Smoothing Time Fixed Effects
Controlling for time fixed effects in analyses on longitudinal data by means of time-dummy variables has long been a standard tool in every applied econometrician’s toolbox. In order to obtain unbiased estimates, time fixed effects are typically put forward to control for macroeconomic shocks and are (almost) automatically implemented when longitudinal data are analyzed. The applied econometrician’s toolbox contains however no standard method to control for time fixed effects when time-dummy variables are not applicable. A number of empirical applications are crucially concerned with both suffering from bias due to omitting time and time-dummies being inapplicable. This paper introduces a simple and readily available parametric approach to approximate time fixed effects in case time dummy variables are not applicable. Applying Monte Carlo simulations, we show that under certain regulatory conditions, trend polynomials (smoothing time fixed effects) yield consistent estimates by controlling for time fixed effects, also in cases time-dummy variables are inapplicable. As the introduced approach implies testing nested hypotheses, a standard testing procedure enables the identification of the order of the trend polynomial. Applications that may considerably suffer from bias in case time fixed effects are neglected are among others cartel overcharge estimations, merger and regulation analyses and analyses of economic and financial crises. These applications typically divide time into event and control periods, such that standard time dummies may not be applicable due to perfect multicollinearity. In turn, their estimates of interest most crucially need to be purged from other (unobserved) time dependent factors to be consistent as time may by construction induce omitted-variable bias.