷt are measured by their actual values, whereas all the other variables are measured bytheir percentage deviation from pre-reform levels.
Table 3 reports welfare consequences arising from the tax changes. Welfare level ismeasured as a consumption equivalent: what constant relative increases in annual consumption per capita must be induced so that households’ pre-reform utility levels equal
the household utility levels in the case where the economy moves to a new steady-state
equilibrium due to the tax change.16
Table 3: Welfare gains of tax changes (benchmark)
Policy change

Unanticipated(Permanent)

Anticipated(Permanent)∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2

−14.0
5.03
13.56
10.86

−11.17
5.67
10.78
9.58

Temporary
−8.19
0.64
7.86
4.87

Note: Welfare gains are measured in consumption equivalent and expressed in percentage points.

16

More formally, welfare diﬀerences are evaluated as follows. U0O (cO , lO , ŷ O , nO ) is deﬁned as a household’s level of the utility in the case where the economy remains in the initial steady-state equilibrium
N
N
N
before a tax change. We deﬁne U0N (cNt , lt , ŷt , nt ) as in the case when the economy moves to the newsteady-state equilibrium due to the tax changes. Here, we measure the consumption equivalent by δ, whichNN
N
is deﬁned as the value that satisﬁes U0O (cO (1 + δ), lO , ŷ O , nO ) = U0N (cNt , lt , ŷt , nt ). See Appendix 6 fordetails on how to calculate household utility levels.

19

4.2

Dividend tax cut

Figure 2-(a) shows the impulse responses by key macro variables to the 10% point permanent dividend tax cut under the benchmark parameter setting. The dashed lines in
the panels of Figure 2-(a) plot the impulse responses in the case where the permanent tax
cut is unanticipated. When the tax cut is implemented (at t = 5), the consumption ratio
and modiﬁed q instantaneously fall, whereas the number of ﬁrms per capita starts to rise.
These variables gradually converge to the new steady-state level. Hours worked reacts in
a contrary manner against the consumption ratio. The growth rate of output per worker
falls from 0.02 to 0.0148 at t = 5 before it converges to 0.0152. The tax cut is detrimental
to quality growth during all transition phases. Since the tax cut proportionally and permanently increases both after-tax gross cash ﬂows and the cost of in-house R&D at thesame time, it therefore has no direct eﬀect on a ﬁrm’s incentive to conduct in-house R&D.
It only directly increases dividend payments and returns on equity, which lead to productproliferation.17 This negatively impacts the incentives to in-house R&D.
Table 3 shows that the tax cut carries welfare costs of around 14% points of per capita
annual consumption. The negative welfare consequence results from the decline of consumption and household leisure times as well as the slowdown of quality growth.
If the permanent tax cut is anticipated, then the impulse responses, which are plottedby the solid lines in Figure 2-(a), become quite diﬀerent. When the news arrives (att = 0), households and ﬁrms can incorporate the future tax cut and change their intertemporal behavior. At t = 0, all variables rather than the state variable (the number ofﬁrms per capita) instantaneously changes. The consumption ratio falls, whereas modiﬁed
q jumps up and the growth rate of per worker output rises from 0.02 to 0.025. During
the announcement phase, the consumption ratio further decreases, whereas modiﬁed q
increases and the growth rate of per worker output continues to rise. The number ofﬁrms per capita gradually rises through the general equilibrium eﬀect. After the tax cut
is implemented (at t = 5), both the consumption ratio and the number of ﬁrms per capita
17

The interest rate (returns to equity) jumps at t = 5 as the tax cut directly increases after-tax dividend
payments. During the transition, however, the interest rate gradually decreases, eventually falling below
the pre-reform level because product proliferation lowers both pre-tax dividend payments as well as capitalgains (which equals rate of quality growth) at the individual-ﬁrm level.

20

gradually increase to converge to a new steady-state level. On the other hand, at t = 5,
modiﬁed q and the growth rate of output per worker drastically drops lower than they
were pre-reform values. Then they also converge to a new steady-state level.
Why does a lag in implementing the tax cut have a positive impact on quality growthduring the announcement phase? Recall that the dividend tax cut proportionally increases
both after-tax gross cash ﬂows and the cost of in-house R&D. However, during the announcement phase, anticipated future tax cuts increases the future after-tax gross cash
ﬂows but do not change the cost of in-house R&D. Since ﬁrms can adjust their investment
plan dynamically, the anticipated tax cut has a direct positive eﬀect on a ﬁrm’s incentive to
conduct in-house R&D activities up to the point when the tax cut is actually implemented.
This positive eﬀect outweighs the negative eﬀect derived from product proliferation during
the announcement phase.
Table 3 shows that the tax cut is estimated to impose the loss of around 11.17% pointsof annual consumption per capita, indicating that the welfare costs are mitigated comparedto the welfare eﬀect of an unanticipated tax cut. This outcome reﬂects the fact that therate of quality growth temporarily increases during the announcement phase, whereas
consumption and hours worked adjust more smoothly.
Figure 2-(b) shows the impulse responses to a temporary 10% point dividend tax cut
under the benchmark setting. When the tax cut is implemented (at t = 0), all variables
other than the state variable instantaneously change. After the tax cut is terminated(at t = 10), all variables gradually revert to their pre-reform levels. Remarkably, during
implementation, modiﬁed q declines more sharply compared to the case of the permanent
tax cut. At t = 0, the growth rate of output per worker falls to 0.0125 and then decrease
further until the tax cut is terminated, in reaction to the temporary increase in the costof conducting in-house R&D. As Table 3 shows, the temporary dividend tax cut yields
welfare costs of an estimated 8.2% points of per capita annual consumption.

