ESTIMATING COST FUNCTION USING OBSERVED BID … · estimating cost function using observed bid data in wholesale electricity italian market carlo andrea bollino ... n 12.15%cn-cs-s-si-sa

ESTIMATINGCOSTFUNCTIONUSINGOBSERVEDBIDDATAINWHOLESALEELECTRICITYITALIANMARKET

Carlo Andrea Bollino – Paolo Polinori

• Introduction & Aims• Methodology• Data• Empirical results• Conclusions

• Introduction & Aims

Relatively Concentration on the Italian Market in2004 :–HHI on generator capacity : 2675–HHI on net production : 2100–Often, Italian market was split in several

regional zones:• 2 zone market: 1/3 of a year• 3 zone market: ¼ of a year• 4+ zone market : 10% of a year

Higher price in Italy than in other Europeancountries (April – December 2004):

0

20

40

60

80

IPX Omel Northpool EEX APX Powernext EXAA

! /

MW

h

average peak off-peak holidays

• Introduction & AimsIn this paper we recover cost function estimates

for major Italian market partecipants

We use only bids information and marketclearing prices and quantities

• MethodologyHp.: Firm is able to observe the market demand and

the bids submitted by all other participants.

It firstly constructs the realized value of its residualdemand function given market demand and bids

Then selects optimal price associated with residualdemand, and marginal cost

• MethodologyLet C(q) be the total variable cost associated

with output q;we write the profit function as:

f.o.c. to compute an estimate of marginal cost atthe observed market clearing price p* as:

( ) ( ) ( )( ) ( ), ,q DR p p C DR p p PC QC! " "= # $ $ $ #

( )( )( )( )

( )

* *,' ' *,

' *,

p QC DR pC DR p

DR p

!!

!

" "=

• Methodology• DR (p*, e) can be directly computed and p* is

directly observed• We compute residual demand to obtain an

estimate of marginal cost of firm at DR (p*, e).

( )( ) ( )* , *,

' *,DR p DR p

DR p! " "

"!

+ #$

Data

There are 18885 hourly zones in the periodApril-December 2004, yielding an average of2,86 zones per hour (as there are 6600 hours inthe period).

In our analysis we use data referring to realdifferent states of nature aggregation and notto ex post statistical averages.

Elementary zones aggregationZones % Zones %

Sa 24.18% N-Cn 2.83%Si 18.95% ITA 2.54%N 12.15% Cn-Cs-S-Si-Sa 1.99%N-Cn-Cs-S (Peninsula) 11.33% Cs-S-Si 1.97%Cn-Cs-S 6.74% Cs-S 1.85%N-Cn-Cs-S-Si 5.90% Cn 0.37%Cn-Cs-S-Si 3.93% Cs-S-Sa 0.15%N-Cn-Cs-S-Sa 3.30% Cs-S-Si-Sa 0.15%Cn-Cs-S-Sa 1.35% Others 0.03%Relative frequency of each realized aggregation zonePeriod: April – December 2004; Hourly clusters. # 18,885

Gen. #. % Variable Mean Std. Dev Sig. Min Max

ENELP 13198 69.88% Price (ph) 55.66 30.40 * 19.00 300.00Quantities 14601.12 12087.87 890.74 46357.41

ENDE 4009 21.23% Price (ph) 69.05 51.62 22.68 500.00Quantities 2132.65 4027.46 434.00 41250.11

EDIS 590 3.12% Price (ph) 44.06 15.44 *** 26.39 152.00Quantities 7545.75 9327.18 1306.55 40642.54

ENELG 407 2.16% Price (ph) 47.28 26.59 * 24.49 194.97Quantities 10681.82 11339.01 986.31 39745.00

AEM 251 1.33% Price (ph) 42.61 11.72 *** 30.00 80.00Quantities 14590.38 10870.74 1479.96 36638.20

*** significant at 1%, ** significant at 5%;* significant at 10%

Equilibrium price makers (18885 hourly zones)

• Empirical resultsWe present preliminary results applying previous

methodWe use the best response price concept in order

to derive estimates of the cost function for abidder in a competitive electricity market

Figures 1 and 2 show the actual DR faced byENEL in a representative off-peak and on-peakdemand period

Fig.1 DR low period April 16, 2004

0

10

20

30

40

50

60

70

80

0 2000 4000 6000 8000

MWh

Pric

e (!

/MW

h)

Fig. 2.DR peak period July 26, 2004

0

100

200

300

400

500

600

0 2000 4000 6000 8000

MWh

Pric

e (!

/MW

h)

