Assessing the palliative aspects of green innovations in the non-linear tendencies of environmental sustainability-financial globalization nexus among West African states

Abstract

A reconciliation of the disagreement on whether financial globalization (FG) affects ecological footprint through the scale, technique and composition effects cannot be achieved without an explicit understanding of the direct and indirect interactions of FG with environmental sustainability. Hence, the novel perspective of this study lies in the investigation of how green innovations moderate the non-linear tendencies in the FG-environmental sustainability link among western African states given the abundance of natural resources and the prevailing pace of economic growth. The core findings are obtained from robust analysis based on cross-sectional autoregressive distributed lag (CS-ARDL) technique, the augmented mean group (AMG) technique, and the common correlated effects mean group (CCEMG) advanced estimators. Firstly, the beneficial ecological impacts of green innovations were observed. As per direct impact, enhanced financial globalization (FG) exhibits non-linear detrimental ecological effects. However, green innovations cushion the observed adverse ecological effects of FG. Furthermore, resource rents reduce ecological footprint within the moderating framework of green innovation as the environmental Kuznets curve (EKC) is validated among the states. Additionally, a bidirectional causal link between financial globalization, green innovations, economic growth, natural resources, and ecological footprint was observed. Thus, the significant policy implication is for the West African states to decisively increase their investments in green innovations while strategically encouraging the share of ecologically friendly resources in total resource utilization to guarantee a more sustainable environment.

Keywords

Green innovations / Ecological footprint / Natural resources / Financial globalization / West Africa

CRediT authorship contribution statement

Mohammed Musah: Conceptualization, Data curation, Formal analysis, Methodology. Stephen Taiwo Onifade: Conceptualization, Methodology, Supervision, Writing – original draft, Writing – review & editing. Elma Satrovic: Data curation, Writing – original draft, Visualization. Joseph Akwasi Nkyi: Writing – original draft.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix.

CS-ARDL model specifications

The study’s CS-ARDL models augmented with the lags of the cross-sectional averages of the input and output variables to account for cross-sectional dependence are specified as;

Interactive Model:(A1)${\mathrm{lnEFP}}_{\mathit{it}}={\mathrm{w}}_{\mathrm{i}}+\sum _{\mathrm{j}=1}^{{\mathrm{p}}_{\mathrm{y}}}{\mathrm{\lambda }}_{\mathit{ij}}{\mathrm{lnEFP}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{1\mathrm{j}}{\mathrm{lnFG}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{2\mathrm{j}}{\mathrm{lnGI}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{3\mathrm{j}}{\mathrm{lnY}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{4\mathrm{j}}{{\mathrm{lnY}}^2}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{5\mathrm{j}}{\mathrm{lnNRR}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathrm{\delta }}_{1\mathrm{j}}{\ln \left(\mathrm{FG}\ast \mathrm{GI}\right)}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{1\mathrm{j}}{\overline{\mathrm{lnEFP}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{2\mathrm{j}}{\overline{\mathrm{lnFG}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{3\mathrm{j}}{\overline{\mathrm{lnGI}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{4\mathrm{j}}{\overline{\mathrm{lnY}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{5\mathrm{j}}{\overline{{\mathrm{lnY}}^2}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{6\mathrm{j}}{\overline{\mathrm{lnNRR}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{7\mathrm{j}}{\overline{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}}_{\mathrm{t}-\mathrm{j}}+{\mathrm{\epsilon }}_{\mathrm{i}\mathrm{t}}$${\mathrm{lnEFP}}_{\mathit{it}}={\mathrm{w}}_{\mathrm{i}}+\sum _{\mathrm{j}=1}^{{\mathrm{p}}_{\mathrm{y}}}{\mathrm{\lambda }}_{\mathit{ij}}{\mathrm{lnEFP}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{1\mathrm{j}}{\mathrm{lnFG}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{2\mathrm{j}}{\mathrm{lnGI}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{3\mathrm{j}}{\mathrm{lnY}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{4\mathrm{j}}{{\mathrm{lnY}}^2}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{5\mathrm{j}}{\mathrm{lnNRR}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathrm{\delta }}_{1\mathrm{j}}{\ln \left(\mathrm{FG}\ast \mathrm{GI}\right)}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{1\mathrm{j}}{\overline{\mathrm{lnEFP}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{2\mathrm{j}}{\overline{\mathrm{lnFG}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{3\mathrm{j}}{\overline{\mathrm{lnGI}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{4\mathrm{j}}{\overline{\mathrm{lnY}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{5\mathrm{j}}{\overline{{\mathrm{lnY}}^2}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{6\mathrm{j}}{\overline{\mathrm{lnNRR}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{7\mathrm{j}}{\overline{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}}_{\mathrm{t}-\mathrm{j}}+{\mathrm{\epsilon }}_{\mathrm{i}\mathrm{t}}$

