Consumption Decisions with Stochastic Wage Income: Testing the Implications of an Approximate Solution

In this paper, I use an approximate solution to model the optimal consumption when the representative consumer faces labor income uncertainty. This approximate consumption function is based on Zeldes' (1989) numerical solution to the optimal consumption problem with CRRA utility and stochastic labor income. Unlike the certainty equivalence solution, this model assumes that the consumer discounts expected future labor income at a rate higher than the real interest rate. It therefore takes into consideration the precautionary savings of the consumer. The first order implications of the approximate consumption function, with and without the liquidity constrained consumers, are tested using quarterly US data. The evidence lends support to the claims of the approximate consumption function, particularly when liquidity constrained consumers are included. The empirical results of this paper imply that current consumption should be Granger caused by variables in the lagged information set. Meanwhile, consumption should be smoother than labor income, even when the latter follows an integrated process. Both implications have been documented in the literature. Based on this evidence, I conclude that the approximate model is a promising way of getting around the difficulties involved in obtaining a closed form solution when utility is of the general decreasing absolute risk aversion type.