What are central banks interested in?

Central banks (we look at the cases of the Federal Reserve and the ECB) can have three types of objectives: Their traditional domestic objectives: inflation, cyclical position, i.e. the Taylor rule; The objective of stabilising asset prices (equities, real estate) or debt (overall, this is "leaning against the wind"); External objectives, concerning the effects of the country’s monetary policy on other countries: stabilisation of exchange rates or other countries’ interest rates. Which of these three groups of objectives does the Federal Reserve and the ECB take into account? We see: No external objective for the Federal Reserve; No asset price objective for the ECB; A debt objective in both cases; An exchange rate objective for the ECB.