These curves have been smotheed using δ = .25 €

Implied marginal cost (quadratic regressions)0

50

10

01

50

MC

_ene

lp

3342.563

0 2000 4000 6000 8000

DR_ENELP

Plot of MC and DR

50

10

01

50

3342.563

0 2000 4000 6000 8000

DR_ENELP

95% CI

Implied MC

Implied MC

05

01

00

15

0

3342.563

0 2000 4000 6000 8000

DR_ENELP

95% CI On-Peak

Off-Peak

Implied MC Off/On-Peak

Source: Data from GME

Implied Marginal Cost - ENEL - Northern of Italy

05

01

00

15

0

MC

_e

ne

lp

0 20004000 6000800010000

0 20004000 6000800010000

DR_ENELP

Average qh = 18253.4

Plot of MC and DR

40

60

80

10

01

20

14

0

0 2000 4000 6000 800010000

0 2000 4000 6000 800010000

DR_ENELP

95% CI

Implied MC


Implied MC

05

01

00

15

0 0 2000 4000 6000 8000 10000

0 2000 4000 6000 8000 10000

DR_ENELP

95% CI On-Peak

Off-Peak




Implied Marginal Cost - ENEL - Peninsula

05

01

00

15

0

MC

_e

ne

lp

0 5000 10000 15000

0 5000 10000 15000

DR_ENELP


Plot of MC and DR

05

01

00

15

0 0 5000 10000 15000

0 5000 10000 15000

DR_ENELP

95% CI

Implied MC


Implied MC

05

01

00

15

0 0 5000 10000 15000

0 5000 10000 15000

DR_ENELP

95% CI On-Peak

Off-Peak




Implied Marginal Cost - ENEL - Peninsula & Sicily

20

40

60

80

10

0

MC

_e

ne

lp

0 5000 10000

0 5000 10000

DR_ENELP


Plot of MC and DR

40

60

80

10

01

20

0 5000 10000

0 5000 10000

DR_ENELP

95% CI

Implied MC


Implied MC

05

01

00

15

0

0 5000 10000

0 5000 10000

DR_ENELP

95% CI On-Peak

Off-Peak




Implied Marginal Cost - ENEL - Peninsula & Sardinia

05

01

00

15

0

MC

_e

ne

lp

0 2000 4000 6000

0 2000 4000 6000

DR_ENELP


Plot of MC and DR

20

40

60

80

10

01

20 0 2000 4000 6000

0 2000 4000 6000

DR_ENELP

95% CI

Implied MC


Implied MC

05

01

00

15

0

0 2000 4000 6000

0 2000 4000 6000

DR_ENELP

95% CI On-Peak

Off-Peak




Implied Marginal Cost - ENEL - Center-Southern Italy

05

01

00

15

0

MC

_e

ne

lp

0 2000 4000 6000

0 2000 4000 6000

DR_ENELP


Plot of MC and DR

05

01

00

15

02

00

0 2000 4000 6000

0 2000 4000 6000

DR_ENELP

95% CI

Implied MC


Implied MC

-50

05

01

00

15

0 0 2000 4000 6000

0 2000 4000 6000

DR_ENELP

95% CI On-Peak

Off-Peak




Implied Marginal Cost - ENEL - Center-Southern Italy & Sicily

05

01

00

15

0

MC

_e

nd

es

1545.74

0 1000 2000 3000 4000

DR_ENDES

Plot of MC and DR

40

60

80

10

01

20

1545.74

0 1000 2000 3000 4000

DR_ENDES

95% CI

Implied MC

Implied MC

-50

05

01

00

15

0

1545.74

0 1000 2000 3000 4000

DR_ENDES

95% CI On-Peak

Off-Peak



Implied Marginal Cost - ENDESA - Sardinia

05

01

00

15

02

00

MC

_e

dis

1691.2

0 500 1000 1500 2000

DR_EDIS

Plot of MC and DR

60

80

10

01

20 1691.2

0 500 1000 1500 2000

DR_EDIS

95% CI

Implied MC

Implied MC

40

60

80

10

01

20 1691.2

0 500 1000 1500 2000

DR_EDIS

95% CI On-Peak

Off-Peak



Implied Marginal Cost - EDISON - Sicily

Nowthemarginalcostfunctionsofthegeneratorsaresimplifiedtoacubicfunction

Implied marginal cost (cubic regressions)0

50

100

150

3342.563

0 2000 4000 6000 8000

DR_ENELP

Fitted values

Marginal cost

Implied MC

05

010

015

020

0

3342.563

0 2000 4000 6000 8000

DR_ENELP

Fit-On On-Peak

Fit-Off Off-Peak


Cubic regressionSource: Data from GME

Implied Marginal Cost - ENEL - Northern of Italy


50

100

150

0 2000 4000 6000 8000 10000

0 2000 4000 6000 8000 10000

DR_ENELP

Fitted values

Marginal cost


Implied MC

05

010

015

0

0 2000 4000 6000 8000 10000

0 2000 4000 6000 8000 10000

DR_ENELP

Fit-On On-Peak

Fit-Off Off-Peak




Implied Marginal Cost - ENEL - Peninsula


50

100

150

1545.74

0 1000 2000 3000 4000

DR_ENDES

Fitted values

Marginal cost

Implied MC

05

010

015

0

1545.74

0 1000 2000 3000 4000

DR_ENDES

Fit-On On-Peak

Fit-Off Off-Peak



Implied Marginal Cost - ENDESA - Sardinia


50

100

150

200

1691.2

0 500 1000 1500 2000

DR_EDIS

Fitted values

Marginal cost

Implied MC

05

010

015

020

0

1691.195

0 500 1000 1500 2000

DR_EDIS

Fit-On On-Peak

Fit-Off Off-Peak



Implied Marginal Cost - EDISON - Sicily

• Nextgraphsshow:

‐‐quadraticMCfunction

‐‐cubicMCfunction

‐‐lowessregressionofobservation(BW.0.8)

05

01

00

15

0

0 2000 4000 6000 8000DR_ENELP

3342.563

95% CI Quad. MC Cub. MC Obs. Lowess

Implied MC ENEL North

05

01

00

15

00 2000 4000 6000 8000 10000DR_ENELP

95% CI Quad. MC Cub. MC Obs. Lowess


Implied MC ENEL Peninsula

• Conclusions

• Marginal cost can be estimated from observedmarket behavior

• Are these estimates reasonable?• The answer is: yes

Thanks for attentionThanks for attention

... suggestions and questions arewelcome…

[email protected], [email protected]

Documents

ESTIMATING COST FUNCTION USING OBSERVED BID … · estimating cost function using observed bid data in wholesale electricity italian market carlo andrea bollino ... n 12.15%cn-cs-s-si-sa