What Moves the Ex Post Variable Profit of Natural-Gas-Fired Generation in California?

We use a large California database of over 32,000 hourly observations in the 45-month period of April 2010 through December 2013 to document the ex post variable profit effects of multiple fundamental drivers on natural-gas-fired electricity generation. These drivers are the natural-gas price, system loads, nuclear capacities available, hydro conditions, and renewable generation. We find that profits are reduced by increases in generation from nuclear plants and wind farms, and are increased by increases in the natural-gas price and loads. Solar generation has a statistically insignificant effect, although this will likely change as solar energy increases its generation share in California’s electricity market. Our findings support California’s adopted resource adequacy program under which the state’s load-serving entities may sign long-term bilateral contracts with generation developers to provide sufficient revenues to enable construction of new natural-gas-fired generation plants.


INTRODUCTION
This paper is motivated by Professor Paul Joskow's insightful observation that: "Revenue adequacy has emerged as a problem in many organized wholesale electricity markets and has been of growing concern in liberalized electricity markets in the U.S. and Europe.The revenue adequacy or 'missing money' problem arises when the expected net revenues from sales of energy and ancillary services at market prices provide inadequate incentives for merchant investors in new generating capacity or equivalent demand-side resources to invest in sufficient new capacity to match administrative reliability criteria at the system and individual load serving entity levels" (Joskow, 2013, p. i).
Consistent with what one would expect, we find that an increase in load within an electric region tends to increase profits from a gas turbine.Profits are reduced by increases in generation from baseload nuclear plants and wind farms.Our data analysis, however, reveals that changes in solar generation have a statistically insignificant effect on the profitability of natural-gas plants, although one may anticipate that this will change as solar energy increases its generation share in California's electricity market.Though raising a natural-gas power-plant's operating cost, an increase in natural-gas prices nonetheless enhances the plant's profits.
This paper makes the following contributions.First, the analysis is new and comprehensive, and extends the extant studies, which in the main focus on the profit effect on market prices of a single resource such as wind generation (Steggals et al., 2011; Traber and Kemfert, 2011; Woo  et al., 2012) or nuclear generation (Traber and Kemfert, 2012).
Second, the paper reports the diminishing investment incentives for natural-gas-fired generation under California's adopted energy policy that promotes DR and renewable energy. 10It corroborates the positive price and profit effects of nuclear-generation-plant shutdowns in Germany, which were estimated by Traber and Kemfert (2012).
Third, its finding of diminishing investment incentives supports the state's adopted resource-adequacy program: "[e]ach LSE [load serving entity] is required to file with the [California Public Utilities] Commission demonstrating that they have procured sufficient capacity resources including reserves needed to serve its aggregate system load on a monthly basis.Each LSE's system requirement is 100 percent of its total forecast load plus a 15 percent reserve, for a total of 115 percent." 11inally, the paper enriches the extant literature by presenting an approach that can be used to analyze the profits from natural-gas-fired generation in other deregulated electricity markets that have data similar to those of California (e.g., Alberta and Ontario in Canada; Texas, PJM, New York and New England in the U.S; Germany and Spain in Europe; and Australia and New Zealand in the Asia Pacific region).For example, the same approach can be used to analyze how the retirement of baseload coal-power plants, aimed at reducing emissions of coal-fired generation (Venkatesh et al., 2012), affects the profit of natural-gas-fired generation.
The paper proceeds as follows: Section 2 provides the background for our analysis; Section 3 presents our methodology; Section 4 describes our data and documents their construction; Section 5 presents our results; and Section 6 provides general conclusions.

BACKGROUND
In addition to the state's size 12 and data availability, 13 we choose California for our study because it has features that enable an estimation of the profit effects of a set of fundamental drivers.First, the CAISO uses a nodal market design with real-time markets (RTM) and day-ahead markets (DAM) that are intended to improve system operation and prevent a repeat of the 2000-2001 energy crisis. 14Based on locational marginal pricing (Bohn et al., 1984; Hogan, 1992), these RTM and DAM prices 15 allow us to compute the per MWH profit of a natural-gas-fired generation plant in each of the state's two major electric regions of NP15 in Northern California and SP15 in Southern California. 16econd, California's generation mix is dominated by natural-gas-fired generation plants, 17 implying that the state's marginal generation unit is likely fueled by natural gas, except for the nonpeak hours during which the market prices can become negative. 18This allows us to analyze the dependence of the realized profit on the natural-gas price. 19The effect on profit of the natural-gas price is unclear a priori.While a decrease in the price of natural gas reduces the operating costs of a natural-gas-fired generation plant, it also reduces the wholesale market price of electricity and therefore the plant's operating revenues.
Third, the state's planned central generation stations are CT and CCGT (CEC, 2014,  p.138).Those stations help replace the capacity of the San Onofre nuclear power plant, which was lost due to its January 31, 2012 shutdown and subsequent retirement caused by the premature wear on over 3,000 tubes in 15,000 places (CEC, 2014, Chapter 6).The San Onofre shutdown was estimated to have increased the state's wholesale market prices by $6 to $9/MWH (Woo 2014a).This suggests a positive profit effect that may also occur elsewhere because of the planned nucleargeneration shutdowns and construction moratorium in the aftermath of the March 11, 2011 Fukushima nuclear disaster (Baetz, 2011; Faris, 2011; Traber and Kemfert, 2012; Joskow and Parson,  2012; Wald, 2013).
Fourth, the state's hourly loads are weather-sensitive, with afternoon demand spikes that typically occur on hot summer weekdays (Miller et al., 2008).A load reduction due to the state's 24.While CEC (2010, p. 14, Table 14) reports the per kW-year fixed O&M costs, we do not include them in our per-MWH variable profit calculation.For a new CT (or CCGT) to be financially viable, its total variable profit per year ( = average per-MWH variable profit * annual MWH output) needs to cover the per kW-year fixed O&M costs, depreciation, and return on investment.activation of its DR programs tends to reduce market prices during severe capacity shortages.The profit effect of the DR-load reduction, however, is not well documented.
Fifth, California has central hydro stations that mainly reside in the north, 20 the outputs of which decline as a result of a prolonged drought, such as the current on-going drought that is not expected to end anytime soon. 21While improved hydro conditions tend to reduce market prices (e.g., Woo et al., 2007, 2013), little is known about their profit effect.
Finally, California's legislated RPS requires renewable generation to meet a preset share of the state's electricity consumption by a targeted year. 22Having adopted a 33% RPS by 2020, the state is now investigating the challenges in achieving a 40% or 50% RPS by 2030. 23The state's rich data on renewable generation help determine the profit effect of the state's renewable energy development.

Profit Formula
We first define the hourly ex post variable profit, whose formula is necessary for our data construction and profit-effect estimation.For expositional ease, where there is minimal risk of confusing the reader, we suppress subscripts whose eventual inclusion in the formal regression model delineates our observations with respect to region (j), hour-of-the-day (h), day-of-the-week (d), month-of-the-year (m), and day-in-the-sample (t).Based on CEC (2010), the daily per MWH variable cost of a natural-gas-fired generation plant is: where H = heat rate (MMBTU/MWH) = rate of converting natural gas into electricity, G = daily natural-gas price ($/MMBTU), T = transportation cost for natural gas ($/MMBTU), and OM = variable O&M cost of generation ($/MWH). 245.The same payoff concept underlies the valuation of a tolling agreement, which is a useful instrument for risk management and project financing (Stern, 1998; Deng et al., 2001; Eydeland and Wolyniec, 2003; Deng and Oren, 2006;  Deng and Xia, 2006; Ryabchenko and Uryasev, 2011; Thompson, 2013).
26. Computing the profit effect of a single driver (e.g., wind generation) based on a Tobit-type model entails a multistep simulation process (e.g., Woo et al., 2012, pp.216-217).When there are multiple drivers to consider, the computation of their profit effects becomes tedious and time-consuming, unlike the relatively simple approach proposed below.
Suppose the hourly market price is P ($/MWH).The plant's hourly profit from 1-MW of generation ownership is: which is also the hourly payoff of an hourly call option with a daily-varying strike price equal to C. 25 As will be shown below, up to 90% of the state's hourly V values are zero.While a Tobit-type model (Maddala, 1983) can reveal how V varies with its drivers (Woo et al., 2012), the profit effects of the drivers are not easily inferred. 26here is an alternative calculation of V whose implications for the profit effects of the drivers from a standard linear-regression analysis are more transparent.Specifically, we define the hourly per MWH procurement cost of a local distribution company (LDC) owning natural-gas-fired generation to be: (3) The latter measures what the LDC pays for 1 MWH of electricity, since the LDC can buy from the market if PϽC, and self-generate otherwise (Woo et al., 2006b).
We can now compute the hourly per MWH profit as: We verify the validity of equation ( 4) by considering the following two cases: • Case 1: PϾC and V = max(P -C, 0) = P -C.As Y = min(P, C) = C, we find P -Y = P -C = V.
Unlike the V data series with many zeros, the P and Y data series have few zeros and can be analyzed using standard regression techniques (e.g., Woo et al., 2006b).
Based on equation (4), the profit effect of a driver X (which can be the natural-gas price, system load, nuclear capacity available, renewable generation, or hydro condition) is the arithmetic difference of two marginal effects: (5) Equation ( 5) enables us to readily infer ∂V/∂X after our estimation of the market price and per MWH procurement cost regressions.While the regression-based approach is not new (Woo et al., 2006b), our innovation lies in the use of the regressions' coefficient estimates to identify and quantify the profit effects of a set of fundamental drivers on natural-gas-fired generation.

Linear Regression Model
Our profit-effect estimates are derived from the parameter estimates for a system of seemingly unrelated regressions (SUR).Based on Woo et al. (2006b, 2014a), we empirically identify six linear regressions for California's two electric regions: (6.a) The left-hand-side (LHS) variables are the hourly RTM price (P jht ), the per MWH procurement costs based on the 1-MW ownership of a CCGT (Y jht ), and the per MWH procurement costs based on the 1-MW ownership of a CT (Z jht ), for region j = 1, 2, during hour h = 1, . . ., 24, on sample day t = 04/20/2010, . . ., 12/31/2013.Section 4 below details the construction of these LHS variables.
The time-dependent intercepts are α jhdmt , β jhdmt , and h jhdmt , which represent linear functions of binary indicators to control for the effects of hour-of-the-day, day-of-the-week, and month-ofyear.Specifically, let: I ht denote the indicator that is equal to unity during hour h, and is zero otherwise; I dt denote the indicator that is equal to unity when day t falls on d = 1 (Monday), . . ., 7 (Sunday), and is zero otherwise; and I mt denote the indicator that is equal to unity when day t occurs during m = 1 (January), . . ., 12 (December), and is zero otherwise.Then, where the respective sums are over h = 1, . . ., 23, d = 1, . . .6, and m = 1, . . ., 11.Hence, the d's are the coefficients to be estimated in the regression process and α j is the regression's constant intercept.The other time-dependent intercepts are similarly determined. 27he right-hand-side (RHS) variables are the profit drivers, including the daily natural-gas price G jt which is region-specific and the metric variables (X 1ht , . . .X 11ht ) that measure hourly system loads, daily nuclear capacities available, hourly hydro conditions measured by three Northern Californian rivers' stream flows, and hourly renewable generation outputs.Section 4 below describes these RHS variables in greater detail.
The slope coefficients of the RHS variables measure the drivers' marginal effects on the hourly RTM price and the per MWH procurement costs.We hypothesize that: (a) the coefficients for the daily natural-gas price and hourly loads are positive, since an increase in each of these drivers should tend to raise both the hourly RTM price and the per MWH procurement costs; and (b) the coefficients for the daily nuclear capacities available, hourly stream flows, and hourly renewable generation are negative, since an increase in each of these drivers should tend to reduce the hourly RTM price and the per MWH procurement costs.
The random-error terms are e jht , l jht and g jht , which may well be contemporaneously and serially correlated.To allow for this contingency, we employ the iterated seemingly unrelated regression (ITSUR) method in PROC MODEL of SAS (2004) to jointly estimate the six regressions for the two electric regions, yielding the results reported in Section 5.
The underlying arguments in support of our chosen specification are as follows: 28.To form these interaction terms, we first define a binary indicator D ht for the standard period definition used in bilateral trading: (a) the on-peak period of 06:00-22:00, Monday-Saturday; and (b) the off-peak period of the remaining hours (Woo et al., 2013).This indicator equals unity if hour h on day t is in the on-peak period, and is zero otherwise.Each interaction term is the product of D ht and a profit driver.Including these interaction terms doubles the number of slope coefficients to be estimated.
• Linear functional form.Equation (4) states that the hourly profit is the arithmetic difference between the hourly market price and the procurement cost, which lends support to our preference for the linear form over, say, a logarithmic functional form.Still further, using a doublelog form would have excluded about 4% of the sample, because of the negative market prices.• Transparent and readily interpreted coefficient estimates.The chosen specification helps achieve our primary goal of estimating the effect upon profits of a given driver.Consider, for example, the estimates for the natural-gas-price coefficients of (α jG , β jG , h jG ), denoted here by a jG , b jG and q jG .Equation ( 5) implies that the profit effect of the natural-gas price is the arithmetic difference of the coefficient estimates: (a jGb jG ) for a CCGT and (a jGq jG ) for a CT.Based on Mood et al. (1974, p. 179), we can readily find each profit-effect estimate's variance (e.g., var(a jGb jG ) = var(a jG ) -2cov(a jG , b jG ) + var(b jG )), which enables us to subject that effect to a t-test of the null hypothesis that there is a zero profit effect.• Large number of slope coefficients.The hourly price data are noisy, making precise detection of profit effects difficult.Even with the parsimonious specification given by equations (6.a)-(6.c),we already have 6 * 12 = 72 slope coefficients to estimate and interpret for the fundamental drivers, to say nothing of the 6 * (23 + 6 + 11) = 240 coefficients attached to the six time-dependent intercepts.Adding more RHS variables would not seem to improve the insights gleaned from our profit-effect estimation.In particular, before settling on our final specification, we did indeed include in our estimations various interaction terms that allowed the slope coefficients to vary by trading period. 28The majority of the expanded regressions' coefficient estimates are statistically insignificant (p-valueϾ0.05),an indication of over-specification that produces imprecise estimates.To account for possible nonlinearities, we also re-estimated the system of equations including both squared and interaction terms formed by the drivers to account for possible nonlinearities.Once again the result was that a majority of the coefficient estimates were statistically insignificant (p-valueϾ0.05).• Serial correlation.Our data decisively reject (p-valueϽ0.0001) the null hypothesis of no serial correlation.As a result, we initially assumed that our random-error terms followed an AR(5) process, which led us to ultimately conclude that an AR(4) process is the empirically appropriate specification that yields the statistically significant (p-valueϽ0.05)parameter estimates shown in Section 5 below.• Empirical plausibility of the results.As discussed below, our regression results are empirically plausible.That is, most of the slope-coefficient estimates have the hypothesized sign and are of plausible size.

Data Construction
This subsection details the construction of our data sample.To construct the per MWH variable cost C as defined in equation (1), we make the following assumptions: Copyright ᭧ 2016 by the IAEE.All rights reserved.
29.We verified that minor variations in H do not materially alter our statistical results.30.These natural-gas prices are used by the CAISO (CAISO, 2013, 2014b).Hence, they can better represent California's marginal fuel costs that drive the CAISO's DAM and RTM prices than the state's wholesale natural-gas prices at hubs like PG&E Citygate and SoCal Citygate.A map of the major Western natural-gas hubs is available from the U.S. Federal Energy Regulatory Commission at https://www.ferc.gov/market-oversight/mkt-gas/western.asp 31.We verified that minor variations in T do not materially alter our statistical results.32.CEC (2010, pp.54-56, Tables 14-16) reports three variable cost ranges: (1) average case: $2.69 to $4.17/MWH; (2) high case: $3.42 to $9.05/MWH; and (3) low case: $0.79-$2.19/MWH.Hence, we assume a $5/MWH variable cost which is approximately the mid-point for the combined range of $0.79-$9.05/MWH.33.We use the 12 5-minute intra-hour RTM prices to compute the average RTM price for each hour.We choose not to use the 5-minute RTM price data in our analysis for the following reasons.First, equation (2) assumes an hourly dispatch, rather than a 5-minute dispatch.Second, except for the daily natural-gas price and nuclear capacity data, all the metric variables are measured through hourly data.Finally, 0.99 is the correlation between (a) the hourly payoffs based on the hourly RTM prices, and (b) the hourly averages of the 5-minute payoffs based on the 5-minute RTM prices.This almost perfect correlation holds for both NP15 and SP15, thus obviating any concern that our use of hourly RTM price data may yield results notably different from those based on the 5-minute RTM price data.
A complete list of California's stream-flow data at 492 sites is available at: http://waterdata.usgs.gov/ca/nwis/current/?type = flow 38.We do not include biogas, biomass, and geothermal for reasons given in supra note 8. 39.We thank a referee for suggesting the analysis in this subsection.40.See CAISO (2014c, pp.66-68).
41. Assuredly, one can use the ARIMA method (e.g., PROC FORECAST in SAS ( 2004)) to make reasonable dayahead forecasts for such drivers as the natural-gas price, nuclear capacities available, and stream flows.The quality and reliability of such forecasts, however, may invite questions as to the empirical validity of our analysis of ex post profits (e.g., "Are the forecasts constructed by the authors reflective of those used by market participants?""Are the authors' forecasts sensitive to the choice of forecasting technique?").While the CAISO publishes day-ahead load forecasts (http:// oasis.caiso.com/mrioasis/logon.doessionid = 8BE96B340BDE4D2C4772E65DB499B2CC), it only publishes day-ahead forecasts for solar and wind generation since December 2012, through its OASIS site (http://oasis.caiso.com/mrioasis/logon.doessionid= 03863D12C2A297D0BB3CBB82798A69A7).As a result, we do not have day-ahead forecast data for the highly unpredictable solar and wind generation for the entire sample period.
• Hourly hydro conditions (000ft 3 /second).The hydro conditions are proxied by the U.S. Geological Survey's hourly average of the 15-minute stream flows for the three major rivers in Northern California: the Klamath near the California-Oregon border, and the American and Sacramento in the Central Valley. 37Figure 1 portrays the daily averages of the 15-minute stream flows of these rivers, which reflect the worsening drought in California.The Klamath's flows are moderately correlated (rϽ0.65) with those of the American and Sacramento rivers.
The flows of the American and Sacramento, however, are highly correlated (r = 0.81).• Hourly renewable generation (MW).The three generation sources are small hydro, solar, and wind generation, the data for which are published by the CAISO. 38

DAM or RTM Prices?
We now consider which of the two price series-the DAM or the RTM-would be more appropriate to use for our profit analysis. 39At first blush, the DAM prices seem preferable, since over 95% of the MWH traded in the CAISO's markets are settled at the DAM prices. 40Nonetheless, we decided to use the RTM prices, thereby circumventing the difficulty noted by Woo et al. (2013)  of obtaining day-ahead forecast data to properly match with the DAM price data. 41ur decision is also supported by the following observations.First, Figures 2 and 3 show that on average a $1/MWH movement in the DAM prices is matched by a $1/MWH movement in the RTM prices.
Second, the owner of a CT (or CCGT) can always choose to transact in the RTM or DAM, even though the RTM has a smaller trading volume than the DAM.The hourly DAM-based profits are likely to be less than the hourly RTM-based profits because (a) these profits are the payoff of a call option, and (b) the hourly DAM prices are less volatile than the hourly RTM prices.Using the cost and price data described in the last subsection, Table 1 confirms that for the entire sample  period, the average DAM-based profits are $0.52/MWH to $2.84/MWH.These profits are substantially less than the average RTM-based profits of $4.70/MWH to $7.79/MWH.

Descriptive Statistics
Panel A of Table 2 reports the descriptive statistics for the RTM price and per MWH procurement-cost data used in our regression analysis.To address possible concerns about a spurious price regression due to non-stationary data (Granger and Newbold, 1974), we apply the Phillips-Perron unit-root test (Phillips and Perron, 1988) and determine that all data series in Panel A are stationary.
The hourly price data have means of $33/MWH for NP15 and $35/MWH for SP15.The data are volatile, as reflected in their respective standard deviations of $39/MWH and $49/MWH, minimum values of -$107/MWH and -$164/MWH, 42 and maximum values of $910/MWH and $1,377/MWH.Relative to the price data, the per MWH procurement-cost data have lower means, and much smaller standard deviations and maximum values, principally because generation ownership caps the per MWH procurement costs well below the market price spikes.
Panel B shows the comparable statistics for the profit drivers.The natural-gas-price data series are non-stationary and have means of $4.17/MMBTU for NP15 and $4.32/MMBTU for SP15.The remaining series, however, are stationary.
The PG&E and SCE hourly load data are volatile and have large standard deviations and maximum values.The statistics for the available nuclear capacities suggest that, during the sample period, each nuclear plant had high capacity availability, unless it was shut down, as in the case of the San Onofre plant.There are three hourly non-dispatchable renewable-generation series: small hydro, solar, and wind.Their statistics suggest that the three series are highly volatile.The average wind generation is about 3.0 times the size of the average small-hydro generation, and 3.6 times the size of the average solar generation.
Rows 2 to 7 of Table 3 report that the hourly prices are positively correlated (r = 0.63).The hourly prices and per MWH procurement costs are also positively correlated and at times strongly so (r ≥ 0.50).Finally, the per MWH procurement costs are highly correlated (rϾ0.88).
The last 12 rows of Table 3 report the coefficients of correlation of the hourly prices and per MWH procurement costs with their respective drivers.Even though these coefficients are quite low ( ⎪ r ⎪ Ͻ0.38), they are broadly consistent with what one would expect: (a) the prices and per MWH procurement costs are positively correlated with the loads and natural-gas prices; and (b) they are negatively correlated with the nuclear capacities available, hydro conditions, and renewable generation.The notable exception is solar generation, which has small but positive correlation coefficients (rϽ0.17).Table 4 reports the share of sample observations with zero hourly profits, as well as the mean hourly profits over the 45-month sample period.The share of hours with zero profit is large, up to 94% for a CT, 43 showing that natural-gas-fired generation is unprofitable for a majority of the year. 44These data also highlight the necessity of using a Tobit-type model to directly analyze the ex post profit data in a regression analysis (Maddala, 1983), unless one circumvents the problem, as we do here.For the entire sample period, the NP15 mean profit is $5.8/MWH for a CCGT and $4.7/MWH for a CT, about $2/MWH less than the corresponding SP15 mean profits.

Regression Results
Table 5 presents our hourly regression results that do not include the coefficient estimates related to the time-dependent intercepts.The following observations speak to the empirical plausibility of these results.First, the adjusted R 2 is 0.20 for the NP15 price regression and 0.16 for that of SP15.These relatively modest values reflect the noisy and volatile hourly price data.By contrast, the hourly per MWH procurement-cost regressions have adjusted R 2 values above 0.56, chiefly because the per MWH procurement costs are far less volatile than the market prices.
Second, relying on the criterion of a p-valueϽ0.05,which is used throughout the rest of the paper, the positive AR parameter estimates are statistically significant.Their regression-specific sum is less than 0.6, thus suggesting a stationary AR(4) error process.Hence, the regression residuals do not follow a random walk and the regression results in Table 5 are not subject to spurious interpretation (Davidson and MacKinnon, 1993, Chapter 19).
Third, most of the slope-coefficient estimates for the drivers are statistically significant and have the hypothesized sign.Specifically, 59 (82%) of the 72 slope-coefficient estimates are statistically significant.There are two insignificant load-related estimates: (1) Northern California's hourly PG&E load in the Southern California SP15 price regression; and (2) Southern California's hourly SCE load in the Northern California NP15 price regression.The statistical insignificance of these estimates is understandable, because of the locational difference between loads and prices and the occasional transmission congestion on the Path 15 interface between Northern and Southern California.Out of the 18 estimates associated with the stream flows of the three rivers, 12 are insignificant.In response to a referee's comment, however, we retain the stream flows as RHS variables to explicitly account for the impact of hydro conditions.
Fourth, all of the estimated slope coefficients have the "right" sign, except for the three that are associated with the stream flow of the Klamath River and that of the American River.The Klamath River's stream flow has two statistically significant coefficient estimates in the price regressions.These two estimates are judged to have the "wrong" sign, because one would expect improved hydro conditions to induce lower market prices.45.The market-based heat-rate interpretation is based on a competitive electricity market in which the market price tracks the per MWH variable cost of the marginal generation unit.Suppose there is no capacity shortage so that the market price of P ($/MWH) is equal to the unit's per MWH cost C in equation ( 1).The marginal effect of the natural-gas price G ($/MMBTU) on P is ∂P/∂G = (∂P/∂C) (∂C/∂G).While ∂P/∂C = 1, we need to find ∂C/∂G.Let TVC denote the unit's total variable cost for producing Q MWH.Invoking Shephard's Lemma (Varian, 1992, p. 74), ∂TVC/∂G is the plant's total naturalgas consumption.As ∂(TVC/Q)/∂G = ∂C/∂G is the per MWH fuel requirement, we find ∂P/∂G = ∂C/∂G is the marginal market-based heat rate (MMBTU/MWH).
Finally, the sizes of the estimated slope coefficients pass the test of plausibility.In particular, the coefficient estimates for the natural-gas price in both price regressions indicate that the market-based marginal heat rate over the sample period is 8.65 MMBTU/MWH in Northern California and 9.63 per MMBTU/MWH in Southern California. 45These market-based marginal heat rates are in line with our heat-rate assumptions of 7 MMBTU/MWH for the CCGT and 9 MMBTU/ MWH for the CT.
The coefficient estimates for the other drivers in the price regressions, namely, hourly loads, daily nuclear capacities available, and hourly renewable generation, are very similar to those reported in Woo et al. (2014a) for the 33-month sample period of April 2010 through December 2012.The interpretation of these coefficient estimates as marginal effects is straightforward, and we omit it for the sake of conciseness.
Turning our attention to the coefficient estimates for the per MWH procurement-cost regressions, we find that (a) they generally have the same sign as those in the price regressions, and (b) they are generally smaller in size than those in the price regressions.These results again would be in line with our prior conjectures in light of the capping effect of generation ownership on the per MWH procurement costs.

Profit Effects
Based on equation ( 5), Table 6 reports the estimated profit effects of each of the 12 fundamental drivers.Each estimate measures the marginal change in profit due to a marginal increase in the associated driver.These profit-effect estimates lead to the following inferences.
First, the estimated profit effect of the natural-gas price suggests that a $1/MMBTU increase tends to increase profit by as much as $1.80/MWH for SP15 at the assumed heat rate of H = 7 MMBTU/MWH for a CCGT.Only that one estimate, however, is statistically significant, although under a more lax standard of statistical significance, say a p-value ≤ 0.10, the estimate of $1.06/MWH at H = 7 MMBTU/MWH for NP15 would also pass muster.All four estimates, however, have the hypothesized sign.
Second, a 1-MW increase in the PG&E (SCE) load has a small, positive and statistically significant effect on the NP15 (SP15) profit, but has no impact on the SP15 (NP15) profit.
Third, increasing nuclear generation tends to reduce profits, but its estimated effects are only significant for the San Onofre and Palo Verde plants in the SP15 and NP 15 regions, respectively.
Fourth, the profit effects of the river flows are mixed.The flow at the Klamath River has a positive and statistically significant profit effect, in both regions, which in the main is due to the unanticipated result shown in Table 5 of the river's stream flow having a positive effect on price.
Fifth, small-hydro and solar generation in Northern California have statistically insignificant profit-effect estimates.This is in accordance with the estimates in Table 5 that show that smallhydro and solar generation have comparable impacts on both price and procurement costs in the 46.For example, California is expanding its solar-energy development under the state's solar-energy initiative (http:/ /www.gosolarcalifornia.ca.gov/csi/index.php).This may introduce a structural change that our regressions cannot capture.Nonetheless, an outright rejection of the results of our regression analysis by reason of a possible structural change is unproductive, because the same reason can rule out any regression analysis of ex post prices and profits that are necessarily recorded from actual market data.
north.In Southern California, however, where solar generation plays a greater role, the negative profit of solar generation is more pronounced and close to being statistically significant (pvalue = 0.053) at the assumed heat rate of H = 7 MMBTU/MWH for a CCGT.The magnitude of this effect, however, is less than half that of wind.
Finally, wind generation has negative and statistically significant profit effects, which is consistent with the main finding in the extant literature on the merit-order effect of wind generation, and its ensuing impact on generation investment incentives.

Profit Changes
As an illustrative application of our profit-effect estimates, we estimate the profit changes resulting from each of a series of hypothetical events.These profit-change estimates aid our understanding of how each event may impact the incentives to invest in natural-gas-fired generation.One should bear in mind, however, that rather than being predictive, the estimated changes are only indicative of what might occur in the future, because the hypothetical events will not necessarily materialize in that future, and our parameter estimates may not be sufficiently robust over more extended sample periods to shore up our confidence in any predictions about that future. 46Notes: (1) The profit numbers in the "no change" row are the sample mean profits in Table 2.An estimated profit change is the estimated profit effect multiplied by the change in the driver due to the event.(2) We do not compute the estimated profit change for the San Onofre plant because the average profit numbers in Table 2 have already captured the effect of the plant's shutdown.More importantly, a counter-factual computation for the San Onofre plant is meaningless, as the plant's shutdown is permanent.(3) We assume that the 50% increase [ = (50%/33%) -1Ϸ0.5)] in renewable generation is caused by California's raising the 33%-RPS to a 50%-RPS.
47.The EIA identified export scenarios resulting in U.S. natural-gas prices for producers at 4% to 11% more than the AEO 2014 reference case over the 2015-40 period (http://www.eia.gov/analysis/requests/fe/pdf/lng.pdf).That study indicates that larger gas demand from higher economic growth assumptions could also lead to projected increases in gas prices by more than $1/MMBTU in the 2020-2025 period.
Table 7 describes these hypothetical events and reports the estimated profit changes under the ceteris paribus assumption: Suppose there is a $1/MMBTU increase in the natural-gas price.That increase reflects the increasing demand for natural gas due to the U.S. economic recovery and rising natural-gas exports. 47The estimated profit increases can be as high as 23% of the sample's mean profits, as shown by the statistically-significant SP15 estimate for a CCGT with H = 7 MMBTU/MWH.The profit effects, however, are relatively small and statistically insignificant for a CT with H = 9 MMBTU/ MWH, chiefly because the natural-gas price increase has similar impacts on the market price and the CT's fuel cost.
• Suppose there is a 1,000-MW DR-load reduction that occurs 60 hours per year, reflecting our assumption of 10 DR days per year during California's peak hours of 12:00-18:00 (Moore  et al., 2010).The 1,000-MW DR-load reduction is based on the state's DR target of 5% and PG&E's and SCE's system annual peaks in 2013.We find the change in estimated profit as 48.To be sure, the estimate reported here reflects the average profit effect of a load change, based on our regression analysis.That profit effect can be smaller than the profit effect during the peak hours.Our possible understatement of the profit impact, however, is mitigated by the load increase that likely occurs in the shoulder-peak hours immediately before and after a DR-event.For example, critical-peak pricing tends to shift end-use loads in the critical-peak hours to the shoulderpeak hours (e.g., Faruqui and Segici, 2010).Thus, when the DR-load reduction during the peak hours is compensated for by the load increase in the shoulder-peak hours, the profit effect estimable from our regression analysis is empirically plausible.
49.This is based on a 26% reduction in profit ‫נ‬ 50% increase in wind generation.50.This is based on a 32% reduction in profit ‫נ‬ 50% increase in wind generation.51.This is based on the estimated profit reduction of 8% to 13% caused by a 40% increase in wind generation.52.This is based on the estimated profit reduction of 12% to 33% caused by a doubling in wind generation.
the hourly load's average profit effect * 1,000 MW * (60 hours / 8760 hours).Though statistically significant, the estimated profit reductions are less than 1% of the sample's mean profits, implying that when the number of DR hours is small, the estimated profit reductions are also likely to be small. 48• Suppose the Diablo Canyon nuclear plant loses one of its two reactors.While statistically insignificant, the estimated profit increases are about 20% of the sample's mean profits.• Suppose the Palo Verde nuclear plant loses one of its three reactors.The estimated profit increases are large and statistically significant for NP15, and mount up to 60% of the sample's mean profits.This may be attributable to the increased exports from the NP15 to SP15 region after loss of the unit.• Suppose there is a 50% (175.5 MW) increase in the average small-hydro generation due to California's raising its RPS from 33% to 50% of electricity usage.The estimated profit changes are mixed and statistically insignificant.• Suppose there is a 50% increase (146 MW) in the average solar generation due to the state raising its RPS from 33% to 50% of electricity usage.The profit-reduction estimates are statistically insignificant and equal to only 0% to 4% of the sample's mean profits.• Suppose there is a 50% increase (525 MW) in the average wind generation due to California's raising its RPS from 33% to 50% of electricity usage.The estimated profit reductions are statistically significant and equal to 26% to 32% of the mean profits.These estimated reductions imply that wind generation's negative profit-elasticity estimates are -0.53 49 to -0.64, 50 which are larger in size than the negative estimates of -0.20 to -0.33 for Texas (Woo et al.,  2012) 51 and -0.12 to -0.33 for Germany (Trabert and Kamfert, 2011). 52 In summary, these estimated profit changes show that the natural-gas price, DR-based load reduction, nuclear capacity available, and wind generation can have statistically significant impacts on the ex post profits of natural-gas-fired generation.Except for the DR-load reduction, the estimated impacts can be quite large, which corroborates the commonly held view regarding the "missing money" problem.

CONCLUSION
The profit-change estimates in Table 7 suggest that an increase in generation investment incentives in California might occur given an increase in natural-gas prices and the loss of a nuclear reactor, whose occurrence is uncertain.In contrast, we know with certainty that California has a ment in natural-gas-fired generation, which would justify the development and use of a marketsimulation model along the lines of Morales and Conejo ( 2011) and Traber and Kemfert (2011,  2012).

FigureFigure 2 :Figure 3 :
Figure 1: Daily Stream Flows (000ft 3 per second) for the Klamath River (KLA), American River (AME), and Sacramento River (SAC); Sample Period: 04/20/2010-01/31/2013 20.The stations constituted 15.7% of the state's 2013 in-state installed capacity of 78,133 MW (http://energyalmanac.ca.gov/electricity/electric_generation_capacity.html).21."WithCalifornia facing one of the most severe droughts on record, Governor Brown declared a drought State of Emergency in January[2015]and directed state officials to take all necessary actions to prepare for water shortages.The state has continued to lead the way to make sure California is able to cope with an unprecedented drought."(http://ca.

•
Sample period.Our sample period is the 45-month period of 04/20/2010 to 12/31/2013, which results in 32,448 hourly observations.The starting date reflects when the CAISO first reported hourly renewable generation.The ending date reflects the end of the calendar year of 2013.•Hourly market prices ($/MWH).These prices are RTM and DAM hourly prices that are available from the CAISO.
33These prices, along with the variable costs per MWH, allow us to use equation (3) to compute the procurement costs per MWH for electric region j = 1 for NP15 and j = 2 for SP15.The resultant per MWH procurement costs for region j are: Y jht = min[P jht , 7 * (G jt + T) + OM] for the CCGT and Z jht = min[P jht , 9 * (G jt + T) + OM] for the CT.• Hourly system loads (MW).These are the hourly loads published by the CAISO for the state's two large LDCs: PG&E in Northern California and Southern California Edison (SCE) in Southern California.• Daily nuclear capacities available (MW).A nuclear plant's daily capacity available is its installed capacity multiplied by the plant's daily availability factor.PG&E's Diablo Canyon plant's installed capacity is 2,160 MW and that of SCE's San Onofre plant was 2,150 MW. 34 The Palo Verde plant in Arizona has an installed capacity of 3,739 MW and is partially owned by SCE (15.8%), the Southern California Public Power Authority (10.2%), and the Los Angeles Department of Water and Power (5.7%). 35The daily availability factors for the three plants come from the U.S. Nuclear Regulatory Commission. 36

Table 1 : Descriptive Statistics for DAM-and RTM-based Profits ($/MWH) for the Period of 04/20/2010 through 12/31/2013 under the Heat Rate Assumptions of H = 7 MMBTU/MWH for a CCGT and H = 9 MMBTU/MWH for a CT
42.The share of negative prices is 4.28% for NP15 and 4.20% for SP15.

Table 2 : Descriptive Statistics, where h = hour index = 1, . . . , 24, t = day index = 04/20/2010, . . . , 12/31/2013 under the Heat Rate Assumptions of H = 7 MMBTU/MWH for a CCGT and H = 9 MMBTU/MWH for a CT Panel A: Real-time Market Prices and per MWH Procurement Costs
The San Onofre plant's descriptive statistics are based on the observations before the plant's shutdown on January 31, 2012, as the plant's capacity available is zero after the shutdown.Negative wind generation occurs due to on-site plant use.

Table 3 : Correlation Coefficients; the San Onofre Plant's Correlation Based on the Data before the Plant's Shutdown on January 31, 2012 under the Heat Rate Assumptions of H = 7 MMBTU/MWH for a CCGT and H = 9 MMBTU/MWH for a CT
43.Woo et al. (2012)document similarly large shares for the ERCOT market.44.There is a noticeable drop in the share of zero-profit hours for the CCGT's heat rate of H = 7 MMBTU/MWH between 2012 and 2013, which may be attributable to the state's worsening drought.

Table 5 : Hourly Regression Results with p-values in ( ) for the Period of 04/20/2011 through 12/31/2013 under the Heat Rate Assumptions of H = 7 MMBTU/MWH for a CCGT and H = 9 MMBTU/MWH for a CT
Note: For brevity, this table does not report the coefficient estimates for the intercept and the binary indicators that indicate statistically-significant (p-value ≤ 0.05) time-dependence of the hourly real-time market prices and procurement costs.