Final answer:
The central bank's loss function illustrates the trade-offs it makes between inflation and output stability, represented by the parameter β. A central bank with a high β places more emphasis on stabilizing inflation, potentially leading to quicker adjustments after inflation shocks but with greater output volatility. Inflation targeting is popular among central banks, though some, like the Federal Reserve, also consider unemployment.
Step-by-step explanation:
The central bank's loss function is a theoretical representation of the trade-offs it faces when attempting to stabilise inflation and output. The loss function reflects the central bank's preferences for inflation and output variability and is often represented with the parameters β, which indicates the bank's relative weight on stabilizing inflation versus output.
When β = 1, it implies that the central bank gives equal weight to inflation and output variability. In the case of β < 1, this means the central bank places a greater emphasis on stabilizing output, and with β > 1, the central bank is more concerned about keeping inflation stable.
If an inflation shock occurs, the central bank with a higher β (greater than 1) will likely reduce inflation back to the target quickest because it places a higher penalty on deviations from the target inflation. However, this policy stance may entail a downside of potentially greater volatility in output, since less weight is given to stabilizing output.
Regarding whether central banks should target inflation or unemployment, it depends on their legislative mandate and economic philosophy. Inflation targeting has become a common practice for many central banks, but some, like the U.S. Federal Reserve, are mandated to consider both unemployment and inflation in their policy decisions. This dual-mandate approach acknowledges that both price stability and employment are important macroeconomic objectives.