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
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.