21

4.3

Corporate tax cut

Figures 3-(a, b) show the impulse responses to a 10% point corporate tax cut under thebenchmark parameter setting. Except for modiﬁed q and the growth rate of output per
workers, the impulse responses are qualitatively similar to those found in the case of thedividend tax cut. If the tax cut is unanticipated, then at t = 5, modiﬁed q jumps up andthe growth rate of output per workers rises to 0.0219. These variables then further increase
to the new steady-state level. If the tax cut is anticipated, then at t = 0, modiﬁed q jumps
up and the growth rate of output per workers rises to 0.0210. Again, these variables thenfurther increase to the new steady-state level. If the tax cut is temporary, the eﬀect on
quality growth is also positive during all transitional phases.
Why does the tax cut unambiguously exert a positive impact on the quality growthduring all phases of the transition irrespective of implementation? Recall that under thebenchmark parameter setting, in-house R&D expenditures are not deductible against corporate tax (σ = 0). Therefore, while tax cut directly increases after-tax gross cash ﬂows,
it does not change the cost to conduct in-house R&D. Hence, the tax cut has a direct positive eﬀect on incentives to conduct in-house R&D, and also leads to product proliferation,
which results in a negative eﬀect on incentives to conduct in-house R&D. However, theformer positive direct eﬀect outweighs the latter negative eﬀect. Table 3 shows that thewelfare eﬀect is positive irrespective of implementation method.

4.4

Capital gains tax cut

Figure 4-(a) shows the impulse the responses to the unanticipated (or anticipated) andpermanent 10% point capital gains tax cut under the benchmark parameter setting. Although the steady-state eﬀect of a capital gains tax cut on quality growth is qualitatively
ambiguous, our calibration shows that the tax cut increases the quality growth rate in the
new steady state.18 If the permanent tax cut is unanticipated, modiﬁed q initially rises
before converging to the new steady-state level. During all transition phases, the quality
growth rate is higher than its pre-reform level. Table 3 shows that the tax cut yields welfare
18

The subsequent robustness checks shows that the steady state eﬀect on quality growth is positive.

22

gains of around 13.56% points of per capita annual consumption.
If the permanent tax cut is anticipated, however, quality growth slows during theannouncement phase. The future capital gains tax cut reduces the future cost of conducting
in-house R&D so that ﬁrms have an opportunity to dynamically adjust their investment
plans and thus delay in-house R&D investments. This eﬀect dominates the other eﬀects.
Although the overall eﬀect of the capital gains tax cut on welfare remains positive, thetemporary slowdown of quality growth has a negative eﬀect on welfare. On the other hand,the anticipated tax cut makes household behavior more smoothly, resulting in a positiveeﬀect on welfare. However, the latter positive eﬀect cannot outweigh the former negativeeﬀect. As a result, the anticipated tax cut reduces welfare gains by 2.77% points comparedto the welfare eﬀect of the unanticipated tax cut.
Figure 4-(b) shows the impulse response to a temporary 10% point capital gains tax
cut under the benchmark parameter setting. Remarkably, quality growth accelerates during its implementation. This temporary acceleration of quality growth is more signiﬁcantcompared to the steady-state eﬀect of the permanent tax cut. Mainly, this occurs because
the temporary tax cut reduces the cost of conducting in-house R&D during its implementation. As Table 3 shows, the temporary tax cut also yields welfare gains of an estimated
7.86% points of per capita annual consumption.

4.5

Increases in the R&D tax credit rate

Figure 5-(a) shows impulse responses to the unanticipated (or anticipated) 20% point
permanent increase in the R&D tax credit rate under the benchmark parameter setting.
The tax change increases the steady-state rate of quality growth. Remarkably, in the steadystate, the tax changes is shown to be self-ﬁnancing: the ratio of distortionary tax revenues
to output is higher than pre-reform levels. If the permanent tax change is unanticipated,then during all transition phases, both the growth rate of outputs per workers and theconsumption ratio are higher than their pre-reform levels. As Table 3 shows, the tax
change yields welfare gains estimated to be around 10.86% points of per capita annual
consumption.

23

On the other hand, if the permanent tax change is anticipated, modiﬁed q and thegrowth rate of output per workers are lower than their pre-reform levels during the announcement phase. This ﬁndings parallel that in the case of the anticipated capital gains
tax cut. Future rises of the R&D tax credit rate directly reduce the future cost of conducting in-house R&D, leading ﬁrms to delay in-house R&D investments until after thetax change is implemented. This negative eﬀect dominates the other eﬀects. As a result, although the tax cut has an overall positive eﬀect on welfare, the implementation
lags from the tax change reduce these welfare gains by 1.28% points of per capita annual
consumption, compared to the welfare eﬀect of the unanticipated tax change.
Figure 5-(b) shows the impulse responses to a temporary 20% point increase in the tax
credit rate under the benchmark parameter setting. The eﬀect on quality growth parallels
that found in the case of the temporary capital gains tax cut. Temporary increases in
the R&D tax credit rate reduce the cost of conducting in-house R&D during its implementation. Furthermore, the temporary acceleration of quality growth is more signiﬁcantcompared to the steady-state eﬀect of the permanent tax change. As Table 3 shows, thetemporary tax change also yields welfare gains estimated to be around 4.87% points of percapita annual consumption.