Nonlinear Model:(A2)${\mathrm{lnEFP}}_{\mathit{it}}={\mathrm{w}}_{\mathrm{i}}+\sum _{\mathrm{j}=1}^{{\mathrm{p}}_{\mathrm{y}}}{\mathrm{\lambda }}_{\mathit{ij}}{\mathrm{lnEFP}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{1\mathrm{j}}{\mathrm{lnFG}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{2\mathrm{j}}{\mathrm{lnGI}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{3\mathrm{j}}{\mathrm{lnY}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{4\mathrm{j}}{{\mathrm{lnY}}^2}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{5\mathrm{j}}{\mathrm{lnNRR}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathrm{\pi }}_{1\mathrm{j}}{{\mathrm{lnFG}}^2}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{1\mathrm{j}}\overline{\mathrm{lnEFP}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{2\mathrm{j}}\overline{\mathrm{lnFG}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{3\mathrm{j}}\overline{\mathrm{lnGI}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{4\mathrm{j}}\overline{\mathrm{lnY}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{5\mathrm{j}}\overline{{\mathrm{lnY}}^2}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{6\mathrm{j}}{\overline{\mathrm{lnNRR}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{7\mathrm{j}}\overline{{\mathrm{lnFG}}^2}}_{\mathrm{t}-\mathrm{j}}+{\mathrm{\epsilon }}_{\mathrm{i}\mathrm{t}}$${\mathrm{lnEFP}}_{\mathit{it}}={\mathrm{w}}_{\mathrm{i}}+\sum _{\mathrm{j}=1}^{{\mathrm{p}}_{\mathrm{y}}}{\mathrm{\lambda }}_{\mathit{ij}}{\mathrm{lnEFP}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{1\mathrm{j}}{\mathrm{lnFG}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{2\mathrm{j}}{\mathrm{lnGI}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{3\mathrm{j}}{\mathrm{lnY}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{4\mathrm{j}}{{\mathrm{lnY}}^2}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathit{\beta }}_{5\mathrm{j}}{\mathrm{lnNRR}}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{{\mathrm{p}}_{\mathrm{x}}}{\mathrm{\pi }}_{1\mathrm{j}}{{\mathrm{lnFG}}^2}_{\mathit{it}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{1\mathrm{j}}\overline{\mathrm{lnEFP}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{2\mathrm{j}}\overline{\mathrm{lnFG}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{3\mathrm{j}}\overline{\mathrm{lnGI}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{4\mathrm{j}}\overline{\mathrm{lnY}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{5\mathrm{j}}\overline{{\mathrm{lnY}}^2}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{\mathrm{\gamma }}_{6\mathrm{j}}{\overline{\mathrm{lnNRR}}}_{\mathrm{t}-\mathrm{j}}+\sum _{\mathrm{j}=0}^{\mathrm{p}}{{\mathrm{\gamma }}_{7\mathrm{j}}\overline{{\mathrm{lnFG}}^2}}_{\mathrm{t}-\mathrm{j}}+{\mathrm{\epsilon }}_{\mathrm{i}\mathrm{t}}$where $\overline{\mathrm{lnEFP}}$$\overline{\mathrm{lnEFP}}$, $\overline{\mathrm{lnFG}}$$\overline{\mathrm{lnFG}}$, $\overline{\mathrm{lnGI}}$$\overline{\mathrm{lnGI}}$, $\overline{\mathrm{lnY}}$$\overline{\mathrm{lnY}}$, $\overline{{\mathrm{lnY}}^2},\overline{\mathrm{lnNRR}}$$\overline{{\mathrm{lnY}}^2},\overline{\mathrm{lnNRR}}$, $\overline{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}$$\overline{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}$, and $\overline{{\mathrm{lnFG}}^2}$$\overline{{\mathrm{lnFG}}^2}$ are the cross-sectional means of the endogenous and exogenous series correspondingly.

