Accelerating the Adoption of Residential Solar Power Systems: Policy Analysis using a Dynamic Structural Model

Sebastián Souyris; Jason A. Duan; Anantaram Balakrishnan; Varun Rai

econ.EMAug 24, 2026

Accelerating the Adoption of Residential Solar Power Systems: Policy Analysis using a Dynamic Structural Model

Authors: Sebastián Souyris, Jason A. Duan, Anantaram Balakrishnan, Varun Rai

Organizations: Lally School of Management, Rensselaer Polytechnic Institute · McCombs School of Business, The University of Texas at Austin · LBJ School of Public Affairs, The University of Texas at Austin

Abstract

Problem definition: Solar electricity generation is a strategic component of energy portfolios designed to meet growing demand and reduce carbon emissions. Governments and municipalities encourage household photovoltaic (PV) adoption through upfront rebates and tax credits. Limited budgets require principled, data-driven policies that account for the drivers of adoption and the effects of incentives on adoption rates. Methodology/results: We develop a dynamic structural model of residential PV diffusion based on adoption decisions by forward-looking households that weigh the economic trade-offs between installing now and later. Adoption depends on return on investment and influence from neighboring adopters. The model segments households by home value and urbanization level, incorporates unobserved heterogeneity, and captures spatiotemporal installation dynamics. We estimate the model using Bayesian methods and detailed household-level data from Austin, Texas. In out-of-sample tests, it predicts installations more accurately than contemporary alternatives. We simulate counterfactual policies within the dynamic equilibrium of PV diffusion to evaluate rebate designs. The framework can also be adapted to study the adoption of other durable technologies. Managerial implications: A rebate offered for a limited period generates more adoption and emissions reductions than a prolonged, costlier program. This counterintuitive result arises from forward-looking behavior, neighbor influence, and accelerated adoption before the rebate expires. We also evaluate phased reductions and rebates differentiated by household segment. A two-step reduction outperforms multiple small reductions. Geographic differentiation improves policy performance, whereas differentiation by home value offers little advantage over a uniform rebate.

Figures & tables

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

$\text{NPV}_{it}$ coefficient	Estimate	S.E.	p-value
Model with temporal fixed effects	$2.36\times 10^{-6}$	$0.085\times 10^{-6}$	$\simeq 0$
Model without temporal fixed effects	$2.31\times 10^{-6}$	$0.072\times 10^{-6}$	$\simeq 0$

Appendix

Table 1: Sensitivity of the net-present-value coefficient

\beta_{1}

to temporal fixed effects in the discrete hazard model.

Panel of Figure 1 — Figure 1: PV current adopters and potential future adopters in 2013, Austin, TX.

Figure 2: MCMC trace plots of the best model, Model (4)H, structural parameters.

Figure 3: Counterfactual trajectory under the one-step rebate switching policy RSP(40).

	Economic Segment ( ${E}$ )	Neighborhood Radial Ring ( ${D}$ )	MAE (StdMAE)		MAPE (StdMAPE) [%]
Model	Home Mkt Value ($’000)	Radial Distance Brackets (Miles)	NH	H	NH	H
(1)	[0, $\infty$ )	no neighborhood effects	67.726 (5.994)	71.482 (4.974)	29.778 (2.852)	31.552 (2.373)
(2)	[0, $\infty$ )	[0,1)	37.343 (12.247)	32.656 (6.721)	19.314 (6.036)	16.956 (3.496)
(3)	[0,300),[300, $\infty$ )	no neighborhood effects	85.001 (3.871)	85.511 (3.661)	38.144 (1.861)	38.386 (1.764)
(4)	[0,300),[300, $\infty$ )	[0,1)	45.768 (14.155)	31.845 (2.412)	23.407 (6.641)	15.599 (1.552)
(5)	[0,300),[300,600),[600, $\infty$ )	no neighborhood effects	69.011 (4.542)	69.627 (4.353)	30.889 (2.151)	31.177 (2.061)

Appendix

Table 2: Comparison of various model specifications.

