1.5 Canceled: A New Reliability Incentive Month Year Vol Issue H23, L11, L94,
Q41 energy-only markets, ERCOT, orthogonalization, price incentives,
reliability

# Canceled: A New Reliability Incentive for Energy-Only Electricity Markets

Devin Mounts and Robin M. Cross Mounts: Department of Applied Economics;
Oregon State University, 213 Ballard Hall, Corvallis, OR 97331 and Portland
General Electric, 121 SW Salmon St. Portland, OR, 97204.
<EMAIL_ADDRESS>Cross: Dept. of Applied Economics; Oregon State
University, 221B Ballard Hall, Corvallis, OR 97331,
<EMAIL_ADDRESS>Acknowledgments: We extend appreciation to
Severine Borenstein for his market participant response suggestions provided
as part of the Energy, Resources and Environmental Economics Student Seminar
at U.C. Berkeley, which are incorporated as Section V of this paper, Carey
King from the University of Texas Energy Institute and Joshua D. Rhodes from
the University of Texas Webber Energy Group for providing critical background
in ERCOT’s market protocols and data, Ryan King, Pamela Shaw, Jonas Kersulis,
Jian Chen, Zhengguo Chu, Haibo You, and Fred Adadjo from the ERCOT Market
Design Group for their review of market structure assumptions and findings and
William Hogan from Harvard’s Kennedy School for his clarifications on the
ERCOT’s original incentive design and dynamics. We declare no financial
interests related to the research within this paper. Disclaimer: This research
was prepared by Devin Mounts in his personal capacity. The opinions in this
article are the author’s own and do not reflect the view of Portland General
Electric.

###### Abstract

This paper considers the reliability problem in energy-only markets. Following
widespread blackouts in 2011, Texas introduced a reliability price incentive
to attract two GW of net additional natural gas-generating capacity. The
incentive is unusual because energy buyers pay the incentive directly to
producers in a real-time spot market. The program has created $13 billion in
direct payments to generators annually since 2015 and is now being implemented
or considered in several major energy markets in the US and abroad. We assess
the incentive’s impact on the Texas market from three perspectives: First, we
derive the incentive’s equilibrium effect on the electricity market price in a
monopolistic market from first principles using a standard partial equilibrium
economic model. We then empirically test whether the incentive encouraged net
entry into the market or the generating applicant pool, controlling for market
and climatic conditions using monthly capacity data. Finally, we look for
direct evidence of an incentive response among active traders using real-time
market trading data. The three approaches suggest buyers and producers cancel
out the incentive, and the price-only program does not encourage new
generation capacity to enter the market.

Under intense pressure to improve grid reliability following the state-wide
blackouts of 2011, Texas enacted its first producer reliability incentive
program in 2014 (the Incentive). The Incentive pays producers a price premium
that increases as scarcity conditions in the market worsen. It is unique
because buyers pay the price premium directly to producers as a lump sum per
megawatt in real time. The Electric Reliability Council of Texas (ERCOT)
anticipated the Incentive would generate an additional $1.12B in annual energy
profits necessary to replace 8,000 MW of gas generation capacity expected to
retire due to tighter emissions standards and to attract 2,000 MW of net new
capacity (Hogan, 2013, ERCOT, 2011). Since ERCOT’s implementation, the program
has generated an average of $13.3 billion in incentive payments to generators
annually, and several major U.S. wholesale power markets are considering or
implementing a similar buyer-paid incentive approach. However, only 407 MW of
net new capacity has entered the market.111Scarcity pricing models are being
implemented by the Southwest Power Pool, New York Independent System Operator,
Independent System Operator New England, Midcontinent Independent System
Operator, and the Pennsylvania-New Jersey-Maryland Interconnection (PJM)
(Hogan, 2012; Pennsylvania New Jersey Maryland Interconnection, 2023)].

Crampton and Stoft (2006) and Fabra (2018) questioned the potential impact of
short-run payments on long-run capacity growth. Texas reliability is again
under increased scrutiny after ERCOT was forced to conduct the largest rolling
blackout in US history in 2021.222FERC and the N. Am. Elecitric Reliability
Corp., 2021, pg. 9 In this research, we analyze whether the simultaneous tax
and subsidy policy canceled itself out or promoted additional natural gas
capacity as intended.,333Net growth is a result of forecast retirements
(ERCOT, 2011), additional energy payments resulting from policy (Hogan, 2013),
and estimated cost of entry for natural gas generators (S. Newell, K. Spees,
J. Pfeifenberger, R. Mudge, M. DeLucia and R. Carlton, 2012)

The reliability of an electrical system is not only a measure of total grid
capacity but also the availability of that capacity to meet demand when
required. This is made more difficult as the amount of renewable capacity in a
market increases since the reliability contribution of a dispatchable
resource, one that can be turned on and off, such as natural gas, is not equal
to that of an intermittent resource which produces when the weather conditions
allow, such as wind and solar.

Figure 1: Generation by Resource Type for Peak Day of Month in ERCOT

Figure 1 highlights the complementary relationship between renewables and
natural gas generation and the role of readily dispatchable generation from
sources such as natural gas in providing reliability. Here, we see natural gas
and renewable generation during two days in 2022: February (left) and
September (right). In February, total generation peaked in the morning and
again in the evening due to heating demand. As the sun set, generation from
renewables fell by approximately 2,000 MWh, requiring a 3,000 MWh increase
from natural gas to meet evening peak demand. There was a more prominent
single peak in September, driven by cooling demand. Again, as the sun set,
renewable generation subsided, and natural gas generators increased production
to compensate. The mirrored natural gas and renewable generation curves
illustrate each resource’s complementary contribution toward reliability.

Figure 2: Daily Ratio of Reserves to Demand at Peak (A) and Sunset (B) Hours

The challenge of measuring reliability in a market with large quantities of
renewable generation is depicted in Figure 2. Panel A shows the ratio of
reserves to generation in ERCOT at the peak hour of each day from 2014, when
the Incentive was implemented, through 2022.444Daily reserve point estimates
are smoothed using a generalized additive model. The dotted line displays the
upward trend in this ratio at the peak hour of the day, which averages 4:00 pm
in the Summer and 12:30 pm in the Winter. The horizontal line indicates the
policy’s 2,000 MW net growth goal. Reserves surpass this goal in 2021,
suggesting that the policy was successful. Panel B, in contrast, shows the
same ratio at the sunset hour, on average 8:15 pm in the Summer and 5:30 pm in
the Winter. The sunset hour ratio shows a flat-to-declining trend from 2016,
never reaching the additional 2,000 MW of dispatchable reserves marked by the
horizontal line. As suggested in Figure 1, generation from renewables declines
at or near sunset, suggesting Panel B more accurately reflects the changes in
grid reliability over time. However, this illustration is not scientific
because it does not measure how much capacity entered the market and whether
that entry was a result of the policy or other market changes relevant to the
firm’s entry decision, areas we will focus on in this study.

The implications of our research go beyond whether ERCOT’s approach has worked
for Texas. Many large US energy markets are undergoing a rapid energy
transition as 75% of US coal generation is estimated to retire by 2040 to curb
climate change (Davis, Holladay and Sims, 2022). The US’s largest wholesale
power market, Pennsylvania-New Jersey-Maryland Interconnection (PJM),
announced a projected 21% reduction in capacity by 2030 as 40,000 MW of
fossil-fueled generation resources are expected to retire due to environmental
and carbon emissions regulations and industry goals for clean energy
(Pennsylvania New Jersey Maryland Interconnection, 2023). The PJM recently
implemented a price-based policy approach, similar to ERCOT’s, in addition to
a secondary market to promote long-term capacity. Other markets are adopting
ERCOT’s approach to reliability, even though the effect of this policy is
still unknown.

Three features of Texas’ ERCOT market make it a valuable setting for testing
the effect of this policy design. First, the Incentive is the only reliability
policy in ERCOT, where other markets are incorporating this approach in
addition to creating markets specifically to procure additional reserve
generation capacity. Second, ERCOT is not integrated with other US electricity
markets. This lack of integration results in ERCOT relying solely on
generation within its own market, as it cannot import or export large
quantities of power. Finally, supply changes in ERCOT’s generation portfolio
reflect transitions underway in other US markets, as the retirement of coal
facilities and the substantial growth of intermittent renewable resources
cause dispatchable natural gas to shoulder the burden of reliability. These
factors create a unique environment where we can test the impact of the
Incentive on capacity growth in the ERCOT market over the past seven years.

Our research extends the literature in three areas. First, we extend the study
of subsidies and taxation, explored by Jenkin ’s (1871-72) seminal work on
physical neutrality and extended to imperfectly competitive markets by Weyl
and Fabringer (2013).555We refer to the Incentive here as a simultaneous buyer
tax and producer subsidy to frame it in terms of the partial equilibrium
theory results of Jenkin (1871-72) and Weyl and Fabringer (2013), but
alternative terms such as surcharge (Economides and Henriques, 2011), user fee
(Gertler, Locay and Sanderson, 1987), and incentive (Mirrlees, 1976) are also
relevant. We are the first to formally identify and analyze a firm subsidy
paid directly by the consumer in a competitive and monopolistic market. We
develop a theoretical model to formalize the Incentive and demonstrate how it
influences behavior among profit-maximizing market participants. Second, we
extend the literature on energy-only markets, price caps, and reliability
through our empirical analysis of the Incentive’s impact on entry into and
exit from the ERCOT generating pool using a recursive structural model.
Earlier work by Cabral and Riordan (1991) suggested price caps reduce capital
investment in monopolistic markets. Hogan (2005) then proposed a price-only
incentive program to counter under-investment, presented as a solution to
reliability in ERCOT (Hogan, 2012). Crampton and Stoft (2006) critiqued
Hogan’s incentive design, suggesting short-run price incentives alone are too
erratic to support a reliable surplus of supply, and proposed a separate
market for reserve capacity to provide a longer-term incentive. The separate-
market design was simulated for ERCOT by Bajo-Buenestado (2017), who found
increased reliability and prices. Our analysis suggests that the Incentive
does not increase firm profits, does not encourage additional generating
capacity in ERCOT, and has an unintended net negative effect on market prices.
Finally, our findings add to the ongoing examination of reliability and market
power within the ERCOT energy market (Hortaçsu and Puller, 2008; Dyer, 2011;
Newell et al., 2012).

Although we critique the direct consumer payment and price-only aspects of
ERCOT’s Incentive design, we do not suggest that other approaches to
reliability, whether regulated reserve margins or capacity markets, might not
improve reliability in ERCOT. Finally, we do not claim that future reliability
in the market is dependent only on natural gas but rather that ERCOT has
failed to encourage entry from such dispatchable sources through the
Incentive.

The rest of the paper is organized as follows: Section I provides background
on ERCOT’s Incentive and describes the data. Section II presents the partial
equilibrium framework and shows that the Incentive does not influence firm
profits. Section III tests the framework empirically, introducing a structural
model to capture the firm’s entry decision and remove multicollinearity and
then testing the Incentive’s impact, controlling for energy prices, weather
events, and other market factors. Section IV tests for evidence traders lower
bids and asks in response to the Incentive level, as predicted in the partial
equilibrium model, using real-time market data, and Section V concludes.