CCEMG model specifications

In the CCEMG procedure, the estimated model is augmented with cross-sectional averages of the regressors to account for cross-sectional correlations. Our study’s augmented CCEMG models to control for cross-sectional dependence are specified as;

Interactive Model:(A3)${\mathrm{lnEFP}}_{\mathit{it}}={\mathit{\alpha }}_0+{\mathit{\beta }}_1{\mathrm{lnFG}}_{\mathit{it}}{+{\mathit{\beta }}_2{\mathrm{lnGI}}_{\mathit{it}}+{\mathit{\beta }}_3{\mathrm{lnY}}_{\mathit{it}}+\mathit{\beta }}_4{{\mathrm{lnY}}^2}_{\mathit{it}}+{\mathit{\beta }}_5{\mathrm{lnNRR}}_{\mathit{it}}+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+{\mathrm{\psi }}_1\overline{{\mathrm{lnFG}}_{\mathit{it}}}+{\mathrm{\psi }}_2\overline{{\mathrm{lnGI}}_{\mathit{it}}}+{\mathrm{\psi }}_3\overline{{\mathrm{lnY}}_{\mathit{it}}}+{\mathrm{\psi }}_4\overline{{{\mathrm{lnY}}^2}_{\mathit{it}}}+{\mathrm{\psi }}_5\overline{{\mathrm{lnNRR}}_{\mathit{it}}}+{\mathrm{\psi }}_6\overline{{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}}{+\mathrm{\epsilon }}_{\mathit{it}}$${\mathrm{lnEFP}}_{\mathit{it}}={\mathit{\alpha }}_0+{\mathit{\beta }}_1{\mathrm{lnFG}}_{\mathit{it}}{+{\mathit{\beta }}_2{\mathrm{lnGI}}_{\mathit{it}}+{\mathit{\beta }}_3{\mathrm{lnY}}_{\mathit{it}}+\mathit{\beta }}_4{{\mathrm{lnY}}^2}_{\mathit{it}}+{\mathit{\beta }}_5{\mathrm{lnNRR}}_{\mathit{it}}+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+{\mathrm{\psi }}_1\overline{{\mathrm{lnFG}}_{\mathit{it}}}+{\mathrm{\psi }}_2\overline{{\mathrm{lnGI}}_{\mathit{it}}}+{\mathrm{\psi }}_3\overline{{\mathrm{lnY}}_{\mathit{it}}}+{\mathrm{\psi }}_4\overline{{{\mathrm{lnY}}^2}_{\mathit{it}}}+{\mathrm{\psi }}_5\overline{{\mathrm{lnNRR}}_{\mathit{it}}}+{\mathrm{\psi }}_6\overline{{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}}{+\mathrm{\epsilon }}_{\mathit{it}}$

Nonlinear Model:(A4)${\mathrm{lnEFP}}_{\mathit{it}}={\mathit{\alpha }}_0+{\mathit{\beta }}_1{\mathrm{lnFG}}_{\mathit{it}}{+{\mathit{\beta }}_2{\mathrm{lnGI}}_{\mathit{it}}+{\mathit{\beta }}_3{\mathrm{lnY}}_{\mathit{it}}+\mathit{\beta }}_4{{\mathrm{lnY}}^2}_{\mathit{it}}+{\mathit{\beta }}_5{\mathrm{lnNRR}}_{\mathit{it}}+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+{\mathrm{\Omega }}_1\overline{{\mathrm{lnFG}}_{\mathit{it}}}+{\mathrm{\Omega }}_2\overline{{\mathrm{lnGI}}_{\mathit{it}}}+{\mathrm{\Omega }}_3\overline{{\mathrm{lnY}}_{\mathit{it}}}+{\mathrm{\Omega }}_4\overline{{{\mathrm{lnY}}^2}_{\mathit{it}}}+{\mathrm{\Omega }}_5\overline{{\mathrm{lnNRR}}_{\mathit{it}}}+{\mathrm{\Omega }}_6\overline{{{\mathrm{lnFG}}^2}_{\mathit{it}}}{+\mathrm{\epsilon }}_{\mathit{it}}$${\mathrm{lnEFP}}_{\mathit{it}}={\mathit{\alpha }}_0+{\mathit{\beta }}_1{\mathrm{lnFG}}_{\mathit{it}}{+{\mathit{\beta }}_2{\mathrm{lnGI}}_{\mathit{it}}+{\mathit{\beta }}_3{\mathrm{lnY}}_{\mathit{it}}+\mathit{\beta }}_4{{\mathrm{lnY}}^2}_{\mathit{it}}+{\mathit{\beta }}_5{\mathrm{lnNRR}}_{\mathit{it}}+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+{\mathrm{\Omega }}_1\overline{{\mathrm{lnFG}}_{\mathit{it}}}+{\mathrm{\Omega }}_2\overline{{\mathrm{lnGI}}_{\mathit{it}}}+{\mathrm{\Omega }}_3\overline{{\mathrm{lnY}}_{\mathit{it}}}+{\mathrm{\Omega }}_4\overline{{{\mathrm{lnY}}^2}_{\mathit{it}}}+{\mathrm{\Omega }}_5\overline{{\mathrm{lnNRR}}_{\mathit{it}}}+{\mathrm{\Omega }}_6\overline{{{\mathrm{lnFG}}^2}_{\mathit{it}}}{+\mathrm{\epsilon }}_{\mathit{it}}$From the above equations $\overline{{\mathrm{lnFG}}_{\mathit{it}}}$$\overline{{\mathrm{lnFG}}_{\mathit{it}}}$, $\overline{{\mathrm{lnGI}}_{\mathit{it}}}$$\overline{{\mathrm{lnGI}}_{\mathit{it}}}$, $\overline{{\mathrm{lnY}}_{\mathit{it}}}$$\overline{{\mathrm{lnY}}_{\mathit{it}}}$, $\overline{{{\mathrm{lnY}}^2}_{\mathit{it}},}$$\overline{{{\mathrm{lnY}}^2}_{\mathit{it}},}$ $\overline{{\mathrm{lnNRR}}_{\mathit{it}}}$$\overline{{\mathrm{lnNRR}}_{\mathit{it}}}$, $\overline{{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}}$$\overline{{\ln \left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}}$, and $\overline{{{\mathrm{lnFG}}^2}_{\mathit{it}}}$$\overline{{{\mathrm{lnFG}}^2}_{\mathit{it}}}$ denote the cross-sectional averages of the input variables.

AMG model specifications

The AMG approach follows a two-staged process. At the first stage, Eqs. (1), (2), and (3) are specified in a T−1 dummies and first differenced form as;

Interactive Model:(A5)${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\mathit{\alpha }}_0{+\mathit{\beta }}_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\mathit{\beta }}_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\mathit{\beta }}_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\mathit{\beta }}_4\mathrm{\Delta }{{\mathrm{lnY}}^2}_{\mathit{it}}+{\mathit{\beta }}_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+\sum _{\mathrm{t}=2}^{\mathrm{T}}{\mathrm{\varnothing }}_{\mathrm{t}}\left({\mathrm{\Delta }\mathrm{D}}_{\mathrm{t}}\right){+\mathrm{\epsilon }}_{\mathit{it}}$${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\mathit{\alpha }}_0{+\mathit{\beta }}_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\mathit{\beta }}_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\mathit{\beta }}_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\mathit{\beta }}_4\mathrm{\Delta }{{\mathrm{lnY}}^2}_{\mathit{it}}+{\mathit{\beta }}_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+\sum _{\mathrm{t}=2}^{\mathrm{T}}{\mathrm{\varnothing }}_{\mathrm{t}}\left({\mathrm{\Delta }\mathrm{D}}_{\mathrm{t}}\right){+\mathrm{\epsilon }}_{\mathit{it}}$

Nonlinear Model:(A6)${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\alpha }_0{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+\sum _{t=2}^T{\mathrm{\varnothing }}_t\left({\mathrm{\Delta }D}_t\right){+\epsilon }_{\mathit{it}}$${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\alpha }_0{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+\sum _{t=2}^T{\mathrm{\varnothing }}_t\left({\mathrm{\Delta }D}_t\right){+\epsilon }_{\mathit{it}}$From the equations above, ${\mathrm{\Delta }\mathrm{D}}_{\mathrm{t}}$${\mathrm{\Delta }\mathrm{D}}_{\mathrm{t}}$ is the first difference order of T−1 dummies, and ${\mathrm{\varnothing }}_{\mathrm{t}}$${\mathrm{\varnothing }}_{\mathrm{t}}$ is its coefficient.

