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4.5 Concluding remarks
In this Chapter, we examine the short-run and long-run e¤ects of capital taxation on economic growth in an R&D-based growth model with endogenous market structure. In earlier traditional AK-type growth models, raising the capital tax has a harmful long-run e¤ect on growth. In our analysis, however, we show that the negative growth e¤ect sustains only in the short run. In the short run where the number of intermediate …rms is …xed, raising the capital tax depresses growth because labor ‡ows out from the in-house R&D sector. During the transitional period, 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 leads to a zero long-term e¤ect on economic growth. Our analytical results succeed in matching some empirical observations that the negative growth e¤ect of capital taxation may be neglectably small in the long run (Lucas, 1990; Stokey and Rebelo, 1995).
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This appendix solves the dynamic system of the model under tax shifting from labor income taxes to capital income taxes. The set of equations under the model is expressed by:
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From eq. (A14), we can infer the folowing expression:
Lt = Lt(zt; ct; LY;t; K); (A15)
We now turn to deal with the transitional dynamics of the model. From eqs (A12) and (A13) we can infer:
N = N_ t Lt
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Combining eqs (A15), (A16), and (A17) together yields:
N =_ Lt(zt; ct; LY;t; K) 1 + (1 '
) LY;t : (A18)
To simplify the notation, in what follows we suppress those arguments of the laobr supply function. Substituting eq. (A17) into eq. (A8) yields:
Z_t
Zt = ' 1 ' LY;t
Nt : (A19)
From eqs (A1), (A2), (A6), (A11), ct Ct=Kt, and zt Zt=Kt, we can infer:
C_t
Ct = (1 K) 2(ztLY;t)1 (A20)
Based on eqs (A2), (A4), (A6), (A11), ct Ct=Kt, and zt Zt=Kt, we can obtain:
K_t Kt
= (1 ) 2(ztLY;t)1 ct (A21)
From eqs (A5) and (A11), we have:
wt = (1 )Kt(ZtLY;t)1
LYt (A22)
Taking logarithms of eq. (A22) and di¤erentiating the resulting equation with respect to time yields:
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Substituting eqs (A19), (A20), and (A21) into eq. (A23) and then combining the resulting equation with eq. (A24) together, we thus infer the following expression:
L_Y;t
From eqs (A18), (A19),(A20), (A21), (A25), (A26), and (A27), the dynamic system can be expressed as:
_z=z = ' 1 ' LY;t
Linearizing eqs (A28a), (A28b), (A28c), and (A28d) around the steady-state equilibrium yields:
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Due to the complicated calculations, we do not list the analytical results for bij, where i 2 f1; 2; 3; 4; 5g and j 2 f1; 2; 3; 4; 5g:Let 1, 2, 3, and 4be the four characteristic roots of the dynamic system.
Due to the complexity calculations of the four characteristic roots, we do not try to prove the saddle-point stability analytically. Instead, we show that the dynamic system exists two positive and two negative characteristic roots via a numerical simulation. For expository convenience, in what follows let 1 and 2 be the negative root as well as 3 and 4 be the positive roots.
The general general solution is given by:
2 3 2 3 2 32 3
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where D1, D2, D3, and D4 are undetermined coe¢ cients and
j
b12 b13 b14 b22 j b23 b24 b32 b33 j b34
; j 2 f1; 2; 3; 4g (A31b)
h2j =
j b11 b13 b14
b21 b23 b24 b31 b33 j b34
= j ; j 2 f1; 2; 3; 4g (A31b)
h3j =
b12 j b11 b14
b22 j b21 b24 b32 b31 b34
= j ; j 2 f1; 2; 3; 4g (A31c)
h4j =
b12 u13 j b11
b22 j b23 b21
b32 b33 j b31
= j ; j 2 f1; 2; 3; 4g (A31e)
The government changes the capital tax rate K from K0 to K1 at t = 0, based on eqs (A31a)-(A31e), we can employ the following equations to discribe the dynamic adjustment of zt; Nt; ct;and LY;t :
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where 0 and 0+ denote the instant before and after the policy implementation, respectively.The values for D1, D2, D3 and D4 are determined by:
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Substituting eqs (A33c), (A33d), (A34a), and (A34b) into eqs (A32a)-(A32d), the time path for zt; Nt; ct and LY;t can then be described as:
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CHAPTER 5
CONCLUSION
This dissertation has provided a systematic analysis regarding the growth and welfare e¤ects of capital taxation with distinct R&D-based growth models. More speci…cally, we have dealt with the growth and welfare e¤ects of capital income taxation in three di¤erent types of R&D models, namely, the …rst-generation R&D-based growth model developed by Romer (1990), the semi-endogenous growth model developed by Jones and Williams (2000), and the second-generation R&D-based growth model developed by Dinopoulos and Thompson (1998) and Peretto (1998). The main …ndings of each chapter can be summarized as follows.
In Chapter 2, we have constructed a …rst-generation R&D-based growth model to examine the e¤cts of capital taxation on innovation and economic growth. We have found that capital taxation has drastically di¤rent e¤cts in the short run and in the long run. An increase in the capital income tax rate has both a consump-tion e¤ct and a tax-shifting e¤ct on the equilibrium growth rates of technology and output. In the long run, the tax-shifting e¤ct dominates the consumption ef-fect, yielding an overall positive e¤ct of capital taxation on steady-state economic growth. However, in the short run the consumption e¤ect becomes the dominant force, causing an initial negative e¤ct of capital taxation on the equilibrium growth rates. These contrasting e¤cts of capital taxation at di¤rent time horizons may provide a plausible explanation for the mixed evidence in the empirical literature
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capital income tax is positive, at a rate of around 11.9 percent. We have also found that the result of a positive optimal capital income tax is robust with respect to varying the degrees of various types of R&D externalities.
In Chapter 4, we have built up a second-generation R&D-based growth model which features endogenous market structure, and examined the short-run and long-run e¤ects of capital taxation on economic growth. In this chapter, we have shown that the negative growth e¤ect sustains only working in the short run. Speci…cally, in the short run the number of intermediate …rms is …xed, a rise in the capital tax rate tends to lower the growth rate because labor ‡ows out from the in-house R&D sector. During the transitional period, 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 leads to a zero long-term e¤ect on economic growth. Our analytical results have succeeded in matching some empirical observations that the negative growth e¤ect of capital taxation may be neglectably small in the long run (Lucas, 1990; Stokey and Rebelo, 1995).
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