Discrete Choice Modeling of a Firm’sDecision to Adopt Photovoltaic Technology

Chrystie BurrMay 2, 2011

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Firm’s Decision in Adopting PV Technology

Research Aims• Develop an understanding of how firms respond

differently to upfront subsidies and production subsidies.

• Develop a policy optimization framework for solar technology (policy target).

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Firm’s Decision in Adopting PV Technology

Introduction:Photovoltaic(PV) System diagram

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Firm’s Decision in Adopting PV Technology

Introduction: What is grid-connected PV?

• Grid-connected solar power system

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Firm’s Decision in Adopting PV Technology

Background - U.S. PV MarketCumulative Installation (1996-2008)

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Firm’s Decision in Adopting PV Technology

Background Global Market Share

Solar PV Existing Capacity, 2009 (source: REN21)

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Firm’s Decision in Adopting PV Technology

Trends in Photovoltaic Application• Fastest growing energy technology in the last 5

years.

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Firm’s Decision in Adopting PV Technology

Driver for the PV boom• Lower cost

• Government Incentive Programs

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Average PV Module Cost 1975 - 2006

PV m

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)

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Firm’s Decision in Adopting PV Technology

Background- PV Price Trends• Price of crystalline modules declined by 50-60% from

$3.5/W to $2/W in 2008/2009.

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Firm’s Decision in Adopting PV Technology

Incentive Programs in the U.S.

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Firm’s Decision in Adopting PV Technology

Data• Annual installed capacity (2002-2008) by states: Larry

Sherwood (IREC)

• Subsidy: Dollar amount recovered from DSIRE database

• Electricity price: EIA

• Solar Irradiation: NREL

• # businesses: US small business admin.

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Firm’s Decision in Adopting PV Technology

Summary StatisticsVariable Mean Std. Dev. Min Max

share 0.18% 0.00459 0 0.302

revenue 28,214 2,145 -319 15,179

upfront % sub. 0.269 0.183 0.1 0.8

upfront (size) sub. 33,438 66,998 0 41,500

elec. price 9.67 3.55 5.8 29.95

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Firm’s Decision in Adopting PV Technology

Assumptions• Potential market: 30%• Annual discount rate: 8%• System lifespan: 20 years• Average PV size: 20kW• Elec. escalation rate: 10 year average• Maintenance cost: $0.01/kWh• Inverter cost: $0.75/W• Annual degradation factor: 1%• Solar electricity conversion factor: 76%• Net metering: null• Company located in the largest metropolitan area in a

state

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Firm’s Decision in Adopting PV Technology

Discrete Choice Model• At each time period, a non-residential unit

(commercial firm) can choose to install an average sized PV panel or not adopt PV technology

• Decision is based on the annual revenue generated by the system and the upfront cost, both affected by the incentive programs.

• The purchasers leave the market.

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Firm’s Decision in Adopting PV Technology

Model• Firm’s profit function

mtimtufmtmt

Pmt

iomtijmt PR 11

if not installed

if installed

• R: NPV of the future benefit and costs

• Avoided utility cost• Production incentive

• FC: Upfront installed cost

• τuf: Upfront subsidy (% based)

• ξmt: Fixed effect

• f(ε) = eε/(1+ eε )

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Firm’s Decision in Adopting PV Technology

Model

mtimtufmtmt

Fmt

iomtijmt PR 11

if not installed

if installed

• CAC: Avoided electricity cost for next 20 years

• Local solar Irradiation• Electricity price

• τp: Production subsidy• X: Increased revenue from

improved brand image

• PAV: Ave. cost of 20kW system• W: State wage deviation from

national mean• L: Learning effect. f(cum. install)• Code: Building codes depend on

seismic activity and hurricane

mtpmt

PSACmt

ACimt XCR codeLWPP AV

tmt %%%1

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Firm’s Decision in Adopting PV Technology

EstimationHierarchical Bayesian approach

®A Ci ;®F

i ;®P S

ACi F

i PS

• Let A = , Bi = [ ]T ~ lognormal(b, D),

• Prior: b ~ N(0, s) s ∞, D ~ IW(3, V0)

• Likelihood:

• Posterior: K(Bi, b, D| Y)

• Conditional posterior:

PS ACi F

i

),3(~),,|(

),(~),,|(

),|()|(),,|(

*VNIWYbBDKNDbNYDiBbK

DbBgBYPYDbBK

i

i

iiii

ii

X

imt dfe

eBAYPSimtXmt

imtmt

)(1

),|1( )

)

ii BB

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Firm’s Decision in Adopting PV Technology

EstimationBayesian Procedure on BLP model

®A Ci ;®F

i ;®P S

Yang, S., Y. Chen, and G. Allenby (2003), ‘Bayesian analysis of simultaneous demand and supply’, Quantitative Marketing and Economics 1.Jiang, R., P. Manchanda, and P. Rossi (2009), ‘Bayesian analysis of random coefficient logit models using aggregate data’, Journal of Econometrics 149(2).

Bayesian Approach GMM ApproachIn addition to the distribution

assumption, need assumption on the unobserved characteristics.

Distribution assumption on the demand function, and on

heterogeneity.Lower mean squared error Higher MSE

Able to conduct inference for model parameters and functions

of model parameters.

Standard errors for these functions

of model parameters require supplemental computations

outside of the estimation algorithm.

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Firm’s Decision in Adopting PV Technology

U.S. Solar Potential Map