Model	Economic segments $E$	$\rho$	$\sigma_{\xi}$	$\alpha_{1}$	$\alpha_{2}$	$\alpha_{3}$
(2)	$[0,\infty)$	$-$ 6.80990	0.05094	0.00041
		( $-$ 6.94269, $-$ 6.70937)	(0.04839, 0.05364)	(0.00038, 0.00047)
(4)	$[0,300),[300,\infty)$	$-$ 6.79158	0.05098	0.00029	0.00064
		( $-$ 6.89602, $-$ 6.71202)	(0.04851, 0.05368)	(0.00026, 0.00032)	(0.00059, 0.00070)
(6)	$[0,300),[300,600),[600,\infty)$	$-$ 6.81902	0.05180	0.00029	0.00086	0.00052
		( $-$ 6.91498, $-$ 6.73623)	(0.04924, 0.05443)	(0.00026, 0.00033)	(0.00081, 0.00093)	(0.00024, 0.00097)

Appendix

Table 3: Posterior mean and 95% credible interval of

\rho,\sigma_{\xi},\alpha

of Models (2), (4), and (6) to (15).

		Inner ring			Outer ring
Model	Rings $D$	urban	suburban	rural	urban	suburban	rural
(2)	$[0,1)$	0.04703	0.05135	0.13372
		(0.02800, 0.08690)	(0.04685, 0.05984)	(0.11403, 0.19105)
(4)	$[0,1)$	0.03611	0.04932	0.12135
		(0.02695, 0.05801)	(0.04518, 0.05853)	(0.10514, 0.15563)
(6)	$[0,1)$	0.03726	0.04689	0.10768

Appendix

Table 4: Posterior mean and 95% credible interval of

\gamma

of Models (2), (4), and (6) to (15).

Figure 4: Stability of the structural parameters across economic-segment and radial-ring specifications.

Note: (a) Training periods: 1-33, test periods: 34-38;
Specification of h in utility	MAE (StdMAE)	MAPE (StdMAPE) [%]
$h$	31.845 (2.412)	15.599 (1.552)
$\log(1+h)$	106.901 (6.648)	54.746 (4.221)
$\sqrt{h}$	74.434 (5.631)	37.672 (4.208)
(b) In estimation: $\hat{h}_{it+1}=h_{it+1}$ , in prediction: $\hat{h}_{it+1}=\lambda_{i}\hat{h}_{it}$ ;
(c) Economic Segments ( ${E}$ ): $[0,300),[300,\infty)$ ;

Appendix

Table 5: Predicted performance of models using alternative function specifications of h in the utility function.

Parameter	$T=26$	$T=28$	$T=30$	$T=32$	$T=33$	$T=34$	$T=36$
$\rho$	$-$ 7.10438	$-$ 7.14538	$-$ 7.19179	$-$ 7.04018	$-$ 6.79158	$-$ 6.76025	$-$ 6.84665
	( $-$ 7.19273, $-$ 7.01396)	( $-$ 7.22766, $-$ 7.07685)	( $-$ 7.26856, $-$ 7.10772)	( $-$ 7.11829, $-$ 6.96704)	( $-$ 6.89602, $-$ 6.71202)	( $-$ 6.82481, $-$ 6.69228)	( $-$ 6.90845, $-$ 6.78334)
$\alpha_{[0,300\mathrm{K})}$	0.00040	0.00039	0.00042	0.00033	0.00029	0.00028	0.00040
	(0.00036, 0.00044)	(0.00036, 0.00043)	(0.00038, 0.00046)	(0.00030, 0.00037)	(0.00026, 0.00032)	(0.00025, 0.00031)	(0.00037, 0.00043)
$\alpha_{[300\mathrm{K},\infty)}$	0.00023	0.00018	0.00025	0.00065	0.00064	0.00076	0.00088
	(0.00017, 0.00031)	(0.00012, 0.00027)	(0.00019, 0.00036)	(0.00060, 0.00070)	(0.00059, 0.00070)	(0.00071, 0.00082)	(0.00085, 0.00090)

Appendix

Table 6: Posterior mean and 95% credible interval of the structural parameters of Model (4)H across expanding estimation windows

Figure 5: Expanding-window estimates of the structural parameters of Model (4)H.

