Growth and International Knowledge Spillovers with Firm Heterogeneity

Abstract

Using theoretical analysis, this study explores the effects of trade and foreign direct investment (FDI) liberalization on productivity growth in a model with heterogeneous firms. Baldwin and Robert-Nicoud (2008, BRN hereafter) show that freer trade has an ambiguous impact on growth rate in a heterogeneous firms model. Their main findings are in contrast to the notions shared by most literature on the endogenous growth of homogeneous firms, which says that trade liberalization promotes economic growth. Although BRN mainly focus on the diffusion of international knowledge by trade, we can see that some countries benefit not only from international trade but also from FDI by foreign firms in the process of development. That is, FDI liberalization can influence knowledge spillovers among local companies and promote the development of the host country. In contrast to BRN, this chapter considers whether trade and FDI liberalization could push up economic growth in the steady state or not. This chapter finds that FDI liberalization tends to have more positive growth promoting effects than trade liberalization does. On the other hand, trade liberalization is prone to have an ambiguous impact on growth rates.

Appendix

1.1 A.1 Derivation of the Free Entry Condition in Eq. (2.24)

Free entry ensures that ex ante expected discounted profits must equal ex ante expected fixed costs of developing a profitable variety.

$$ G\left({a}_{\mathrm{D}}\right)\left\{{\int}_0^{a_{\mathrm{D}}}\frac{\left(1-\alpha \right)E/n}{r+{\dot{K}}_n/{K}_n}{\left[\frac{a}{\overset{\sim }{a}}\right]}^{1-\sigma}\frac{g(a)}{G\left({a}_{\mathrm{D}}\right)}\mathrm{d}a-\frac{f_{\mathrm{D}}}{K_n}\right\}+\left(G\left({a}_{\mathrm{X}}\right)-G\left({a}_{\mathrm{X}}\right)\right)\left\{{\int}_{a_{\mathrm{X}}}^{a_{\mathrm{F}}}\frac{\left(1-\alpha \right)E/n}{r+{\dot{K}}_n/{K}_n}{\left[\frac{\tau a}{\overset{\sim }{a}}\right]}^{1-\sigma}\frac{g(a)}{G\left({a}_{\mathrm{X}}\right)-G\left({a}_{\mathrm{F}}\right)}\mathrm{d}a-\frac{f_{\mathrm{X}}}{K_n}\right\}+G\left({a}_{\mathrm{F}}\right)\left\{{\int}_0^{a_{\mathrm{F}}}\frac{\left(1-\alpha \right)E/n}{r+{\dot{K}}_n/{K}_n}{\left[\frac{a}{\overset{\sim }{a}}\right]}^{1-\sigma}\frac{g(a)}{G\left({a}_{\mathrm{F}}\right)}\mathrm{d}a-\frac{f_{\mathrm{F}}}{K_n}\right\}=\frac{f_I}{K_n}\iff \frac{\left(1-\alpha \right)E/n}{r+{\dot{K}}_n/{K}_n}{\left[\frac{1}{\overset{\sim }{a}}\right]}^{1-\sigma}\left[{\int}_0^{\infty }{a}^{1-\sigma }{\mu}_{\mathrm{D}}(a)\mathrm{d}a+{p}_{\mathrm{X}}\phi {\int}_0^{\infty }{a}^{1-\sigma }{\mu}_{\mathrm{X}}(a)\mathrm{d}a+{p}_{\mathrm{F}}{\int}_0^{\infty }{a}^{1-\sigma }{\mu}_{\mathrm{F}}(a)\mathrm{d}a\right]=\frac{1}{K_n}\left(\frac{1}{G\left({a}_{\mathrm{D}}\right)}{f}_I+{f}_{\mathrm{D}}+\frac{G\left({a}_{\mathrm{X}}\right)-G\left({a}_{\mathrm{F}}\right)}{G\left({a}_{\mathrm{D}}\right)}{f}_{\mathrm{X}}+\frac{G\left({a}_{\mathrm{F}}\right)}{G\left({a}_{\mathrm{D}}\right)}{f}_{\mathrm{F}}\right)\iff \frac{\left(1-\alpha \right)E/n}{r+{\dot{K}}_n/{K}_n}=\frac{\overline{f}}{K_n} $$

