I have been staring for weeks now at what I have come to call equation (11):
ΔW is the (marginal) change in social welfare induced by a (marginal) change ΔG in this-period government purchases
rd is the real social rate of time discount
g is the real growth rate of the economy
η is the labor-side hysteresis parameter--the share of today's boost to employment/output that is permanent because deep recessions cast shadows and reduce aggregate supply by increasing failures in the labor market
δ is the deadweight loss from raising a dollar of tax money in the future
m is the multiplier, net of any central bank neutralization of fiscal stimulus
τ is the current tax rate
ρ is the (if positive) default premium interest rate that the government must pay over and above the social rate of time discount, or (if negative) the value to investors of having safe government paper backstopped by the taxing power to invest in).
I think that there are a number of lessons to be drawn from this equation:
First, expansionary fiscal policy at the margin has net benefits as long as the this-period net-of-monetary offset multiplier parameter m is greater than the deadweight loss from additional tax revenue parameter δ. In a normal situation expansionary fiscal policy is not worth undertaking: the deadweight tax loss parameter δ is greater than the within-period multiplier parameter m, whether because labor or capacity constraints keep increases in nominal spending from raising production and employment by any significant amount or because the monetary authority takes steps that raise interest rates and so neutralize fiscal policy out of its desire to maintain price stability. But the situation right now is not normal.
If there is value to investors in holding safe government debt--if ρ is negative and large enough in magnitude that rd - g + ρ is less than zero--then expansionary fiscal policy at the margin has net benefits for any positive multiplier parameter m, no matter how low. This is the “free money” point: if rd - g + ρ < 0, the attractiveness of government debt to wealthholders as a safe savings vehicle is sufficiently great that at the margin there is no financing burden of government debt on taxpayers. A national debt is then, in the words of first U.S. Treasury Secretary Alexander Hamilton, “a national blessing”—and more debt is a bigger blessing. In such a situation to sell new government debt and use the money to buy something useful in any way--or indeed to buy something useless--is social welfare-improving.
It certainly looks right now as though rd - g + ρ < 0: if we had a real Treasury consol right now, its duration would be about 70 years and its interest rate would be in the range from 1.2%/year to 1.7%/year, comfortably less than the projected real growth rate of the economy. Where this comes from is an interesteing research question. Is it the equity premium puzzle by another name? Is it because investors are irrationally attached to what they regard as safety? Is it because financial markets are really lousy at mobilizing the risk-bearing capacity of the economy, while governments via taxation can do so easily? It looks as though the 1980s and the 1990s are the only times since the Gilded Age in which rd - g + ρ has not been less than zero. If so, that would have implications for optimal fiscal policy that would run far beyond the desirability of Keynesian expansion at the margins in deep depressions.
Under the ancillary assumption that the appropriate social rate of time discount is surely not that much larger than the expected real growth rate of the American economy, positive hysteresis effects from labor-market attachment are highly likely to make expansionary fiscal policy at the margin worthwhile even if the multiplier is so low and the deadweight loss from taxation so high that even right now m < δ. Whatever costs are incurred as a result of deadweight losses of financing for debt and whatever current year benefits are obtained from a stronger economy are swamped did fiscal stimulus now manages to boost the permanent capital stock or reduce structural employment in the economy at all.
If there is a substantial multiplier or significant hysteresis effects right now, the only consideration that could militate against the desirability of expansionary fiscal policy at the margin would be the emergence of a large positive risk-and-default premium ρ on government debt. Unless and until we turn into Greece in some bizarre way, there is nothing else in (11) that could mke expansionary fiscal policy at the margin a bad idea.
The cost of financing the extra deficits generated by expansionary fiscal policy are lower than one would think becasue the multipier works in the short run to diminish the increment to the debt that must then be financed.
Anything that I have missed?