Evaluating a consumption function with precautionary savings and habit formation under a general income process

In order to derive closed-form solutions for the consumption function under precautionary motive, the literature adopts restrictive assumptions about the consumer's income process, ranging from a stationary process to a random walk. To avoid such restrictions, I derive a consumption function with precautionary savings and habit formation under any ARIMA(p, 1, q) process. Empirically, I evaluate this general consumption function for aggregate U.S. data using different approaches to set the structural parameters. The findings imply that the larger the habit strength, the larger the level of income risk necessary to make the precautionary motive relevant. And, for reasonable parameters values, the aggregate time series on income is incapable of eliciting expressive precautionary savings.