Identifying Elasticities in Autocorrelated Time Series Using Causal Mechanism Graphs

Instrumental variable (IV) methods are widely used to estimate the price elasticity of demand from observational data. However, naive IV estimators may be inconsistent in settings with autocorrelated time series. We argue that causal graphs taking into account time structure can simplify IV identification and help select consistent estimators. More precisely, we propose to model equilibrium conditions using causal mechanism time graphs. These (acyclic) graphs allow us to maintain the assumption of a simultaneous determination of prices and quantities and come with an interpretable notion of intervention. They further allow us to exploit recent advances in graphical inference to derive valid IV estimators that are consistent under weak assumptions. Finally, we argue that observing significant differences between the estimates of presumably valid estimators can help to reject false model assumptions, thereby improving our understanding of underlying economic dynamics. We apply our approach to the German electricity market, estimating the price elasticity of demand from simulated and real-world data. The findings underscore the importance of accounting for structural autocorrelation in IV-based analysis.