A note on the time series measure of conservatism

Asymmetric persistence of accounting income is often tested in a regression of changes in earnings on lagged changes in earnings, including an interaction term for negative changes (see Basu [1997] or Ball et al. [2009] for a recent overview). In this note we propose an alternative, but closely related measure of conservatism - regressing the changes in earnings on the lagged levels, similar to the threshold-unit root test specification of Enders and Granger [1998]. We argue that this approach has three distinct advantages compared to the conventional setup: (i) a smooth, non-oscillating impulse response pattern to an unexpected shock in earnings (ii) a return to the old equilibrium of earnings in the long run and (iii) it can be extended to higher order autoregressive processes. We illustrate the differences between the two approaches, when applied to a common data set of firms, as well as a data set from a Monte Carlo simulation.