This paper analyses the effect of measurement error in the output gap on
efficient monetary policy rules in a simple estimated model of the US economy.
While it is a well-known result that such additive uncertainty does not affect
the optimal feedback rule in a linear-quadratic framework, it is shown that
output gap uncertainty can have a significant effect on the efficient response
coefficients in restricted instrument rules such as the popular Taylor rule.
Output gap uncertainty reduces the response to the current estimated output gap
relative to current inflation and may partly explain why the parameters in
estimated Taylor rules are often much lower than suggested by optimal control
exercises which assume the state of the economy is known.
