Empirical development of parsimonious model for international diffusion of residential solar

Abstract

We develop a new parsimonious model of residential solar diffusion that, with only two regression parameters and one independent variable, reasonably explains empirical observations. Additional solar customers resulting from an increase in Net Present Value (NPV) are modeled as a normal distribution. This leads to adoption as a function of NPV being the integral of the Gaussian, producing the error function, which demonstrates S-curve behavior commonly seen in technology diffusion. Empirical analysis for five regions (three U.S. states: Arizona, California, and Massachusetts; and two countries: Germany and Japan) from 2005 to 2016 shows a consistent relationship between annual adoption per million households and NPV. Non-linear regression indicates good agreement between data and the error function model, the adoption rate peaking at an NPV of $7100/kW with standard deviation of $4110/kW. Consumer purchases of rooftop solar across multiple regions are explained with a single variable, making this model simpler than traditional diffusion approaches. A novel implication of the model is that the subsidy cost to stimulate additional solar adoption increases as the technology becomes cheaper. This is because the same subsidy is paid to all consumers, including those who would have purchased solar without subsidy.