A Cybernetic Delay Analysis of the Energy–Economy–Emission Nexus in India via a Bistage Operational Amplifier Network

Abstract

In analyzing the decoupling of emissions from economic growth, current literature foregoes the nonlinear complexities of macroeconomic systems, leading to ineffective energy transition policies, specifically for developing countries. This study focuses on the Indian energy–economy–emission nexus to establish a control system that internalizes inflation, trade openness, and fossil fuel imports with economic growth and macro-emissions to visualize the complex pathways of decoupling. Through long-term cointegration and vector error correction modeling, it was found that GDP and energy affect capital, inflation and energy imports, which are locked in a long-run negative feedback loop that ultimately increases emissions. Capital growth enables decoupling at 0.7% CO2 emissions reduction for every 1% capital growth, while 1% inflation growth inhibits decoupling by increasing CO2 emissions by 0.8%. A cybernetic fractional circuit of R-C elements and operational amplifiers was utilized to examine the delay of pulses from GDP to the loop elements, which revealed that capital is periodic with GDP pulses. However, inflation, being aperiodic with the clock pulses of GDP, causes the pulse-width of capital to decrease and fossil fuel imports to increase. Through the circuital model, it was possible to determine the exact policy intervention schedule in business cycle growth and recession phases that could build clean energy capital and limit inflation-induced recoupling.