Even here, however, we encounter important technical difficulties: These inflation compensation measures are "contaminated" both by an inflation risk premium and by differences in liquidity between the markets for nominal and indexed Treasury securities.
More fundamentally, even a "rational" forecast of inflation from financial markets provides only part of the information needed to form monetary policy because it gives only a sense of where inflation is expected to go, not why it is going there. The latter question is often important for assessing the appropriate stance of policy.