5

Sensitivity analysis

5.1

Parameter changes

We now conduct robustness checks for identiﬁed tax changes eﬀects by changing certain
parameters. First, we consider increasing or decreasing the value of the unclear parameter,
β and h. Speciﬁcally, we increase or decrease the values of β and h by 50% points.19 In
all these cases, we re-estimate α and ϕ so that the consumption ratio and the growth rateof output in the pre-reform steady-state equilibrium remain the same as in the benchmark
parameter setting. We ﬁnd that the impulse responses are qualitatively the same as in
the benchmark analysis. As Table 4 reports, the welfare consequences of tax changes are19

If we reduce the value of h by 50% points (i.e., we set to h = 6.0), the growth rate of output per
workers becomes negative. To assure an interior solution, we set h = 8.0 alternatively.

24

quantitatively modiﬁed but our main ﬁndings in the benchmark analysis qualitatively hold.
Second, we consider the case of σ = 1.0. In fact, the U.S. tax code sets σ = 1.0 eventhough in the benchmark analysis, we set to σ = 0.0. Our analysis shows that except
for the case of the corporate tax cut, the impulse responses and welfare consequences
remain qualitatively the same as in the benchmark analysis. We also ﬁnd that the impulse
responses to the corporate tax cut are qualitatively the same as those to the dividend tax
cut. As Table 4 reports, the welfare consequence is almost identical to that found in thedividend tax cut.20 This similarity reﬂects the fact that a corporate tax cut has the sameeﬀects as a divided tax cut if in-house R&D investments are fully tax deductible.
We then consider the case in which labor supply is inelastic (i.e., ζ = 0). The impulse
responses in ζ = 0 are qualitatively the same as those found in the benchmark analysis.
As Table 4 reports, the welfare consequences of tax changes are quantitatively modiﬁed
but our main ﬁndings in the benchmark analysis qualitatively hold.

5.2

Social returns to product variety

In the model as described thus far, and as (18) shows, the number of ﬁrms (productvariety) per capita does not directly contribute to the production of ﬁnal goods. Given
the aggregate market demand for intermediate goods, changes in the number of ﬁrms per
capita merely aﬀect the market structure for intermediate goods ﬁrms. The policy that
leads to a higher number of ﬁrms per capita indirectly distorts incentives for a ﬁrm to
conduct in-house R&D. In this section, we relax this somewhat extreme feature. Alongthe lines of Peretto (2007, 2011), we consider the case where socially positive returns to
product variety exist for the production of ﬁnal goods as follows:∫ Nt
Yt = nvt)1−θ
(di, v > 0,
Xitθ Zitα Z̄t1−α Lit

0where the contribution of product variety on ﬁnal goods output is assumed to be external
to all agents. In this case, the reduced-form production function of ﬁnal goods can be

20

Note that initially, the corporate tax rate is set to 0.335, whereas the dividend tax rate is set to 0.35.

25

rewritten by
Yt = nκt Ωl(ct )eλt Zt , κ ≡

v
.
1−θ

The dynamic system of the economy is modiﬁed as follows:[][] Ωl(ct )(Sqt )2 − 1nt
2ṅt = 1 − θ − g − c+ βλ,−κ − ϕ +
2h
β
βnt
[
]
Sqt − 1ṅtċt = ct [1 + Γct ] rt − ρ −
−κ
,
h
nt
1
αθ(1 − θ) Ωl(ct ) (Sqt − 1)2q̇t =r t qt −−,1 − τV
Sη
2Sh
n1−κ
t
where
[
]
(1 − τV )Ωl(ct )
(Sqt )2 − 1
Sqt − 1rt =
θ(1 − θ) 1−κ − ϕ − η+ (1 − τV )
.
βSη
2h
h
nt
The growth rate of output per workers is given by q̃th−1 + κ ṅntt . Since the steady-state
number of ﬁrms per capita is constant, the steady-state growth rate of output is only
dependent of modiﬁed q, as is also the case for κ = 0. If κ > 0, then the steady-state
1

number of ﬁrms per capita is given by (n∗ ) 1−κ , where n∗ is consistent with the steady-statevalue in the case of κ = 0. The other steady-state values coincide with those in the caseof κ = 0. That is, social returns to product variety (κ > 0) simply add to the direct
positive eﬀect on the production of ﬁnal goods, and they only change the steady-statevalue of the number of ﬁrms per capita; thus, the steady-state eﬀect from tax changes
upon macroeconomic variables is consistent with the case of κ = 0.
The impulse responses of key macro variables not involving the growth rate of output
per workers are qualitatively the same as in the case of κ = 0. The growth rate of output per
workers is also dependent on the transition growth rate of the number of ﬁrms per capita. If
the intensity of the growth rate for the number of ﬁrms per capita dominates that for quality
growth, then the impulse response of the growth rate of output per workers is modiﬁed.
As an example, Figures 6 (a, b) depict the impulse responses to a 10% point dividend
tax cut in the case of κ = 0.3. The ﬁgure shows that even if the tax cut is unanticipatedand permanent (or temporary), the growth rate of output per workers initially shows a26

sharp increase. That is, the positive growth rate in the number of ﬁrms per capita initiallyoutweighs the slowdown in quality growth.
In the case of κ > 0, household welfare is also dependent of the number of ﬁrms per
capita. Higher product variety directly increases household welfare. Table 5 reports thewelfare consequences of tax changes in the cases of η = 0.1, 0.3, 0.5, and 0.7. As theintensity of social return to product variety, η, increases, welfare losses arising from thedividend tax cut are mitigated, while the welfare gains resulting from the corporate tax cut
increase signiﬁcantly. On the other hand, the welfare gains resulting from the capital gains
tax cut increase, while the welfare gains resulting from increases in the R&D tax credit rate
are reduced, but these variations are not signiﬁcant compared to the impacts from cutsin the rate of dividend and corporate taxes. In any tax change, however, the sign of thewelfare eﬀect does not change, and the eﬀect of implementation lags holds qualitatively,
as in the case of the benchmark analysis.

