More on Interest Rates

According to Taylor's original version of the rule, the nominal interest rate should respond to divergences of actual inflation rates from target inflation rates and of actual Gross Domestic Product (GDP) from potential GDP:

$\mathrm{i}_{\mathrm{t}}=\pi_{\mathrm{t}}+\mathrm{r}_{\mathrm{t}}^{*}+\alpha_{\pi}\left(\pi_{\mathrm{t}}-\pi^{*}{ }_{t}\right)+\alpha_{y}\left(\mathrm{y}_{\mathrm{t}}-\mathrm{y}^{*} \mathrm{t}\right)$

In this equation, $i_{t}$ is the target short-term nominal interest rate (e.g., the federal fund rates in the United States), $\pi_{t}$ is the rate of inflation as measured by the GDP deflator, $\pi_{t}^{*}$ is the desired rate of inflation, $r_{t}^{*}$ is the assumed equilibrium real interest rate, $y_{t}$ is the logarithm of real GDP, and $\mathrm{y}_{\mathrm{t}}^{*}$ is the logarithm of potential output, as determined by a linear trend.

In other words, $\left(\pi_{t}-\pi_{t}^{*}\right)$ is inflation expectations that influence interest rates. Most economies generally exhibit inflation, meaning a given amount of money buys fewer goods in the future than it will now. The borrower needs to compensate the lender for this. If the inflationary expectation goes up, then so does the market interest rate and vice versa.