Friday, February 13, 2009

Uncertainty and the MPC

I try not to spend too much time on this blog correcting journalists' spurious economic arguments. After all, the target is too easy, and time is too scarce. But I will make an exception for this Newsweek article by Daniel Gross, in part because he invokes my name so prominently and in part because his error is so edifying.

Essentially, what Gross says is that (1) people now face a lot of uncertainty, (2) therefore they are inclined to save rather than spend, and (3) therefore any tax cuts they might receive would have only a small effect on their spending.

On its face, that argument sounds reasonable. But there is a subtle logical leap that, I believe, does not bear up under closer scrutiny. The step from (1) to (2) makes perfect sense in the context of models of precautionary saving. (For the econ wonks out there, I am envisioning an intertemporal consumption model with either a positive third derivative of utility, so certainty equivalence fails, or the possibility of borrowing constraints). Essentially, what the precautionary-saving literature says is that more uncertainty reduces the average propensity to consume (APC), the ratio of consumption to income.

But statement (3) does not concern the average propensity to consume. It is about the marginal propensity to consume (MPC), which is the extra consumption generated by a dollar of extra income. Gross implicitly assumes that when uncertainty reduces the APC, it also reduces the MPC. The precautionary-saving literature, however, suggests otherwise.

Suppose we were to graph a household's consumer spending as a function of cash-on-hand, which equals current income plus liquid assets, holding constant expected future income. In a permanent-income world without precautionary saving effects, that consumption function would have a constant slope of r, the rate at which the consumer annuitizes wealth. That slope is the marginal propensity to consume.

Now introduce uncertainty and precautionary saving effects. That uncertainty would depress consumption at all levels of cash-on-hand, but it would depress consumption more at low levels of cash. Those with high cash levels can more easily bear the effects of the uncertainty and would change their consumption less. But if consumption is depressed more at lower levels of cash than at higher levels, then it follows, as a sheer mathematical matter, that the marginal propensity to consume from an extra dollar of cash has gone up. In other words, uncertainty lowers the APC but raises the MPC. People save more in response to uncertainty, but their spending becomes more sensitive to current cash flow.

Gross makes another, unrelated mistake. He suggests that, as a Harvard professor, I am an example of a person with a particularly stable income. (That is why, he intimates, I fail to appreciate the consumption decisions facing real people who face substantial uncertainty.) It is true that my university salary is reasonably secure, but more of my income comes from book royalties than salary, and that income is anything but stable. Any day now, someone could come along with a better textbook and put me out of business.

On this last point, of course, I am speaking hypothetically.