Understanding the householder solar panel consumer: A Markovian model and its societal implications

TL;DR

This paper studies household rooftop PV adoption as a diffusion process shaped by social influence and investment payoffs. It develops two Markovian agent-based models, the second with a procrastination loop via a Planner state, and derives a mean-field ODE system that tracks fractions in each state. Calibrated to Italian data (2006–2020) and used for 2020–2026 scenario analysis, the study shows hyperbolic discounting and present bias can dampen or amplify diffusion depending on policy mix. The findings highlight that commitment devices and social-norm strategies can substantially raise PV uptake and its spillover emissions benefits, informing more effective, behaviorally informed policy portfolios.

Abstract

Household adoption of rooftop photovoltaic (PV) systems is central to the green energy transition, yet diffusion depends on social influence and behavioral biases, as well as payback economics. This study develops a parsimonious Markovian model in which households move sequentially from being unengaged (Carbon) to informed, to planning, and finally to adoption (Green). Transition rates are micro-founded by two mechanisms: (i) social contagion/communication, proxied by the current share of adopters, and (ii) economic profitability, proxied by payback time computed from a Net Present Value framework. Novel to this diffusion setting, bounded rationality is introduced via hyperbolic discounting, creating a procrastination loop that delays adoption even when PV is economically attractive in a long-run perspective. Calibrated on the Italian residential PV diffusion path (2006-2020) and assessed in national and regional applications, the model reproduces observed trajectories and enables forward-looking scenario analysis (2020-2026). Results show that policies yielding similar payback improvements can produce different outcomes once present bias is accounted for and that behaviorally informed intervention are stronger. The findings contribute a micro-to-macro bridge between behavioral economics and technology diffusion modeling and imply that effective policy portfolios (and PV business models) should complement incentives with commitment devices and social-norm peer strategies to accelerate PV uptake and its spillover emissions benefits.

Figures (14)

• Figure 1: Evolution of Italy's renewable electricity production by sources: "Solar" (red line), "Hydro" (blue line), "Wind" (green line) over 2006--2020. Data Source : Terna Spa (https://www.terna.it).
• Figure 2: Evolution of Italy's electricity production, source "Solar", by categories: "Agriculture" (blue line), "Domestic" (black line), "Services" (red line), "Industry" (green line) over 2006--2020. Data Source : GSE (https://www.gse.it/dati-e-scenari/statistiche).
• Figure 3: Pictorial representation of the economic utility in Equation \ref{['eq:econ']} as a function of $n_G(t):=\frac{N_G(X_t)}{N}$ for a fixed $t$ for different discount factors $g^{i}(t, s, n_G(t))$ as defined in Equation \ref{['eq:discountfactor']}.
• Figure 4: Turnkey PV system price per installed W of a PV system over 2007-2020, residential buildings. Data Source : National Survey Report of PV Power Applications in Italy.
• Figure 5: Influence of the weights $w_{\text{ec}}$, $w_{\text{soc}}$ and $w_{\text{irr}}$ obtained by calibrating the model on the $2/3$ of times series of Italy and of the three different regions.

Theorems & Definitions (2)

• Remark 2.1
• Remark 4.1