In this paper, we formalize the secular stagnation hypothesis in an overlapping generations model with nominal wage rigidity. We show that, in this setting, any combination of a permanent collateral (deleveraging) shock, slowdown in population growth, or an increase in inequality can lead to a permanent output shortfall by lowering the natural rate of interest below zero on a sustained basis. Absent a higher inflation target, the zero lower bound on nominal rates will bind, real wages will exceed their market clearing rate, and output will fall below the full employment level.

The paper is by Gauti Eggertsson and Neil Mehrotra, here. I have been clamoring for someone to formalize the secular stagnation hypothesis, and this is an interesting approach. EDIT: See new footnote.*

This is a 3-period OLG model without capital. The standard shock is contraction of an exogenous borrowing constraint, inducing deleveraging among borrowers (the young). A persistent savings glut is driven by generational concerns: having borrowed less when I was young, I now have more to save when I am middle aged. This keeps the interest rate from returning to a higher level. Deleveraging shocks, even temporary ones, have persistent consequences, potentially resulting in a new steady state with a very low, even negative, interest rate. More generally, any shock that results in low aggregate borrowing among the young has persistent effects, including a lower birth rate. Within-cohort income concentration can also reduce the interest rate through the standard mechanism associated with marginal propensity to consume. Nominal rigidities (in particular, downwardly rigid wages) make things worse, resulting in permanently lower output. If the interest rate falls below zero, the central bank can't put Humpty Dumpty together again.

The authors plan to extend the model to include capital, which seems important. A world in which consumption is the only source of demand doesn't make a lot of sense to me for this question, but it seems to be what some people in the blogosphere are assuming. And what if there is an equity premium? The standard response to my complaints that stagnationists are ignoring investment is that the ZLB prevents investment from really getting going; I guess the implication is that people will just hold cash instead of buying widget machines. But the natural interest rate would have to be

*really*low for the rate on equity to fall below zero. This investment market still clears.

At the margin, should fans of Piketty be rejoicing at the prospect of permanently low r? Arnold Kling has been asking for a reconciliation of these stories; he got a really interesting response from the brilliant Matt Rognlie (in the Kling's comments):

One way to reconcile the two is to say that Piketty's return on capital includes the equity premium (and other premia for privately held businesses, etc.), whereas the secular stagnation idea of a perpetual ZLB deals with only the riskfree rate. If the equity premium is large, it's possible that Piketty's return on capital is high but the equilibrium real rate is low.

Is this plausible? Rognlie does some back-of-the-envelope thinking that suggests it may not be:

A decline in the real interest rate from 2% to -1% implies a decline in user cost r+delta from 4.5% to 1.5%, of a factor of three. If the demand for structures is unit elastic . . ., this would imply a threefold increase in the steady-state quantity. Since structures are already 175% of GDP this would imply an additional increase of 350% of GDP, more than doubling the overall private capital stock and nearly doubling national net worth.

Needless to say, getting there would require a huge investment boom.

Rognlie's is a very rough parameterization, and it's partial equilibrium, but the point is that we haven't grappled with this yet. I'm looking forward to the next iteration from Eggertsson and Mehrotra; the existing paper has convinced me that this question deserves serious attention.

*There has been some debate about particulars of the model and whether this paper is very good. I think it is a good paper; we have been complaining about the lack of formal exposition of secular stagnation, and now we have a start. In my view starting with a simple model is useful, even though it lacks some key aspects of reality (primarily capital) and assumes the result to some degree (with its totally exogenous borrowing constraint). I am a skeptic of secular stagnation, so it's important to me that its proponents make their argument transparently and formally. Starting simple is the most honest and transparent way to build the case so that we can all see the man behind the curtain. The next serious step is capital, and then we will really have something to talk about.

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