Abstract
Based on the advanceretreat 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.
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Notes
 1.
Data source: http://www.wto.org/english/res_e/statis_e/statis_e.htm.
 2.
Data source: http://www.whitehouse.gov/omb/budget/Historicals.
 3.
Data source: http://www.wto.org/english/res_e/statis_e/statis_e.htm.
References
Anderson JE, Marcouiller D (2005) Anarchy and autarky: endogenous predation as a barrier to trade. Int Econ Rev 46:189–213
Anderson JA, Van Wincoop E (2003) Gravity with gravitas: a solution to the border puzzle. Am Econ Rev 93:170–192
Appleyard D, Field A (2001) International economics, McGrawHill Companies, Inc
Barro RJ (2008) Macroeconomics: a modern approach. Thomson SouthWestern, a part of Cengage Learning.
Barro RJ, SalaiMartin X (1995) Economic growth. McGraw Hill, New York
Beladi H, Oladi R (2011) An elementary proposition on technical progress and nontraded goods. J Math Econ 47:68–71
Cipollina M, Salvatici L (2010) The trade impact of European Union agricultural preferences. J Econ Policy Reform 13:87–106
Dai F, Liang L, Wu S (2013) Money supply and economic growth under environmental pressure: the strategy for Regrowth. Int J Monet Econ Financ 6(1):55–80. doi:10.1504/IJMEF.2013.055717
Dai F, Wu S, Liang L (2014) Capital and innovation aggregation with environmental pressure: an optimal evolution. Cogent Econ Financ 2:988401. doi:10.1080/23322039.2014.988401
Dai F, Li P, Liang L (2015) Longterm economic growth under environmental pressure: an optimal path. The Quarterly Review of Economics and Finance. doi:10.1016/j.qref.2015.03.008
Deardorff AV (1994) The possibility of factor price equalization, revisited. J Int Econ 36:167–175
Deardorff AV (2007) The Ricardian model. University of Michigan in its series Working Papers with number 564, http://ideas.repec.org/p/mie/wpaper/564.html.
Debaere P (2005) Monopolistic competition and trade, revisited: testing the model without testing for gravity. J Int Econ 66:249–266
Dutt P, Mitra D, Ranjan P (2009) International trade and unemployment: theory and crossnational evidence. J Int Econ 78:32–44
Francois J, Wooton I (2010) Market structure and market access. World Econ 33:873–893
Harrigan J (2010) Airplanes and comparative advantage. J Int Econ 82:181–194
Jones RW (1965) The structure of simple general equilibrium models. J Polit Econ 73:557–572
Jones R (1971) A threefactor model in theory, trade and history. In J. Bhagwati et al., eds. Trade, balance of payments, and growth. Amsterdam: Northholland, 3–21
Kraay A, Ventura J (2002) Trade integration and risk sharing. Eur Econ Rev 46:1023–1048
Leung HM (1998) On wageinequalities in the North and in the South. J Int Trade Econ Dev 7:299–315
Matsuyama K (2000) A ricardian model with a continuum of goods under nonhomothetic preferences: demand complementarities, income distribution, and north–south trade. J Polit Econ 108:1093–1120
Melvin J, Waschik R (2001) The neoclassical ambiguity in the specific factor model. J Int Trade Econ Dev 10:321–337
Opp MM (2010) Tariff wars in the Ricardian Model with a continuum of goods. J Int Econ 80:212–225
Pelletiere D, Reinert KA (2004) Used automobile protection and trade: gravity and ordered probit analysis. Empir Econ 29:737–751
Reed W (2001) The Pareto Zpif and other Power law. Econ Lett 74:15–19
Roldos JE (1991) Tariffs, investment and the current account. Int Econ Rev 32:175–94
Samuelson P (1971) Ohlin was right. Swed J Econ 73:365–384
Sanchez JR, GonzalezEstevez J, LopezRuiz R, Cosenza MG (2007) A model of coupled maps with Pareto behavior. http://arxiv.org in its series Quantitative Finance Papers with number nlin/0701016.
Schoenberg FP, Peng R, Woods J (2003) On the distribution of wildfire sizes. Environmetrics 14:583–592
Simon JE, Wolfgang K (2002) On theories explaining the success of the gravity equation. J Polit Econ 110:281–316
Solow RM (1956) A contribution to the theory of economic growth. Q J Econ 70:65–94
Solow RM (1957) Technical change and the aggregate production function. Rev Econ Stat 39:312–320
Stack M, Pentecost E (2011) Regional integration and trade: a panel cointegration approach to estimating the gravity model. J Int Trade Econ Dev 20:53–65
Syropoulos C (2002) On tariff preferences and delegation decisions in customs unions: a heckscherohlin approach. Econ J 112:625–648
Thompson H, Francis J (2009) Tariff elimination and the wage Gap in an industrial specific factors model. Rev Int Econ 17:447–460
Tinbergen J (1962) Shaping the world economy: suggestions for an international economic policy. The Twentieth Century Fund, New York
Acknowledgments
The authors acknowledge PhD Raj Chetty (Department of Economics, Harvard University) for his appreciation and encouragement for the work in the paper.
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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), OGDEG (6) and services exports σ = q∙μ ^{*}:

(i).
If \( \left[1+q\left(1/w1/\overline{\theta}\right)\right]{q}^{\overline{\theta}1}<v/\left(\overline{\theta}w\right) \), 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 OGDEG 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.
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Dai, F., Wu, S., Liang, L. et al. Bilateral Trade under Environmental Pressure: Balanced Growth. J Ind Compet Trade 16, 209–231 (2016). https://doi.org/10.1007/s1084201502059
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Keywords
 Import–export model
 Trade environmental pressure
 Policy index
 Bilateral trade balance
 Balanced growth
JEL Classification
 C53
 F43
 F47
 O44