Staff Report 96

Estimating Linear Filters With Errors in Variables Using the Hilbert Transform

Warren E. Weber | Retired Economist
Melvin J. Hinich

Revised August 1, 1992

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.

Published In: Signal Processing (Num 37, Vol. 2, May 1994, pp. 215-228)

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