What do “residuals” from first-order conditions reveal about DGE models?

The first-order condition (FOC) associated with labour in many dynamic general equilibrium models involves only current period variables. Residuals constructed from this FOC are inconsistent with aggregate US data in that they are very large and highly persistent. The persistence suggests that models which introduce dynamic terms in the labour FOC may be more consistent with the data. Three such models (one with learning by doing, one with habit formation, and one with labour adjustment costs) confirm that they can reduce the persistence in the residuals making the models more consistent with the joint dynamics of consumption, output and hours.