Bilateral Trade under Environmental Pressure: Balanced Growth

Abstract

Based on the advance-retreat course (ARC) model - a growth model under environmental pressure, this paper builds a bilateral import and export trade growth model under environmental pressure. By using the model, the paper analyzes the impacts of innovation on import and export growth, presents a method for computing the optimal levels of imports and exports, derives the limit values of imports and exports, and obtains the limit equilibrium between exports and imports. Finally, a strategy for promoting import and export growth and achieving a bilateral trade balance according to the limit equilibrium is designed. The findings are the following: (i) innovation growth will gradually reduce goods import and export, and services import and export will increase, (ii) the U.S. import–export structure is more reasonable than that of China, and (iii) there is big room for services import and export growth for China.

Appendices

Appendix 1

Without loss of generality, let 1 < θ < 3 and θ = θ ₀ + x (θ ₀ = 2, −1 < x < 1), where θ is the policy index; and let Δ = 0.1, θ ^Δ _i = θ ₀ + i · Δ (i = −9, · · ·, −1, 0, 1, · · ·, 9), then an algorithm is designed as follows:

• (i). Do the regression calculation based on θ ^Δ _i , we will obtain the coefficient of determination R ² _i (i = −9, · · ·,-1, 0, 1, · · ·, 9);

• (ii). Denote ${R}_{i_0}^2=\underset{i}{ \max}\left\{{R}_i^2\right\}$, correspondingly, θ ₁ = ${\theta}_{i_0}^{\varDelta }$.

  Afterwards, let

  $$ {\varDelta}_1=0.01,\;{\theta}_i^{\varDelta }={\theta}_1+i\bullet {\varDelta}_1\left(i=-9,\cdots, -1,\;0,\;1,\cdots,\;9\;\right) $$

  And

  $$ {\varDelta}_2=0.001,\;{\theta}_i^{\varDelta }={\theta}_2+i\bullet {\varDelta}_2\left(i=-9,\cdots,\;1,\;0,\;1,\cdots, 9\right) $$

  Using the above algorithm repeatedly, and then, the coefficient of determination is maximised.

Appendix 2

We have the following conclusions for OGE (5), OGDE-G (6) and services exports σ = q∙μ ^*:

• (i). If $\left[1+q\left(1/w-1/\overline{\theta}\right)\right]{q}^{\overline{\theta}-1}<v/\left(\overline{\theta}w\right)$, innovation growth causes OGE to grow.

• (ii). If $q<{\left(\overline{\theta}v/w\right)}^{1/\left(\overline{\theta}-1\right)}$, innovation growth causes services exports, σ = q∙μ ^*, to grow.

• (iii). if $q<{\left(v/w\right)}^{1/\left(\overline{\theta}-1\right)}$, innovation growth causes OGDE-G to grow.

  Proof. Let ${\scriptscriptstyle \frac{d{\mu}^{*}}{dq}}>0$, ${\scriptscriptstyle \frac{d}{dq}}\left({\mu}^{*}\cdot q\right)>0$ and ${\scriptscriptstyle \frac{d}{dq}}\left({\left.{Y}_E\right|}_{\mu ={\mu}^{*}}\right)>0$ separately, and Appendix 2 is as follows.