1.2 A.2 Derivation of the Average Productivities in Eq. (2.29)

$$ \overset{\sim }{a}={\left(\frac{1}{G\left({a}_{\mathrm{D}}\right)}\right)}^{1/\left(1-\sigma \right)}{\left[{\int}_0^{a_{\mathrm{D}}}{a}^{1-\sigma }g(a)\mathrm{d}a+\phi {\int}_{a_{\mathrm{F}}}^{a_{\mathrm{X}}}{a}^{1-\sigma }g(a)\mathrm{d}a+{\int}_0^{a_{\mathrm{F}}}{a}^{1-\sigma }g(a)\mathrm{d}a\right]}^{1/\left(1-\sigma \right)}={\left(\frac{1}{a_{\mathrm{D}}^k}\right)}^{1/\left(1-\sigma \right)}{\left[{\int}_0^{a_{\mathrm{D}}}{a}^{1-\sigma }k{a}^{k-1}\mathrm{d}a+\phi {\int}_{a_{\mathrm{F}}}^{a_{\mathrm{X}}}{a}^{1-\sigma }k{a}^{k-1}\mathrm{d}a+{\int}_0^{a_{\mathrm{F}}}{a}^{1-\sigma }k{a}^{k-1}\mathrm{d}a\right]}^{1/\left(1-\sigma \right)}={\left(\frac{k}{a_{\mathrm{D}}^k}\right)}^{1/\left(1-\sigma \right)}{\left[{\int}_0^{a_{\mathrm{D}}}{a}^{k-\sigma}\mathrm{d}a+\phi {\int}_{a_{\mathrm{F}}}^{a_{\mathrm{X}}}{a}^{k-\sigma}\mathrm{d}a+{\int}_0^{a_{\mathrm{F}}}{a}^{k-\sigma}\mathrm{d}a\right]}^{1/\left(1-\sigma \right)} $$

$$ ={\left(\frac{k}{a_{\mathrm{D}}^k}\right)}^{1/\left(1-\sigma \right)}{\left[{\left[\frac{1}{k-\sigma +1}{a}^{k-\sigma +1}\right]}_0^{a_{\mathrm{D}}}+\phi {\left[\frac{1}{k-\sigma +1}{a}^{k-\sigma +1}\right]}_{a_{\mathrm{F}}}^{a_{\mathrm{X}}}+{\left[\frac{1}{k-\sigma +1}{a}^{k-\sigma +1}\right]}_0^{a_{\mathrm{F}}}\right]}^{1/\left(1-\sigma \right)}={\left(\frac{k}{a_{\mathrm{D}}^k}\right)}^{1/\left(1-\sigma \right)}{\left[\frac{1}{k-\sigma +1}{a}_{\mathrm{D}}^{k-\sigma +1}+\phi \frac{1}{k-\sigma +1}{a}_{\mathrm{F}}^{k-\sigma +1}+\left(1-\phi \right)\frac{1}{k-\sigma +1}{a}_{\mathrm{F}}^{k-\sigma +1}\right]}^{1/\left(1-\sigma \right)}={\left(\frac{k}{k-\sigma +1}\right)}^{1/\left(1-\sigma \right)}{\left[{a}_{\mathrm{D}}^{1-\sigma }+\phi {a}_{\mathrm{D}}^{1-\sigma }{\left(\frac{T}{\phi}\right)}^{\left(k-\sigma +1\right)/\left(1-\sigma \right)}+\left(1-\phi \right){a}_{\mathrm{D}}^{1-\sigma }T{\prime}^{\left(k-\sigma +1\right)/\left(1-\sigma \right)}\right]}^{\frac{1}{1-\sigma }}={\left(\frac{\beta }{\beta -1}\right)}^{1/\left(1-\sigma \right)}{\left[1+{T}^{1-\beta }{\phi}^{\beta }+\left(1-\phi \right)T{\prime}^{1-\beta}\right]}^{1/\left(1-\sigma \right)}{a}_{\mathrm{D}} $$