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

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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.

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Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

NPVit\text{NPV}_{it} coefficientEstimateS.E.p-value
Model with temporal fixed effects2.36×10−62.36\times 10^{-6}0.085×10−60.085\times 10^{-6}≃0\simeq 0
Model without temporal fixed effects2.31×10−62.31\times 10^{-6}0.072×10−60.072\times 10^{-6}≃0\simeq 0
Appendix
Table 1: Sensitivity of the net-present-value coefficient β1\beta_{1} to temporal fixed effects in the discrete hazard model.
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{E} )Neighborhood Radial Ring ( D{D} )MAE (StdMAE)MAPE (StdMAPE) [%]
ModelHome Mkt Value ($’000)Radial Distance Brackets (Miles)NHHNHH
(1)[0, ∞\infty )no neighborhood effects67.726 (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 effects85.001 (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 effects69.011 (4.542)69.627 (4.353)30.889 (2.151)31.177 (2.061)
Appendix
Table 2: Comparison of various model specifications.
ModelEconomic segments EEρ\rhoσξ\sigma_{\xi}α1\alpha_{1}α2\alpha_{2}α3\alpha_{3}
(2)[0,∞)[0,\infty)−- 6.809900.050940.00041  
  ( −- 6.94269, −- 6.70937)(0.04839, 0.05364)(0.00038, 0.00047)  
(4)[0,300),[300,∞)[0,300),[300,\infty)−- 6.791580.050980.000290.00064 
  ( −- 6.89602, −- 6.71202)(0.04851, 0.05368)(0.00026, 0.00032)(0.00059, 0.00070) 
(6)[0,300),[300,600),[600,∞)[0,300),[300,600),[600,\infty)−- 6.819020.051800.000290.000860.00052
  ( −- 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 ρ,σξ,α\rho,\sigma_{\xi},\alpha of Models (2), (4), and (6) to (15).
  Inner ringOuter ring
ModelRings DDurbansuburbanruralurbansuburbanrural
(2)[0,1)[0,1)0.047030.051350.13372   
  (0.02800, 0.08690)(0.04685, 0.05984)(0.11403, 0.19105)   
(4)[0,1)[0,1)0.036110.049320.12135   
  (0.02695, 0.05801)(0.04518, 0.05853)(0.10514, 0.15563)   
(6)[0,1)[0,1)0.037260.046890.10768   
Appendix
Table 4: Posterior mean and 95% credible interval of γ\gamma of Models (2), (4), and (6) to (15).
Figure 4: Stability of the structural parameters across economic-segment and radial-ring specifications.
Specification of h in utilityMAE (StdMAE)MAPE (StdMAPE) [%]
hh31.845 (2.412)15.599 (1.552)
log⁡(1+h)\log(1+h)106.901 (6.648)54.746 (4.221)
h\sqrt{h}74.434 (5.631)37.672 (4.208)
Note: (a) Training periods: 1-33, test periods: 34-38;
(b) In estimation: h^it+1=hit+1\hat{h}_{it+1}=h_{it+1} , in prediction: h^it+1=λih^it\hat{h}_{it+1}=\lambda_{i}\hat{h}_{it} ;
(c) Economic Segments ( E{E} ): [0,300),[300,∞)[0,300),[300,\infty) ;
Appendix
Table 5: Predicted performance of models using alternative function specifications of h in the utility function.
ParameterT=26T=26T=28T=28T=30T=30T=32T=32T=33T=33T=34T=34T=36T=36
ρ\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)
α[0,300K)\alpha_{[0,300\mathrm{K})}0.000400.000390.000420.000330.000290.000280.00040
 (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)
α[300K,∞)\alpha_{[300\mathrm{K},\infty)}0.000230.000180.000250.000650.000640.000760.00088
 (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.
CoefficientsEstimateS.E.p-value
Intercept−7.23-7.231.611.617.34×10−67.34\times 10^{-6}
NPVit\text{NPV}_{it}2.15×10−42.15\times 10^{-4}0.12×10−40.12\times 10^{-4}≃0\simeq 0
NPVHit\text{NPV}_{H_{it}}−9.19×10−6-9.19\times 10^{-6}1.08×10−61.08\times 10^{-6}≃0\simeq 0
HitH_{it}3.57×10−23.57\times 10^{-2}0.18×10−20.18\times 10^{-2}≃0\simeq 0
FootPrint2TreeCoveri\text{FootPrint2TreeCover}_{i}2.93×10−42.93\times 10^{-4}0.72×10−40.72\times 10^{-4}4.81×10−54.81\times 10^{-5}
SunlightReceivedi\text{SunlightReceived}_{i}4.47×10−44.47\times 10^{-4}0.64×10−40.64\times 10^{-4}2.71×10−122.71\times 10^{-12}
Appendix
Table 7: Estimated coefficients of the hazard benchmark model (b).
ModelSpecificationMAEMAPE [%]
(4)HDynamic discrete choice model (best model)31.84515.599
(a)Hazard model (individual level)41.45321.831
(b)Myopic choice model (static NPV logit)78.15843.376
(c)Partially forward-looking model48.16726.352
(d)Bass diffusion model (aggregate data)106.17247.208
Appendix
Table 8: Out-of-sample predictive performance of the benchmark models.
 (1)(2)(3)
Dependent variableAdoptionAdoptionDeviation from budget line
Budget ($ million)94.86  
 (3.15)  
Urban multiplier murbanm_{\mathrm{urban}} −- 544.05−- 141.87
  (9.21)(7.10)
Suburban multiplier msuburbanm_{\mathrm{suburban}} −- 752.4152.74
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 policyBudget ($M)Installed MWCarbon savings
402RSP(32)29.615.7174.2
443RSP(36)32.621.8250.8
484RSP(36)32.627.1347.9
525RSP(36)32.632.3466.5
566RSP(36)32.636.4604.2
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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