Instrumental variables and wavelet decompositions
The application of wavelet analysis provides an orthogonal decomposition of a time series by time scale, thereby facilitating the decomposition of a data series into the sum of a structural component and a random error component. The structural components revealed by the wavelet analysis yield nearly ideal instrumental variables for variables observed with error and for co-endogenous variables in simultaneous equation models. Wavelets also provide an efficient way to explore the path of the structural component of the series to be analyzed and can be used to detect some specification errors. The methodology described in this paper is applied to the errors in variables problem and simultaneous equations case using some simulation exercises and to the analysis of a version of the Phillips curve with interesting results.
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