  Demand response aims to stimulate electricity consumers to modify their loads
at critical time periods. In this paper, we consider signals in demand response
programs as a binary treatment to the customers and estimate the average
treatment effect, which is the average change in consumption under the demand
response signals. More specifically, we propose to estimate this effect by
linear regression models and derive several estimators based on the different
models. From both synthetic and real data, we show that including more
information about the customers does not always improve estimation accuracy:
the interaction between the side information and the demand response signal
must be carefully modeled. In addition, we compare the traditional linear
regression model with the modified covariate method which models the
interaction between treatment effect and covariates. We analyze the variances
of these estimators and discuss different cases where each respective estimator
works the best. The purpose of these comparisons is not to claim the
superiority of the different methods, rather we aim to provide practical
guidance on the most suitable estimator to use under different settings. Our
results are validated using data collected by Pecan Street and EnergyPlus.
