Lately everyone is blogging multipliers. It is frequently suggested that the multiplier today is best estimated at 1.5 or 1.6. My point today is this: if you postulate a potent multiplier you cannot easily also postulate a liquidity trap. The whole point of the multiplier is that if the government buys cement from my company (say for a road) I as the company owner take those cash receipts and spend them elsewhere. Maybe so but that means people are willing to spend cash when they receive it. It means that a helicopter drop (and maybe other forms of monetary policy as well) would stimulate AD quite readily and for free. You don't need exotic or balance sheet-distorting QE here, a simple injection of cash will do.
Indeed, the Christiano, Eichenbaum, and Rebelo model of fiscal policy in a liquidity trap, no matter what you think of it (e.g., I am not sure that the derivation of equations 2.19 and 2.20 takes the non-smooth, black hole properties of the liquidity trap assumption seriously enough; also the critical p.13 sentence about how the MU of consumption rises with employment is the kind of Minnesota macro that Krugman justly complains about) both implies and states that monetary policy will work too. And if that monetary policy is truly a free lunch in terms of gdp, it should be quite credible (if it's not credible in the real world maybe the problem wasn't AD in the first place).
There are other models in which fiscal policy has a potent multiplier yet there is a liquidity trap. For instance fiscal policy may be a "sunspot" which gets you out of the liquidity trap. I have at least two objections. First, these models are question-begging. (Might not monetary policy be the sunspot? Why is fiscal policy the sunspot if indeed fiscal policy would otherwise not have much of a multiplier?) Second, no one much believed these models ex ante, before the current set of policy debates came along.
I am also puzzled by Paul Krugman's point:
…this [Barro's paper] tells us very little about what would happen under current
conditions: during World War II there, um, was a war on: consumption
goods were rationed, construction required special permits, and so on.
The government was, in other words, deliberately suppressing private
spending, through direct controls. So WWII is not a useful data point
for determining what the multiplier is under other conditions.
As I view it, during the war the government suppressed private spending because the government did not in fact believe there was much of a multiplier (at least at those margins). The suppression of private spending was not an exogenous accident but rather it reflected the very real trade-offs which had to be faced between guns and butter. At the beginning of the war unemployment was still quite high yet rationing came quickly, not only after full employment was restored, precisely because the trade-offs were faced quickly. Are we to believe that without rationing U.S. private consumption would have risen during WWII? Something like the following can be argued: "there is a multiplier for small acts of public investment but at some margin, such as we faced in WWII, that multiplier goes away for sufficiently large acts of public investment." I don't read Krugman as making that claim, but it would be his best available response to Barro.