Coefficients	Estimate	S.E.	p-value
Intercept	$-7.23$	$1.61$	$7.34\times 10^{-6}$
$\text{NPV}_{it}$	$2.15\times 10^{-4}$	$0.12\times 10^{-4}$	$\simeq 0$
$\text{NPV}_{H_{it}}$	$-9.19\times 10^{-6}$	$1.08\times 10^{-6}$	$\simeq 0$
$H_{it}$	$3.57\times 10^{-2}$	$0.18\times 10^{-2}$	$\simeq 0$
$\text{FootPrint2TreeCover}_{i}$	$2.93\times 10^{-4}$	$0.72\times 10^{-4}$	$4.81\times 10^{-5}$
$\text{SunlightReceived}_{i}$	$4.47\times 10^{-4}$	$0.64\times 10^{-4}$	$2.71\times 10^{-12}$

Appendix

Table 7: Estimated coefficients of the hazard benchmark model (b).

Model	Specification	MAE	MAPE [%]
(4)H	Dynamic discrete choice model (best model)	31.845	15.599
(a)	Hazard model (individual level)	41.453	21.831
(b)	Myopic choice model (static NPV logit)	78.158	43.376
(c)	Partially forward-looking model	48.167	26.352
(d)	Bass diffusion model (aggregate data)	106.172	47.208

Appendix

Table 8: Out-of-sample predictive performance of the benchmark models.

	(1)	(2)	(3)
Dependent variable	Adoption	Adoption	Deviation from budget line
Budget ($ million)	94.86
	(3.15)
Urban multiplier $m_{\mathrm{urban}}$		$-$ 544.05	$-$ 141.87
		(9.21)	(7.10)
Suburban multiplier $m_{\mathrm{suburban}}$		$-$ 752.41	52.74

Appendix

Table 9: Regression summary of the 27 geographically differentiated rebate policies at period 56.

Figure 6: Home-value differentiated rebate policies at period 56.

Horizon (period)	Years beyond est.	Carbon-max policy	Budget ($M)	Installed MW	Carbon savings
40	2	RSP(32)	29.6	15.7	174.2
44	3	RSP(36)	32.6	21.8	250.8
48	4	RSP(36)	32.6	27.1	347.9
52	5	RSP(36)	32.6	32.3	466.5
56	6	RSP(36)	32.6	36.4	604.2

Appendix

Table 10: Horizon robustness of the one-step cost-effectiveness frontier.

Figure 7: One-step cost-effectiveness frontier at five simulation horizons.

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Sep 4, 2026J/K move · Enter open · S save

Reinforcement Learning for Sequential Solar PV Policy Design under Uncertainty: An Agent-Based Approach

Iias Faiud, Jonaid Shianifar, Michael Schukat, Karl Mason

School of Computer Science, University of Galway Galway, Ireland, H91 TK33

Policy Optimization Reinforcement Learning

Open paper AskPDF arXiv

Designing effective and fiscally sustainable policies for solar photovoltaic (PV) adoption requires balancing adoption gains against public expenditure under uncertainty and heterogeneous decision-making. This study formulates PV policy design as a sequential decision problem and integrates reinforcement learning (RL) with a stochastic agent-based model (ABM) that simulates yearly solar PV adoption under uncertainty. A policymaker agent selects annual incentives, including capital grants, subsidised loan rates, and feed-in tariffs, over a 16-year horizon. Adoption--cost trade-offs are explored by varying policy preferences within a scalarised reward framework. Policies are learned using PPO, SAC, and TD3 and evaluated under stochastic simulation. The results show that this approach produces a clear trade-off structure: the highest-adoption policy (TD3,

w_{\text{cost}}=0.5

) achieves approximately 4,145 adopters at a cost of EUR 41.73 million, while the lowest-cost policy (PPO,

w_{\text{cost}}=2.0

) reduces expenditure to EUR 7.27 million with 2,682 adopters. The balanced policy (PPO,

w_{\text{cost}}=1.6

) achieves 3,495 adopters at a cost of EUR 22.47 million. Across algorithms, consistent trade-off patterns are observed, indicating robustness of the adoption--cost relationship. Compared with static baseline policies, the RL framework explores a broader range of policy configurations. These findings demonstrate the potential of RL as a flexible tool for adaptive policy design under uncertainty.

Abstract

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