##  1 Background and Data

###  1.1 Background and Relevant Literature

ERCOT implemented its Incentive in June 2014, as initially proposed by Hogan
(2012), to offset the potential loss of revenue from a newly imposed price cap
(Crampton and Stoft, 2006) and to improve reliability. From Hogan’s analysis,
ERCOT estimated the Incentive would have increased the profitability of a gas-
fueled generator by 17% during 2011, or an additional $21,794 to $125,001 of
profit during the year per generator (Hogan, 2013, pp. 10–11). For comparison,
the estimated cost for a one MW gas generator to enter the market in that same
year was $116,000 (Newell et al., 2012, p. 48).

Since its implementation, we have found no studies that analyze the causal
influence of the Incentive on capacity growth. ERCOT’s internal estimates
suggest a correlation between a higher Incentive and the quantity of reserves
in the market over time. Recent adjustments to the Incentive design are
reported to have improved reserve capacity, as illustrated in Figure 2 panel
A. However, their analysis does not control for economic, climatic, or market
factors that influence capacity growth (ERCOT, 2022).

Several studies have raised concerns over the theoretical justification for
the Incentive design initially outlined by Hogan (2005). Crampton and Stoft
(2006) agree prices are one aspect of an efficient reliability incentive but
argue a price-only incentive does not provide a stable signal of long-term
cost recovery that investors require to enter the market and propose instead a
separate Capacity Market to pay producers to maintain offline reserve
capacity. Bajo-Buenestado (2017) extends the Capacity Market approach by
simulating the impact of offline capacity payments in the ERCOT market setting
and finds these payments would increase reliability in the market and raise
the cost to the consumer. In addition to the literature, we note one concern
an anonymous ERCOT staff member raised during the Incentive design process
pertinent to our examination: that producers may reduce bids to offset the
Incentive (ERCOT, 2013). This concern provides the intuition behind our
theoretical and empirical findings.

###  1.2 Data

Two primary data sets are used for our analysis. First, monthly inventories of
proposed, generating, postponed, and retired generation units are provided by
the US Energy Information Administration (EIA) Form 860M from July 2015
through December 2022. The data provides generator-level information on
capacity, status, fuel source, plant, operator, first operation date,
retirement date, and geo-coordinates for all US plants with more than one MW
of capacity. We narrowed this sample to 2,249 verifiable generators within
ERCOT during the analysis period.666See the appendix for details about sample
construction.

Table 1 summarizes active ERCOT generators by count and capacity in our
sample, grouped into three fuel source categories: Natural Gas, Renewables
(Wind and Solar), and Other (Coal, Nuclear, Hydro, etc.). Using our monthly
observations, we measure the entry and exit of capacity for these three
categories and the generators present in the initial period (July 2015) and
the final period (December 2022). From this information, we can see that the
total capacity in ERCOT increased from 97,654 MW to 125,860 MW for a net
growth of 28,206 MW (entry minus exit), or 29% from 2015. 407 MW of this
growth resulted from the entry of 367 natural gas generator units. These 367
new natural gas generators each have 15 MW of capacity on average, 94 MW
smaller than the average retired. Renewable capacity increased by 31,272 MW,
growing from 15% of total market share in 2015 to 36% by the end of 2022 and
accounting for 80% of entry in ERCOT. Finally, 5,718 MW from Other generators
exited the market, primarily Coal, 60% of the total market exit.

Table 1: Form 860M: ERCOT Active Generators - Entry and Exit Group | Measure | NG | Renewables | Other | Total
---|---|---|---|---|---
Initial Period | Generating Units | 500 | 112 | 476 | 1,088
| Share Total Units | ( 0.46 ) | ( 0.10 ) | ( 0.44 ) | ( 1 )
| Mean MW | 115.09 | 130.08 | 53.89 | 89.92
| Total MW | 57,542.60 | 14,568.50 | 25,543.00 | 97,654.10
| Share Total MW | ( 0.59 ) | ( 0.15 ) | ( 0.26 ) | ( 1 )
Entrants | Generating Units | 367 | 205 | 63 | 635
| Share Total Units | ( 0.58 ) | ( 0.32 ) | ( 0.10 ) | ( 1 )
| Mean MW | 15.43 | 154.44 | 35.65 | 62.17
| Total MW | 5,664.40 | 31,506.00 | 2,246.20 | 39,416.60
| Share Total MW | ( 0.14 ) | ( 0.80 ) | ( 0.06 ) | ( 1 )
Exits | Generating Units | 48 | 3 | 76 | 127
| Share Total Units | ( 0.38 ) | ( 0.02 ) | ( 0.60 ) | ( 1 )
| Mean MW | 109.54 | 78.00 | 75.25 | 88.27
| Total MW | 5,257.90 | 234.00 | 5,718.70 | 11,210.60
| Share Total MW | ( 0.47 ) | ( 0.02 ) | ( 0.51 ) | ( 1 )
Final Period | Generating Units | 819 | 314 | 463 | 1,596
| Share Total Units | ( 0.51 ) | ( 0.2 ) | ( 0.29 ) | ( 1 )
| Mean MW | 70.76 | 146.46 | 47.88 | 79.01
| Total MW | 57,949.10 | 45,840.50 | 22,070.50 | 125,860.10
| Share Total MW | ( 0.46 ) | ( 0.36 ) | ( 0.18 ) | ( 1 )
Values in parenthesis denote share of total

Generator entry is identified for units recorded with either ”Operating” or
”Stand-by/Backup” status during a month more recent than our initial
observation period. Generator exits are identified when the generator’s status
is no longer recorded as ”Operating,” ”Stand-by,” or ”Out of Service, but
expected to return to service in the next calendar year,” i.e., it is recorded
as out of service or retired. By grouping available capacity by the three fuel
source categories, we measure the generating capacity for every month in the
analysis period.

While we can identify when a generator enters operation or retires with dates
recorded in the data, we cannot confidently determine when a unit enters or
exits any of the six applicant pool stages that precede operation. There are
six applicant statuses before operation begins, spanning from ”Planned for
installation, but regulatory approvals not initiated” to ”Construction
Complete, but not yet in commercial operation.” A total of 93% of our sample’s
megawatts from natural gas generators appear in at least one of the six
applicant pool phases before generation. However, only 2% of the megawatts
from these generators appear in the first applicant pool phase. Considering
our inability to track entry into the applicant pool, we focus our empirical
analysis on changes to generating capacity actively operating in the market.
Given that most units appear in at least one phase of the applicant pool
before operating, we consider the sum of all units in any stage of the
applicant pool statuses as a representative measure of the applicant pool in
any given month for the same three fuel source categories, Natural Gas,
Renewables and Other.

The second data set comes from ERCOT’s Real-time Prices Report and the
Historical Real-Time ORDC and Reliability Deployment Price Adders and Reserves
Report, which provides market-level price and generation at fifteen-minute
intervals and supply reserves and the Incentive at five-minute intervals. We
use this data in both of our empirical analyses. First, in Strategy 2, we
calculate monthly statistics from this market data and relate those statistics
to our monthly observations of capacity in ERCOT. Strategy 3 uses the 15- and
5-minute market data to look for real-time trader responses to the Incentive.
Additionally, we use daily economic data from the Bureau of Labor and
Statistics and weather data for Texas from NOAA to calculate monthly economic
and climatic controls and annual Levelized Cost of Electricity data from
Berkeley National Laboratory to control for renewable installation costs.

Table 2 describes the mean values of the ERCOT real-time market data,
including select values of capacity from EIA Form 860M and weather from NOAA.
Statistics are grouped into three Incentive ranges: (1) all intervals, (2)
intervals where the Incentive is inactive, and (3) those where it is active.
Producers receive the Incentive in addition to the Energy Only Price.

The average Incentive was $11.00, $0.00, and $55.31 during All, Inactive, and
Active intervals, respectively. The Incentive is positive (Incentive Active)
in 20% of all intervals. The energy price averaged $30.70, decreasing to
$21.84 during inactive intervals and increasing to $66.38 during active
intervals.

Table 2: Means of ERCOT Real-time Market by Incentive State | All Intervals | Incentive Inactive | Incentive Active
---|---|---|---
| (1) | (2) | (3)
Price - $/MW | 30.70 | 21.84 | 66.38
Incentive Active - share | 0.20 | 0.00 | 1.00
Incentive - $/MW | 11.00 | 0.00 | 55.31
Supply Nat. Gas - GW | 4.76 | 4.29 | 6.66
Supply Renewable - GW | 2.38 | 2.52 | 1.85
Supply Other - GW | 3.70 | 3.59 | 4.15
Capacity Utilization - % | 43.30 | 40.13 | 56.08
Reserves - GW | 14.61 | 15.75 | 10.03
Nat. Gas Capacity - GW | 56.47 | 56.45 | 56.57
Renewable Capacity - GW | 26.78 | 26.48 | 28.01
Other Capacity - GW | 22.12 | 22.16 | 21.98
Cent. Midpoint Temp. - ${}^{\circ}C$ | -0.00 | 0.18 | -0.72
Cent. Midpoint Temp. Sq. - ${}^{\circ}C$ | 43.54 | 41.98 | 49.81
Nat. Gas Price - $/MMBtu | 3.32 | 3.21 | 3.74
Wind speed - Km/hr | 0.88 | 0.99 | 0.45
Year | 2018.66 | 2018.59 | 2018.92
Month | 6.61 | 6.60 | 6.67
Hour | 11.50 | 10.75 | 14.52
Minute | 22.50 | 22.41 | 22.84
Observations | 257,252 | 206,096 | 51,156

Natural gas provided an average of 4.76 GW of supply during all intervals, 44%
of total supply, while renewables provided 2.3 GW of supply, 22% of the total.
During active intervals, supply by natural gas generators increased by 1.90
GW, and supply by renewable generators decreased by 0.53 GW on average. The
average Capacity Utilization, the ratio of demand over demand plus remaining
reserves, was 43%, 40%, and 56% for all inactive and active intervals,
respectively. Reserves averaged 14.61 GW across all intervals and 15.75 GW and
10.03 GW during inactive and active, respectively. Capacity averaged 56.47 GW,
26.78 GW, and 22.12 GW across all intervals for natural gas, renewables, and
other generating sources, respectively, varying only slightly in inactive and
active intervals. The average midpoint temperature was $0.18^{\circ}C$ above
the mean during inactive intervals and $-.72^{\circ}C$ below the mean for
active intervals. The natural gas price increased from $3.21 during inactive
intervals to $3.74 during active intervals. Average wind speeds decrease from
0.99 km/hr during inactive intervals to 0.45 km/hr in active intervals.
Finally, active intervals are approximately 4 hours later in the day on
average than inactive intervals, as the hour of active intervals averages 2:30
pm while inactive intervals average approximately 10:45 am.

Using our data, we will examine whether the Incentive increased natural gas
capacity in ERCOT and how traders responded in real-time when the Incentive
was active. However, before exploring these questions empirically, we check
the policy’s theoretical impact on a profit-maximizing firm’s decision to
enter or exit the market.

##  2 Strategy 1: Theoretical Impact on Market Entry

Figure 2 suggests some market entry has occurred since the beginning of the
Incentive program, but not from dispatchable NG generators initially targeted
by the program and, therefore, not at the critical sunset hour demand. To
explore whether or not the program’s design encourages market entry, we use a
classic partial equilibrium framework and compare the firm’s profit-maximizing
output with and without the Incentive. The Incentive increases as energy
reserves become scarce, that is, as energy generation (demand) grows relative
to total generating capacity (supply). We will consider both the monopoly and
competitive market cases.

$Q$$P$$S$$P$$MC$$MC-S$$P_{P}$$P_{E}$$P_{C}$$Q_{E}$$Q_{S}$Firm subsidy
$S$(a)$0$$Q$$P$$T$$P$$P-T$$MC$$P_{C}$$P_{E}$$P_{P}$$Q_{T}$$Q_{E}$Consumer tax
$T$(b)$0$

Figure 4: Impact on competitive partial equilibrium output $Q$ from a firm
subsidy $S$, panel (a), and consumer tax $T$, panel (b).

Figure 4(a) shows how a unit subsidy $S$ shifts the supply curve $MC$ down by
the subsidy amount, increasing the competitive equilibrium quantity exchanged
from $Q_{E}$ to $Q_{S}$ and raising the producer price received to $P_{P}$.
The consumer pays a price $P_{C}$, which is lower than the original
equilibrium price $P_{E}$ but by less than the full subsidy amount. Consumer
and producer welfare gains are shaded gray and green, respectively.

Panel (b) shows how a unit tax $T$ shifts the aggregate demand curve lower by
the tax amount, lowering equilibrium output to $Q_{T}$ and raising the total
cost to the consumer to $P_{C}$. The producer receives price $P_{P}$, lower
than the original equilibrium price $P_{E}$ but by less than the total tax
amount. Consumer and producer welfare losses are shaded gray and green,
respectively.

It appears the quantity reduction under the tax may fully offset the expansion
under the subsidy. We will formalize this result for the competitive and
monopoly markets in the Lemmas subsection after a few preliminaries.

###  2.1 Preliminaries

Departing from the commonly studied subsidy scenarios (Jenkin, 1871-72), the
consumer pays the ERCOT Incentive directly to the producer, effectively
creating an energy tax $T$ on the consumer and subsidy $S$ to the producer,
the two amounts equal $S=T$.

In the ERCOT real-time energy market, consumers and producers submit bid and
offer schedules, listing prices and quantities, at the beginning of each
15-minute trading period. Clearing prices are calculated, and contracts are
settled at the end of each period. The level of energy scarcity is measured
every five minutes and the Incentive is calculated based on the average of the
last three five-minute scarcity values. In this analysis, we will ignore the
time subscript on the subsidy amount $S$ for two reasons: First, ERCOT’s
15-minute ahead forecast is intended to be accessible to all market
participants and accurate enough to make short-term discrepancies between the
forecasted and actual payments uninteresting; Second, we will show our
equilibrium result does not depend on the specification of the Incentive, so
long as the tax and subsidy amounts remain identical.

In the standard monopoly case, buyers negotiate to purchase quantity $Q$ at a
price $P(Q)$ from a profit-maximizing firm with a cost of production $C(Q)$.
Under the standard partial equilibrium assumptions, the profit $\pi$ for the
firm can be formulated as total revenue less total cost

$\displaystyle\pi=P(Q)Q-C(Q),$

with an equilibrium price solution $P_{E}$ equal to the difference between
marginal cost and marginal revenue,

(1) $\displaystyle P_{E}=C^{\prime}(Q)-P^{\prime}(Q)Q.$

The monopoly price is above marginal cost in proportion to the concavity of
consumer preferences, observable in the balancing equation,

$\displaystyle P_{E}=C^{\prime}(Q)\frac{1}{1+\eta},$

where $\eta$ is the inverted own-price elasticity $1/\epsilon$. Equilibrium
output can be written in closed form:

(2) $\displaystyle Q_{E}=\frac{C^{\prime}(Q)-P(Q)}{P^{\prime}(Q)}.$

In the perfectly competitive case, in contrast, equilibrium price $P_{E}$
cannot be written as a closed form function of $Q$, but equilibrium quantity
satisfies the condition that price equals marginal cost:

$\displaystyle P_{E}=C^{\prime}(Q).$

To examine a subsidy $S$ paid by an external source to the monopoly firm for
each unit of output, the profit function includes revenues from both the
consumer and the subsidy:

(3) $\displaystyle\pi=P(Q)Q+SQ-C(Q).$

The equilibrium price under the subsidy $P_{S}$, paid by the consumer, is now
the difference between marginal cost and marginal revenue, less the subsidy,

$\displaystyle P_{S}=C^{\prime}(Q)-P^{\prime}(Q)Q-S.$

As shown in Figure 4(a), the price paid by the consumer is lower than the non-
subsidized case, in equation (1), but by a smaller amount than the full
subsidy $S$, in proportion to the price elasticity. This can be seen from the
balancing equation,

$\displaystyle P_{S}=C^{\prime}(Q)\frac{1}{1+\eta}-S\frac{1}{1+\eta}.$

Equilibrium output can be expressed in terms of the subsidy,

(4) $\displaystyle
Q_{S}=\frac{C^{\prime}(Q)-P(Q)}{P^{\prime}(Q)}+\frac{S}{P^{\prime}(Q)},$

which is greater than the non-subsidized monopoly quantity in equation (2) for
a positive subsidy in proportion to the concavity of consumer preference.

In the perfectly competitive case, no closed-form solution exists for
equilibrium quantity. Profit is maximized at the quantity that equates the
consumer paid price with marginal cost, less the subsidy:

$\displaystyle P_{S}=C^{\prime}(Q)-S.$

This price is lower than the non-subsidized competitive equilibrium price by
the full subsidy $S$, suggesting the subsidy pass-through to the consumer is
100% (Weyl and Fabringer, 2013).

A tax $T$ levied against the monopoly firm by an external source acts as a
negative subsidy, replacing the subsidy amount $S$ with a negative tax amount
$-T$. Now, the firm pays the production cost and tax:

$\displaystyle\pi=P(Q)Q-C(Q)-TQ.$

The total equilibrium price facing the consumer is higher under the tax

$\displaystyle P_{T}=C^{\prime}(Q)+T-P^{\prime}(Q)Q,$

and quantity is lower

$\displaystyle
Q_{T}=\frac{C^{\prime}(Q)-P(Q)}{P^{\prime}(Q)}-\frac{T}{P^{\prime}(Q)}.$

Fortunately, equilibrium prices $P$ and outputs $Q$ do not depend on which
party physically receives or pays the subsidy or tax. This is the Principle of
Physical Neutrality first examined in competitive markets by Jenkin (1871-72)
and extended to imperfectly competitive markets by Weyl and Fabringer (2013).
This principle can be demonstrated by comparing the profit functions under the
firm subsidy and consumer subsidy cases.

When the consumer receives a subsidy, the monopolistic firm first observes
that consumer demand has been shifted upward by the subsidy, from $P(Q)$ to
$(P(Q)+SQ)$, opposite to the consumer tax case in Figure 4(b). With this in
mind, the profit function is formed:

$\displaystyle\pi=P(Q)Q+SQ-C(Q).$

This matches exactly the objective function in the firm-subsidy model of
equation (3), and the subsidy output solution of equation (4) follows
directly. The principal holds, similarly, for subsidy and taxation in both the
monopoly and competitive cases.

###  2.2 The cancelled subsidy lemmas

We may now turn to the paper’s central question and ask if the Incentive, paid
by consumers to producers, leads to market entry, specifically, should
equilibrium energy capacity increase under the Incentive?

Define the equilibrium price and quantity solution under a simultaneous tax
and subsidy, $P_{ST}$ and $Q_{ST}$, respectively, and the equilibrium solution
pair under no subsidy or tax $P_{E}$ and $Q_{E}$. Under the standard
equilibrium assumptions, the following lemma holds.

Lemma 1: The monopolistic partial equilibrium solution is unchanged by a
fixed, identical, unit subsidy $S$ and tax $T$, regardless of the physically
responsible parties: $Q_{ST}=Q_{E}\>\>\text{and }\>P_{ST}=P_{E}$.

To check this condition, we can form the profit function for a monopoly firm
receiving a subsidy $S$, which is paid directly and instantaneously by a
consumer tax $T$:

$\displaystyle\pi=P(Q)Q+SQ-TQ-C(Q).$

Here, the firm observes that consumer demand has shifted downward by the total
tax $TQ$ and that firm revenues have increased by the subsidy payment $SQ$.

Because the payment is made directly and instantaneously between the two
parties, the tax and subsidy are identical $T=S$, and the two products cancel.
The profit function is simplified to

$\displaystyle\pi=P(Q)Q-C(Q),$

an objective function identical to the standard monopoly problem, with an
identical equilibrium solution pair, $P_{E}$ and $Q_{E}$ from equations (1)
and (2), respectively, demonstrating our result.

The outcome is independent of which entity physically bears the subsidy or
tax, according to the Principle of Physical Neutrality, since the positive and
negative payments are canceled if held by any single party or if the parties
are reversed.

The result also holds for the firm operating in a competitive market, which we
state next.

Lemma 2: The competitive partial equilibrium solution is unchanged by a fixed,
identical, unit subsidy $S$ and tax $T$: $Q_{ST}=Q_{E}\>\>\text{and
}\>P_{ST}=P_{E}$.

The only change for the competitive case is a fixed price $P$ specified in the
profit function:

$\displaystyle\pi=PQ+SQ-TQ-C(Q).$

Finally, the above results hold for any functional form of tax and subsidy,
including uncertain or lagged payments, since the two payments are canceled
under identical specifications. To formalize this, consider subsidy and tax
functions $S(X_{t})$ and $T(X_{t})$, respectively, where $X_{t}$ is a random
variable with the usual triplet ($\Omega,P,\mathscr{F}_{t}$), with $\Omega$
the set of all possible events, $P$ the probability rule, and
$\mathscr{F}_{t}$ the filtration containing all information up to time $t$.
The following then holds.

Lemma 3: The partial equilibrium solution is unchanged by any identical
subsidy and tax functions $S(X_{t})$ and $T(X_{t})$, respectively:
$Q_{ST}=Q_{E}\>\>\text{and }\>P_{ST}=P_{E}$.

To verify, we can reform the profit function for the monopoly firm with
subsidy function $S(X_{t})$, paid for by consumer tax function $T(X_{t})$:

$\displaystyle\pi=P(Q)Q+S(X_{t})-T(X_{t})-C(Q),$

which cancel, so long as $S(X_{t})=T(X_{t})$. Independence from the physically
responsible party follows from Lemma 1 and extends to the competitive market
from Lemma 2.

##  3 Strategy 2: Empirical Impact on Market Entry

The third canceled subsidy lemma suggests the Incentive should not impact
entry into the ERCOT generation market. To test this empirically, we estimate
the Incentive’s direct and total effects using a structural model of the
firm’s decision to enter ERCOT’s applicant pool and eventually proceed into
production.

###  3.1 Model

Before firms introduce generating capacity $G_{t}$ to the market in time $t$,
they must first enter the ERCOT applicant pool $A_{t-n}$ some $n$ months
prior. Firms apply after assessing market and climate conditions $X_{t-n}$ and
the Incentive $I_{t-n}$. Twelve months ($n=12$) is within the time range firms
spend in the pool before either withdrawing from the pool or entering
production.777Many other lags were tested for robustness with little impact on
conclusions; see Variable Lags Appendix for more detail. The Incentive,
observed by prospective firms, is also determined by market and climate
conditions $X_{t-n}$. These three steps in the structural model are then:

(5) $\displaystyle I_{t-12}$
$\displaystyle=\alpha_{X,I}X_{t-12}+\boldsymbol{\upsilon}_{I,\,t-12}$ (6)
$\displaystyle A_{t-12}$
$\displaystyle=\alpha_{X,A}X_{t-12}+\alpha_{I,A}I_{t-12}+\boldsymbol{\upsilon}_{A,\,t-12}$
(7) $\displaystyle G_{t}$
$\displaystyle=\alpha_{X,G}X_{t-12}+\alpha_{I,G}I_{t-12}+\alpha_{A,G}A_{t-12}+\boldsymbol{\upsilon}_{G_{t}}.$

Coefficients are estimated consistently with Ordinary Least Squares (OLS), and
the parameters are interpreted as the usual direct effects. Our coefficient of
interest is the market entry coefficient $\alpha_{G,I}$, representing the
increase in megawatts of generating capacity $G_{t}$ at time $t$ for each
dollar of the Incentive $I_{t-12}$ paid out during period $t-12$, holding all
other variables constant. A positive and significant entry coefficient
estimate would reject the no-entry hypothesis posed by the canceled subsidy
Lemma 3.

Because we expect the applicant pool $A$ to respond causally to the incentive
$I$ and market controls $X$, as in equation (6), we would expect
multicollinearity to reduce statistical significance. In addition, coefficient
signs would be less reliable since coefficient covariance is negative when
controls are correlated. It turns out we can eliminate multicollinearity and
its statistical impacts when we obtain the reduced form.

Solving the system of equations in terms of orthogonal residuals, we find the
reduced form:

(8) $\displaystyle I_{t-12}$
$\displaystyle=\beta_{X,I}X_{t-12}+\boldsymbol{\upsilon}_{I,\,t-12}$ (9)
$\displaystyle A_{t-12}$
$\displaystyle=\beta_{X,A}X_{t-12}+\beta_{I,A}\,\boldsymbol{\upsilon}_{I,\,t-12}+\boldsymbol{\upsilon}_{A,\,t-12}$
(10) $\displaystyle G_{t}$
$\displaystyle=\beta_{X,G}X_{i,t-12}+\beta_{I,G}\,\boldsymbol{\upsilon}_{I,\,t-12}+\beta_{A,G}\,\boldsymbol{\upsilon}_{A,\,t-12}+\boldsymbol{\upsilon}_{G_{i,t}}.$

Coefficients now represent the total effect of each independent variable on
the dependent variable. In our case, the entry coefficient $\beta_{I,G}$ is
the total effect on generating capacity from each Incentive dollar:

(11) $\displaystyle\beta_{I,G}$
$\displaystyle=\alpha_{I,G}+\alpha_{I,A}\,\alpha_{A,G}.$

The total effect of the Incentive consists of its direct effect on generating
capacity $\alpha_{I,G}$, plus its impact on the applicant pool $\alpha_{I,A}$,
moderated by the propensity of applicants to move into production
$\alpha_{A,G}$. A positive and significant total effect estimate of
$\beta_{I,G}$ would also reject the no-entry hypothesis of the canceled
subsidy Lemma 3. However, this would be a weaker indication since rejection
can be due to the Incentive’s direct effect on market entry, its indirect
impact on the applicant pool, or both.

Reduced-form coefficients can be estimated consistently with OLS equation-by-
equation, recursively replacing each of the three variables with the
corresponding residual as shown by Wold (1960) and Pearl (2000). By exploiting
the temporally separated and recursive nature of the structural system and
noticing that the substitution of residuals in the reduced-form system
corresponds to the Gram-Schmidt orthogonalization process, we can go one step
beyond consistency to show that our covariate estimate of $\beta_{I,G}$ in
equation (11) is an unbiased estimate of the total effect
$\alpha_{I,G}+\alpha_{I,A}\,\alpha_{A,G}$, free from multicollinearity, and
more efficient than the OLS estimate.

Assume $X\subseteq\mathcal{R}^{[N\times K]}$ is a full-rank, ordered regressor
matrix including dependent variable $G_{t}=x_{K}$; $X$ has positive degrees of
freedom $N>K$; the error vectors have zero conditional means,
$E[\upsilon_{i}|x_{j}]=0$, $j=1,...,i-1$, and are free of autocorrelation and
heteroscedasticity,
$E[\upsilon_{i}\upsilon_{i}^{\prime}|\mathbf{X}]=\sigma_{i}^{2}\mathbf{I}$.
Referring to the proposed estimation model as Gram-Schmidt least squares
(GSLS), define the GSLS coefficient estimates $c_{i,j}$, OLS coefficient
estimates $b_{i,j}$, and OLS residuals $u_{i}$.

Theorem 1: Under the above assumptions, GSLS estimation of the reduced-form
system in equations (8) - (10) achieves the following properties:

(A) | Regressors are orthogonal, $u_{i}\perp u_{j}$;
---|---
(B) | Coefficients are stable, $Cov[c_{ij},c_{ji}]=0$;
(C) | Coefficients are unbiased, $E[c_{ij}]=\beta_{ij}$; and
(D) | GSLS is more efficient than OLS, $V[c_{ij}]\leq V[b_{ij}]$.

A proof is provided in the appendix.

To avoid endogeneity bias, whenever covariates are determined simultaneously,
such as temperature and wind speed or online and offline capacity, these
covariate groups are regressed upon all prior covariates but not upon one
another. This way, across-group multicollinearity will be removed, and only
within-group multicollinearity will remain. In the following sections, we will
apply this model to all ordered datasets and present total effects from the
GSLS model alongside direct effect estimates from OLS.

###  3.2 Results and discussion - Market Entry

Columns 1 and 2 of Table 3 show direct and total effects for a select set of
covariates on natural gas generation capacity operating in the market. Neither
the direct nor total Incentive effects $\alpha_{I,G}$ and $\beta_{I,G}$,
estimated by the Incentive coefficients, are significant, failing to reject
the canceled subsidy hypothesis of Lemma 3. The only highly significant direct
effect on natural gas capacity is wind speed, where a one km/hr increase in
the 3-month rolling mean (lagged 12 months) causes 2.4 GW of capacity to exit
the market, suggesting competition between wind and natural gas generation.
Wind speed’s total effect on the exit of natural gas capacity is lower than
the direct effect, tempered by downstream economic and market influences, yet
still causes 0.92 GW to exit for each additional average kilometer-per-hour at
99.9% confidence. Increases in Offline Capacity have a positive and somewhat
significant effect, both directly (95% confidence) and in total (99%
confidence). In further examining total effects, inflation reduces natural gas
capacity by 115 MW per inflation percentage point when accounting for
downstream impacts, and the Shadow Price of bringing online one more offline
generating unit increases capacity by 32 MW per $1 increase in marginal
generation cost. Lastly, there is a slightly significant (95% confidence)
positive total effect from increased Capacity Utilization, suggesting that
scarcity, as measured through sustained decreases in reserves, may encourage
the entry of natural gas capacity in total, if not directly.

Table 3: Total Megawatts Generating - Select Covariates Dep. Var.: |  |  |  |
---|---|---|---|---
Generating Cap. (MW) | Natural Gas | Renewables
| Direct | Total | Direct | Total
| (1) | (2) | (3) | (4)
Midpoint Temp. - ∘C 12mo mean | $-202.53$ | $-81.44$ | $77.33$ | $-236.32^{*}$
Midpoint Temp. Sq. - ∘C 12mo Mean | $182.44$ | $155.23^{*}$ | $171.56$ | $324.48^{***}$
Mean Windspeed - km/hr 12mo Mean | $-2,432.79^{***}$ | $-919.20^{***}$ | $-956.74^{*}$ | $-743.13^{***}$
Labor Force Pop. - Millions | $363.92$ | $308.88$ | $99.95$ | $6,591.84^{***}$
Unemp. Rate | $-47.92$ | $-5.49$ | $-22.58$ | $211.92^{**}$
CPI | $-82.50$ | $-115.02^{**}$ | $-30.12$ | $50.35$
Interest Rate | $369.12$ | $368.29$ | $238.81$ | $-1,636.90^{***}$
Cost Wind Installation - $/MWh | $-64.63$ | $-42.05$ | $51.45$ | $-264.90^{***}$
Cost PV Installation - $/MWh | $2.22$ | $37.54$ | $-26.43$ | $136.85^{***}$
Natural Gas Price - $/MMBtu | $-436.63$ | $-17.21$ | $-322.33$ | $112.17$
Online Capacity - GW | $10.44$ | $37.51$ | $103.30$ | $-301.11^{***}$
Offline Capacity - GW | $919.01^{*}$ | $804.84^{**}$ | $-617.20$ | $-665.78^{*}$
Capacity Utilization - % | $475.85$ | $772.47^{*}$ | $-1,162.50^{*}$ | $-1,023.50^{**}$
Shadow Price - $/MW | $4.45$ | $32.20^{*}$ | $-113.66$ | $-30.74^{**}$
Energy Only Price - $/MW | $12.15$ | $3.78$ | $65.68$ | $29.44^{***}$
Incentive - $/MW | $-34.13$ | $-21.80$ | $-51.55^{*}$ | $-24.03$
Change Peaker Net Margin - $/GW | $1,080.57$ | $1,213.13$ | $884.36$ | $-1,326.20$
NG GINI Index | $-72.67$ | $-8.10$ | $-191.19$ | $1.70$
Wind GINI Index | $109.22$ | $165.13$ | $231.34$ | $302.94^{*}$
Renewable Appl. Pool - MW | $-0.08$ | $-0.09$ | $0.35^{*}$ | $0.30^{*}$
NG Appl. Pool - MW | $-0.18$ | $-0.16$ | $-0.59^{***}$ | $-0.69^{***}$
Note: |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

Columns 3 and 4 of Table 3 display the corresponding model output for
renewable generating capacity for comparison. There are two notable results in
comparison to the natural gas segment. First, the Incentive continues to have
a negative and insignificant or weakly significant effect on renewable
capacity entry, supporting the Cancelled Incentive Lemma. Second, many more
coefficients are statistically significant for renewable capacity, suggesting
entry and exit may be less restricted in the renewable market in response to
changing economic and climatic conditions. In total, increased inflation and
installation costs are significant drivers of exit in the renewables market,
while greater population and energy prices appear to encourage entry.
Directly, the NG Applicant Pool coefficient is also negative and significant,
suggesting some crowding out may occur between natural gas and renewables
capacity.

These results suggest that the Incentive and scarcity, more broadly, do not
appear to promote natural gas capacity growth directly. The lack of
responsiveness from the natural gas segment and potential crowding out of
generating renewable capacity motivates our next section, where we will
further examine the effects of the incentive on the applicant pools.

###  3.3 Strategy 2. B: Empirical Impact on the Applicant Pool

Past research has noted the concentration of generating capacity in ERCOT
(Hortaçsu and Puller, 2008; Newell et al., 2012) and questioned the market’s
competitiveness (Dyer, 2011), suggesting the lack of a Capacity Market in
ERCOT results in higher price volatility and less reliability than long-term
capacity incentives (Bajo-Buenestado, 2017). So, we explore whether investors
enter the applicant pool but fail to reach generating status due to factors
beyond the production costs, returns, and incentives captured by our model.
Applicants representing eight GW of natural gas capacity, or about 48% of the
applicant pool, exited before reaching operation. In comparison, only three
GW, or 5%, of the renewable pool exited over the same period. However, these
figures don’t explain why a generator in the applicant pool failed to become
operational.

Columns 1 and 2 of Table 4 compare natural gas application pool total effects
from equation (9) with the generating capacity total effects, already shown in
Column 2 of Table 3. First, the applicant pool appears much more responsive to
drivers of entry and exit. Wind generation continues to compete with natural
gas in the applicant pool, as a one-dollar decrease in the cost of wind
installation results in 0.2 GW of natural gas entry into the pool. Entry into
the natural gas pool also increases with natural gas concentration (NG GINI
Index), at 99.9% confidence, yet fails to become operational (Column 2), as we
saw in Table 3. Finally, the Incentive coefficient $\beta_{I,A}$ is
insignificant consistent with the canceled incentive Lemma 3.

Table 4: Comparison Applicant Pool to Generating - Select Covariates | Natural Gas | Renewables
---|---|---
Dependent Variable: (MW) | Appl. Pool | Gen. Cap. | Appl. Pool | Gen. Cap,
| (1) | (2) | (3) | (4)
Midpoint Temp. - ∘C 12mo mean | $781.47^{***}$ | $-81.44$ | $112.23$ | $-236.32^{*}$
Midpoint Temp. Sq. - ∘C 12mo mean | $48.68$ | $155.23^{*}$ | $291.71^{***}$ | $324.48^{***}$
Mean Wind speed - km/hr 12mo mean | $-1,521.35^{***}$ | $-919.20^{***}$ | $-1,352.60^{***}$ | $-743.13^{***}$
Labor Force Pop. - Millions | $-5,302.81^{***}$ | $308.88$ | $2,984.89^{***}$ | $6,591.84^{***}$
Unemp. Rate | $-252.97^{*}$ | $-5.49$ | $-81.58$ | $211.92^{**}$
CPI | $-39.47$ | $-115.02^{**}$ | $16.67$ | $50.35$
Interest Rate | $1,650.64^{***}$ | $368.29$ | $-1,330.31^{***}$ | $-1,636.90^{***}$
Cost Wind Installation - $/MWh | $297.06^{**}$ | $-42.05$ | $5.38$ | $-264.90^{***}$
Cost PV Installation - $/MWh | $-211.04^{***}$ | $37.54$ | $-22.49$ | $136.85^{***}$
Natural Gas Price - $/MMBtu | $-767.11^{***}$ | $-17.21$ | $227.93$ | $112.17$
Online Capacity - GW | $619.91^{***}$ | $37.51$ | $-63.99$ | $-301.11^{***}$
Offline Capacity - GW | $-2,053.85^{***}$ | $804.84^{**}$ | $-351.79$ | $-665.78^{*}$
Capacity Utilization - % | $368.73$ | $772.47^{*}$ | $-217.99$ | $-1,023.50^{**}$
Shadow Price - $/MW | $40.73^{*}$ | $32.20^{*}$ | $-33.97^{**}$ | $-30.74^{**}$
Energy Only Price - $/MW | $-1.90$ | $3.78$ | $15.53^{*}$ | $29.44^{***}$
Incentive - $/MW | $-31.71$ | $-21.80$ | $19.31$ | $-24.03$
Change Peaker Net Margin - $/GW | $-5,397.12^{***}$ | $1,213.13$ | $-2,601.29^{**}$ | $-1,326.20$
NG GINI Index | $136.93^{***}$ | $-8.10$ | $26.88^{***}$ | $1.70$
Wind GINI Index | $-190.87$ | $165.13$ | $-72.43$ | $302.94^{*}$
Renewable Appl. Pool - MW |  | $-0.09$ |  | $0.30^{*}$
NG Appl. Pool - MW |  | $-0.16$ |  | $-0.69^{***}$
Note: |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

To validate these results, Columns 3 and 4 of Table 4 make the same comparison
between the applicant pool capacity and generating capacity in the renewables
segment. This comparison reinforces the insignificance of the renewable
segment to the Incentive. Further, the applicant pool and generating capacity
respond negatively and significantly to the Shadow Price, contracting by 36 MW
and 31 MW, respectively, for each dollar increase in marginal cost. Growth in
the applicant pool is positive and significant as the concentration of natural
gas resources increases (Column 3). However, similar to natural gas, this
growth is not realized as operational capacity (Column 4).

The results from our comparison of the applicant pool reinforce findings from
Strategy 2, namely, the Incentive is not a significant cause of entry.

##  4 Strategy 3: Market Participant Response

The lack of natural gas entry in response to the Incentive in Strategy 2a and
the negative response in 2b suggest the Incentive fails to attract and may be
discouraging capacity growth. The canceled subsidy Lemma 3 suggests market
participants will optimally lower their bids and offers to offset the
Incentive. But how is this accomplished in practice? ERCOT adds the Incentive
to the energy price at the end of each 15-minute trading period. A perfect
offset would require market participants to have excellent information about
the Incentive and to be able to adjust bids and asks incrementally lower, all
in near real-time. In this section, we empirically test for evidence of a bid
or ask response to the Incentive.

###  4.1 Model

To test whether market participants actively lower their bids, either directly
or indirectly, in response to the Incentive, we will allow for either a fixed
response $\beta_{1}$, an amount by which participants may lower their bid
whenever the Incentive is active, $Incentive_{t}>0$, or a proportional
response $\beta_{2}$, an amount participants may lower their bid for each
dollar paid through the Incentive.

To test for these two possible responses simultaneously, we estimate direct
and total effects for the following model:

(12) $\displaystyle
P_{t}=\beta_{1}\mathbb{1}(Incentive_{t}>0)+\beta_{2}Incentive_{t}+\alpha\textbf{X}_{t}+\epsilon_{t}.$

Here, $P_{t}$ is the clearing price of energy before the Incentive in the
15-minute interval $t$, and $X$ is a vector of annual and monthly fixed
effects and the covariates described in Table 2.

Two extreme trading responses exactly fulfill Lemma 3. A fixed-only response,
in which participants lower their bids by a fixed amount $\beta_{1}=$ $55.31
whenever the Incentive is active, $\mathbb{1}(Incentive_{t}>0)$. This would
offset the average Incentive over all active 15-minute trading intervals with
no proportional response $\beta_{2}=0$. Such a response might be reasonable if
Incentive information is delayed or costly to incorporate into future bids,
but information about the average Incentive is known. Alternatively, in a
proportional-only response, participants would lower their bid by one dollar
for each dollar to be paid out under the Incentive $\beta_{2}=-1$ in the
upcoming 15-minute trading interval. This would exactly offset the Incentive
with no fixed response, $\beta_{1}=0$. This might be reasonable when the
Incentive amounts are known perfectly in real-time and easily incorporated
into the bid-ask schedules. A combination of these two strategies could also
fully cancel out the Incentive in line with Lemma 3.

An imbalance exists between the number of active and inactive intervals in our
data set, as shown in the summary statistics in Table 2. This introduces a
potential weighting error that may bias our OLS estimates (Ruben, 1973). Table
2 shows that the Incentive is active in only 20% of intervals. To check for
potential weighting bias, we rebalance the treatment and control set using a
covariate matching method that minimizes the Mahalanobis distance between the
means and variances of characteristics in the two groups (Dehejia and Wahba,
2002). We then re-estimate equation (12) for the average (direct) treatment
effect (ATET), $\beta_{1}$, with the re-weighted data in Table 6.

###  4.2 Results and discussion

Direct and total effects for the two responses in Equation 12 are presented in
Table 5 for selected covariates with the original observation weighting.

Table 5: Underbidding Direct and Total Effects - Fixed Effects Omitted | Dependent variable:
---|---
| Energy Price
| Direct | Total
| (1) | (2)
Nat. Gas Capacity - GW | $-11.25^{***}$ | $-24.51^{***}$
Renewable Capacity - GW | $-17.15^{***}$ | $-24.28^{***}$
Other Capacity - GW | $-17.58^{***}$ | $67.87^{***}$
Midpoint Temp. | $-2.29^{***}$ | $-2.15^{***}$
Midpoint Temp. Sq. | $0.63^{***}$ | $0.76^{***}$
Wind speed km/hr | $-1.03^{***}$ | $-1.33^{***}$
Natural Gas Price - $/MMBtu | $32.36^{***}$ | $31.01^{***}$
Supply Nat. Gas - GW | $-63.35^{***}$ | $16.37^{***}$
Supply Renewables - GW | $-57.07^{***}$ | $0.63$
Supply Other - GW | $-106.98^{***}$ | $-15.20^{***}$
Reserve Capacity - GW | $36.57^{***}$ | $-7.35^{***}$
Capacity Utilization - % | $31.68^{***}$ | $23.73^{***}$
Incentive Active - Y/N | $-79.97^{***}$ | $-79.13^{***}$
Incentive Payment - $/MW | $-0.05^{***}$ | $-0.05^{***}$
Note: |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

The results suggest market participants may use a mixed strategy of fixed and
proportional bid offsets. The direct fixed offset $\beta_{1}$ (Incentive
Active) is a negative and significant $79.97, with an additional proportional
offset of $0.05 for every dollar increase in the incentive. The combined
direct offset of $82.74 is $27.43 greater than the amount required to fully
offset the average Incentive of $55.31 from Table 2. The total offset of
$79.13 is $23.82 greater than the amount required to match the average
Incentive. The apparent overreaction suggests traders may be highly aware of
the need to cancel out the pending Incentive, in line with Lemma 3, but lack
accurate real-time information about the magnitude and timing of the
Incentive. The $82.74 drop is more in line with the extreme Incentive payouts,
such as those seen during the 2021 Texas energy crises, than with normal
scarcity conditions.888Results for periods excluding Winter Storm Uri and
other outlier events are included in the appendix.

Other dynamics in the Texas energy market appear to function normally.
Additional capacity from both natural gas and renewable sources lowers the
energy price significantly, both directly and in total. Increases in capacity
from Natural Gas and Renewables have a similarly significant and negative
effect on the energy price, with an additional GW of capacity reducing the
energy price by $11.25 and $17.15, respectively. Wind has a significant and
negative impact on the energy price, with a one km/hr increase in wind speed
reducing the energy price by $1.03 per MW. This price-depressing effect of
wind speed increases slightly when accounting for downstream covariates, such
as natural gas price and the Reserve Capacity in the system, reducing the
energy price by $1.33 in total. The market is responsive to natural gas
prices, increasing $32.36 per MW for every $1.00 increase in the price of
natural gas. The total effect is somewhat depressed at $31.01, accounting for
impacts on reserve capacity and other downstream covariates. Scarcity has a
positive and significant effect, increasing the energy price by $31.68 per MW
for every one percentage-point increase in generating capacity utilization.

Table 6: Incentive Active Effect on Energy Price With Matched Data | Coefficient | Std. error | z | P
---|---|---|---|---
Active Incentive | -494.744 | 19.668 | -25.155 | 1.2e-139
| Standardized Differences | Variance Ratio
| Raw | Matched | Raw | Matched
Supply Nat. Gas - GW | 1.124 | 0.170 | 1.726 | 1.176
Supply Renewables - GW | -0.512 | -0.125 | 0.853 | 1.004
Supply Other - GW | 0.645 | 0.095 | 0.997 | 1.014
Capacity Utilization - % | 1.739 | 0.390 | 1.745 | 1.248
Reserve Capacity - GW | -1.592 | -0.405 | 0.853 | 1.232
Nat. Gas Capacity - GW | 0.118 | -0.004 | 1.122 | 0.996
Renewable Capacity - GW | 0.171 | -0.007 | 1.238 | 0.996
Other Capacity - GW | -0.082 | 0.000 | 0.910 | 1.002
Midpoint Temp. - $C^{\circ}$ | -0.134 | -0.020 | 1.175 | 1.021
Natural Gas Price - $/MMBtu | 0.268 | -0.000 | 2.058 | 1.012
Wind speed - Km/hr | -0.218 | -0.011 | 0.909 | 1.017
Year | 0.148 | -0.006 | 1.109 | 0.993
Month | 0.021 | 0.002 | 0.775 | 0.989
Day | -.051 | 0.006 | 1.032 | 1.022
Hour | 0.609 | 0.052 | .519 | 0.980
Minute | 0.026 | 0.007 | 0.984 | 0.999

To check for the potential bias from fewer active Incentive observations,
Table 6 shows the average treatment effect (ATET) of the fixed response when
the Incentive is active (treatment) compared to inactive (control). Matched
standardized differences (differences in means) are near zero except for
Reserve Capacity and Capacity Utilization, which are closely tied to active
Incentive conditions. Matched variance ratios are close to unity, suggesting
that rebalancing reduces most differences between active and inactive
Incentive probability moments despite significant differences in the original
data.

Rebalanced treatment effect estimates cannot be compared directly to the OLS
and GSLS results in Table 5. By rebalancing the observations in the control
and treatment groups, we also rebalance the Incentive amounts paid to the
group, which may be more or less than the $494.74 offset. Rebalancing results
reinforce the idea that traders were aware of the Incentive and lowered prices
by a significant amount when the Incentive was active.

##  5 Conclusion

ERCOT’s policy to ensure reliability in Texas’ energy market aimed to improve
reliability by increasing natural gas generating capacity by 2,000 MW. The
results from our research suggest that the Incentive did not encourage entry
into the Texas energy market and did not contribute to reliability. The
partial equilibrium solution to the Incentive does not raise profits for
generators, as intended, since market participants lower bid and ask prices
and effectively cancel out the Incentive. The theoretical findings are
supported by our causal analysis of generating capacity, which showed the
Incentive did not contribute directly or in total to entry by natural gas
generators. Finally, market participants appear to know and practice the
canceling strategy, lowering bids and asking prices whenever the Incentive is
active. Clearing prices were reduced by more than the actual Incentive value,
suggesting traders were aware of the need to lower prices but may not have had
ready access to complete Incentive information or found implementing finer
price adjustments difficult or costly.

We do not examine how the program was initially designed or why it was
implemented in its current form. Several alternative policies are standard in
energy markets that would avoid the canceling-out effect observed in this
analysis. Due to grid instability, ERCOT has faced pressure to come under
greater regulatory authority from the Federal Energy Regulatory Commission.
The promise of improved reliability from additional natural gas generation
capacity might assuage such pressure. However, the adopted policy’s unusual
self-canceling feature fails to improve pricing, market competition, or grid
reliability.

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##  Appendix A Appendix

This appendix provides additional data discussion, proof of Theorem 1, and
robustness checks. Data and code to replicate the main results can be accessed
at https://github.com/devinmounts/ercot_incentive_effects.

###  A.1 Firm Profits

Figure A1 shows profit margins for six ERCOT firms as reported through annual
SEC filings and fiscal reports. Profit margins are calculated based on
operating revenues minus expenses or earnings before interest, taxes,
depreciation, and amortization (EBITDA) for Texas or ERCOT-specific generation
operations. These firms account for roughly 36% of ERCOT’s natural gas
capacity in 2022. While this is not a scientific analysis, comparing profit
margin to annual Incentive value does not demonstrate a positive relationship.

Figure 3: Firm Profits and Annual Incentive Value

###  A.2 Sample Construction

69% of the 3,845 generators listed on EIA FORM 860M in Texas have null
balancing authority codes at some point in the record during the analysis
period. Of all null values, 92% are concentrated in the first 12 months of the
data. To identify generators within the ERCOT market, we replaced null
balancing authority codes with the balancing authority identified for the same
plant in future observations. Two hundred ninety-eight generators retain null
balancing authority codes. 40% of the generators with remaining null balancing
authority codes are located within ERCOT’s boundary. These 119 generators are
assigned to ERCOT due to their geo-location. Of these 119 generators, 16, 11,
and 9 operating or applicant natural gas, renewable, and other generators,
respectively, come into our analysis. The sample is limited to the 2,249
generators assigned to the ERCOT balancing authority.

###  A.3 Proof of Theorem 1

The proof here is adapted from Cross and Bucolla (2024).

(A) The orthogonality of the regressors is shown by Wong (1935, pp. 57-59).

(B) Stability of coefficients follows directly from their orthogonality (A)
since coefficient covariance

$Cov[c_{ik},c_{jk}]=\sigma_{\upsilon_{k}}^{2}\frac{-r_{u_{i},u_{j}}}{1-r_{u_{i},u_{j}}^{2}}$

is linear in regressor correlation
$r_{u_{i},u_{j}}=u_{i}^{\prime}u_{j}/\surd(u_{i}^{\prime}u_{i}\;u_{j}^{\prime}u_{j})$
and zero for any recursive regressor pair.

(C) Unbiasedness. Coefficients $a_{ij}$ of reduced-form parameter matrix A can
be expressed as the recursive sequence

$a_{ij}=\beta_{ij}+\sum_{n=i+1}^{j-1}a_{in}\beta_{nj},$

for $i<j$, and zero otherwise.

Define vector $k_{i}=u_{i}^{\prime}/(u_{i}^{\prime}u_{i})$ and note that
$k_{i}^{\prime}x_{i}=k_{i}^{\prime}u_{i}=1$.

Now, equivalence in expectation between Gram-Schmidt coefficient matrix $C$
and the reduced-form true, underlying matrix A, $E[c_{ij}]=a_{ij}$, can be
shown recursively, since by assumptions and Theorem 1(A) for each coefficient:

(13) $\displaystyle E[c_{ij}]$ $\displaystyle=E[k_{i}^{\prime}\,x_{j}],$ (14)
$\displaystyle=E[k_{i}^{\prime}(\sum_{n=1}^{j-1}x_{n}\,\beta_{nj}+\upsilon_{j})],$
(15)
$\displaystyle=E[\sum_{n=i}^{j-1}k_{i}^{\prime}\,x_{n}\,\beta_{nj}+k_{i}^{\prime}\,\upsilon_{j}],$
(16) $\displaystyle=\beta_{ij}+\sum_{n=i+1}^{j-1}E[c_{in}]\beta_{nj},$ (17)
$\displaystyle=\beta_{ij}+\sum_{n=i+1}^{j-1}a_{in}\beta_{nj},$

for $i<j$, and zero otherwise. Line (17) holds because $E[c_{ij}]=a_{ij}$
follows directly from (16) for $j=i+1$, proving the $j=i+2$ case, and so forth
through $j=K$.

(D) Gram-Schmidt coefficient variance is lower than OLS. Define (i) $X_{-i}$
as the regressor set $X$ excluding regressor $x_{i}$; (ii) $X_{<i}$ as the
regressor set excluding later-determined regressors $x_{i},...,x_{K}$; (iii)
$B\subseteq\mathcal{R}^{[j-1\times 1]}$ as the OLS coefficient vector; and
(iv) $C_{i}\subseteq\mathcal{R}^{[K\times 1]}$ as the $i^{\text{th}}$ Gram-
Schmidt coefficient vector. Consider the non-trivial case when $\beta_{ij}\neq
0$.

Lemma A1: The coefficient of determination weakly declines as regressors are
excluded:

$\displaystyle R_{x_{i}\;X_{<i}}^{2}\leq R_{x_{i}\;X_{-i}}^{2}.$

This lemma is true for any regressor order, though for convenience, we specify
order-of-exclusion in terms of regressors determined after $x_{i}$. The proof
is standard and omitted here.

The variance of OLS coefficient $b_{ij}$ is a function of the $i^{\text{th}}$
diagonal element of the variance-covariance matrix, which can be expressed by
the Schur Complement (see Zhang, 2010), in terms of the $j^{th}$ regression
coefficient of determination:

$\displaystyle Var[b_{ij}]$
$\displaystyle=\sigma_{\upsilon_{u_{j}}}(X^{\prime}X)_{ii}^{-1},$
$\displaystyle=\sigma_{\upsilon_{u_{j}}}(x_{i}^{\prime}x_{i}-B_{-i}^{\prime}(X_{-i}^{\prime}X_{-i})B_{-i})^{-1},$
$\displaystyle=\sigma_{\upsilon_{u_{j}}}(x_{i}^{\prime}x_{i}(1-R_{x_{i}\;X_{-i}}^{2}))^{-1}.$

The variance of Gram-Schmidt coefficient $c_{ij}$ is by 1(A) a function of the
residual $u_{i}$, which by 1(A) and Lemma A1 is:

$\displaystyle Var[c_{ij}]$
$\displaystyle=\sigma_{\upsilon_{u_{j}}}(u_{i}^{\prime}u_{i})^{-1},$
$\displaystyle=\sigma_{\upsilon_{u_{j}}}(x_{i}^{\prime}x_{i}-C_{i}^{\prime}(X^{\prime}X)C_{i})^{-1},$
$\displaystyle=\sigma_{\upsilon_{u_{j}}}(x_{i}^{\prime}x_{i}(1-R_{x_{i}\;X_{<i}}^{2}))^{-1},$
$\displaystyle\leq\sigma_{\upsilon_{u_{j}}}(x_{i}^{\prime}x_{i}(1-R_{x_{i}\;X_{-i}}^{2}))^{-1}.$

The result holds with strict inequality for $i=1,...j-2$ and with strict
equality for $i=j-1$ because the excluded regressor set is identical between
the terminal Gram-Schmidt and the OLS coefficient.

###  A.4 Full Regression Results

Table 7: Total Megawatts Generating - Full Covariates Dep. Var.: |  |  |  |
---|---|---|---|---
Generating Cap. (MW) | Natural Gas | Renewables
| Direct | Total | Direct | Total
| (1) | (2) | (3) | (4)
2022-year | $7,842.43$ | $2,846.69^{***}$ | $20,310.79^{***}$ | $25,566.32^{***}$
2021-year | $6,377.75$ | $2,421.75^{***}$ | $16,632.67^{***}$ | $18,388.01^{***}$
2020-year | $5,418.43$ | $2,049.98^{***}$ | $13,294.30^{***}$ | $12,068.58^{***}$
2019-year | $3,308.18$ | $886.71^{***}$ | $9,810.73^{***}$ | $7,760.83^{***}$
2018-year | $2,902.03$ | $618.95^{***}$ | $6,419.09^{***}$ | $4,900.03^{***}$
2017-year | $1,569.90$ | $682.33^{***}$ | $2,737.63^{**}$ | $2,488.76^{***}$
12-month | $1,305.20$ | $528.36^{**}$ | $3,079.93^{***}$ | $4,302.72^{***}$
11-month | $717.79$ | $488.62^{**}$ | $2,646.77^{**}$ | $3,233.86^{***}$
10-month | $185.83$ | $449.29^{**}$ | $3,141.17^{**}$ | $2,915.30^{***}$
9-month | $-45.64$ | $416.27^{*}$ | $3,135.82^{*}$ | $2,602.40^{***}$
8-month | $-154.38$ | $399.19^{*}$ | $2,793.48^{*}$ | $2,333.20^{***}$
7-month | $-1.57$ | $382.39^{*}$ | $2,052.31^{*}$ | $1,981.36^{***}$
6-month | $408.58$ | $180.13$ | $1,166.16$ | $1,546.45^{***}$
5-month | $283.63$ | $-153.82$ | $182.47$ | $886.42^{***}$
3-month | $-622.97$ | $-267.15$ | $206.07$ | $477.22^{**}$
4-month | $-169.27$ | $-215.15$ | $65.38$ | $622.58^{***}$
2-month | $-381.80$ | $-87.70$ | $295.95$ | $179.55$
Midpoint Temp. - ∘C 12mo mean | $-202.53$ | $-81.44$ | $77.33$ | $-236.32^{*}$
Midpoint Temp. Sq. - ∘C 12mo Mean | $182.44$ | $155.23^{*}$ | $171.56$ | $324.48^{***}$
Mean Wind speed - km/hr 12mo mean | $-2,432.79^{***}$ | $-919.20^{***}$ | $-956.74^{*}$ | $-743.13^{***}$
Labor Force Pop. - Millions | $363.92$ | $308.88$ | $99.95$ | $6,591.84^{***}$
Unemp. Rate | $-47.92$ | $-5.49$ | $-22.58$ | $211.92^{**}$
CPI | $-82.50$ | $-115.02^{**}$ | $-30.12$ | $50.35$
Interest Rate | $369.12$ | $368.29$ | $238.81$ | $-1,636.90^{***}$
Cost Wind Installation - $/MWh | $-64.63$ | $-42.05$ | $51.45$ | $-264.90^{***}$
Cost PV Installation - $/MWh | $2.22$ | $37.54$ | $-26.43$ | $136.85^{***}$
Natural Gas Price - $/MMBtu | $-436.63$ | $-17.21$ | $-322.33$ | $112.17$
Online Capacity - GW | $10.44$ | $37.51$ | $103.30$ | $-301.11^{***}$
Offline Capacity - GW | $919.01^{*}$ | $804.84^{**}$ | $-617.20$ | $-665.78^{*}$
Capacity Utilization - % | $475.85$ | $772.47^{*}$ | $-1,162.50^{*}$ | $-1,023.50^{**}$
Shadow Price - $/MW | $4.45$ | $32.20^{*}$ | $-113.66$ | $-30.74^{**}$
Energy Only Price - $/MW | $12.15$ | $3.78$ | $65.68$ | $29.44^{***}$
Incentive - $/MW | $-34.13$ | $-21.80$ | $-51.55^{*}$ | $-24.03$
Change Peaker Net Margin - $/GW | $1,080.57$ | $1,213.13$ | $884.36$ | $-1,326.20$
NG GINI Index | $-72.67$ | $-8.10$ | $-191.19$ | $1.70$
Wind GINI Index | $109.22$ | $165.13$ | $231.34$ | $302.94^{*}$
Renewable Appl. Pool - MW | $-0.08$ | $-0.09$ | $0.35^{*}$ | $0.30^{*}$
NG Appl. Pool - MW | $-0.18$ | $-0.16$ | $-0.59^{***}$ | $-0.69^{***}$
Mean Status Phase - Renewables | $-4.02$ | $-4.02$ | $661.84$ | $661.84$
Mean Status Phase - NG | $-152.18$ | $-152.18$ | $617.50$ | $617.50$
Constant | $67,125.29^{*}$ | $56,893.43^{***}$ | $29,068.73$ | $28,993.32^{***}$
Observations | 78 | 78 | 78 | 78
R2 | 0.96 | 0.96 | 1.00 | 1.00
Adjusted R2 | 0.92 | 0.92 | 1.00 | 1.00
Note: $R^{2}$ values for Renewables |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001
shown as 1 due to rounding. |

Table 8: Comparison Application Pool to Generating - Full Covariates | Natural Gas | Renewables
---|---|---
Dependent Variable: (MW) | Appl. Pool | Gen. Cap. | Appl. Pool | Gen. Cap,
| (1) | (2) | (3) | (4)
2022-year | $-4,006.19^{***}$ | $2,846.69^{***}$ | $9,548.61^{***}$ | $25,566.32^{***}$
2021-year | $-2,340.79^{***}$ | $2,421.75^{***}$ | $4,398.01^{***}$ | $18,388.01^{***}$
2020-year | $-117.62$ | $2,049.98^{***}$ | $2,086.68^{***}$ | $12,068.58^{***}$
2019-year | $2,538.28^{***}$ | $886.71^{***}$ | $2,162.48^{***}$ | $7,760.83^{***}$
2018-year | $3,907.97^{***}$ | $618.95^{***}$ | $2,135.86^{***}$ | $4,900.03^{***}$
2017-year | $4,048.45^{***}$ | $682.33^{***}$ | $1,804.40^{***}$ | $2,488.76^{***}$
12-month | $-703.11^{**}$ | $528.36^{**}$ | $1,612.50^{***}$ | $4,302.72^{***}$
11-month | $-671.70^{*}$ | $488.62^{**}$ | $1,278.86^{***}$ | $3,233.86^{***}$
10-month | $-592.84^{*}$ | $449.29^{**}$ | $968.80^{***}$ | $2,915.30^{***}$
9-month | $-516.51$ | $416.27^{*}$ | $844.23^{***}$ | $2,602.40^{***}$
8-month | $-1,130.32^{***}$ | $399.19^{*}$ | $678.61^{***}$ | $2,333.20^{***}$
7-month | $-1,571.52^{***}$ | $382.39^{*}$ | $354.18^{*}$ | $1,981.36^{***}$
6-month | $-341.24$ | $180.13$ | $297.82$ | $1,546.45^{***}$
5-month | $-306.24$ | $-153.82$ | $256.02$ | $886.42^{***}$
3-month | $-247.32$ | $-267.15$ | $-16.52$ | $477.22^{**}$
4-month | $-268.91$ | $-215.15$ | $169.94$ | $622.58^{***}$
2-month | $-133.56$ | $-87.70$ | $-96.47$ | $179.55$
Midpoint Temp. - ∘C 12mo mean | $781.47^{***}$ | $-81.44$ | $112.23$ | $-236.32^{*}$
Midpoint Temp. Sq. - ∘C 12mo mean | $48.68$ | $155.23^{*}$ | $291.71^{***}$ | $324.48^{***}$
Mean Wind speed - km/hr 12mo mean | $-1,521.35^{***}$ | $-919.20^{***}$ | $-1,352.60^{***}$ | $-743.13^{***}$
Labor Force Pop. - Millions | $-5,302.81^{***}$ | $308.88$ | $2,984.89^{***}$ | $6,591.84^{***}$
Unemp. Rate | $-252.97^{*}$ | $-5.49$ | $-81.58$ | $211.92^{**}$
CPI | $-39.47$ | $-115.02^{**}$ | $16.67$ | $50.35$
Interest Rate | $1,650.64^{***}$ | $368.29$ | $-1,330.31^{***}$ | $-1,636.90^{***}$
Cost Wind Installation - $/MWh | $297.06^{**}$ | $-42.05$ | $5.38$ | $-264.90^{***}$
Cost PV Installation - $/MWh | $-211.04^{***}$ | $37.54$ | $-22.49$ | $136.85^{***}$
Natural Gas Price - $/MMBtu | $-767.11^{***}$ | $-17.21$ | $227.93$ | $112.17$
Online Capacity - GW | $619.91^{***}$ | $37.51$ | $-63.99$ | $-301.11^{***}$
Offline Capacity - GW | $-2,053.85^{***}$ | $804.84^{**}$ | $-351.79$ | $-665.78^{*}$
Capacity Utilization - % | $368.73$ | $772.47^{*}$ | $-217.99$ | $-1,023.50^{**}$
Shadow Price - $/MW | $40.73^{*}$ | $32.20^{*}$ | $-33.97^{**}$ | $-30.74^{**}$
Energy Only Price - $/MW | $-1.90$ | $3.78$ | $15.53^{*}$ | $29.44^{***}$
Incentive - $/MW | $-31.71$ | $-21.80$ | $19.31$ | $-24.03$
Change Peaker Net Margin - $/GW | $-5,397.12^{***}$ | $1,213.13$ | $-2,601.29^{**}$ | $-1,326.20$
NG GINI Index | $136.93^{***}$ | $-8.10$ | $26.88^{***}$ | $1.70$
Wind GINI Index | $-190.87$ | $165.13$ | $-72.43$ | $302.94^{*}$
Renewable Appl. Pool - MW |  | $-0.09$ |  | $0.30^{*}$
NG Appl. Pool - MW |  | $-0.16$ |  | $-0.69^{***}$
Mean Status Phase - Renewables |  | $-4.02$ |  | $661.84$
Mean Status Phase - NG |  | $-152.18$ |  | $617.50$
Constant | $7,080.37^{***}$ | $56,893.43^{***}$ | $4,699.32^{***}$ | $28,993.32^{***}$
Observations | 78 | 78 | 78 | 78
R2 | 0.99 | 0.96 | 0.99 | 1.00
Adjusted R2 | 0.98 | 0.92 | 0.99 | 1.00
Note: $R^{2}$ values for Renewables |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001
shown as 1 due to rounding. |

###  A.5 Additional Robustness Checks

A.5.1 Autocorrelation

When autocorrelation is present, coefficient estimates remain unbiased but no
longer achieve minimum variance. To test for the presence and impact of
autocorrelation, we run a Generalized Least Squares model (Goldberger, 1962)
with a lagged error term of one-period (AR1) and 10-periods (AR10). Results
are compared in Tables 9, 10, and 14. Positive first-order autocorrelation is
detected with a coefficient for the lagged error of 0.86 and 0.67 in the two
models, respectively, both significant at the 0.1% confidence level,
suggesting trader pricing errors are persistent. The incentive coefficient of
interest remains negative and significant across all models.

Table 9: AR1 Underbidding Direct and Total Effects - Omitting FE Dependent variable: | Energy Price
---|---
| Direct | Total
| (1) | (2)
Nat. Gas Capacity - GW | $-10.71^{***}$ | $-24.51^{***}$
Renewable Capacity - GW | $-21.04^{***}$ | $-24.28^{***}$
Other Capacity - GW | $-19.41^{***}$ | $67.87^{***}$
Midpoint Temp. - ∘C | $-2.38^{***}$ | $-2.15^{***}$
Midpoint Temp. Sq. - ∘C | $0.68^{***}$ | $0.76^{***}$
Wind speed - Km/hr | $-1.17^{***}$ | $-1.33^{***}$
Natural Gas Price - $/MMBtu | $36.21^{***}$ | $31.01^{***}$
15min AR Error | $0.86^{***}$ | $0.86^{***}$
Supply Nat. Gas - GW | $-51.02^{***}$ | $16.14^{***}$
Supply Renewables - GW | $-44.10^{***}$ | $0.68^{***}$
Supply Other - GW | $-93.28^{***}$ | $-15.24^{***}$
Reserve Capacity - GW | $30.46^{***}$ | $-7.09^{***}$
Capacity Utilization - % | $25.65^{***}$ | $22.86^{***}$
Incentive Active - Y/N | $-14.07^{***}$ | $-13.31^{***}$
Incentive Payment - $/MW | $-0.09^{***}$ | $-0.09^{***}$
Constant | $441.55^{***}$ | $30.70^{***}$
Observations | 257,251 | 257,251
R2 | 0.82 | 0.82
Adjusted R2 | 0.82 | 0.82
Note:Excludes Fixed Effects |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

Table 10: AR10 Underbidding Direct and Total Effects - Omitting FE | Dependent variable:
---|---
| Energy Price
| (1) | (2)
Nat. Gas Capacity - GW | $-11.54^{***}$ | $-24.52^{***}$
Renewables Capacity - GW | $-22.78^{***}$ | $-24.28^{***}$
Other Capacity - GW | $-19.02^{***}$ | $67.89^{***}$
120hr AR Error | $-0.01^{***}$ | $0.01^{***}$
96hr AR Error | $0.02^{***}$ | $0.06^{***}$
72hr AR Error | $0.03^{***}$ | $0.09^{***}$
48hr AR Error | $0.04^{***}$ | $0.32^{***}$
24hr AR Error | $0.04^{***}$ | $0.37^{***}$
Midpoint Temp. - ∘C | $-2.49^{***}$ | $-2.29^{***}$
Midpoint Temp. Sq. - ∘C | $0.68^{***}$ | $0.67^{***}$
Wind speed - Km/hr | $-1.29^{***}$ | $-1.34^{***}$
Natural Gas Price - $/MMBtu | $37.80^{***}$ | $25.90^{***}$
75min AR Error | $0.04^{***}$ | $0.59^{***}$
60min AR Error | $0.09^{***}$ | $0.45^{***}$
45min AR Error | $-0.01^{***}$ | $0.44^{***}$
30min AR Error | $0.10^{***}$ | $0.57^{***}$
15min AR Error | $0.67^{***}$ | $0.69^{***}$
Supply Nat. Gas - GW | $-50.47^{***}$ | $16.37^{***}$
Supply Renewables - GW | $-43.58^{***}$ | $1.02^{***}$
Supply Other - GW | $-93.33^{***}$ | $-14.91^{***}$
Reserve Capacity - GW | $30.34^{***}$ | $-6.86^{***}$
Capacity Utilization - % | $25.48^{***}$ | $22.35^{***}$
Incentive Active - Y/N | $-12.00^{***}$ | $-10.90^{***}$
Incentive Payment - $/MW | $-0.13^{***}$ | $-0.13^{***}$
Constant | $503.15^{***}$ | $30.72^{***}$
Observations | 256,772 | 256,772
R2 | 0.83 | 0.83
Adjusted R2 | 0.83 | 0.83
Note: |  ∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

A.5.2 Extreme Events and Covariate Exclusion

To test for the influence of omitted variables and extreme events on
Generating Capacity, covariate groups and extreme event observations are
excluded sequentially in the table below. Covariates are grouped by Fixed
Effects (annual), Seasonal Effects (monthly), climatic effects (temperature
and wind), economic effects (Labor Force, Unemp. Rate, CPI, Interest Rate,
Cost Wind & PV Installation, Natural Gas Price), Upstream Market Effects
(Online & Offline Capacity, Capacity Utilization, Shadow Price, Energy Only
Price) and Downstream Market Effects (Compensation Adder, Change Pekaer Net
Margin, NG & Renewable GINI Index, Renewable & NG Applicant Pool, and
Renewable & NG Status Phase). Results are shown for 12, 24, and 36-month
lagged models. Exclusion of Winter Storm Uri (Feb. 2021) is also shown.

Table 11: Covariate Sequencing - Generating Capacity Incentive Effect: 12 Month Lag | (1) | (2) | (3) | (4) | (5) | (6) | (7)
---|---|---|---|---|---|---|---
Incentive | -0.971 | 0.175 | 1.122 | 1.115 | -21.796 | -34.131 | -30.208
Fixed Effects | X | X | X | X | X | X | X
Seasonal Effects |  | X | X | X | X | X | X
Climatic Eff. |  |  | X | X | X | X | X
Economic Eff. |  |  |  | X | X | X | X
Upstream Market Eff. |  |  |  |  | X | X | X
Downstream Market Eff. |  |  |  |  |  | X | X
Exclude Storm Uri |  |  |  |  |  |  | X
Obs | 78 | 78 | 78 | 78 | 78 | 78 | 77
R2 | 0.822 | 0.889 | 0.918 | 0.935 | 0.956 | 0.963 | 0.962
AIC | 1190.462 | 1175.691 | 1158.004 | 1153.788 | 1134.030 | 1134.050 | 1123.497
BIC | 1211.672 | 1222.825 | 1212.209 | 1224.489 | 1216.515 | 1233.032 | 1221.937
F Statistic | 46.141 | 26.207 | 29.832 | 25.188 | 28.724 | 24.021 | 22.706
Table 12: Covariate Sequencing - Generating Capacity Incentive Effect: 24 Month Lag | (1) | (2) | (3) | (4) | (5) | (6) | (7)
---|---|---|---|---|---|---|---
Incentive | -0.973 | -0.514 | -0.523 | -1.1* | 16.109* | 5.145 | -0.684
Fixed Effects | X | X | X | X | X | X | X
Seasonal Effects |  | X | X | X | X | X | X
Climatic Eff. |  |  | X | X | X | X | X
Economic Eff. |  |  |  | X | X | X | X
Upstream Market Eff. |  |  |  |  | X | X | X
Downstream Market Eff. |  |  |  |  |  | X | X
Exclude Storm Uri |  |  |  |  |  |  | X
Obs | 66 | 66 | 66 | 66 | 66 | 66 | 65
R2 | 0.914 | 0.946 | 0.959 | 0.976 | 0.985 | 0.991 | 0.992
AIC | 934.806 | 926.979 | 914.337 | 892.913 | 873.106 | 853.943 | 836.642
BIC | 952.323 | 968.582 | 962.510 | 956.413 | 947.555 | 943.719 | 925.792
F Statistic | 105.168 | 49.064 | 52.593 | 57.268 | 66.504 | 71.494 | 76.080
Table 13: Covariate Sequencing - Generating Capacity Incentive Effect: 36 Month Lag | (1) | (2) | (3) | (4) | (5) | (6) | (7)
---|---|---|---|---|---|---|---
Incentive | -0.973* | -0.612 | -0.704* | -0.687* | -1.414 | -8.819 | -4.895
Fixed Effects | X | X | X | X | X | X | X
Seasonal Effects |  | X | X | X | X | X | X
Climatic Eff. |  |  | X | X | X | X | X
Economic Eff. |  |  |  | X | X | X | X
Upstream Market Eff. |  |  |  |  | X | X | X
Downstream Market Eff. |  |  |  |  |  | X | X
Exclude Storm Uri |  |  |  |  |  |  | X
Obs | 54 | 54 | 54 | 54 | 54 | 54 | 53
R2 | 0.926 | 0.971 | 0.981 | 0.996 | 0.996 | 0.998 | 0.998
AIC | 753.927 | 724.613 | 707.436 | 640.688 | 644.292 | 634.977 | 625.207
BIC | 767.850 | 760.415 | 749.205 | 696.379 | 709.929 | 714.536 | 704.019
F Statistic | 119.692 | 78.239 | 93.956 | 246.819 | 189.972 | 162.935 | 153.457

To test the influence of omitted variables and outlier observations on the
Direct Underbidding effect and the Average Treatment Effect, covariate groups
are added, and rare event observations are removed sequentially in the table
below. Columns (1)-(3) compare Control covariates excluding rare events,
including observations occurring during Storm Uri, and those when the total
energy price, including incentives, is within $2,000 of the regulatory cap.
Columns (4)-(5) examine the layering of one-period (AR1) and 10-period (AR10)
lagged error covariates excluding regulatory cap observations. Columns (6)-(8)
report the average total incentive for covariate matching when excluding Storm
Uri observations(6), regulatory cap observations (7), and with the inclusion
of AR1 and AR10 covariates while excluding regulatory cap observations(8). The
Average Active Incentive per megawatt is included for each data subset for
comparison.

Table 14: Underbidding Incentive Effect - Direct and Treatment Effect Robustness | Direct | ATET
---|---|---
Dep.: Energy Price - $/MW | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
Active Incentive Effect |  -79.96∗∗∗ |  -15.14∗∗∗ |  -15.19∗∗∗ |  -5.27∗∗∗ |  -5.78∗∗∗ |  -224.78∗∗∗ |  -390.98∗∗∗ |  -24.91∗∗∗
Incentive Effect |  -0.05∗∗∗ |  0.24∗∗∗ |  0.07∗∗∗ |  -0.21∗∗∗ |  -0.26∗∗∗ | - | - | -
Avg. Active Incentive -$/MW | 55.31 | 12.20 | 31.72 | 12.20 | 12.20 | 12.20 | 31.72 | 12.20
Avg. Underbid -$/MW | 79.73 | 12.21 | 12.97 | 7.83 | 8.95 | 224.78 | 390.98 | 24.91
FE and Controls | X | X | X | X | X | X | X | X
AR1 |  |  |  | X | X |  |  | X
AR10 |  |  |  |  | X |  |  | X
Matching |  |  |  |  |  | X | X | X
Excl. Tot. Payment $>$$7,000 |  | X |  | X | X | X |  | X
Exclude Uri |  |  | X |  |  |  | X |
Obs | 257,252 | 256,850 | 256,484 | 256,849 | 256,370 | 101,620 | 101,220 | 101,460
R2 | 0.312 | 0.170 | 0.132 | 0.714 | 0.732 | - | - | -
AIC | 3,281,245 | 3,006,953 | 2,926,943 | 2,732,782 | 2711664 | - | - | -
BIC | 3,282,144 | 3,007,851 | 2,927,843 | 2,733,692 | 2712668 | - | - | -
F Statistic | 1,373 | 617 | 458 | 7,469 | 7,377 | - | - | -

A.5.3 Information Lags and Covariate Exclusion

Figure 4 displays a histogram and density plot of coefficient p-values for 222
model alternatives for both Natural Gas and Renewable Capacity shown in Table
3. Covariates lags range from zero to 36 months. For each lag, three fixed
effects permutations are evaluated: no fixed effects, annual fixed effects,
and both annual and seasonal fixed effects. Each version is repeated with and
without a polynomial expansion on temperature. The Incentive coefficient of
interest was found to be both positive and significant at the 95% confidence
level in one model, or 0.45% of those evaluated. No Renewable Capacity models
were significant at the 95% confidence level or above.

Figure 4: Robustness Results: Incentive Significance and Direction

[Note] Negative p-values indicate negative Incentive coefficient estimates.

A.5.4 Rebalancing

The covariate matching method in of Table 6 resulted in the following
observation counts.

Table 15: Underbidding - Covariate Matching Observation Count | Raw | Matched
---|---|---
Number of obs | 256,772 | 102,152
Treated obs | 51,076 | 51,076
Control obs | 205,696 | 51,076