Timing is Everything: A New Way to Estimate Strategic Behavior

Many applied economic studies aim to estimate strategic behavior through reaction curves. Examples include two-sided conflicts, or economic trade wars, and algorithmic pricing between firms. Analysis is usually performed at a prespecified time interval, such as days, weeks, months, or years, using a vector autoregression (VAR). Yet sides may respond within a day to one action, but wait a month after another. If data is recorded in arbitrary time intervals, then the researcher may mistake waiting to act for inaction. We analytically show that VAR analyses do not recover true reaction curves if the timing of reaction is not accurately recorded. This misspecification can cause the sign of the VAR coefficient to reverse and misspecified standard errors leading to erroneous inference. We discuss an alternative structural approach rooted in game theory to estimate reaction curves and investigate its usefulness in a Monte Carlo simulation.