On the functional form of short-term electricity demand response - insights from high-price years in Germany

Demand response is crucial for balancing supply and demand in the presence of intermittent electricity generation, particularly during scarcity situations with high prices. In 2021/2022, wholesale power prices in Germany have been dramatically higher than ever before, which offers the opportunity to investigate the demand response in high-price situations. This paper, thus, discusses the applicability of the two common functional forms of demand response under these circumstances, namely linear and log-log. Using a two-stage least squares approach, the short-term own-price elasticity of electricity demand in Germany is estimated for the period from 2015 to 2022, employing the two assumptions for the functional form of the demand function. The day-ahead forecast of wind power generation serves as an instrumental variable for the day-ahead price. The analysis shows that for low prices, the linear assumption tends to yield similar average elasticities to the constant elasticity obtained from the log-log specification. However, estimators based on linear functions exhibit significant variations depending on whether low or high prices are considered. This discrepancy arises from the observation that remaining demand at high prices tends to have limited flexibility, leading to distinct estimations. In contrast, the log-log approach provides smaller differences between estimates based on low and high prices. The exponential nature of the log-log function effectively captures the decrease in absolute demand response at high prices, resulting in more consistent estimations across the price range.