One of the most basic tenets of economic modeling (Samuelson and Solow for example) has been that in a stationary economy the interest rate is defined by the rate of growth of the population. If population is decreasing we get negative interest rates and if population is increasing we get positive ones. I have to admit that I had not given much thought about that until recently since I just considered it to be just another of the great simplifications economists make when they want their models to work. Yet, after reading Samuelson's original model, it somehow got into my head. If one also remembers Krugman's points on Japan and the relationship population has with inflation then the relationship between population, the economy and the interest rate is not as vague as it appears.

It is more often true than not that interest rates reflect inflation. If inflation is high (low), interest rates are also high. Yet inflation is not only governed by population, money supply, both commercial bank-created and central bank-created, matters much more in establishing the price level in the short run as do corporate profit margins, import prices and other (for more details see this). If this holds, which it does, it would mean that the shorter the duration of an instrument the larger the effect of the current price level on it. With respect to interest rates, it would mean that the short-run interest rate (e.g. on Treasuries) is more prone to changes in the price level than the long-run rate (e.g. on 20-year Bonds).* This can also be seen in inverted yield curves in times of high inflation.

Continuing with our rationale, it appears that long-term rates are affected by much more things than short-term ones. For example, a fall in the rate of population growth will probably not be visible for the next 5 or so years; new regulations or expected long-term projects and future inflation rates can also be included in this category. However, this should not be confused with long-term equilibria of any kind: this is not something, which will work in the long term if nothing changes (e.g. that GDP will rise in the long run even if it has been falling in the short run). This is the idea that results of some action are not visible now either because the change is very little every year or because it takes time for the whole plan to be completed. Think of it this way: we will find out if there is oil in area X but until all the studies and drillings are made 5 or so years will have to pass.

Thus, we can admit that there are variables, which take much longer to manifest are not having any effect in short-term interest rates but have an effect in long-term ones. In the graph, which follows, the correlation between bond yields and population growth can be observed. The further right you move along a line the longer the bond duration.

The correlation, although not being an exact science, points out something very interesting. It appears that irrespective of whether the correlation is positive or negative, the longer the horizon of a bond, the higher the correlation (in absolute numbers). Although correlation does not mean causation, seeing that long-term demographic trends tend to have great effects on interest rates is quite important. The reverse may also hold but in a much broader sense: it does not just take low interest rates to affect population growth, yet an economy in a bad state may have some effect on that. This is not a generalized result however, if it was all the underdeveloped countries would face diminishing populations and all prospering ones would have huge population growth rates. Real life begs to differ with theory here.

Yet the main result is that population matters when it comes to interest rates. For example, have a look at Japan's data since the early 1960s (population growth is reflected on the right-hand axis):

Although changes in the population growth rate are rather small and interest rates are high, it can be clearly seen that the trend is quite similar. As population growth declines the yields in 7- and 10-year bonds follow the same trend. For example, the spike in the population growth rate in the early 1970s was followed by a spike in interest rates in the mid- to late-1970s. Obviously, the spike could also be attributed to other variables changing thus I will not insist too much on it. Still, the long-term trend is more revealing than anything else.

The spikes in yields over the time frame seen above are not contradictory to what is being described in this post. They are actually more supportive than anything, since there is a magnitude of variables, which affect long-term interest rates. As these variables have different effects on the rates it makes more sense for yields to fluctuate over time, depending on which effect is stronger. Nonetheless, interest rates and the economy in general have a strong tendency to prefer growing populations over falling ones for the obvious reason of increased demand. Thus, as correlations and trends indicate, population growth does make a difference in the long-term yields, even if its effects are almost zero in the short term.

*For those readers who are thinking about the annuity formula, which shows that if we increase the market interest rate longer annuity have greater fluctuations than shorter-term ones I would like to remind that the formula assumes that the same market rate will prevail in all future cases. Yet, if for example, we consider the interest to rise for two years and the return to some lower level, the change in the 20-year bond will be far less than the change in the 1-year or 2-year bond since it will affect just 10% of the former's payments and none at all the present value of the maturity price while it will affect all payments in the latter's case including the maturity value.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.