Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis

This paper argues that the typical household’s saving is better described by a “buffer-stock” version of the Life Cycle/Permanent Income Hypothesis (LC/PIH) model than by the traditional, certainty-equivalent version of that model. Buffer-stock behavior emerges when consumers who face important, uninsurable income uncertainty are also “prudent” (they have a precautionary saving motive, in Miles Kimball’s sense) and “impatient” (if future income were known with certainty, they would want to consume more than their current income). Such consumers hold a target wealth-to-permanent-income ratio: below the target, prudence dominates and they save; above it, impatience dominates and they dissave. Carroll shows analytically, in an infinite-horizon version of the model, that this configuration implies average consumption growth equals average labor-income growth for the typical household – even though consumers obey the standard consumption Euler equation – because the endogenous variance of consumption growth, which prior research typically assumed away, adjusts to make it so. A finite-horizon version of the model, calibrated to US household age/income data, generates buffer-stock behavior over most of the working lifetime (until roughly age 45-50), switching toward more conventional life-cycle saving only in the last years before retirement. Carroll argues this buffer-stock model, unlike the standard LC/PIH model, a simple Keynesian consumption function, or the Campbell-Mankiw hybrid of the two, can jointly explain three stylized facts: the “consumption/income parallel” documented by Carroll and Summers [1991]; the “consumption/income divergence” long known from household-level survey data; and the empirical stability of the household age/wealth profile despite a sharp post-1973 slowdown in expected income growth, which the standard model implies should have produced a large increase in wealth-to-income ratios. The model implies a much higher marginal propensity to consume out of transitory income (15-50 percent across the parameter values considered, versus at most about 8 percent in the standard model) and a much smaller marginal propensity to consume out of anticipated future (“human”) income than the standard model. Carroll argues that, read carefully, this buffer-stock model is close to Friedman’s [1957] original conception of the Permanent Income Hypothesis, though he is explicit that it is not a complete theory of household wealth: it does not describe the very wealthy, explicit life-cycle savers using pension plans, housing investment, or the sharp asset decumulation of retirees implied by the model’s assumption of a certain date of death.

Christopher D. Carroll | Macro Paper Warehouse

Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis