Time-varying (S, s) band models: Properties and interpretation

A recent strand of empirical work uses (S, s) models with time-varying stochastic bands to describe infrequent adjustments of prices and other variables. The present paper examines some properties of this model, which encompasses most micro-founded adjustment rules rationalizing infrequent changes. We illustrate that this model is flexible enough to fit data characterized by infrequent adjustment and variable adjustment size. We show that, to the extent that there is variability in the size of adjustments (e.g. if both small and large price changes are observed), (i) a large band parameter is needed to fit the data and (ii) the average band of inaction underlying the model may differ strikingly from the typical observed size of adjustment. The paper thus provides a rationalization for a recurrent empirical result: very large estimated values for the parameters measuring the band of inaction.