Creator: Hinich, Melvin J. and Weber, Warren E. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 096 Abstract:
In this paper we present a consistent estimator for a linear filter (distributed lag) when the independent variable is subject to observational error. Unlike the standard errors-in-variables estimator which uses instrumental variables, our estimator works directly with observed data. It is based on the Hilbert transform relationship between the phase and the log gain of a minimum phase-lag linear filter. The results of using our method to estimate a known filter and to estimate the relationship between consumption and income demonstrate that the method performs quite well even when the noise-to-signal ratio for the observed independent variable is large. We also develop a criterion for determining whether an estimated phase function is minimum phase-lag.
Keyword: Hilbert transform, Minimum phase-lag, Phase unwrapping, Linear filter, and Errors-in-variables