Many people have asked me recently why interest rates continue to grind lower. As can be seen in Figure 1 below, when viewed over the course of 3 decades, interest rates have declined almost linearly since 1982. In fact, the same trend holds true for many western countries. Why might that be the case?

Solow (1956) is one of the most important papers in the history of Macroeconomics. (In fact, Robert Solow won the Nobel Prize in Economics in large part due due to this paper.) In it, he presents a model of long term economic growth that has since come to be known as Solow Growth Model. He makes a set of assumptions in the paper and from there derives an equation which characterizes the development of the economy over a “long” period of time. One implication of the model is that interest rates are related macroeconomic factors like population growth and productivity and, by implication, not monetary policy.

Assumptions of the Model

  1. The population grows as a constant rate n
  2. Labor productivity grows as a constant rate g
  3. Capital and labor exhibit constant returns to scale i.e., if you double both labor and capital, you double total output
  4. A constant proportion (s) of output is saved
  5. Savings equals investment
  6. Capital increases at the rate of investment minus a constant depreciation rate d

Results of the model

There are a few implications of the model. One is that the only thing that increases long term per capita income and consumption is productivity. I won’t discuss this further since it’s consistent with our intuition.

A second implication is that, in the long run, real interest rates can be described by the following equation: $$r_{real} = \frac{\alpha}{s}(n+g+d) - d$$ where \(\alpha\) represents the proportion of income that goes to investors and has historically averaged around 0.33 in the United States. Empirically, the quantity \(\frac{\alpha}{s}\) is greater than 1 in every country and, in the United States, it has hovered around 2. If we assume 2, we get $$r_{real} = 2n+2g+d$$ Since 2000, population growth has declined by ~1% and labor productivity growth has declined by 3-4%. Based on the above equation, we’d expect a 8-10% decline in rates. In actual fact, rates have declined by just 6%, implying that the bond market rally could continue.

We can also consider how/why real interest rates might become negative: $$r_{real} = \frac{\alpha}{s}(n+g+d) - d < 0$$ or $$n+g<-d\left(1-\frac{s}{\alpha}\right)$$

In other words, if \(n+g\) turn sufficiently negative, then we would expect to see negative interest rates.

While this model doesn’t provide a clear prediction for the level of rates, it doesn’t rebut a common refrain these days that interest rates are being driven artificially low by central banks.

References

Solow, Robert M. (February 1956). “A contribution to the theory of economic growth”. Quarterly Journal of Economics. 70 (1): 65–94.