A first clue is that the movements in distant forward real rates that we document appear to reflect changes in term premiums, as opposed to changes in expectations about short-term real rates far into the future.
Said differently, if the Fed eases policy today and yields on long-term TIPs go down, this does not mean that the real short rate is expected to be lower 10 years from now – but rather that TIPs have gotten more expensive relative to the expected future path of short rates.