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CHAPTER 4
SHORT-RUN AND LONG-RUN EFFECTS OF CAPITAL TAXATION ON ECONOMIC GROWTH IN A R&D-BASED
MODEL WITH ENDOGENOUS MARKET STRUCTURE
4.1 Introduction
The linkage between capital taxation and economic growth has been studied ex-tensively in the …eld of macroeconomics. In general, the existing studies on this topic can be classi…ed into two strands of literature. The …rst strand emphasizes the growth engine of capital accumulation, and …nds that capital taxation sti‡e economic growth. To be more speci…c, the tax imposed on capital income leads the household to reduce its accumulation of physical capital, and hence is detrimental to economic growth. The relevant literature in this strand includes Judd (1985), Chamley (1986), King and Rebelo (1990), Jones et al. (1993), Devereux and Love (1994), and Milesi-Ferretti and Roubini (1998).
The second strand instead highlights the growth engine of R&D investment, and …nds that mixed relationship between capital taxation and economic growth.
More speci…cally, a rise in the capital income tax rate motivates intermediate …rms to lower its demand for physical capital, thereby causing a decline in the pro…t of intermediate …rms. This in turn lowers R&D investment and economic growth.
However, if the government adopt a tax shifting scheme to balance its budget (i.e.,
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growth.1 As a consequence, if this additional e¤ect is taken into consideration, capital taxation may either spur or sti‡e economic growth. The relevant literature in this strand includes Lin and Russo (1999), Zeng and Zhang (2002), Aghion et al. (2013), and Chen et al. (2016).2
With regard to the empirical studies on capital taxation and economic growth, there is also lack of consensus within the existing literature. Lee and Gordon (2005), Hungerford (2010), Arnold et al. (2011), and Mertens and Ravn (2013)
…nd that capital taxation, such as corporate pro…t tax, capital gains tax, dividends tax, has an adverse e¤ect on economic growth, while Mendoza et al. (1997), Angelopoulos et al. (2007), and ten Kate and Milionis (2015) …nd that capital taxation may be neutral with or even bene…cial to economic growth.
The main purpose of this chapter is to explain these mixed observations from the perspective of time horizon. To this end, we set up a second-generation R&D-based growth model developed by Dinopoulos and Thompson (1998) and Peretto (1998). As is well known, some salient features are exhibited in the second-generation R&D-based growth model. The …rst feature is that both vertical and horizontal innovations are present simultaneously. In the vertical dimension, each of incumbent …rms engages in in-house R&D to improve the quality of their speci…c product. In the horizontal dimension, …rms enter the market through the creation new products. The second feature is that the economic growth rate is crucially related to the rate of returns to the …rm’s in-house R&D. The third feature is that
1With this additional reduction in the labor income tax rate, the household is inclined to provide higher labor supply, causing the good …rm to raise its production. Then, the …nal-goods …rm will increase its demand for intermediate …nal-goods, thereby resulting in a rise in the pro…t of intermediate …rms and boosting R&D investment and economic growth.
2Yilmaz (2013) speci…es that an increase in the capital income tax rate is coupled with a rise in the subsidy on R&D to balance the government budget. Based on the fact that the additional subsidy e¤ect is bene…cial to R&D investment and economic growth, his analysis also shows that capital taxation may either boost or depress economic growth.
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the returns to the …rm’s in-house R&D are determined by its market size rather than aggregate market size. With the second and third features, an expansion in the scale of the aggregate economy is completely fragmented by the proliferation of endogenous product varieties, causing the second-generation R&D-based growth model to be able to eliminate the undesirable scale e¤ect.
Based on these features, our Schumpeterian growth model with endogenous market structure (EMS) …nds that, in response to a change in the capital tax rate, the long-run and short-run responses of the economic growth rate exhibit distinct patterns.3 To be more precise, in the short run where the number of …rms is …xed, a higher capital income tax rate is harmful to economic growth. During the transitional process, with the number of …rms adjust endogenously, economic growth keeps on rising as each of the in-house R&D …rms continues to expand its market size. In the long run, with the equal counteracting strength between the short run and the transition period, capital taxation is neutral with economic growth. This provides a plausible explanation for the mixed empirical observations between capital taxation and economic growth.
