Can there be an equilibrium real rate of interest that is

negative? In general, the answer is no. If we think of a steady-state where

consumption is constant, then because the household discounts the future, the

real rate of interest has to be strictly positive. The real interest rate corresponds to the

marginal product of capital. In a representative agent economy, a negative real

interest rate is possible as a transitory phenomenon, and would correspond to a

decumulation of capital indicating that the capital stock was too large and

hence the household would seek to reduce it by maintaining a high level of

consumption with possible dis-saving (consumption in excess of income). A

negative real interest rate would be a temporary phenomenon on the path to

steady-state: along the path, as the capital stock is reduced, the real

interest would get back into the positive territory. In the Ramsey model, a

very large initial capital stock yielding a negative marginal product would

result in a high level of consumption which fell over time, with

dis-investment.

Matters are different in OLG models, which are not in

general dynamically efficient. In a simple exchange economy without production,

it is possible to get a negative real interest rate in equilibrium. If current consumption is cheaper than future

consumption, you need to give up more now to get less in the future. The key assumption needed is that there is no

storage or capital: one generation trades with another. Eggertson et al (2017)

have a model where people live for three periods: they have endowments middle

age and when old: they borrow when young.

Assuming that the endowment is largest in middle-age, consumption smoothing

indicates that they will borrow when young, and save when middle aged to

augment their retirement consumption (the old consume everything they

have). At any time, there are all three

generations living together. The middle aged at time t can only save for when

they are old in t+1 by lending to the young at time t, who will repay the old

at t+1. Here, the young demand loans

(consumption) from the middle aged; the middle aged lend to them so that next

period they get paid back and their old aged consumption is increased. The real interest rate here can be positive

or negative, depending on the balance between the supply and demand for loans.

In order to link this monetary policy, we need to introduce

nominal wages, nominal prices and a nominal interest rate. Making various

assumptions, Eggertsson et al show that there can exist “*a unique, locally
determinate secular stagnation equilibrium” *

*(*

*Proposition 1, page 21. Figures 4 just above the proposition make the essential*

role of deflation clear).

However, the secular stagnation

role of deflation clear).

equilibrium must have deflation: negative inflation. If inflation is positive,

then there will be full employment. This

is because the mechanism reducing output is the increase in real wages. So, in

a secular stagnation equilibrium, the nominal interest rate is at the ZLB (zero

lower bound), output is below full employment, inflation is negative and real

wages above their full employment level (due to downward rigidity). The actual real interest rate is positive

(equal to minus the deflation rate): it is a hypothetical real rate that is

negative (the real rate that would restore full employment). The ZLB does not lead to an equilibrium

negative real interest rate: it prevents the real interest rate from becoming

negative when inflation turns negative.

Have we observed

negative inflation? In the UK and the US just the occasional month in 2016 and

(depending on whether you use CPI or RPI) perhaps for a month or two at the

height of the crisis. Japan has had more

disinflation since the late 90s (disinflation “peaked” at just over -2% in

2009). The Eurozone is a mixed bag: the

aggregate inflation rate has mainly been strictly positive with a few

exceptions as in the UK and US. For

individual countries the story is more heterogeneous. So, if we look at the

major economies, there is no evidence of sustained disinflation that might give

rise to the high real rates required for Eggertsson Stagnation. In fact we find

the exact opposite. The ZLB is combined not with negative inflation, but

positive inflation. Rather than positive real rates, we find real rates are

negative.

This brings us to

the most important an obscure part of the paper: section 8, the model with over

100 equations. Here there are lots of

generations and capital is introduced. The key equations are buried in the

appendix: A81 and A82. The marginal productivity for capital A81 is the usual:

the marginal product of capital will be strictly positive. Then there is

A82. This is a little different: there

is a price of capital goods term. Greg Thwaites has developed a model of

falling real interest rates driven (in part) by the falling price of investment

goods. There has been a downward trend in the prices of investment goods

(relative to consumption goods), which means that savings leads to more

investment (but possibly lower investment expenditure). This can drive down the

marginal product of capital. However, in Thwaites model the real interest rate

may be low, but is always positive. So what is it in the Eggesrtsson model that

can give you their figure 7: secular stagnation with strictly positive

inflation (recall, this was impossible in the world of proposition1). I must

admit, that I have read the paper and am none the wiser about how this might be

possible. The paper just presents a

calibration and reports that this is what happens. Unlike the world of

proposition 1 there is no clear story or intuition.

I do not doubt that with sufficient

inventiveness a model with equilibrium negative real interest rates can be

constructed. But it would not be a basis for monetary policy. Monetary policy

needs to be based on robust models that have passed the test of time, not on

exotica. I will continue to believe that real interest rates should be strictly

positive in equilibrium.

The two papers mentioned are:

A Model of Secular Stagnation: Theory and Quantitative Evlauation,Gauti B. Eggertsson, Neil R. Mehrotra, Jacob A. Robbins. NBER Working Paper

23093 (2017).

Why are real interest rates so low? Secular stagnation and, Greg Thwaites. Bank of England workingthe relative price of investment goods

paper 564 (2015).