# Multiplicative Interactions in Error Correction Models

## Flávio Souza (Texas A&M University)

Abstract: Error correction modeling (ECM) is a common time-series strategy when both dependent and independent variables contain a unit root and are cointegrated. But one of its principal drawbacks is its inflexibility—since it requires that every independent variable enter the right-hand side of the equation in first differences and first lags. This complicates testing the effects of multiplicative interactions. Researchers often ask themselves, for example, whether they should lag before interacting or lag the interaction term itself. Much confusion remains as to whether interactions are even appropriate with these models in the first place. In this paper, I suggest that multiplicative interactions can and should be included in ECMs when theoretically warranted. I explore the technicalities of this modeling choice and use a series of Monte Carlo simulations to evaluate the bias and efficiency trade-offs over alternative strategies.