# Estimating the relationship between short-term intretes rates and 10Y bond yields

On the 16th of March 2020, the Polish Central Bank announced its first-ever round of Quantitative Easing. I am conducting an event study on how this announcement impacted the term structure.

The main obstacle is the fact that in the same press announcement the central bank also lowered its policy rate by 50 bps. My goal is to get an estimate of the reduction in the 10Y bond yield that would follow ONLY from the policy rate cut, based on the historical data. I have considered estimating the following equation:

\begin{align*} \Delta10Y\_Yield_{t}=\beta_{0}+\beta_{1}\Delta Policy\_Rate_{t}+\beta_{2}\Delta Policy\_Rate_{t}^{2}+u_{t} \end{align*}

What could be an alternative approach? Are you aware of any relevant literature?

• You might want to consider whether or not the cut was a surprise relative to what was priced. Not obvious to me that a fully-priced move in the policy rate should have an impact on the 10Y. Jul 6 at 15:20

A good discussion about the complex and still unsettled relationship between short- and long-term interest rates (along with a literature review) can be found here in Section 3 of the paper below:

The causal relationship between short- and long-term interest rates

Some of the issues that you might want to take a look at in the context of your regression model:

• Omitted variables: theory argues that the relationship between short and long-term rates should also contain time-varying "term premia" that depend on uncertainty about inflation, real activity and the future path of monetary policy. Liquidity may also play a role.

• Time window over which you will calculate your delta: the sensitivity of long-term yields to changes in short-term rates shows dependence on the time horizon considered. See The sensitivity of Long-Term Interest Rates: A Tale of Two Frequencies

There are many other issues to consider but this should hopefully give you a good starting point.