6Concluding remarks

We ﬁrst summarize our results and then discuss their implications.
A dividend tax cut reduces the level of welfare irrespective of implementation method.
After implementation, the tax cut is detrimental to both in-house R&D and aggregate
growth. Consumption and household leisure time also decrease. Therefore, the tax cut
yields overall welfare losses. However, an anticipated tax cut stimulates in-house R&D andaggregate growth during the pre-implementation announcement phase. Households also
can adjust the timing of their consumption and leisure more smoothly. Both these eﬀects
arising from the foreknowledge of the tax cut have a positive eﬀect on welfare. Therefore,
pre-announcement mitigates the welfare losses compared to the case of an unanticipatedtax cut, although the overall welfare eﬀect still remains negative. On the other hand, thepolicy eﬀect of a corporate tax cut is dependent on the speciﬁc R&D tax credit rate.
A capital gains tax cut and increases in the R&D tax credit rate lead to welfare gains
irrespective of implementation method. After implementation, these tax changes stimulate
in-house R&D and aggregate growth. The acceleration of quality growth yields welfare
27gains. However, anticipated tax changes are detrimental to in-house R&D and aggregate
growth during the pre-implementation announcement phase. Although anticipated tax
changes lead households to smooth their behavior, which yields a positive eﬀect on welfare,this positive eﬀect cannot outweigh the negative welfare eﬀect derived from temporary
slowdowns of quality growth. As a result, the pre-announcement of these tax changes
worsens their eﬀectiveness, although the overall welfare eﬀect still remains positive.
Our analysis suggests that a capital gains tax cut and increases in the R&D tax credit
rate are eﬀective policy instruments. However, when considering their implementation interms of scope and timing, policy makers should be careful to ensure that their eﬀectivenessis maximized.

References[1] Abel, A. B. (1982) “Dynamic eﬀects of permanent and temporary tax policies in a q
model of investment,” Journal of Monetary Economics, Vol. 9, No. 3, pp. 353-373.
[2] Abel, A. B. and O. J. Blanchard (1983) “An intertemporal model of savings and investment,” Econometrica, Vol. 51, No. 3, pp. 675-692.
[3] Adams, J. D. and A. B. Jaﬀe (1996) “Bounding the eﬀects of R&D: An investigation
using matched establishment-ﬁrm data,” The RAND Journal of Economics, Vol. 27,
No. 4, pp. 700-721.
[4] Ang, J. B. and J. B. Madsen (2011) “Can second-generations endogenous growth models
explain the productivity and knowledge production in the asian miracle economies?,”
The Review of Economics and Statistics, Vol. 93, No. 4, pp. 1360-1373.
[5] Auerbach, A. and L. Kotilikoﬀ (1987) “Dynamic ﬁscal policy,” Cambridge Univ. Press.
[6] Bernstein, J. I. and M. I. Nadiri (1989) “Rates of return on physical and R&D capitaland structure of the production process: Cross section and time series evidence,” Advances in Econometrics and Modelling, Kluwer Academic Publishing, Dordrecht, pp.
169-185.
28

[7] Brown, J. R. and B. C. Petersen (2011) “Cash holdings and R&D smoothing,” Journalof Corporate Finance, Vol. 17, No. 3, pp. 694-709.
[8] Cohen, W. M. and S. Klepper (1996) “Firm size and the nature of innovation within
industries: The case of process and product R&D,” Review of Economics and Statistics,
Vol. 78, No. 2, pp. 232-243.
[9] Grossman, G. M. and E. Helpman (1991) “Innovation and growth in the global economy,” The MIT Press.
[10] Futagami, K. and Y. Ohkusa (2003) “The quality ladder and product variety: Larger
economies may not grow faster,” Japanese Economic Review, Vol. 54, No. 3, pp. 336351.
[11] Ha, J. and P. Howitt (2007) “Accounting for trends in productivity and R&D: A
schumpeterian critique of semi-endogenous growth theory,” Journal of Money, Credit
and Banking, Vol. 39, No. 4, pp. 733-744.
[12] Hassett, K. A. and R. G. Hubbard (2002) “Chapter 20-tax policy and business investment,” Handbook of Public Economics, Vol. 3, pp. 1293-1343.
[13] Hall, B. and J. V. Reenen (2000) “How eﬀective are ﬁscal incentives for R&D? A
review of the evidence,” Research Policy, Vol. 29, No. 4-5, pp. 449-469.
[14] Hayashi, F. (1982) “Tobin’s marginal q and average q: A neoclassical interpretation,”
Econometrica, Vol. 50, No. 1, pp. 213-224.
[15] Himmelberg, C. P. and B. C. Petersen (1994) “R&D and internal ﬁnance: A panel
study of small ﬁrms in high-tech industries,” Review of Economics and Statistics, Vol.
76, No. 1, pp. 38-51.
[16] Howitt, P. (1999) “Steady endogenous growth with population and R&D inputs growing,” Journal of Political Economy, Vol. 107, No. 4, pp. 715-730.
[17] Jones, C. I. (1995a) “Time series tests of endogenous growth models,” The Quarterly
Journal of Economics, Vol. 110, No. 2, pp. 495-525.
29

