# Real yields and growth [closed]

Found the following very interesting statement on bond prices,

"The yield on a risk-free government bond should equal the growth in nominal GDP since that represents the opportunity cost of holding a government bond both in terms of investment opportunities (real GDP) and the time value of money (inflation)"

http://globalfinancialdata.com/7-centuries-of-government-bond-yields/

Question) How does one square the circle of this statement and the "expectations hypothesis"?

Most significant factors in the price of a goverments bonds

Question)Is future growth or short term rates that determine longer rate? or are these two the same somehow?

• should is a big word here. There is no human, divine or natural law which says this, though there are arguments as to why it might make sense – Henry Jun 9 at 10:21
• @Henry right, lets say it should, what are the arguments that connects these two dots? – Vlad Jun 9 at 11:05
• Individuals' utility from marginal consumption may vary with their total consumption or income which in aggregate may be related to the size of the economy. So if people personally move some of their consumption from one year to another (forwards or backwards by lending or borrowing) it may balance across the economy when it represents the same proportion of the economy in both years. A way to have this happen may be to have interest rates equal to the change in nominal GDP. There are a lot of mays there, so it may not be true. – Henry Jun 9 at 12:56
• Compare the FRED data for annual nominal GDP change with the effective Federal Funds rate fred.stlouisfed.org/graph/?g=rdQK to see how different these have been in the past. Then consider whether interest rates were "wrong" when the big differences occur – Henry Jun 9 at 13:13

The first statement is a result from an old economic model.

The two views can be reconciled by the following argument: the central bank is constrained by the structure of the economy as to its choice of the policy rate. If persistently too low, inflation rises, and if persistently too high, the economy risks falling into deflation.

In this case, the central bank allegedly needs to keep the real policy rate near the growth rate of real GDP. Arguably, not many people are convinced that is precisely the case, rather that there is a “natural rate if interest” (now preferably referred to as $$r^*$$) that the policy rate needs to revert to.

The argument is then that bond investors will be aware of this tendency, and thus bond yields will revert to the long-term average.

However, one would need to search for the modern literature on $$r^*$$ to get a better handle on preferred ways to estimate it. I am in the camp that $$r^*$$ does not exist, so I am not the person to offer such references.

• Thanks for answering, heard about this $r^{*}$ before. And so CBs are basically "targeting" this $r^{*}$? but how does growth expecations relate to $r^{*}$? – Vlad Jun 9 at 11:52
• r* is an equilibrium level, so the policy rate is supposed to be higher/lower than it depending where the economy is (e.g. you lower rates in a recession). Is there a strong relationship between growth and r*? That is discussed in the fiscal sustainability literature. I don’t see a relationship, so I have not pursued the literature. Fairly easily to search for recent papers on google scholar. – Brian Romanchuk Jun 9 at 12:16
• Anyway, so easily put, expected growth is one of the factors that determines short rate policy which in turn is one factors in the long rates? – Vlad Jun 9 at 16:35
• Growth rates are a factor in how central banks set the policy rate, yes. But note that is not what the first quote says: that the growth rate and the neutral rate are equal. There is little empirical evidence of this. – Brian Romanchuk Jun 9 at 17:09