We develop an estimated time-series model of revisions of U.S. payroll employment in order to obtain more accurate filtered estimates of the "true" or underlying condition of U.S. employment. Our estimates of "true" employment are filtered, according to an estimated signal-plus-noise (S+N) model, so as to remove serially correlated observation errors. We are motivated by the perception that raw unfiltered employment estimates based on payroll surveys often overestimate true employment in business-cycle downturns and underestimate it in upturns. Our analysis and estimates operate in real time in the sense that they explicitly account for the timing of initial data releases and revisions and do not simply consider a historical sample of the most revised data as is often done. We view each datum as the sum of a true signal value plus an observation error or noise. Accordingly, we estimate a S+N time-series model, in which each true signal value in the sample is observed multiple times as an initial release followed by revisions, such that the signal and noises are generated by separate autoregressive processes. The signal follows a univariate process and the noises follow a vector process whose dimension depends on the number of vintages of observations in the sample. We use payroll employment data from 1969-2003 to estimate by maximum likelihood an S+N model and use the estimated model to obtain filtered estimates of true employment for each period in the sample. Intuitively, the S+N model structure is sufficiently restrictive to allow us to exploit own- and cross-serial correlations in the data to estimate separate models of the signal and the noises and, thereby, to obtain more accurate estimates of true employment than are indicated directly by raw and unfiltered data
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Find related papers by JEL classification: C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications