Simulation Model Bias Corrections

A.3.3.1 Bias from Inexact Matches

As with traditional matching estimators, some bias may be introduced due to the fact that matched observations in a pair will not be exactly identical to their counterparts on observed covariates. If matched days systematically differ from their target day counterparts in demand and/or temperature, our estimated differences in electricity market outcomes could be driven in part by differences in these variables in addition to differences in gas prices.77 We are concerned that this type of bias may arise in our setting because within the local neighborhood of 56 first-stage match days for each target day there is likely to be a relationship between gas price and other determinants of demand. This means that when sampling three lower gas price days from the counterfactual scenario from among the 56 potential matches, we are more likely to choose days with lower electricity demand and higher temperature as well, and our final estimates would be driven in a small part by differences in these other variables.

We employ a simple regression-based bias correction procedure that adjusts gas prices for potential match days to remove variation due to temperature and electricity demand.78 _{Within each neighborhood of 56 potential match days, we estimate the} relationship between the gas price, electricity demand, and temperature (HDD):79

P_tG = α0+ α1DEt + α2HDDt+ ut

We then construct a bias-correct gas price for each potential match day ePG

t by

77_{In this section, we refer to the original day as the “target day.” Each target day in the sample}

is matched with three “match days” that are similar in electricity demand and temperature and either a.) the gas price or b.) our estimated counterfactual gas price, depending on the scenario.

78_{While gas prices are also correlated with oil and coal prices to some extent, we do not include}

them in our bias correction to keep it consistent across all plants for which we employ matching.

79_{Although the relationships between these variables within the subsample 56 potential match}

days will be reflective of broader relationships for the entire population, estimating them within first-stage subsamples flexibly allows these relationships to be nonlinear in all first-stage variables.

taking the predicted price for the target day (indexed using ξ) and adding in the the residual for each match day:

e

P_tG =α_b0+αb1D E

ξ +αb2HDDξ+ ut

We then select the three second-stage match days using the difference between ePG t and either PG

t or bP

G,cf

t , depending on the scenario. In this framework, ePtG incorporates only variation in gas price due to weather and demand of the target day plus only variation in the gas price that is not driven by these determinants in the target day (such as variation that may be driven by capacity withholding).

This bias correction procedure improves the quality of matches on first stage variables. Before employing it, match days for our counterfactual scenario are about .5 ◦_{F warmer than target days on average and their peak demand is about 65 MW lower.} By systematically matching days that are slightly warmer and have slightly lower demand than the target day, we would be overestimating the impact of withholding. After employing the bias correction, match days are only about .018 ◦F warmer than target days and their peak demand is only about 13 MW lower.

A.3.3.2 Bias from Out-of-Merit-Order Dispatch during Congestion The core of our simulation model consists of reconstructing and clearing the day-ahead energy market using generators’ actual day-ahead bids and day-ahead demand. This simplification of ISO-NE’s actual market clearing process makes it possible to exploit the properties of nearest-neighbor matching estimators to identify how a change in the gas price would affect electricity prices, but necessarily introduces some discrepancy with real world outcomes. In particular, we note that simulated prices will likely deviate from actual day-ahead prices because we do not incorporate imports/exports, startup costs, or transmission constraints in our model. While all three introduce

noise, we believe the last in particular may bias our results because transmission constraints are more likely to come into play when the set of available generators is restricted by limited gas supply. Furthermore, this bias will inherently be greater at high electricity prices. Reconstructing and clearing the market without resampling and without applying a bias-correction to demand, we find that simulated prices closely track actual prices when prices are low but are skewed downward when prices are high (see Panel A of Figure 19).

Our bias correction procedure first solves our simulation model with actual bids ¯_{bit backwards to calculate the implied demand necessary to rationalize the observed} day-ahead electricity price for each hour in our study period _eqe

h. We then estimate the relationship between _eqe

h and actual day-ahead demand qhe, and use predicted demand from that model_bqe

h in place of actual demand in all simulations in the main text of this paper. Because we are specifically interested in correcting for a nonlinear relationship, we estimate _bq_he using a fractional polynomial specification:

e q_he = θ0+ θ1(qhe) α_{+ θ} 2(qhe) β _{+ ν} t (1)

We estimate this relationship for the entire sample and then separately estimate it for winter and the rest of the year, finding that the latter model is a much closer fit, as shown in Panels C and D of Figure 19. We therefore use the relationships recovered from the seasonal model to predict q_be

h, which structurally removes the nonlinearity between actual levels of day-ahead demand and levels required to rationalize observed prices in our simulation model as shown in Panel E. As Panel B illustrates, this adjustment significantly improves the fit of our simulation model price results for prices above $200/MWh. As a robustness check, we perform a full run of our simulation model without applying this bias correction, finding that it only slightly affects our estimate of energy costs, as shown in Panel F. We proceed to use the q_be_h in place of q_he

Figure 19: Bias correction to adjust demand for transmission constraint on high-priced days.