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Time-separability of utility means that past work and consumption do not influence current and future tastes. This form of preferences does not restrict the size of intertemporal-substitution effects, but does place constraints on the relative responses of leisure and consumption to changes in relative prices and in permanent income. These constraints are important for evaluating the impact of shifts in expectations about the future, which play a key role in equilibrium models of the business cycle. Further, if consumption and effort are to be positively correlated over the cycle, then equilibrium theories with time-separable preferences predict a procyclical behavior for the real wage rate.
Barro et al. (Thu,) studied this question.