## 3 Regression Analysis of Price (USD/MWh) Data for West, North, and Houston Regions in ERCOT
### Analysis of Hourly Models for West Region Price Data  
Recall the following from Section 2: Could incentivizing renewable resource electricity generation via tax policies, such as Texas Code Chapter 313, lead to reductions in the cost of electricity in the real-time, wholesale energy market in the ERCOT? That is, is there an association between tax-incentivized power generation and wholesale prices in the energy market? Additionally, from the perspective of economic dispatch, increased electricity demand throughout the ERCOT is first met by those resources that are the cheapest to generate and deliver to the grid--the renewable resources, wind and solar. From a pricing perspective, the merit-order effect (MOE) of this dispatching protocol should contribute toward lowering real-time wholesale electricity prices throughout the state. The parameter estimates of the nuclear, wind, and solar generation variables will quantify the MOE. The following empirical analyses will address the above salient points, in addition to other insights. Using STATA, under the assumption of normally distributed errors, the regression parameters were estimated using least squares. Under the assumption that the errors follow a skew-t distribution, the regression parameters are maximum likelihood estimates, which were obtained iteratively. Refer to Table 3 and focus on the Hour 3 AM skew-t regression estimates for the West region. All the regressor variables are statistically significant (\(p<0.0001\), and coefficient signs are as expected). The standard errors are given in parentheses. * WSapp18: The focus of this research is to study the impact of tax policies on the wholesale price of electricity. Let us begin by considering the marginal effect of the variable WSapp18, whose coefficient estimate equals \(-0.0492\). When the number of active wind and solar applications is at least 18, the price per MWh declines by about 5% (=\(0.0492\)) at 3 AM in the West region, which is a statistically significant reduction in price. Note that, even though there is no solar generation at 3 AM, it may be possible to produce and store solar energy, which could then be used if demand was high. * MOE: Of interest here is the merit-order effect (MOE) of nuclear and wind generation. Each 1% increase in nuclear generation, namely LN(Ngen), is associated with a 0.11% drop in price per MWh. A 1% increase in wind generation (LN(Wgen)) is associated with a 0.0851% reduction in price per MWh. Hence, a 10% increase in either energy source will lead to roughly 1.107% (=\(1.10^{0.1119}\)) and 0.81% (=\(1.10^{0.0851}\)) reductions in price per MWh, respectively. Coupled with the marginal effect of WSapp18, we can conclude that a tax policy aimed at incentivizing the number of active wind and solar applications is associated with declines in the wholesale price of electricity, ceteris paribus, since it will increase wind and solar generation--the less expensive renewable resources. Price Dummies: Next, consider the impact of extremely small and large prices in the price data distribution (see Table 2 in Section 2 for the minimum and maximum summary statistics). From Table 3, for the variable Wprice1, when prices are at most USD 1, there is a roughly 1493% decline in price, compared to when prices are greater than USD 1. This drastic reduction in price is likely induced by the LMP. Recall from Section 2 that LMP is a wholesale electricity price construct that quantifies the value of electric power at different regions in the ERCOT, taking into consideration factors such as demand, generation, and the supply constraints inherent in the ERCOT's state-wide transmission system. Theoretically and practically, LMP values can turn negative. This happens when there is a surplus of generation that cannot be delivered outside of its zone due to transmission constraints. In such instances, the prices of certain resources, typically wind, are forced down to curtail generation.