Correlation or causation?
Energy consumption is a result of labor applied to tools and technology for production. It is not mere correlation, but it is also not the cause, it is one measurable downstream effect.
China, in fact, used energy consumption as the measure for GDP reporting. For this reason, local leadership in cities and provinces would game the system by running the coal plants at peak and turning on all lights in a city day and night to juice the numbers so they'd show higher GDP (Beijing used to do this before they hosted the Olympics, for example).
In other words, when potential economic growth buds up against energy supply, energy prices rise and they rise non-linearly. This causes a reduction in potential economic growth. If there is a decline in economic growth, then demand falls below supply and prices drop. As prices drop they enable more economic growth.
In other words, the economy grows as much as energy supply allows. A 10% decline in available energy means a 10% decline in GDP. It really is that linear.
