Section IV
Historical data on interest rates supports the theory: preliminaries
In section I, we gave theoretical intuition for why higher expected growth or higher existential risk would result in higher interest rates: expectations for such high growth or mortality risk would lead people to want to save less and borrow more today. In this section and the next two, we showcase some simple empirical evidence that the predicted relationships hold in the available data.
Measuring real rates. To compare historical real interest rates to historical growth, we need to measure real interest rates.
Most bonds historically have been nominal, where the yield is not adjusted for changes in inflation. Therefore, the vast majority of research studying real interest rates starts with nominal interest rates, attempts to construct an estimate of expected inflation using some statistical model, and then subtracts this estimate of expected inflation from the nominal rate to get an estimated real interest rate. However, constructing measures of inflation expectations is extremely difficult, and as a result most papers in this literature are not very informative.
Additionally, most bonds historically have had some risk of default. Adjusting for this default premium is also extremely difficult, which in particular complicates analysis of long-run interest rate trends.
The difficulty in measuring real rates is one of the main causes, in our view, of Tyler Cowen’s Third Law: “all propositions about real interest rates are wrong”. Throughout this piece, we are badly violating this (Godelian) Third Law. In appendix 2, we expand on our argument that the source of Tyler’s Third Law is measurement issues in the extant literature, together with some separate, frequent conceptual errors.
Our approach. We take a more direct approach.
Real rates. For our primary analysis, we instead use market real interest rates from inflation-linked bonds. Because we use interest rates directly from inflation-linked bonds – instead of constructing shoddy estimates of inflation expectations to use with nominal interest rates – this approach avoids the measurement issue just discussed (and, we argue, allows us to escape Cowen’s Third Law).
To our knowledge, prior literature has not used real rates from inflation-linked bonds only because these bonds are comparatively new. Using inflation-linked bonds confines our sample to the last ∼20 years in the US, the last ∼30 in the UK/Australia/Canada. Before that, inflation-linked bonds didn’t exist. Other countries have data for even fewer years and less liquid bond markets.
(The yields on inflation-linked bonds are not perfect measures of real rates, because of risk premia, liquidity issues, and some subtle issues with the way these securities are structured. You can build a model and attempt to strip out these issues; here, we will just use the raw rates. If you prefer to think of these empirics as “are inflation-linked bond yields predictive of future real growth” rather than “are real rates predictive of future real growth”, that interpretation is still sufficient for the logic of this post.)
Nominal rates. Because there are only 20 or 30 years of data on real interest rates from inflation-linked bonds, we supplement our data by also considering unadjusted nominal interest rates. Nominal interest rates reflect real interest rates plus inflation expectations, so it is not appropriate to compare nominal interest rates to real GDP growth.
Instead, analogously to comparing real interest rates to real GDP growth, we compare nominal interest rates to nominal GDP growth. The latter is not an ideal comparison under economic theory – and inflation variability could swamp real growth variability – but we argue that this approach is simple and transparent.
Looking at nominal rates allows us to have a very large sample of countries for many decades: we use OECD data on nominal rates available for up to 70 years across 39 countries.