Some empirical studies support the features exhibited in the second-generation R&D-based growth model. As mentioned previously, a prominent advantage in this strand of the literature is that an expansion in the scale of the aggregate economy is perfectly fragmented by the proliferation of endogenous product varieties. This makes the undesirable scale e¤ect be eliminated. Laincz and Peretto (2006) use the US data over the period 1964-2001, and …nd that the empirical evidence supports
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market size (total amount of R&D), which is also the main feature of this strand of the literature.
Several existing studies on taxation and economic growth in the R&D-based growth model are closely related to our paper. By using a non-scale R&D growth model developed by Howitt (1999), Zeng and Zhang (2002) show that the balanced growth rate of per capita output is independent of labor income tax and consump-tion tax, while it is negatively related to capital income tax. Conversely, Lin and Russo (1999) analyze how the taxes imposed on distinct sources of capital income a¤ects the long-run growth rate, and …nd that a higher capital income tax rate for innovative …rms could stimulate economic growth if the tax system allows tax credits for R&D spending. In departing from these two papers, this paper instead highlights that the dynamic adjustment of the …rm’s market size is crucial for de-termining the e¤ects of capital taxation on economic growth in both the short run and the transition period. More recently, Aghion et al. (2013) and Hong (2014) develop a quality-ladder R&D-based growth model to deal with optimal capital taxation. More speci…cally, they turn their main focus to the normative analysis to examine the validity of the Chamley-Judd (Chamley 1986; Judd 1985) result, i.e., a zero optimal capital tax. This paper instead sets up a second-generation R&D-based growth model, and focuses on the positive analysis regarding how capital taxation a¤ects economic growth in both the short run and the long run.
The rest of the paper is arranged as follows. Section 4.2 sets up a R&D-based growth model featuring EMS. Section 4.3 analyzes the e¤ects of capital taxation on economic growth and market structure. Section 4.4 calibrates the parameters and provides a quantitative analysis of capital taxation. Finally, some concluding remarks are provided in Section 4.5.
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4.2 The model
4.2.1 Households
Households are homogenous, in…nitely-lived, and endowed with one unit of time which can be allocated between work and leisure. The representative household maximizes the following lifetime utility:4
U = Z 1
0
e t[ln Ct+ (1 Lt)] dt; > 0; 0; (1)
subject to:
K_t+ _At= rA;tAt+ (1 K;t)rK;tKt+ (1 L;t)wtLt Ct: (2)
In eq. (1), Ct is consumption of …nal goods and Lt is total labor supply so that 1 Lt is leisure time. The parameter is time preference, and the parameter re‡ects the preference for leisure. In eq. (2), Kt is physical capital and rK;t is the return on capital. Atis the value of equity shares issued by intermediate …rms and rA;t is the return on equity shares. Physical capital and R&D stocks are perfectly substitute, so that the returns on these two assets follow the no-arbitrage condition:
rA;t= (1 K;t)rK;t. We assume perfectly mobile labor; accordingly a uniform wage rate, denoted by wt, will hold across sectors. The government imposes the capital income tax K;t and the labor income tax L;t on the households.
From standard dynamic optimization, we can derive the usual Keynes-Ramsey
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and the optimality condition for labor supply determines the wage rate:
(1 L;t)wt= Ct: (4)
4.2.2 The …nal goods sector
There is a competitive representative …rm producing a single …nal good Yt (nu-meraire). Following Peretto (2007, 2011) and Chu and Ji (2016), the production function is speci…ed as:5
Yt = average quality of all intermediate goods, which represents the knowledge stock in the economy. The productivity of intermediate good Xt(j) is positively related to its respective quality Zt(j) and also to the existing knowledge stock Zt because of R&D spillovers. LY;t is labor used in …nal goods production. Notice that since the …nal goods producer uses total Nt types of intermediate goods, the amount of labor input collocated with each type of intermediate good is LY;t=Nt.
The …rst-order conditions for the pro…t maximization problem of the …nal goods producer yield conditional demand functions for labor and intermediate goods:
wt= (1 ) Yt
5Peretto (2013) considers a more general speci…cation LY=Nt; where 0 < < 1 measures the soical return to varieties. Under tax shifting from labor income taxes to capital income taxes, our neutral result of capital taxation on long-run economic growth is robust to such a more general setting.
