International integration and the determinants of regional development in China

Abstract

Concerns about the duration of China’s growth and hence the question of a permanent significant contribution of China to world economic growth relate, amongst other things, to the problem of reducing regional disparity in China. While China’s high average growth is driven by a small number of rapidly developing provinces, the majority of provinces have experienced a more moderate development. To obtain broad continuos growth it is important to identify the determinants of provincial growth. Therefore, we introduce a stylized model of regional development which is characterized by two pillars: (1) International integration indicated by FDI and/or trade lead to imitation of international technologies, technology spill overs and temporary dynamic scale economies, and (2) domestic factors indicated by human and real capital available through interregional factor mobility. Using panel data analysis and GMM estimates our empirical analysis supports the predictions from our theoretical model of regional development. Positive and significant coefficients for FDI and trade support the importance of international integration and technology imitation. A negative and significant lagged GDP per capita indicates a catching up, non steady state process across China’s provinces. Highly significant human and real capital identifies the importance of these domestic growth restricting factors. However, other potentially important factors like labor or government expenditures are (surprisingly) insignificant or even negative. Extending the model using an unbalanced panel leads to a positive effect of the quality of governance and institutions on development.

Appendix

1.1 Appendix 1

Determining the aggregate production level of the region:

$$ \begin{aligned} y_{i} &=A_{i}H_{i}^{\alpha }\left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}y_{i}\right) ^{\beta }K_{i}^{1-\alpha -\beta } \\ y_{i} &=A_{i}{}^{{\frac{1} {1-\beta }}}H_{i}^{{\frac{\alpha } {1-\beta }}} \left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}} \right) ^{{\frac{\beta } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}} \\ Y_{i} &={\frac{y_{i}} {A^{{\frac{1} {1-\beta }}}}} \quad \hbox {hence}\quad Y_{i} =\omega _{i}^{{\frac{1} {1-\beta }}} H_{i}^{{\frac{\alpha } {1-\beta }}} \left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}\right) ^{{\frac{\beta}{1-\beta}}} K_{i}^{{\frac{1-\beta -\alpha } { 1-\beta }}}\\ \end{aligned} $$

1.2 Appendix 2

Steady state determination and reactions of ω ^* _i when H _i , K _i , τ _i , τ ^ex _i and γ are changing:

Solve for $\dot{\omega}$ by plugging in:

$$ \begin{aligned} \dot{\omega}_{i}(t) &=G(t)_{i}^{\delta _{G}}F(t)_{i}^{\delta _{F}}-\omega (t), \\ \dot{\omega}_{i}(t) &=\gamma ^{\delta _{G}}\left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}\right) ^{\delta _{F}}y(t)_{i}^{\delta }-\omega (t)\\ y_{i}&=\omega _{i}^{{\frac{1} {1-\beta }}}H_{i}^{{\frac{\alpha } {1-\beta }}}\left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}} \right) ^{{\frac{\beta } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\\ \dot{\omega}_{i}(t) &=\gamma ^{\delta _{G}}\left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}\right) ^{\delta _{F}} \left[ \omega (t)_{i}^{{\frac{1} {1-\beta }}}H_{i}^{{\frac{\alpha } {1-\beta }}}({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}})^{ {\frac{\beta } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{\delta }-\omega (t)\\ \dot{\omega}_{i}(t) &=\gamma ^{\delta _{G}}\left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}\right) ^{\delta _{F}+{\frac{\beta } {1-\beta }}\delta }\left[ H_{i}^{{\frac{\alpha } {1-\beta }} }K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{\delta }\omega (t)_{i}^{ {\frac{\delta } {1-\beta }}}-\omega (t).\\ {\frac{d\dot{\omega}_{i}(t)} {d\omega (t)}} &={\frac{\delta } {1-\beta }}\Psi _{i} \left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } { 1-\beta }}}\right] ^{\delta }\omega (t)_{i}^{{\frac{\delta -1+\beta } {1-\beta }} }-1<0\end{aligned} $$

