The price of a default-free nominal coupon-paying bond can be expressed as:
= additional return required by investors to compensate for inflation
= risk premium for uncertainty in future inflation
With short-term nominal interest rates inflation uncertainty can be ignored and short-term T-bills can be priced as:
Short-term nominal interest rates are positively related to short-term real interest rates and short-term inflation expectations. The interest rates are higher in economies with higher inflation and higher, more volatile growth.
Central banks set short-term interest rates in response to the economy’s position in the business cycle.
The Taylor rule is a rule for setting policy rates and determining whether the rate is at an appropriate level. The rule is given below:
= the policy rate at time t
= the level of real short-term interest rates that balance long-term savings and borrowing in the economy
= the rate of inflation
= the target rate of inflation
= the logarithmic levels of actual and potential real GDP respectively.
A neutral policy rate is the policy rate that neither spurs nor impedes real economic activity.