Historical data on interest rates supports the theory: graphs

The goal of this section is to show that real interest rates have correlated with future real economic growth, and secondarily, that nominal interest rates have correlated with future nominal economic growth. We also briefly discuss the state of empirical evidence on the correlation between real rates and existential risk.

Real rates vs. real growth. A first cut at the data suggests that, indeed, higher real rates today predict higher real growth in the future:

To see how to read these graphs, take the left-most graph (“10-year horizon”) for example. The x-axis shows the level of the real interest rate, as reflected on 10-year inflation linked bonds. The y-axis shows average real GDP growth over the following 10 years.

The middle and right hand graphs show the same, at the 15-year and 20-year horizons. The scatter plot shows all available data for the US (since 1999), the UK (since 1985), Australia (since 1995), and Canada (since 1991). (Data for Australia and Canada is only available at the 10-year horizon, and comes from Augur Labs.)

Eyeballing the figure, there appears to be a strong relationship between real interest rates today and future economic growth over the next 10-20 years.

To our knowledge, this simple stylized fact is novel.

Caveats. “Eyeballing it” is not a formal econometric method; but, this is a blog post not a journal article (TIABPNAJA). We do not perform any formal statistical tests here, but we do want to acknowledge some important statistical points and other caveats.

First, the data points in the scatter plot are not statistically independent: real rates and growth are both persistent variables; the data points contain overlapping periods; and growth rates in these four countries are correlated. These issues are evident even from eyeballing the time series. Second, of course this relationship is not causally identified: we do not have exogenous variation in real growth rates. (If you have ideas for identifying the causal effect of higher real growth expectations on real rates, we would love to discuss with you.)

Relatedly, many other things are changing in the world which are likely to affect real rates. Population growth is slowing, retirement is lengthening, the population is aging. But under AI-driven “explosive” growth – again say 30%+ annual growth, following the excellent analysis of Davidson (2021) – then, we might reasonably expect that this massive of an increase in the growth rate would drown out the impact of any other factors.

Nominal rates vs. nominal growth. Turning now to evidence from nominal interest rates, recall that the usefulness of this exercise is that while there only exists 20 or 30 years of data on real interest rates for two countries, there is much more data on nominal interest rates.

We simply take all available data on 10-year nominal rates from the set of 39 OECD countries since 1954. The following scatterplot compares the 10-year nominal interest versus nominal GDP growth over the succeeding ten years by country:

Again, there is a strong positive – if certainly not perfect – relationship. (For example, the outlier brown dots at the bottom of the graph are Greece, whose high interest rates despite negative NGDP growth reflect high default risk during an economic depression.)

The same set of nontrivial caveats apply to this analysis as above.

We consider this data from nominal rates to be significantly weaker evidence than the evidence from real rates, but corroboration nonetheless.

Backing out market-implied timelines. Taking the univariate pooled OLS results from the real rate data far too seriously, the fact that the 10-year real rate in the US ended 2022 at 1.6% would predict average annual real GDP growth of 2.6% over the next 10 years in the US; the analogous interest rate of -0.2% in the UK would predict 0.7% annual growth over the next 10 years in the UK. Such growth rates, clearly, are not compatible with the arrival of transformative aligned AI within this horizon.