UPDATE (01/25/12): This post is erroneous and none of its conclusions should be relied upon.
OK, so it has come down to this. I just asserted that the way to translate Lucas and Cochrane into the Keynesian model is to set the mpc equal to zero. In that case, any increase in government spending that is offset by taxes causes no net increase in income, because as, Lucas puts it, the increase in government spending is exactly offset by a decrease in consumption of an equal amount thanks to the reduction in after-tax income. This exercise is predicated on the assumption that the equal increase in government spending and taxes is permanent. But in the exercise proposed by Wren-Lewis, the increase in government spending is temporary and the increase in taxes is also temporary. How does the transitory nature of the increase in government spending and taxes alter the analysis under a Lucasian version of the Keynesian model?
Wren-Lewis claimed that you get a stimulative effect. The increase in government spending is concentrated in the present, but the reduction in spending is spread out over the future, leaving a net positive effect in the current period.
Thanks to Scott Sumner’s comment on my previous post (which I too confidently pronounced definitive), I now see where Wren-Lewis and the rest of us went wrong. The stimulative effect of the government spending is depends on the existence of a simple multiplier greater than 1 (i.e., an mpc greater than 0) [This is in error, a stimulative effect is present for any value of the MPC less than 1 for which a unique equilibrium exists in the simple Keynesian model.]. So to say that government spending must be stimulative, even if offset by taxation, begs the question whether government spending generates any increase in income beyond the amount of initial spending. If you assume fully rational maximizing on the part of households (Ricardian equivalence), their mpc is equal to 0 (though that may perhaps be subject to some quibble, in which case there would still be room for argument on the effect of tax-financed government spending). [The balanced budget multiplier is 1 in the simple Keynesian model even if the MPC equals 0.]
But if you are willing to grant for the sake of argument that the mpc is equal to 0, then it does seem that even a temporary increase in government spending would imply no net increase in income because of the absence of multiplier effects. The increase in government spending would be offset by an equal decrease in consumption spending caused either by 1) increased taxes today or 2) by increased saving today in the expectation of future tax payments. (I am now a bit troubled that this doesn’t seem to accord with Nick Rowe’s analysis, but I will have to live with that until he weighs in again on the subject.) [I should have realized that I was confused at this point and started over.]
Note that I didn’t need to say anything about accounting identities to get to this result. (Gotta find that silver lining somewhere.) But Scott can still feel good about having convinced me that his basic intuition was right. The should teach us all to remember the old maxim, “Don’t Mess with Scott.”
PS At this stage, I am fully prepared to be proven wrong yet again, so I will be reading your comments very carefully to find the next surprise lying in store for me.