The …rst empirical strategy essentially implements the graphical exercise econometrically. I es-timate a model of the relationship between unit-level capacity utilization and the factors that should- in theory- determine short run utilization decisions:
cfit= iy+ 0iXit+ i t+ "it (11)
The dependent variable is the capacity factor at unit i in hour t. One di¤erence between this exercise and the graphical analysis is that this estimating equation controls for lagged and expected future electricity market conditions. If the day ahead forecast is for electricity prices to increase in future hours, plants that face binding ramping constraints may want to increase operation, even if costs exceed prices in the current hour. If the electricity price was recently high, a plant with binding ramp down constraints may still be running in an hour where costs exceed the price paid. The Xit matrix includes fuel-based operating costs, variable operations and maintenance costs, contemporaneous hourly wholesale electricity prices, lagged electricity prices, and day ahead forecasts of electricity prices in future hours. To …t this function ‡exibly to the data, all continuous variables enter as third degree polynomials.
Real-time and day ahead hourly locational marginal prices are matched to each unit using detailed hourly data made available by the Independent System Operators.34 Day-ahead prices are used to proxy for expected prices in future hours. These electricity prices will be correlated with the error term ij if unobserved supply shocks a¤ect both market clearing prices and unit-level supply decisions. ISO-speci…c hourly demand and demand forecasts are used to instrument for
34 "Locational marginal pricing" is used in the PJM Interconnection, New York, and New England markets.
the LMPs. These instruments are highly correlated with realized electricity prices in a given hour but independent of unobserved supply shocks. Electricity prices are treated as a linear function of these instruments and the other exogenous regressors. I use two-stage least squares to estimate [11].
The direct e¤ects of the unit speci…c operating constraints, represented by i in [9], are captured by unit-…xed e¤ects. I allow these iy to vary across years within a unit. This will be important if facilities make changes to their operating processes over the course of the study period.
Because these unobserved, unit-speci…c constraints will also a¤ect how the unit can respond to changing market conditions, I allow all of the coe¢ cients in the model to vary by unit. For each of the 550 electricity generating units, I estimate [11] separately.
I am interested in separating the e¤ect of the subsidies conferred under allocation updating regimes from the e¤ect of direct compliance costs. Unfortunately, there is very little within unit variation in ei and si.35 Moreover, spot permit prices are highly correlated with futures prices. As a consequence, these countervailing e¤ects cannot be disentangled using only within-unit variation. Only the contemporaneous permit price enters these unit-speci…c estimating equations.
Conditional on the observable variables in Xit and the unobserved time invariant factors captured by the iy, the i coe¢ cient captures the average relationship between variation in the permit price and unit-level capacity utilization choices. More precisely, this coe¢ cient captures the net e¤ect of the explicit tax (i.e. t e
iei) and the implicit subsidy ( t+l s
isi) on capacity utilization decisions.
In a second stage, I regress this estimated permit price coe¢ cient on unit-level emissions rates and the subsidy parameters:
bi = 0+ eei+ ssi+ i; (12)
Emissions rates ei at units exempt from the NOx Budget Program are set to zero.36 If the
35There is some within-unit variation in emissions rates and heat rates across years due to reto…ts and combustion modi…cations that occur during the study period. However, this variation is extremely limited as compared to the signi…cant cross-sectional variation in emissions rates and implicit production subsidies
36I treat unit-level emissions rates as …xed. No attempt is made to account for the stochastic properties of these unit-speci…c operating parameters (see Appendix 4). Future work will explore alternative approaches to
costs of holding permits to o¤set emissions during ozone season are signi…cantly a¤ecting capacity utilization rates at NBP units, we should expect e < 0. If the implicit subsidies conferred under allocation updating regimes are signi…cantly in‡uencing how plant managers conduct their operations, we expect s > 0: Holding constant all of the variables contained in X, we should not expect to …nd a signi…cant correlation between capacity utilization rates and permit prices at exempt units or units with very low emissions rates and zero subsidies.
