Transcript Document

Testing Models of Strategic
Bidding in Auctions:
A Case Study of the Texas
Electricity Spot Market
Ali Hortaçsu, University of Chicago
Steve Puller, Texas A&M
Motivations
1. “Deregulation” of electricity markets
– Optimal mechanism for procurement?
2. Empirical auction literature
– Bid data + equilibrium model  valuation
– Analog in “New Empirical IO”
• Eqbm (p,q) data + demand elasticity + behavioral assumption
 MC
– Can equilibrium models be tested?
• Laboratory experiments
– Electricity markets are a great place to study firm
pricing behavior
– This paper measures deviations from theoretical
benchmark & explores reasons
Texas Electricity Market
• Largest electric grid control area in U.S.
(ERCOT)
• Market opened August 2001
• Incumbents
– Implicit contracts to serve non-switching customers at
regulated price
• Various merchant generators
Electricity Market Mechanics
• Forward contracting
– Generators contract w/ buyers beforehand for a delivery
quantity and price
– Day before production: fixed quantities of supply and
demand are scheduled w/ grid operator
– (Generators may be net short or long on their contract
quantity)
• Spot (balancing) market
– Centralized market to balance realized demand with
scheduled supply
– Generators submit “supply functions” to increase or
decrease production from day-ahead schedule
Balancing Energy Market
• Spot market run in “real-time” to balance supply
(generation) and demand (load)
– Adjusts for demand and cost shocks (e.g. weather, plant
outage)
• Approx 2-5% of energy traded (“up” and “down”)
– “up”  bidding price to receive to produce more
– “down”  bidding price to pay to produce less
• Uniform-price auction using hourly portfolio bids that
clear every 15-minute interval
• Bids: monotonic step functions with up to 40 “elbow
points” (20 up and 20 down)
• Market separated into zones if transmission lines
congested – we focus on uncongested hours
.0004
Quantity Traded in Balancing Market
.0002
0
.0001
Density
.0003
Mean = -24
Stdev = 1068
Min = -3700
25th Pctile = -709
75th Pctile = 615
Max = 2713
-4000
-2000
0
2000
Net Volume Traded in Balancing Market (MW)
4000
Sample: Sept 2001-January 2003, 6:00-6:15pm, weekdays, no transmission congestion
Who are the Players?
Incentives to Exercise Market Power
• Suppose no further contract obligations
upon entering balancing market
• INCremental demand periods
– Bid above MC to raise revenue on
inframarginal sales
– Just “monopolist on residual demand”
• DECremental demand periods
– Bid below MC to reduce output
– Make yourself “short” but drive down the
price of buying your short position
(monopsony)
Empirical Strategy
Price
MR1
Sio (p,QCi)
B
D
MCi(q)
A
QCi
RD1
Quantity
Empirical Strategy
Price
MR2
MR1
Sio (p,QCi)
B
D
MCi(q)
C
A
RD1
RD2
QCi
Quantity
Empirical Strategy
Price
MR2
Sixpo (p,QCi)
MR1
Sio (p,QCi)
B
D
MCi(q)
C
A
RD1
RD2
QCi
Quantity
Reliant on June 4, 2002 6:00-6:15pm
50
45
Reliant’s
Residual Demand
40
Price ($/MWh)
35
Reliant’s
MC
30
25
Ex Post
Optimal Bid
Schedule
Reliant’s
Bid Schedule
20
15
10
5
-2000
-1500
-1000
-500
0
500
Balancing Market Quantity (MW)
1000
1500
Preview of Results
• Largest firm bids close to benchmarks for
optimal bidding
• Small firms significantly deviate, but
there’s some evidence of improvement
over time
• Efficiency losses from “unsophisticated”
bidding at least as large as losses from
“market power”
Methods to Test Expected Profit
Maximizing Behavior
Difficult to compare actual to ex-ante optimal bids
–
Wolak (2000,2001)  solving ex-ante optimal bid strategy
(under equilibrium beliefs about uncertainty) is computationally
difficult
Options
1) Restrict economic environment so ex-post optimal =
ex-ante optimal
•
Intuitively, uncertainty and private information shift
RD in parallel fashion
2) Check (local) optimality of observed bids (Wolak,
2001)
• Do bids violate F.O.C. of Eε[π(p,ε)]?
3) Can simple trading rules improve upon realized
profits?
Uniform-Price Auction Model of ERCOT
• Setup
–
–
–
–
–
Static game, N firms, costs of generation Cit(q)
Contract quantity (QCit) and price (PCit)
~
Total demand D
t  D  t
Generators bid supply functions Sit(p)
Note: in “balancing market” terminology, these bids
take form of INCrements and DECrements from “dayahead” scheduled quantities
• Market-clearing price (pc) given by (removing t
subscript from now on):
N
~
c
S
(
p
)

D
 i
i 1
Model (cont’d)
•
Ex-post profit:
i  Si ( pc ) pc  Ci ( Si ( pc ))  ( pc  PCi )QCi
•
Information Structure
– Ci(q) common knowledge
– Private information:
•
•
QCi
PCi – but does not affect maximization problem
•
Rival contract positions (QC-i) and total demand (ε)
~
– D is unknown, but this is aggregate uncertainty
 important sources of uncertainty from perspective of
bidder i
Sample Genscape Interface
Characterization of Bayesian Nash Equilibrium
Strategies: Si ( p, QCi )
~
~
QCi , D have joint distribution F (QCi , D | QCi ) (possibly correlated)
FollowingWilson's (1979)share auctionmodel,define theprobability
distribution of market- clearing price,conditional on supply function
Sˆi ( p ) and QCi , given thatotherfirmsfollowstrategyprofileS i ( p, QCi ) :
H ( p, Sˆi ( p ))  P r{p c  p QCi , Sˆi ( p )}
~
 P r{ S j ( p, QC j )  Sˆi ( p )  D QCi , Sˆi ( p )}
j i

QC  i 
1{  S j ( p, QC j )  Sˆi ( p )  D   }dF (QCi ,  | QCi )
j i
Equilibrium (cont’d)
Bidders choose supply functions to maximize expected profits
p
 ( p )  C ( S ( p ))  ( p  PC )QC dH ( p, S ( p ); QC )
max
pS
i
i
i
i
i
i
i
 i

Si ( p )
p
If H(.) is differentiable, necessary condition for pointwise
optimality of Si* ( p ):
*
H
(
p
,
S
*
*
S
i ( p ); QCi )
p  Ci( Si ( p ))  ( Si ( p )  QCi )
H p ( p, Si* ( p ); QCi )
Note: also holds under risk aversion (maximizing E (U ( ))
where U   0)
Equilibrium (cont’d)
CLAIM: If we restrict the class of supply functions:
Si ( p )   i ( p )  i ( QCi )
then (ex ante) equilibrium bids are ex post best responses:
RDi ( p )  QCi
p  Ci( S ( p )) 
RDi( p )
*
i
where
RDi ( p )  D( p )   S j ( p )
j i
Computing Ex Post Optimal Bids (Prop 3)
Ex post best response is Bayesian Nash Eqbm
 Uncertainty shifts residual demand parallel in & out
(observed realization of uncertainty provides
“data” on RDi'(p) for all other possible realizations)
 Can trace out ex post optimal/equilibrium bidpoint
for every realization of uncertainty (distribution of
uncertainty doesn’t matter)
Unknown


*
S
i ( p)  QCi
*
p  MCi ( Si ( p)) 

RDi( p)
Unknown
("inverse elasticity rule")
Do We Expect to See Optimal Bidding?
• First year of market
– Some traders experienced while others brought over
from generation and transmission sectors
• Many bidding & optimization decisions being
made
• Real-time information?
– Frequency charts & Genscape sensor data  rival costs
– Aggregate bid stacks with 2-3 day lag  “adaptive
best-response” bidding?
• Is there enough $$ at stake in balancing market?
– Several hundred to several thousand per hour
• “Bounded rationality”
Sample Bidding Interface
Sample Bidder’s Operations Interface
Data (Sept 2001 thru Jan 2003)
• 6:00-6:15pm each day
• Bids
– Hourly firm-level bids
• Demand in balancing market – assumed perfectly
inelastic
• Marginal Costs for each operating fossil fuel unit
• Fuel efficiency – average “heat rates”
• Fuel costs – daily natural gas spot prices & monthly
average coal spot prices
• Variable O&M
• SO2 permit costs
– Each unit’s daily capacity & day-ahead schedule
Measuring Marginal Cost in Balancing Market
• Use coal and gas-fired generating units that are “on” and
the daily capacity declaration
• Calculate how much generation from those units is already
scheduled == Day-Ahead Schedule
Price Residual MC Total MC
Day-Ahead
Schedule
MW
Reliant (biggest seller) Example
Reliant on February 26, 2002 6:00-6:15pm
50
45
40
Residual Demand
Ex-post optimal bid
MC curve
Actual Bid curve
Price ($/MWh)
35
30
25
20
15
10
5
0
-2000
-1500
-1000
-500
0
500
1000
Balancing Market Quantity (MW)
1500
2000
TXU (2nd biggest seller) Example
TXU on March 6, 2002 6:00-6:15pm
50
45
40
Residual Demand
Ex-post optimal bid
MC curve
Actual Bid curve
Price ($/MWh)
35
30
25
20
15
10
5
0
-2000
-1500
-1000
-500
0
500
1000
Balancing Market Quantity (MW)
1500
2000
Guadalupe (small seller) Example
Guadalupe on May 3, 2002 6:00-6:15pm
50
45
40
Price ($/MWh)
35
30
25
20
15
10
Residual Demand
Ex-post optimal bid
MC curve
Actual Bid curve
5
0
-2000
-1500
-1000
-500
0
500
1000
Balancing Market Quantity (MW)
1500
2000
Calculating Deviation from
Optimal Producer Surplus
$
Optimal
Profit  P EPO  qiEPO  TC(qiEPO )  ( P EPO  PC)QCi
Actual
Profit  P BAL  qiBAL  TC(qiBAL )  ( P BAL  PC)QCi
Avoid
BAL
BAL
Profit  PAvoid
 0  TC(0)  ( PAvoid
 PC)QCi
(1) Foregone Profits   Optimal   Actual
 Actual   Avoid
(2) Percent Achieved  Optimal

  Avoid
Testing Expected Profit Maximizing
Behavior
1) Restrict economic environment so ex-post
optimal = ex-ante optimal
2) No restrictions – uncertainty can “shift” and
“pivot” RD
1) Can simple trading rules improve upon realized
profits?
2) Check (local) optimality of observed bids (Wolak,
2001)
“Naïve Best Reply Test” of
Optimality
• Bidders can see aggregate bids with a few
day lag
• Simple trading rule: use bid data from t-3,
assume rivals don’t change bids, and find ex
post optimal bids (under parallel shift
assumption)
• Does this outperform actual bidding?
Generator’s Ex-Ante Problem
• Max Eε[π(p,ε)]
uncertainty (ε) can enter RD(p,ε) very generally
• Wolak test for (local) optimality:
– Ho: Each bidpoint chosen optimally
– Changing the price/quantity of each (pk,qk) will
not incrementally increase profits on average
Test for (Local) Optimality of Bids
Choose bid vector   ( p1, q1, ... pK , qK )
(,  )  RD( p( , ), ) p( , )  C ( S ( p( , ), ))
 ( p( , )  PC)QC
 (,  ) 
  0
E 
 qk 
Moment condition for each bidpoint on day t:
 (,  )  RD
C S  p C S

p( , )  RD( p,  )  QC 

qk
S p  qk S qk
 p
 
H o : Vector of k momentsfor day t  ut  0 ?
T
T
t 1
t 1
T  J T  ([ T1  ut ] ST1 [ T1  ut ]) distributed  k2
Test for (Local) Optimality of Bids
What the Traders Say about Suboptimal Bidding
1. Lack of sophistication at beginning of market
•
Some firms’ bidders have no trading experience; are
employees brought over from generation &
distribution
2. Heuristics
•
•
Most don’t think in terms of “residual demand”
Rival supply not entirely transparent b/c
•
•
•
Eqbm mapping of rival costs to bids too sophisticated
Some firms do not use lagged aggregate bid data
Bid in a markup & have guess where price will be
3. Newer generators
•
If a unit has debt to pay off, bidders follow a formula
of % markup to add
What the Traders Say (cont’d)
4. TXU
•
•
“old school” – would prefer to serve it’s customers
with own expensive generation rather than buy
cheaper power from market
Anecdotal evidence that relying more on market in 2nd
year of market
5. Small players (e.g. munis)
•
•
“scared of market” – afraid of being short w/ high
prices
Don’t want to bid extra capacity into market because
they want extra capacity available in case a unit goes
down
Possible Explanations for Deviations from
Benchmarks
1.
2.
3.
4.
5.
Unmeasured “adjustment costs”
Transmission constraints
Collusion / dynamic pricing
Type of firm
Stakes matter
Adjustment Costs?
1.
Flexible gas-fired units often are marginal
•
70-90% of time for firms serving as own bidders
“Bid-ask” spread smaller for firms closer to benchmark
2.
•
Decreases over time for higher-performing firms
Transmission Constraints?
•
Does bidding strategy from congested hours spillover
into uncongested hours?
•
1 std dev increase in percent congestion  only 3% ↓Pct
Achieved
Collusion?
•
Collusion not consistent with large bid-ask
spreads
–
–
•
Collusion  smaller sales than ex-post optimal
Bid-ask spread  no sales
Would be small(!) players - unlikely
.9
1
Do Stakes Matter?
.5
.6
.7
.8
Reliant *
Bryan**
.4
TXU*
Calpine
.2
.3
City of Austin**
LCRA**
.1
City of Garland**
0
South TX Elec Coop**
0
100
* = Investor Owned Utility
200
300
Volume of Optimal Output
** = Municipal Utility/Cooperative
400
500
Explaining “Percent Achieved” Across Firms
(4) Own Bidders: 1000MWh increase in sales  86 percentage point increase in Pct Achieved
(5) Own Bidders: 1000MWh increase in sales  97 percentage point increase in Pct Achieved
Learning?
Efficiency Losses from Observed Bidding Behavior
• Which source of inefficiency is larger?
– Exercise of market power by large firms?
– Bidding “to avoid the market” by “unsophisticated” firms?
– “Strategic” == top 6 in Pct Achieved
– Total efficiency loss = 27%
– Fraction “strategic” = 19% Fraction “unsophisticated”=81%!!
Conclusions
• Electricity markets are a great “field” setting to
understand firm behavior under uncertainty and
private information
• Stakes appear to matter in strategic sophistication
• Both sophistication (“market power”) and lack of
sophistication (“avoid the market”) contribute to
inefficiency in this market
• Equilibrium bidding models
– For large firms, models closely predict actual bidding
– For small firms/new markets, models less accurate
• Market design
– If strategic complexity imposes large participation
costs, may wish to choose mechanisms with dominant
strategy equilibrium (e.g. Vickrey auction)
The End
Evolution of Bid-Ask Spread