as H _i and K _i are assumed to be sufficiently small

To simplify, this equation is rewritten as

$$ \begin{aligned} \dot{\omega}_{i}(t) &=\Psi _{i}\left[ H_{i}^{\frac{\alpha }{1-\beta } }K_{i}^{\frac{1-\beta -\alpha }{1-\beta }}\right] ^{\delta }\omega (t)^{ \frac{\delta }{1-\beta }}-\omega (t)\quad\text{ see\; (5)}\\ \hbox{with}\quad \Psi _{i} &:=\gamma ^{\delta _{G}}\left({\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta }{\tau _{i}r}}\right) ^{\delta _{F}+\frac{\beta }{1-\beta }\delta }. \end{aligned} $$

(32)

solve for the steady state position:

$$ \begin{aligned} 0 &=\dot{\omega}_{i}(t)=\Psi _{i}\left[ H_{i}^{{\frac{\alpha } {1-\beta }} }K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{\delta }\omega ^{{\frac{ \delta } {1-\beta }}}-\omega \\ \omega &=\Psi _{i}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{ 1-\beta -\alpha } {1-\beta }}}\right] ^{\delta }\omega ^{{\frac{\delta } { 1-\beta }}} \\ \omega ^{*} &=\Psi _{i}^{{\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left(1-\beta \right) } {(1-\beta -\delta)}}}\\\Psi _{i}^{{\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}}&=\gamma _{i}^{\delta _{G}{\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}}\left({ \varphi }_{i}\right) ^{{\frac{\delta _{F}\left(1-\beta \right) +\delta \beta} {(1-\beta -\delta)}}}\\ \omega _{i}^{*}&=\gamma _{i}^{\delta _{G}{\frac{\left(1-\beta \right) } { (1-\beta -\delta)}}}\left({\varphi }_{i}\right) ^{{\frac{\delta _{F}\left(1-\beta \right) +\delta \beta } {(1-\beta -\delta)}}}\left[ H_{i}^{{\frac{ \alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{ \delta \left(1-\beta \right) } {(1-\beta -\delta)}}}\hbox {\qquad see\qquad } \left(\hbox {6}\right) \end{aligned} $$

Steady state reactions ${{{\frac{\partial \omega _{i}^{*}} {\partial K_{i}}} }}$:

$$ \begin{aligned} \omega _{i}^{*} &=\Psi _{i}^{{{\left( 1-\beta \right) } {(1-\beta -\delta )}}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left( 1-\beta \right) } {(1-\beta -\delta )}}} \\ {{{\frac{\partial \omega _{i}^{*}} {\partial K_{i}}}}} &={{\frac{\delta (1-\beta )} {1-\beta -\delta }} {\frac{1-\beta -\alpha } {1-\beta }}\Psi _{i}^{ {\frac{1-\beta } {1-\beta -\delta }}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }} } K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left( 1-\beta \right) } {(1-\beta -\delta )}}-1}K_{i}^{{\frac{1-\beta -\alpha } { 1-\beta }}-1}}H_{i}^{{\frac{\alpha } {1-\beta }}} \\ &={{\frac{\delta (1-\beta -\alpha )} {1-\beta -\delta }}\omega _{i}^{*}K_{i}^{-1}>{0,}}\hbox {{\quad }} \\ \end{aligned} $$

Steady state reactions ${{{\frac{\partial \omega _{i}^{*}} {\partial \tau _{i}}}}}$:

$$ \begin{aligned} {\frac{\partial \omega _{i}^{*}} {\partial \tau _{i}}} &={\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}\Psi _{i}^{{\frac{\delta } {(1-\beta -\delta)}}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left(1-\beta \right) } {(1-\beta -\delta)}}}{\frac{\partial \Psi _{i}} {\partial \tau _{i}}} \\ {\frac{\partial \Psi _{i}} {\partial \tau _{i}}} &=-\left[ \delta _{F}+{\frac{ \beta } {1-\beta }}\delta \right] \gamma ^{\delta _{G}}\left({{\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}}\right) ^{\delta _{F} +{\frac{\beta } {1-\beta }}\delta -1}{{\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}}\tau _{i}^{-1} \\ &=-\left[ \delta _{F}+{\frac{\beta } {1-\beta }}\delta \right] \gamma ^{\delta _{G}} \left({{\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } { \tau _{i}r}}}\right) ^{\delta _{F}+{\frac{\beta } {1-\beta }}\delta }\tau _{i}^{-1} =-\left[ \delta _{F}+{\frac{\beta } {1-\beta }}\delta \right] \Psi _{i}\tau _{i}^{-1}\\ {\frac{\partial \omega _{i}^{*}} {\partial \tau _{i}}} &=-{\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}\Psi _{i}^{{\frac{\delta } {(1-\beta -\delta)}}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left(1-\beta \right) } {(1-\beta -\delta)}}}\left[ \delta _{F}+{\frac{\beta } {1-\beta }}\delta \right] \Psi _{i}\tau _{i}^{-1} \\ &=-\left[ {\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}\right] \left[ \delta _{F}+{\frac{\beta} {1-\beta }}\delta \right] \omega ^{*}\tau _{i}^{-1}<0\hbox {\qquad see\qquad }\left(7\right) \\ \end{aligned} $$

Steady state reactions ${{{\frac{\partial \omega _{i}^{*}} {\partial \tau _{i}^{ex}}}}}$:

$$ \begin{aligned} {\frac{\partial \omega _{i}^{*}} {\partial \tau _{i}^{ex}}}&={\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}\Psi _{i}^{{\frac{\delta } {(1-\beta -\delta)}}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left(1-\beta \right) } {(1-\beta -\delta)}}}\frac{\partial \Psi _{i}} {\partial \tau _{i}^{ex}}\\ {\frac{\partial \Psi _{i}} {\partial \tau _{i}^{ex}}} &=-\left[ \delta _{F} + {\frac{\beta } {1-\beta }}\delta \right] \gamma ^{\delta _{G}}\left({{\frac{ (1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}}\right) ^{\delta _{F} +{\frac{\beta } {1-\beta }}\delta -1}{{\frac{\beta } {\tau _{i}r}}} \\ &=-\left[ \delta _{F}+{\frac{\beta } {1-\beta }}\delta \right] \Psi _{i}(1-\tau _{i}^{ex})^{-1} \\ {\frac{\partial \omega _{i}^{*}} {\partial \tau _{i}^{ex}}} &=-{\frac{ \left(1-\beta \right) } {(1-\beta -\delta)}}\Psi _{i}^{{\frac{\delta } { (1-\beta -\delta)}}}\left[ H_{i}^{{\frac{\alpha } {1-\beta }}}K_{i}^{{\frac{ 1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left(1-\beta \right) } {(1-\beta -\delta)}}}\left[ \delta _{F}+{\frac{\beta } {1-\beta }} \delta \right] \Psi _{i}(1-\tau _{i}^{ex})^{-1} \\ &=-{\frac{\left(1-\beta \right) } {(1-\beta -\delta)}}\left[ \delta _{F} + {\frac{\beta } {1-\beta }}\delta \right] \omega _{i}^{*}\left(1-\tau _{i}^{ex}\right) ^{-1}\hbox {\qquad see\qquad }\left(9 \right) \\ \end{aligned} $$