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where pt(j)is the price of Xt(j).
4.2.3 The intermediate goods sector
The intermediate goods sector is monopolistically competitive and comprised by a continuum of mass Nt of incumbent …rms, each of which produces a single in-termediate good Xt(j), j 2 [0; Nt] with a perpetually protected patent for that good. Intermediate …rms produce intermediate goods using capital as inputs with the technology that one unit of capital is used to produce one unit of intermediate goods, i.e., Xt(j) = kt(j) where kt(j)is the amount of capital employed by …rm j.
Intermediate …rms also undertake in-house R&D that improves the quality of the good they produce. In-house R&D (vertical R&D) requires labor as inputs. The innovation technology is:
Z_t(j) = 'Zt(j)lZ;t(j); (8) where ' re‡ects the productivity of in-house R&D, and lZ;t(j) is research labor employed by intermediate …rm j.
The pro…t function of incumbent intermediate …rm j is given by:6
t(j) = pt(j)Xt(j) rK;tkt(j) wtlZ;t(j): (9) The value of the jth monopolistic …rm is:
Vt(j) = Z 1
t
exp
Z s t
rvdv s(j)ds; (10)
where r is the interest rate.
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where t(j)is the co-state variable of Zt(j). eq. (11a) indicates that intermedi-ate …rms are symmetric. By taking log of eq. (11b) and total di¤erentiating with respect to time we can obtain _wt=wt = _t= t+ _Zt=Zt. Then, inserting eqs (11a) and (11c) into the above expression yields:
rt= 'Zt
in which we have used the symmetry condition.
4.2.4 Entrants
Following Peretto (1998), it is assumed that a (potential) entrepreneur can create a new …rm by running an R&D project. It hires labor to develop the blueprint that creates new a type of intermediate good and simultaneously expands the number of intermediate …rms. The entry technology is speci…ed as:
N = L_ N;t; (13a)
where is the productivity in the variety R&D sector, and LN;tis the total amount of labor used for variety R&D. Since the value of an incumbent is Vtand the entry cost for each potential entrant is wt= , the no-arbitrage condition for entry is Vt= wt= .
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In the horizontal R&D secotr (entry), the familiar Bellman equation is:
rt= t Vt +
V_t
Vt (13b)
4.2.5 Government
The government levies capital income taxes, labor income taxes, and lump-sum taxes to …nance its public spending Gt. The balanced government budget con-straint can be expressed as:
K;trK;tKt+ L;twtLt= Gt (14)
The government spending is a …xed proportion 2 (0; 1) of …nal output, namely:
Gt= Yt: (15)
4.2.6 Markets clearing and aggregation
Given that the intermediate …rms are symmetric, the capital market clearing con-dition is Kt = Ntkt. The stock market clearing conditions are At = NtVt and rt= rA;t. The labor market clearing condition is Lt= LY;t+ LN;t+ LZ;t, in which LZ;t=RNt
lZ;t(j)dj = NtlZ;t is the aggregate labor used for vertical R&D. By using
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the symmetric condition we can also obtain the aggregate production function for
…nal goods:
Yt= Kt(ZtLY;t)1 : (16)
4.2.7 Decentralized equilibrium
The decentralized equilibrium is de…ned as an in…nite sequence of allocations fCt; Kt; At; Yt; Xt; Lt; LY;t; LN;t; LZ;t; Gtg1t=0, prices fwt; rt; rA;t; rK;t; pt(j); Vt(j)g1t=0, policies f K;t; L;tg, such that at any instant of time:
a. households choose fCt; Kt; At; Ltg to maximize lifetime utility (1) taking prices and policies as given;
b. competitive …nal goods …rms choose fXt(j); LY;tg to maximize pro…t taking prices as given;
c. monopolistic intermediate …rms j 2 [0; Nt] choose fkt(j); pt(j); lZ;t(j)g to maximize pro…t taking frt; rK;t; wt; K;tg as given;
d. entrants make entry decisions taking fVt; wtg as given;
e. the …nal goods market, capital market and labor market clear;
f. the government budget constraint is balanced: K;trK;tKt+ L;twtLt= Gt.