What variable depends on the other? GDP variations depend on the levels of the risk-free rate or the other way around? The relationship is two-ways indeed.
Reference Interest rates can be imposed by central banks, so they indirectly impact GDP growth. If GDP is impacted by random aggregate demand increments, GDP increases. Therefore, the market will set higher interest rates by its own (very similar to what the central bank would do) and GDP will decrease in consequence. The core idea is that most economy systems are convergent systems, I mean all the relevant variables will force against each other in order to arrive to an equilibrium point.
In conclusion, GDP and interest rates (risk-free rate in the bottom) are positively related. If this was not true, just simulate…
GDP grows > interest rates fall > investment and consumption increase > GDP grows again > so… interest rates fall again? > investment and consumption increases much more > GDP explodes! > rates fall to 0%… > GDP increases again… > KABOOM
This system is not convergent, so it is unreal. The relationship between interest rates and GDP growth can’t be negative. It is positive.
What about volatility? The same. The higher the volatility of GDP, the higher the probability that interest rates and GDP rise each other positively. This means that the higher the volatility of GDP, the higher the volatility of interest rates. Therefore, a positive relationship.
Hope this helps.