The results from the …rst stage of the estimation are summarized in Appendix 6. Each unit-speci…c regression includes year …xed e¤ects, a weekend indicator, the contemporaneous permit price, and a suite of continuous variables that enter as third order polynomials. These include fuel operating costs, variable operations and maintenance costs, two lags, two leads, and the contemporaneous electricity price (instrumented for using lagged, current, and future predicted load).
The NOx price coe¢ cient captures the average e¤ect of an incremental change in the NOx permit price (measured in $/ton NOx) on capacity utilization (measured in percentage terms).
We should expect this average e¤ect to be very small for all units. A one dollar change in the permit price increases the operating costs of a unit with an average NOx emissions rate by less than one cent, whereas the average variable operating cost exceeds $80/MWh. In hours where the price-cost margin is not close to zero, we should not expect a change in the permit price to alter operating decisions (see Figure 2). This NOx price coe¢ cient estimate varies signi…cantly across units. The median estimate is -0.00008. The standard deviation is 0.001.
Table 7 summarizes results from regressing these unit-speci…c permit price coe¢ cients on unit level emissions rates and subsidy parameters si. Standard errors are estimated using a bootstrap approach that clusters at the facility (versus unit) level. The most restrictive speci…cation (1) includes only the demeaned NOx emissions rate, the unit-speci…c subsidy parameters si, and a constant. The NOX emissions rate coe¢ cient is statistically signi…cant and negative at the 1-percent level, suggesting that the relationship between NOx permit prices and hourly output is
incorporating this variation. For example, Joskow and Schmalensee (1985) demonstrate a consistent (adjusted least-squares) technique for using estimated plant operating characteristics as independent variables in crosssection regression analysis.
signi…cantly more (less) negative among units with higher (lower) emissions rates. The coe¢ cient on the implicit subsidy is positive (as expected) but cannot be statistically di¤erentiated from zero. The constant term is statistically signi…cant and positive. This suggests that the permit price coe¢ cient may be picking up the e¤ects of other determinants of utilization rates that are correlated with permit prices.
Column (2) investigates the extent to which these coe¢ cient estimates vary systematically with demeaned operating capacity.37 The interaction with the NOx emissions rate is highly statis-tically signi…cant. This indicates that the negative relationship between permit prices and output, conditional on emissions rate, is stronger (i.e. more negative) at larger facilities.
The model is re-estimated using a dataset that omits observations associated with price cost margins that are large in absolute value (i.e. greater than $50/MWh or less than -$50). These estimates are reported in columns (3) and (4). Figure 3 helps to illustrate why we should expect these coe¢ cient estimates to be larger in absolute value. The estimates reported in columns (1) and (2) describe the relationship between permit prices and capacity utilization decisions averaged across a broad range of price-cost margins. In theory, a change in the permit price should have no e¤ect on utilization decisions when plants are far from the margin. These coe¢ cients are larger in absolute value as expected; the pattern of statistical signi…cance does not change. The …nal two columns re-estimate the model using a data set that omits observations in July and August.
Summer peak hours occur during these months. Dropping these observations (in addition to the months December-February) restricts the sample to more similar hours across the ozone season and o¤ season. Results are robust to this modi…cation.
The coe¢ cients in Table 7 are somewhat di¢ cult to intuitively interpret. For example, the coe¢ cient on the emissions rate measures how the average relationship between the capacity utilization rate (measured in percentage terms) and the permit price (measured in $/ton NOx) changes with unit-level emissions rates (measured in tons NOx/MWh). To put these coe¢ cient estimates in context, consider a one standard deviation increase in the NOx price. This translates into an increase in variable operating costs of approximately 3 percent for a unit with average
37Several alternative speci…cations were tried but none improved the …t of the model. For example, NOx emissions rates and implicit subsidies were also interacted with heat rates, NOx emissions rates, and SO2 emissions rates.
operating costs in a grandfathering regime. This incremental NOx price change increase is asso-ciated with an average decrease in operating capacity of approximately 1% (averaged across units and hours).
In sum, the statistical patterns found in these data are generally consistent with the hypothesis that plant managers account for the costs of holding permits to comply with the NBP in their short-run production decisions. The coe¢ cient on the implicit production subsidy is positive, smaller in absolute value, and less precisely estimated.