Some thoughts on Eggertsson and Mehrotra (2014), the first formalization of the “secular stagnation” thesis. Nothing innovative here, I just wanted to collect my thoughts all in one place.

**Model overview**

First, a brief review of Eggertsson and Mehrotra’s model for easy reference. (Simon Wren-Lewis has a short summary of the math.)

The paper describes a three-period overlapping generations model, where the middle generation receives an endowment (or, in an extension, labors for an income). The young and old generations do not receive incomes; the young borrows from the middle generation, and the old uses money saved from their time in the middle generation. The amount the young can borrow is constrained because of a purely exogenous “debt limit”. The key result is that if this debt constraint (exogenously) drops (a “deleveraging shock”), then the demand for loans drops, forcing the natural rate of interest to permanently fall, potentially to permanently below zero.

Once a price level and downward nominal wage rigidity are introduced, we can then have a permanent zero lower bound situation where the natural rate is permanently and unattainably negative – secular stagnation, by definition. This causes output to be permanently below potential.

Now, various thoughts, from more to less interesting:

**1. Lack of capital**

This model does not include capital. I suspect a model with capital and a negative interest rate would have negative or zero investment, whereas in the economy today we of course have positive net investment.

The authors do note they want to include capital in the next iteration of the model.

**2. Lack of land**

There is also no land in this model. Of course in modern times land is not typically included as a factor in the production function. Solow once joked, “If God had meant there to be more than two factors of production, he would have made it easier for us to draw three-dimensional diagrams.”

But Nick Rowe, I think, makes a good case that in a model attempting to analyze permanently negative interest rates, land must be included.

The argument goes like this: think of land as an asset like any other, where the price of land equals the present discounted value of the future returns to land. It can be shown that as the interest rate approaches the growth rate of the economy, the value of the land goes to infinity.

Back in the real world, of course, we have not seen land prices go to infinity. So perhaps adding land to this model would prevent us from having secular stagnation without the price of land blowing up.

Section three of this Stefan Homburg (2014) paper discusses this further, and Homburg models the result more formally here. Another interesting post from Rowe here, and comments from Matt Rognlie here.

(Side note: by the same logic, perhaps a fall in the natural rate explains the housing “bubble” of the last decade?)

**3. Debt limit as exogenous**

The debt limit is purely exogenous. It seems likely that there would be important and interesting general equilibrium effects if it were endogenized. There is not much to say on this point, but it’s very important.

**4. OLG modelling instead of representative agent**

This model uses OLG as its basic framework instead of a representative agent.

Importantly, this is different from the last decade and a half of research on the liquidity trap (Krugman 1998, Eggertsson and Woodford 2003, Auerbach and Obstfeld 2005) which all used representative agent models. In these models, in the long run steady the natural rate will determined by the discount factor which forces the long run natural rate to be positive. Thus, the economy can only be in a liquidity trap (ZLB) situation temporarily.

It’s only in this OLG environment that we can have a permanently negative natural rate. That seems very interesting to me – what else might we be missing by using the representative agent model? (…Probably not much.)

Turning away from mathematical formalization, I wonder if one way we could think about this is: what if the natural rate was expected to remain at the ZLB for a period longer than the remainder of a person’s life (say >60 years)? Would that create some kind of a trap situation?

**Conclusion**

Overall, I’m simply not convinced that this is a useful model. The idea that the natural rate could be permanently negative simply seems extremely unlikely. Also, the lack of inclusion of land seems to be a big oversight.

**Update**: Josh Hendrickson makes the interesting point that adding money to the economy (with a fixed nominal return of 0%), the Eggertsson-Mehrota does not hold.

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[…] AER paper that adds land to the Solow model in continuous time (ugh why) and verifies the result, discussed last week, that as the rate of return on capital approaches the growth rate of the economy the price of land […]