Secular Stagnation and Fiscal Policy

The latest thing is discussing the possibility that the economy might be in a liquidity trap for a long long time or might repeatedly fall into one.

So I ask what about some permanent fiscal stimulus to deal with secular stagnation. Now this question is an offence against Keynes and, much more, against new Keynesian economics. Keynesians have spent decades insisting that Keynesian theory does not imply higher government spending on average but rather higher spending during recessions and lower spending during expansions. Uh so what happens if the economy is stuck in a depressed steady state?

OK a very simple but new Keynesian type model follows.

The conslusion is that permanent fiscal stimulus works fine with a multiplier greater than one.

The standard result that stimulus should end is due to the standard assumption that the economy exits the liquidity trap as it is assumed that the unemployment rate returns to the natural rate.

First steady state, as always, really means balanced growth such that appropriately scaled variables are constant and the growth rates are constant.

First a depressed steady state is not allowed in standard new Keynesian models (or in 1960s era old keynesian models). The reason is mostly that, for convenience, it is assumed that there is only one steady state, but partly that expectations augmented Phillips curves imply that persistently high unemployment causes ever accelrating deflation (hence not a steady state). HOwver, the data suggest simple downward nominal rigidit. It seems only very high unemployment causes significant decline in nominal wages. Models can, and have, been augmented to give wage inflation equal to the greater of the number from an exectations augmented Phillips curve and zero. So I will just assume that wages and prices stay the same so long as unemployment stays high (which will be forever).

Before going on, I note that something like this fits the data. Persistently high unemployment in the USA has not caused deflation (with convergence to about 2% not 0% which I call not significantly different). Persistently low output in Japan caused steady deflation of around 1 or 2% (again not accelerating and close to zero). Even the original Phillips data showed only two years 1930 an 1931 with major decline of nominal wages and many years of high unemployment and wage growth of very roughly zero (in other years it got down to about -3% but with no trend in deflation even with persistently very high unemployment).

I will assume that utility is logarithmic in consumption and additively separable in consumption and leisure (the desire for leisure doesn’t matter as there is involutary unemployment — people are glad to supply all the labor which is demanded). time is discrete

U = sum (Ln(Ct) + h(Lt))B^2

Lt is labor. h'() With the real interest rate (r) = 0, consupmtion will shrink at the rate of time preference (Ct+1/Ct) = B. Investment is such that Kt+1/Kt = Beta that means that (1-delta)Kt+It = BKt where delta is the rate of depreciation and I is investment.

Sad but all equations check. Note importantly that the decline in capital per capita does *not* cause the return on capital to increase. The ratio of employment to capital is chosen so that the ratio of the marginal product of capital to the marginal product of labor is equal to (r+delta)p/w = (delta)p/w. Shringking capital means srhinking employement not less capital per employed person.

OK now let’s aadd a government which taxes T (lump sum not that it matters) and spends G. I will juast assume a balanced budget so G=T. Note the absense of time subscripts. I assume that G is constant (starting in period 1).

First assume that G is pure waste.

Now old Keyensianly assume that investment depends on r (which doesn’t change). Then guess and check that GDP goes up by G when the permanent stimulus starts and remains exactly G higher than the no stimulus path. OK so national income increases by G. Taxes increase by T. Disposable income is not changed. The real interest rate doesn’t change and so all equations check. The solution is that a perment increase in G causes an identical permanent increase in GDP.

But the old Keynesian assumption is crazy (really abandoned immediately and never used except in examples for undergraduates). In the real worlld investment is high when GDP increases (and low when r is high — that is the accelerator model which fits the data better than any newer model).

In the model, capital can jump and it will Given fixed wages prices and real interest rates the ratio of capital to output is fixed. This means that the introduction of the policy will cause investment to increase by ((G)/GDP)(Kt)B.
in period t>2 it will be higher by ((G)/GDP)Kt(B^(t-1))(delta+B-1). The multiplier is greater than one because of the accelerator effect (which is absurdly huge in the simple model with no adjustment costs).

OK what if G isn’t totally wagest ? Here I think a reasonable benchmark case is one in whcih government spending is investment in public capital which is neither a complement to or a substitute for private capital. G goes to set up state owned enterprises which don’t compete with private firms for labor, because there is involutary unemployment. Public capital grows and converges to G/delta. This causes higher income net of depreciation because workers are paid by the public enterprises. This means that the not totally wasted stimulus spending relaxes the national budget constraint and causes higher consumption.

This is true even if consumers are Ricardian and even if public capital is one tenth as efficient as private capital.

Of course realistically, public capital complements private capital which is another way in which G stimulates I.

I think it is not easy to write down a model of a secularly stagnant economy in which the balanced budget multiplier is a low as 1.