[18] Jones, C. I. (1995b) “R&D-based models of economic growth,” Journal of Political
Economy, Vol. 103, No. 4, pp. 759-784.
[19] Laincz, C. A. and P. F. Peretto (2006) “Scale eﬀects in endogenous growth theory:
an error of aggregation not speciﬁcation,” Journal of Economic Growth, Vol. 11, No.
3, pp. 263-288.
[20] Ortigueira, S. and M. S. Santos (1997) “On the speed of convergence in endogenous
growth models,” The American Economic Review, Vol. 87, No. 3, pp. 383-399.
[21] Pagano, P. and F. Schivardi (2003) “Firm size distribution and growth,” The Scandinavian Journal of Economics, Vol. 105, No. 2, pp. 255-274.
[22] Peretto, P. F. (1998) “Technological change and population growth,” Journal of Economic Growth, Vol. 3, No. 4, pp. 283-311.
[23] Peretto, P. F. (2003) “Fiscal policy and long-run growth in R&D-based models withendogenous market structure,” Journal of Economic Growth, Vol. 8, No. 3, pp. 325-347.
[24] Peretto, P. F. (2007) “Corporate taxes, growth and welfare in a schumpeterian economy,” Journal of Economic Theory, Vol. 137, No. 1, pp. 353-382.
[25] Peretto, P. F. (2011) “The growth and welfare eﬀects of deﬁcit-ﬁnanced dividend tax
cuts,” Journal of Money, Credit, and Banking, Vol. 43, No. 5, pp. 835-869.
[26] Romer, P. M. (1990) “Endogenous technological change,” Journal of Political Economy, Vol. 98, No. 5, pp. S71-S102.
[27] Schubert, S. F. and S. J. Turnovsky (2011) “The impact of oil prices on an oilimporting developing economy,” Journal of Development Economics, Vol. 94, No. 1,
pp. 18-29.
[28] Segerstrom, P. S. (1998) “Endogenous growth without scale eﬀects,” American Economic Review, Vol. 88, No. 5, pp. 1290-1310.

30

[29] Summers, L. H. (1981) “Taxation and corporate investment: A q-theory approach,”
Brookings Papers on Economic Activity, Vol. 1981, No. 1, pp. 67-140.
[30] Trimborn, T., K.-J. Koch and T. M. Steger (2008) “Multi-dimensional transitional
dynamics: A simple numerical procedure,” Macroeconomic Dynamics, Vol. 12, No. 3,
pp. 301-319.
[31] Trimborn, T. and T. M. Steger (2010) “Anticipated tax reforms and temporary tax
cuts,” Journal of Economic Dynamics and Control, Vol. 34, No. 10, pp. 2141-2158.
[32] Turnovsky, S. (2000) “Methods of macroeconomic dynamics,” The MIT Press.
[33] Zeng, J. and J. Zhang (2002) “Long-run growth eﬀects of taxation in a non-scale
growth model with innovation,” Economic Letters, Vol. 75, No. 3, pp. 391-403.

A

AppendicesA.1

Appendix 1

The perfect distribution in the ﬁnal goods sector (letting Lit = Lt ) yields:
θ2 Yt = Nt Xt ,(A-1)

(1 − θ)Yt = Wt Nt Lt .

(A-2)

Using the deﬁnition of ct , (A-2), and the market equilibrium condition of labor, Nt Lt =eλt lt , then (15) can be rewritten as (17). Substituting (2) and the market equilibrium
condition of labor to (1) yields (18).

A.2

Appendix 2

Dividing both sides of (16) by Yt and using the deﬁnition of nt and ct , (A-1), and (18), we
obtain

(
)]
[
nt
ṅt
Φ(Rt , Zt )1 − θ − g − ct =
+β
+λ .
ϕ+
Ωl(ct )
Zt
nt
2

31

(A-3)

Dividing (5) by Zt and using (11), we obtain
Φ(Rt , Zt )(Sqt )2 − 1
=
.
Zt
2h

(A-4)

Substituting (A-4) to (A-3), we obtain (19).
From (A-1) together with the deﬁnition of nt , and (18), we obtain
Ft
=
Zt

(

1−θ
θ

)

Xt
− ϕ,
Zt
Ωl(ct )= θ(1 − θ)
− ϕ.
nt

(A-5)

Using (A-4), (A-5), and (11), we can rewrite (13) as[][](1 − τD )(1 − τΠ )Ωl(ct )
(1 − τD )(1 − στΠ ) (Sqt )2 − 1rt =θ(1 − θ)
−ϕ −
β
nt
β
2h
+ (1 − τV )Sqt − 1.
hThen, from the deﬁnition of S and η, rearranging the above equation yields (22).
From logarithmic diﬀerentiation of ct with respect to time yields
c˙tĊt Ẏt=−= rt − ρ + λ −
ct
Ct Yt

{

˙ t)
l(c
Żt
+λ+
l(ct )
Zt}.

Using (17) and (11), the above equation can be rewritten asc˙t
Γċt
Sqt − 1= rt − ρ +−.
ct
1 + Γcth(A-6)

Rearranging (A-6) yields (20).
From (2), (8), and the market equilibrium condition of labor, we obtainΩl(ct )∂Ft
= αθ(1 − θ)
.
∂Zt
nt

32

(A-7)

Using the deﬁnition of S and η, (11), and (A-7), we can rewrite (10) asαθ(1 − θ) Ωl(ct ) (Sqt − 1)2
1+
rt qt − q̇t .
=
Sη
nt
2Sh
1 − τV
Then, using (17), the above equation is rewritten as (21).

A.3

Appendix 3

The dynamical system of the economy where qt ≤ 1 is constituted by[] Ωl(ct )ntṅt = 1 − θ2 − g − ct
− [ϕ + βλ] ,ββċt = ct [1 + Γct ] [rt − ρ] ,q̇t =1αθ(1 − θ) Ωl(ct )rt qt −,
1 − τVSη
nt

where the interest rate is given by[](1 − τV )Ωl(ct )rt =θ(1 − θ)
−ϕ .
βSη
nt

A.4

Appendix 4

Diﬀerentiating (26) with respect to q̃ yields′

f (q̃) ≡








 1+α−

1 − τV






−

if q̃ ≤ 1.

ρ
1 − τV

,


2




q̃
h

+


1
1 − τV− 1

Sαβ + 1h−ρ
1 − τV

Moreover, second order diﬀerentiation of (26) with respect to q̃ yields

f ′′ (q̃) ≡






1 + α −




0,


2
1 − τVif q̃ ≤ 1.

33



1
h

< 0,

if q̃ > 1,,

if q̃ > 1,

Here,
ραϕ[Sαβ − 1] +,1 − τVη1
lim f ′ (q̃) =[τV (Sαβ − 1) − (1 − α) − hρ] .
q̃→1+0h(1 − τV )f (1) =If Sαβ ≤ 1 − (1−τηρV )αϕ (< 1), f (1) ≤ 0 and limq̃→1+0 f ′ (q̃) < 0. Then, f ′ (q̃) < 0 forq̃ > 1 as f ′′ (q̃) < 0 for q̃ > 1. Therefore, in this case, f (q̃) has only one solution of q̃ with avalue less than one. That is, no steady-state equilibrium exists with a positive growth rateof output. On the other hand, if 1 − (1−τηρV )αϕ < Sαβ, then f (1) > 0. No matter whether
limq̃→1+0 f ′ (q̃) < 0 is positive or negative, f (q̃) has unique solution of q̃ with a value higher
than one, as depicted in Figure 1.

A.5

Appendix 5

Diﬀerentiating the RHS of (26) with respect to τD , τΠ , τV , and σ yields
{
[
]
}
αβ
1
1
∂f (q̃)q̃ − 1=ρ+− 1 αβ
S > 0,∂τD
1 − τV1 − τVh(1 − τD ){[]}∂f (q̃)αβ1τΠq̃ − 1αϕσ=ρ+− 1 αβS+ 2> 0,∂σ1 − τV1 − τVh(1 − στΠ )η (1 − τΠ ){[]}∂f (q̃)αβ1
σq̃ − 1αϕ(1 − σ)=ρ+− 1 αβS−R 0,∂τΠ
1 − τV1 − τVh(1 − στΠ )(1 − στΠ )2= −αϕ < 0, if σ = 0,
{
[
]
}
αβ
1
1
q̃ − 1=ρ+− 1 αβ
S > 0, if σ = 1,
1 − τV1 − τVh(1 − τΠ )[]∂f (q̃)ρq̃ − 1
q̃
=−
q̃ +
Sαβ −
≡ Γ(q̃) R 0.
∂τV
(1 − τV )2h(1 − τV )1 − τV
Since f (q̃) is a decreasing function of q̃ in the neighborhood around the steady-state solution, the above derivations imply that q̃ ∗ is increasing in τD , τΠ (if σ = 1) and is decreasingin σ, τΠ (if σ = 0) and the eﬀects of tax changes in τΠ (if σ ∈ (0, 1)) and τV are ambiguous.

34

In addition, we also ﬁndρ< 0,(1 − τV )2
1
Γ′ (q̃) =[−2q̃ − hρ + 1 + Sαβ(1 − τV )] R 0,
(1 − τV )2 h
2Γ′′ (q̃) = −< 0.
(1 − τV )2 h
Γ(1) = −Then, if Sαβ < (1 + hρ)/(1 − τV ), Γ(q̃) < 0 for q̃ > 1. Therefore, it is shown that if
Sαβ < (1 + hρ)/(1 − τV ), then q̃ ∗ is a decreasing function of τV .

A.6

Appendix 6

1
We deﬁne Ψt ≡ Ut − ρ−λlog Zt . From the deﬁnition of ct , (11), and (18), diﬀerentiating Ψtwith respect to time yields
Ψ̇t = (ρ − λ)Ψt − log Ω − log ct − log lt − ζ log (1 − lt ) −1 Sqt − 1.
ρ−λ hIn the steady state, Ψt is constant over time. Calculating the dynamic path of Ψt numerically using the relaxation algorithm, we can obtain the initial value of Ψt , Ψ0 =1
log Z0 . Without loss of generality, Z0 is normalized to one. Hence, we obtain
U0 − ρ−λU0 = Ψ0 .

35

nmodified qchours worked

1

1.07

0.99

1.12

1.08

1.06

0.98
1.06

1.1

0.97

1.08

0.96

1.04

0.95

1.02

1.06

1.05
1.04
1.03

0.94
1

0.93

1.04
1.02

1.02

0.92

0.98

0.91

0.96

1.01

1

1
0

10

20

0

interest rate

10

20

0

growth rate of y1020

dividend ratio

0.03

0.068

0

10

20

tax revenue ratio
1

1.25

0.995

0.066
0.99

1.2
0.025

0.064

0.985

1.15

0.98

0.062

1.1

0.06

0.02

0.975
0.97

1.05

0.965

0.058

1
0.96

0.056

0.95

0.015
0

10

20

0

10

20

0.955
0

10

20

0

10

20

(a) Anticipated vs. unanticipated permanent reduction in the dividend tax rate by 10
percentage points in the benchmark setting. Solid (Dashed) lines plots the impulse response ofeach variable to the anticipated (unanticipated) tax cut. The circle marks on the left (right) verticalaxis indicates the steady-state level before (after) the tax cut.

ncmodified q

1.04

1

1.02

0.98

1.08

1

0.96

1.06

0.98

0.94

0.96

0.92

hours worked
1.07

1.1

1.06
1.05
1.04
1.03
1.02

1.04
0.94
1.02

1.01
1

0.9

0.99

0.92
0.88

0.98

0.9

1
0

10

20

0

interest rate

10

20

0

10

20

dividend ratio

growth rate of y
0.02

0.066

0.016

0.06

0.014

tax revenue ratio
1

0.985

1.15

0.98
1.1

0.975

0.058

0.012

1.05

0.97

0.056

0.01

1

0.965

0.054

0.95

0.96

0.9

0.955

0.008

0.052
0

10

20

20

0.99

1.2

0.062

10

0.995

1.25

0.018

0.064

0

0

10

20

0

10

20

0

10

20

(b) Temporary reduction in the dividend tax rate by 10 percentage points in the benchmark
setting. The circle mark on the vertical axis indicates the initial level.