In the second stage, common dynamic processes are formed by transforming ${\mathrm{\varnothing }}_{\mathrm{t}}$${\mathrm{\varnothing }}_{\mathrm{t}}$ to ${\mathrm{P}}_{\mathrm{t}}$${\mathrm{P}}_{\mathrm{t}}$(${\mathrm{\varnothing }}_{\mathrm{t}}$${\mathrm{\varnothing }}_{\mathrm{t}}$ = ${\mathrm{P}}_{\mathrm{t}}$${\mathrm{P}}_{\mathrm{t}}$) as;

Interactive Model:(A7)${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\alpha }_{\mathrm{i}}{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+P_t\left(d_t\right){+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+\epsilon }_{\mathit{it}}$${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\alpha }_{\mathrm{i}}{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+P_t\left(d_t\right){+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+\epsilon }_{\mathit{it}}$(A8)${\mathrm{\Delta lnEFP}}_{\mathit{it}}-P_t\left(d_t\right)={\alpha }_i{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}{+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+\epsilon }_{\mathit{it}}$${\mathrm{\Delta lnEFP}}_{\mathit{it}}-P_t\left(d_t\right)={\alpha }_i{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}{+{\mathrm{\delta }}_1\ln {\left(\mathrm{GI}\ast \mathrm{FG}\right)}_{\mathit{it}}+\epsilon }_{\mathit{it}}$

Nonlinear Model:(A9)${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\alpha }_i{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+P_t\left(d_t\right){+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+\epsilon }_{\mathit{it}}$${\mathrm{\Delta lnEFP}}_{\mathit{it}}={\alpha }_i{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}+P_t\left(d_t\right){+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+\epsilon }_{\mathit{it}}$(A10)${\mathrm{\Delta lnEFP}}_{\mathit{it}}-P_t\left(d_t\right)={\alpha }_{\mathrm{i}}{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}{+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+\epsilon }_{\mathit{it}}$${\mathrm{\Delta lnEFP}}_{\mathit{it}}-P_t\left(d_t\right)={\alpha }_{\mathrm{i}}{+\beta }_1{\mathrm{\Delta lnFG}}_{\mathit{it}}+{\beta }_2{\mathrm{\Delta lnGI}}_{\mathit{it}}+{\beta }_3{\mathrm{\Delta lnY}}_{\mathit{it}}+{\beta }_4\mathrm{\Delta ln}{{\mathrm{Y}}^2}_{\mathit{it}}+{\beta }_5{\mathrm{\Delta lnNRR}}_{\mathit{it}}{+{{\mathrm{\pi }}_1{\mathrm{lnFG}}^2}_{\mathit{it}}+\epsilon }_{\mathit{it}}$where ${\mathrm{d}}_{\mathrm{t}}$${\mathrm{d}}_{\mathrm{t}}$ is the dynamic process.

After the transformations, the elasticities of the predictors are respectively computed as;

Interactive Model:(A11)${\mathit{\beta }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{1\mathrm{i}},{\mathit{\beta }}_{2,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{2\mathrm{i}},{\mathit{\beta }}_{3,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{3\mathrm{i}},{\mathit{\beta }}_{4,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{4\mathrm{i}},{\mathit{\beta }}_{5,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{5\mathrm{i}},{\mathrm{\delta }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{\delta }}_{1\mathrm{i}},$${\mathit{\beta }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{1\mathrm{i}},{\mathit{\beta }}_{2,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{2\mathrm{i}},{\mathit{\beta }}_{3,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{3\mathrm{i}},{\mathit{\beta }}_{4,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{4\mathrm{i}},{\mathit{\beta }}_{5,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{5\mathrm{i}},{\mathrm{\delta }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{\delta }}_{1\mathrm{i}},$

Nonlinear Model:(A12)${\mathit{\beta }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{1\mathrm{i}},{\mathit{\beta }}_{2,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{2\mathrm{i}},{\mathit{\beta }}_{3,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{3\mathrm{i}},{\mathit{\beta }}_{4,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{4\mathrm{i}},{\mathit{\beta }}_{5,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{5\mathrm{i}},{\mathrm{\pi }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{\pi }}_{1\mathrm{i}},$${\mathit{\beta }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{1\mathrm{i}},{\mathit{\beta }}_{2,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{2\mathrm{i}},{\mathit{\beta }}_{3,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{3\mathrm{i}},{\mathit{\beta }}_{4,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{4\mathrm{i}},{\mathit{\beta }}_{5,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathit{\beta }}_{5\mathrm{i}},{\mathrm{\pi }}_{1,\mathrm{A}\mathrm{M}\mathrm{G}}=\frac{\mathrm{I}}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{\pi }}_{1\mathrm{i}},$

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