Discrete Choice Modeling of a Firm’s
Decision to Adopt Photovoltaic Technology
Chrystie Burr
May 2, 2011
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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).
Firm’s Decision in Adopting PV Technology
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Introduction:
Photovoltaic(PV) System diagram
Firm’s Decision in Adopting PV Technology
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Introduction:
What is grid-connected PV?
• Grid-connected solar power system
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Background - U.S. PV Market
Cumulative Installation (1996-2008)
Firm’s Decision in Adopting PV Technology
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Background
Global Market Share
Solar PV Existing Capacity, 2009 (source: REN21)
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Trends in Photovoltaic Application
• Fastest growing energy technology in the last 5 years.
US cum. Installed PV
(2002-2008)
Worldwide cum. Installed PV
(1992-2008)
1400
16000
1200
12000
10000
8000
6000
4000
2000
0
Firm’s Decision in Adopting PV Technology
Installed PV (MW)
Installed PV (MW)
14000
1000
800
600
400
200
0
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Driver for the PV boom
• Lower cost
Average PV Module Cost
1975 - 2006
PV module cost ($/W)
120.00
100.00
80.00
60.00
40.00
20.00
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
0.00
• Government Incentive Programs
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Background- PV Price Trends
• Price of crystalline modules declined by 50-60% from $3.5/W
to $2/W in 2008/2009.
120.00
PV module cost ($/W)
100.00
80.00
60.00
40.00
20.00
Firm’s Decision in Adopting PV Technology
2005
2001
2003
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
0.00
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Incentive Programs in the U.S.
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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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Summary Statistics
Variable
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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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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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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Model
• Firm’s profit function
 iomt
 ijmt  
P
uf
R


P
1


mt
mt   mt   i1mt
 mt

•R: NPV of the future benefit
and costs
•Avoided utility cost
•Production incentive
•FC: Upfront installed cost
Firm’s Decision in Adopting PV Technology

if not installed
if installed
• τuf: Upfront subsidy (% based)
• ξmt: Fixed effect
• f(ε) = eε/(1+ eε )
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Model
if not installed
 iomt
 ijmt  
F
uf
R


P
1


mt
mt   mt   i1mt if installed
 mt

Rmt   iAC CmtAC   PS mtp  X mt
• CAC: Avoided electricity cost for
next 20 years
•Local solar Irradiation
•Electricity price
• τp: Production subsidy
• X: Increased revenue from
improved brand image
Firm’s Decision in Adopting PV Technology

Pmt  Pt AV 1  %W  % L  %code 
• 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
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Estimation
Hierarchical Bayesian approach  iAC  iF  PS
• Let A =  , Bi = [  i
PS
AC
 iF ]T ~ lognormal(b, D), Bi  B  i
• Prior: b ~ N(0, s) s ∞, D ~ IW(3, V0)
• Likelihood:
 e mt  X mti ) 
Smt  P(Y  1 | A, Bi )   
 mt  X mti )  f (i ) di
1  e

• Posterior: K(Bi, b, D| Y)
• Conditional posterior:  K ( Bi | b, D, Y )  P(Yi | Bi ) g ( Bi | b, D)

D
 K (b | Bi i, D, Y ) ~ N (b , )
N

 K ( D | Bi , b, Y ) ~ IW (3  N , V * )
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Estimation
Bayesian Procedure on BLP model
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 Approach
In 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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U.S. Solar Potential Map
Firm’s Decision in Adopting PV Technology