## Sentence of enduring value

[F]iscal stimulus is a solution, rather than a way of buying time, only under some particular assumptions that are at the very least rather speculative.

Those particular assumptions are that the economy is in a lower output equilibrium, that fiscal policy is temporary and it is large enough to bump it to the higher output equilibrium. Given Krugman’s rhetoric on deficit spending, he must have these assumptions in mind.

First, he must be assuming we’re in a sustained depression.

Second, he’s assuming we’re stuck in a pessimism induced low output equilibrium. The alternative would be to assume a structural problem causing low investment demand. The candidate problems for having put us into the current depression are the banking crisis and the loss in wealth due to the housing bust. The banking crisis reduces the supply of loanable funds thus increasing real interest rates. This might reduce GDP, but its not getting us closer to a liquidity trap. The housing bust made people poorer but I’m not sure how that would have effected interest rates. So, of those three alternatives, he must have pessimism and multiple equilibria in mind.

I’m not sure how we got to this lower equilibrium assuming we were in the high equilibrium before the crisis. Looking at Krugman’s figure 6, we would identify a move to the low output equilibrium from a standard reduction in planned expenditures by looking at how fast of a decrease in GDP there was in the down-turn. Sudden, deep declines suggest a move to the lower equilibrium. Did I sleep through a large and sudden decrease in GDP?

Third, he must be assuming fiscal policy will be short-lived. This doesn’t seem consist with Obama’s rhetoric of “green” projects and its especially inconsistent with nationalized health care.

Fourth, Krugman assumes fiscal stimulus will be quite large. How big is quite large? Since talk of multiple equilibrium is “just speculative” — we don’t know the shape of the non-linear anticipated expenditures line — its not clear how to quantify the amount of stimulus needed to get to the better equilibrium. Also, there’s an implied trade-off between this assumption and assumption three. The larger the fiscal package the shorter term it must be because taxpayers’ Ricardian impulses will start to kick-in and consumption plans can and will be changed the longer the time horizon. Fully rational consumers suffering from no transition costs make fiscal policy ineffective.

UPDATE: I expanded the points in the paragraph that starts “First, …” and added the point about the trade-off between short-term and large fiscal policy.

UPDATE 2: Krugman has a “paper” up that’s really terrible. He solves an optimization problem without a zero lower bound on interest rates, but uses the lower bound in his discussion the first order conditions and their implications for policy. tsk tsk

UPDATE 3: This paper shows how significant the problem I point out in update 2 can be… Compare the first order conditions in Krugman’s note to the first order conditions here (equations 2.1-2.3); the equations get really ugly when you include that lower bound on nominal interest and they’re not nearly as aminable to easy story-telling as Krugman would like them to be. BTW, these authors, through numerical simulations, find surprising implications of optimal fiscal policy:

We find that it is indeed true that an optimal tax policy involves changing tax rates in response to a situation in which the zero bound is temporarily binding, and we ¯nd furthermore that the optimal change in tax rates is largely temporary. However, the nature of the optimal tax response to a liquidity trap is quite di®erent from traditional Keynesian policy advice. In the case that only taxes with supply-side e®ects are available, we find that it is actually optimal to

raisetaxes while the economy is in a liquidity trap.

As a professor once told me, paraphrasing, in modern macro there are no stories, there’s only solutions to a system of equations.