Seemingly contradictory relationship between bond yields and economic growth?
(Note: there were similar questions in the past, but I did not see an exact match.)
As used in this question, “interest rates” are the rate of interest associated with a policy rate or a deposit. A “yield” is the the rate of return on a bond given its purchase price. For a bond, since the payments are fixed, the yield moves inversely with price.
If we simplify to the case of a zero coupon bond that matures at time T (starting at $t=0$), the price is given as:
$$
P(T) = e^{- \int_0^T f(t)dt},
$$
where $f(t)$ is the instantaneous forward rate. (Based on Rebanato’s “Interest-Rate Option Models”, page 6. Should be in any fixed income textbook.)
Put into words: the price of the bond is given by “averaging” the forward rates over the life of the bond. Higher forward rates implies a lower price (and hence, a higher yield).
The central bank “risk-free” rates for short maturities, and the instantaneous forward rate initially coincides with that rate. Further along the time axis, the forward rate is normally interpreted as the expected policy rate plus a term premium.
If economic growth is expected to be strong, market participants normally expect rate hikes. For example, that is the implied behaviour of “The Taylor Rule,” which the reader can easily find references for.
In a recession, it is entirely possible for the central bank to lower the policy rate, and market participants to expect a strong recovery, and forward rates rise. However, one can look at bond data to see that the policy rate and bond yields are roughly “correlated.”
As for the relationship to equity prices (which show up in the question), the situation is muddled and should be a separate question.