Figure 2

36

c

n

modified q

1

1.1

hours worked

1.02
1.05

0.99
1.08

0.98

1.015

1.04

0.97

1.06

1.03
0.96

1.04

1.01
1.02

0.95
1.005

0.94

1.02

1.01
0.93
1

1
0

10

20

interest rate
0.072

0

10

20

1
0

growth rate of y1020

dividend ratio

0

10

20

tax revenue ratio
1

0.022
0.995

1.2

0.02180.07

0.99

0.02160.068

1.15

0.02140.985

0.0212

0.066

0.021
0.0208

0.064

1.1

0.98

1.05

0.975

0.02060.062

0.97

0.02041
0.965

0.0202

0.06

0.95
0

10

20

0

10

20

0.96
0

10

20

0

10

20

(a) Anticipated vs. unanticipated permanent reduction in the corporate tax rate by 10
percentage points in the benchmark setting. Solid (Dashed) lines plots the impulse response ofeach variable to the anticipated (unanticipated) tax cut. The circle marks on the left (right) verticalaxis indicates the steady-state level before (after) the tax cut.

n

c

1.07

1.02

1.06

1.01

modified q
1.012
1.04

1

1.05

1.01
1.03

0.99
1.04

0.98

1.03

0.97

1.008
1.02
1.006
1.01

0.96
1.02

hours worked
1.05

1.004
1

0.95

1.01

1.002

0.94

0.99

0.93

1
0

10

20

interest rate
0.07
0.068

1
0

10

20

0

10

20

dividend ratio

growth rate of y
0.02140.0212

1.2

0.021

1.15

0

10

20

tax revenue ratio
1
0.995
0.99

0.066

0.985

0.02081.1

0.0206

1.05

0.064

0.98

0.062

0.975
0.0204

1

0.97

0.95

0.965

0.06
0.0202
0.058
0

10

20

0

10

20

0

10

20

0

10

20

(b) Temporary reduction in the corporate tax rate by 10 percentage points in the benchmark setting. The circle mark on the vertical axis indicates the initial level.

Figure 3

37

n

c

modified q

1
1.02

hours worked

1.04

0.998

1.01
1.02

0.996
1.015

1.008

0.994

1

0.992
1.01

1.006
0.98

0.99

1.004

0.988
1.005

0.96

0.986

1.002
0.94

0.984
1

1
0

10

20

0

interest rate

10

20

0

20

dividend ratio

growth rate of y

0.066

10

0

10

20

tax revenue ratio
1

0.024
1.02

0.064

0.998

0.022

0.062

1.01

0.02

1

0.996

0.018

0.99

0.994

0.06
0.058

0.98

0.016

0.992
0.97

0.056
0.014

0.99

0.96

0.054
0

10

20

0

10

20

0

10

20

0

10

20

(a) Anticipated vs. unanticipated permanent reduction in the capital gains tax rate by 10
percentage points in the benchmark setting. Solid (Dashed) lines plots the impulse response ofeach variable to the anticipated (unanticipated) tax cut. The circle marks on the left (right) verticalaxis indicates the steady-state level before (after) the tax cut.

ncmodified q

1
1.001

0.999

1

1.004
1.0035

1.1

1.003

0.998

0.999

hours worked

1.12

1.08
1.0025

0.997

0.998

1.06

1.002

1.04

1.0015

0.996
0.997

1.001

0.995
1.02

0.996

1.0005

0.994
0.995

1
0

10

20

interest rate

0

10

20

1
0

growth rate of y1020

dividend ratio
1.01

0.072

0.032

0.07

0.028

10

20

tax revenue ratio
1

1.005

0.999

1

0.998

0.03

0.068

0

0.997

0.995

0.996

0.066

0.026

0.99

0.064

0.024

0.985

0.994

0.98

0.993

0.062

0.022

0.995

0.992

0.975
0

10

20

0

10

20

0

10

20

0

10

20

(b) Temporary reduction in the capital gains tax rate by 10 percentage points in thebenchmark setting. The circle mark on the vertical axis indicates the initial level.

Figure 4

38

n

c

1

modified q

1.01

1.03

1.008

1.02

hours worked
1.001
1
0.999

0.995

0.99

0.985
0

10

1.006

1.01

1.004

1

0.997

1.002

0.99

0.996

1

0.98

0.998

0.97

20

interest rate

0.998

0.994
0

10

20

10

20

dividend ratio
1.015

0.021

1.005

0.02

1

0.019

0.995

0

10

20

tax revenue ratio
1.0025
1.002

1.01

0.022

0.062

0.993
0

growth rate of y
0.023

0.063

0.995

1.0015
1.001

0.061

1.0005

0.06
0.059

0.018

0.99

0.017

0.985

1
0.9995
0.999

0.058
0

10

20

0

10

20

0.9985
0

10

20

0

10

20

(a) Anticipated vs. unanticipated permanent rise in the tax credit rate by 20 percentage
points in the benchmark setting. Solid (Dashed) lines plots the impulse response of each variable
to the anticipated (unanticipated) change. The circle marks on the left (right) vertical axis indicatesthe steady-state level before (after) rise of the tax credit.

nchours worked

modified q

1

1.07
1.004

0.998
1.06
1.01

0.996

1.002
1.05

0.994

1
1.005

0.992

1.04
0.998

0.99

1.03

0.996

1

0.988

1.02

0.994

1.01

0.992

0.986
0.995

0.984
0.982

1
0

10

20

interest rate

0

10

20

0

0.027

0.065

0.026

20

dividend ratio

growth rate of y

0.066

10

tax revenue ratio

1.0035

1.01

1.003

1.005

1.0025

0.024
0.063
0.023

0.061

20

1.004

1.015

0.025

0.062

10

1.025
1.02

0.064

0

1

1.002

0.995

1.0015

0.022

0.99

0.021

0.985

1.001
1.0005

0.98
0.02
0

10

20

1
0

10

20

0

10

20

0

10

20

(b) Temporary rise in the tax credit rate by 20 percentage points in the benchmark setting.
The circle mark on the vertical axis indicates the initial level.

Figure 539

Table 4: Welfare gains of tax changes (parameter changes)
Tax change

Unanticipated(Permanent)

Anticipated(Permanent)

Temporaryβ = 3.275 (with α = 0.277 and ϕ = 0.125)∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2−14.94
5.09
15.33
11.55

−12.21
5.76
12.63
10.3

−8.52
0.58
8.3
5.05

β = 9.825 (with α = 0.0945 and ϕ = 0.408)∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2

−13.7
5.03
13.04
10.66

−10.85
5.65
10.25
9.36

−8.08
0.66
7.72
4.81

h = 8.0 (with α = 0.133 and ϕ = 0.267)∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2−15.44
5.87
15.1
12.37

−11.41
6.55
11.05
10.37

−9.98
0.89
9.7
6.05

h = 18.0 (with α = 0.153 and ϕ = 0.265)∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2

−12.5
4.2
12.02
9.39

−10.55
4.77
10.15
8.59

−6.64
0.44
6.29
3.88

σ = 1.0 (with α = 0.0955 and ϕ = 0.260)∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2−13.86
−13.6
12.95
17.06

−11.05−10.83
10.15
15.0

−8.08
−7.95
7.69
7.55

ζ=0
∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2−14.23
4.81
13.5
10.87

−9.93
4.64
9.16
8.20

−7.12
0.53
6.72
4.18

Note: Welfare gains are measured in consumption equivalent and expressed in percentage points.
Other values of the tax variables and parameters are sames as the benchmark setting.

40

n

c

1.2

modified q

1

1.03

1.06

0.99

1.15

hours worked
1.035

1.08

1.025
1.04

0.98

1.02
1.02

1.1

1.015

0.97
1

1.01
1.05

0.96

0.98

1.005

0.96

0.95

1

1
0

10

20

0

interest rate

10

20

0

growth rate of y1020

dividend ratio

0

10

20

tax revenue ratio

0.036
0.066

1

0.034

1.2

0.995

0.032
0.064

0.99

0.03

1.15

0.985

0.028

0.062

0.98

0.026

1.1

0.975

0.024

0.06

0.97

0.022
0.058

1.05

0.965

0.02

0.96

0.018
0.056

1

0.955

0.016
0

10

20

0

10

20

0

10

20

0

10

20

(a) Anticipated vs. unanticipated permanent reduction in the dividend tax rate by 10
percentage points in the case of κ = 0.3. Solid (Dashed) lines plots the impulse response of eachvariable to the anticipated (unanticipated) tax cut. The circle marks on the left (right) vertical axis
indicates the steady-state level before (after) the tax cut.

nmodified q

c

1.14

hours worked

1

1.04

0.98

1.03

1.02

1.12

1.01

1.1

1

1.08

0.99

0.96

1.02

0.94
1.01

0.98

1.06

0.92
0.97

1

1.04
1.02

0.96

0.9

0.95

0.88

0.99

1
0

10

20

0

interest rate

10

20

0

growth rate of y1020

dividend ratio

0.022

0.064
0.062

0.02

1.2

0.018

1.15

0.056

tax revenue ratio
1

0.99

1.1

0.012

1.05

0.01

1

0.98
0.975
0.97

0.008

0.054

20

0.985

0.014
0.058

10

0.995

0.016

0.06

0

0.965
0.95

0.006
0.052

0.96
0.9

0.004
0

10

20

0

10

20

0.955
0

10

20

0

10

20

(b) Temporary reduction in the dividend tax cut by 10 percentage points in the case ofκ = 0.3. The circle mark on the vertical axis indicates the initial level.

Figure 641

Table 5: Welfare gains of tax changes (positive social spillover of product variety)Tax change

Unanticipated(Permanent)

Anticipated(Permanent)

Temporaryκ = 0.1∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2−13.08
5.88
13.73
10.72

−10.17
6.59
10.98
9.43

−7.95
0.83
7.86
4.82

κ = 0.3∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2−10.75
8.07
14.17
10.35

−7.78
8.88
11.53
9.1

−7.12
1.42
7.85
4.66

κ = 0.5∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2

−7.57
11.08
14.76
9.87

−4.65
11.93
12.25
8.68

−5.86
2.35
7.85
4.43

κ = 0.7∆tD = −0.1∆tΠ = −0.1
∆tV = −0.1
∆σ = 0.2

−3.07
15.34
15.54
9.23

−0.22
16.22
13.24
8.13

−4.11
3.61
7.86
4.13

Note: Welfare gains are measured in consumption equivalent and expressed in percentage points.
Other values of tax variables and parameters are same as the benchmark setting.

42