The authors argue that it is important to allow for a prolonged decay when studying anomalies or their impact on portfolio choice. Such decays may arise because investors may need time to build models and capabilities or to market the idea to raise funds. There could also be implementation frictions, for example, transaction costs that only slowly decrease over time. Moreover, the market's efficiency may vary over time, as suggested by Lo (2004) and Akbas et al. (2012), which will make some anomalies longer-lived than others.
In the paper, the authors propose a framework for modeling anomalies that specifically allows for a gradual disappearance. Their framework nests, and thus allows for direct tests of various economically motivated special cases: immediate disappearance, no decline, etc.
Estimating this model (or an equivalent model that allows for a decay) would be a valuable part of any paper that identifies a new anomaly or that documents an existing anomaly in a different market or context, the authors assert. The model would allow the authors to better estimate the original full strength of the anomaly (which would be understated if the anomaly already started declining) and would improve out-of-sample predictions for the anomaly (which would be overstated if the decline already began).