Steady state reactions ${{{\frac{\partial \omega _{i}^{*}} {\partial \gamma _{i}}}}}$ :

$$ \begin{aligned} {\frac{\partial \omega _{i}^{*}} {\partial \gamma _{i}}} &={\frac{\left(1-\beta \right) \omega _{i}^{*}} {(1-\beta -\delta)}}\Psi _{i}^{-1}{\frac{ \partial \Psi _{i}} {\partial \gamma _{i}}} \\ {\frac{d\Psi _{i}} {d\gamma _{i}}} &=\delta _{G}\gamma _{i}^{\delta _{G}-1} \left({{\frac{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } { \tau _{i}r}}}\right) ^{\delta _{F}+{\frac{\beta } {1-\beta }}\delta } \\ &-\left(\delta _{F}+{\frac{\beta } {1-\beta }}\delta \right) \gamma _{i}^{\delta _{G}} \left({{{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}}\right) ^{\delta _{F}+{\frac{\beta } {1-\beta }} \delta -1} {{\frac{(1-\tau _{i}^{ex})\beta } {\tau _{i}r}}} \\ &=\Psi _{i}\left[ \delta _{G}\gamma _{i}^{-1}-\left(\delta _{F}+{\frac{ \beta } {1-\beta }}\delta \right) \left(1-\gamma _{i}\right) ^{-1}\right] \\ {\frac{\partial \omega _{i}^{*}} {\partial \gamma _{i}}} &={\frac{\left(1-\beta \right) \omega _{i}^{*}} {(1-\beta -\delta)}} \left[ \delta _{G}\gamma _{i}^{-1}-\left(\delta _{F}+{\frac{\beta } {1-\beta }}\delta \right) \left(1-\gamma _{i}\right) ^{-1}\right] \quad {{\text see}}\quad \left(10\right) \\ \end{aligned} $$

1.3 Appendix 3

Optimal level of government activities

$$ \begin{aligned} \underset{\gamma _{i}}{\max \quad }\omega ^{*} &=\Psi _{i}^{{\frac{ \left(1-\beta \right) } {(1-\beta -\delta)}}}\left[ H_{i}^{{\frac{\alpha } { 1-\beta }}}K_{i}^{{\frac{1-\beta -\alpha } {1-\beta }}}\right] ^{{\frac{\delta \left(1-\beta \right) } {(1-\beta -\delta)}}}\quad \Psi _{i}:=\gamma _{i}^{\delta _{G}} \left({{{(1-\tau _{i}^{ex})\left(1-\gamma _{i}\right) \beta } {\tau _{i}r}}}\right) ^{\delta _{F}+{\frac{\beta } {1-\beta }} \delta } \\ {\frac{\partial \omega _{i}^{*}} {\partial \gamma _{i}}} &={\frac{\left(1-\beta \right) \omega _{i}^{*}} {(1-\beta -\delta)}}\Psi _{i}^{-1}{\frac{ \partial \Psi _{i}} {\partial \gamma _{i}}} \\ {\frac{d\Psi _{i}} {d\gamma _{i}}} &=\Psi _{i} \left[ \delta _{G}\gamma _{i}^{-1}-\left(\delta _{F}+{\frac{\beta } {1-\beta }} \delta \right) \left(1-\gamma _{i}\right) ^{-1}\right] =0 \\ \delta _{G} &=\gamma _{i}\left(\delta _{F}+{\frac{\beta } {1-\beta }}\delta \right) \left(1-\gamma _{i}\right) ^{-1} \\ \gamma _{i}^{*}&={\frac{\delta _{G}} {\left(\delta _{F}+{\frac{\beta } { 1-\beta }}\delta +\delta _{G}\right) }} \\ {\frac{\partial \omega _{i}^{*}} {\partial \gamma _{i}}} &={\frac{\omega _{i}^{*}} {1-\delta }}\Psi _{i}^{-1}{\frac{\partial \Psi _{i}} {\partial \gamma _{i}}}\end{aligned} $$

with

$$ {\frac{\partial \Psi _{i}} {\partial \gamma _{i}}} \left\{ \begin{array}{llll} >0 & & \gamma _{i}<\gamma _{i}^{*}\quad & \hbox {underinvestment, undertaxation}\\ =0 & \hbox {for} & \gamma _{i}=\gamma _{i}^{*}\quad & \hbox {growth maximizing tax rate}\\ <0 & & \gamma _{i}>\gamma _{i}^{*}\quad & \hbox {overinvestment, overtaxation}\\ \end{array} \right. $$