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At last – an economic theory that works?

It will have escaped the attention of very few people active in the financial markets that long-term real rates of interest are low. Very low, in fact. Anyone buying a ten-year index-linked gilt today, and holding it to maturity, is guaranteed a real-terms loss of some 2.0%. That doesn’t seem right, does it?

What should determine a country’s long-run real rate of interest? Economists have a bit of a long-winded answer, and it runs something like this. Ultimately, a country’s real rate of interest must match the return on its capital stock, adjusted for depreciation. In turn, the return on a country’s capital stock will depend on its size, relative to output. The larger is the capital stock, for a given level of output, the smaller will be its return, and vice versa. The size of the capital stock depends on the amount of past investment undertaken. For a closed economy, or for the world as a whole, investment is the same as savings. So, finally, in asking what is an appropriate long-run real rate of interest we are, in a roundabout way, asking how much should be saved today, and how much should be put away so that more can be consumed in future. That is perhaps the fundamental question of economics, and yet we have a mathematician to thank for the answer.

As long ago as 1928, Frank Ramsey derived what has since become known as the modified golden rule. In a world where consumers maximise their lifetime utility, while firms maximise profits, the real rate of interest, r, should satisfy the following equation:

where θ is a parameter of the utility function, often assumed to be one, g is growth in GDP per capita, n is the rate of population growth, and ρ is the time discount rate – effectively a measure of human impatience. A more impatient society will face a higher real rate of interest, and so a higher return on capital. That means its capital stock will be lower and it will consume less in the long run. Such is the penalty for a ‘jam today’ attitude.

What this equation tells us is that, for the case where θ is one, a country’s real rate of interest should be broadly equal to its real rate of growth, with the difference representing the time discount rate. And it turns out that, miraculously, this is a theory that works pretty well. This week’s chart uses data from a fascinating database of long-run economic and financial market data put together by Òscar Jordà, Moritz Schularick, and Alan M. Taylor[1]. It shows real GDP growth and the real long-term rate of interest for the UK economy since 1870. The means of the two series are 2.11% and 2.90% respectively. So the real long-term rate of interest has exceeded real GDP growth in the UK by 79 basis points. For all their variability, these two series are, on average, remarkably close. Similar results hold for all 17 advanced economies in the database.

On the face of it, the empirical success of the modified golden rule over the past century and a half makes today’s bond market pricing all the more puzzling. Fathom is sometimes accused of talking a pessimistic view of the UK economic outlook. But even we would put trend growth somewhere in the range 1.0%-1.5%. It is not -2.0%. Have we become a nation of savers? Have we adopted a ‘jam tomorrow’ attitude, justifying a negative time discount rate? Is there a massive bubble in global bond markets? Or is there something else going on? We will address these questions, and more, in our forthcoming Global Economic and Markets Outlook for 2017 Q2.

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