Ensuring the Validity of the Micro Foundation in DSGE Models with Stochastic and Deterministic Trends

The presence of stochastic and deterministic trends in DSGE models may imply that the values of the agentsobjective functions are in\u85nite. For the households, this might happen if the consumption process has a su ¢ ciently high growth rate and the subjective discount factor is very close to 1. The problem associated with objective functions attaining in\u85nite values is that they do not have an optimum. Hence, DSGE models with trends may have invalid micro foundations because the optimal behavior of the agents is indetermined. In a rich DSGE model we derive su ¢ cient conditions which ensure that the householdsand the rmsobjective functions do not attain in\u85nite values. Based on these results we test the validity of the micro foundation in four calibrated or estimated DSGE models from the literature