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This dissertation estimates a time series of the natural rate of unemployment via competing methods, and evaluates such methods both within sample and for forecasting purposes. The methods used include the Kalman and Hodrick-Prescott filters. Evaluation proceeds along two lines. First, a Phillips curve is used in order to assess how well deviations of actual inflation from expected inflation are explained by deviations of the actual unemployment rate from estimated natural rates within a given sample period. The evaluative criterion is the overall fit of each regression. The analysis indicates that the in-sample fit of the Phillips curve changes little when different estimators of the natural rate of unemployment are considered. However, incorporating the 12-month-ahead forecast of inflation given by the Livingston survey improves the overall fit of the curve. Beyond the within-sample overall fit of a Phillips curve, analysis is conducted in order to assess the usefulness of various estimators of the natural rate for purposes of forecasting and policymaking. In order to test “out-of-sample,” recursive least squares is used in a Phillips curve context in order to estimate the natural rate and generate a corresponding forecast of inflation for next period. Additionally, estimates of the natural rate derived from a Kalman filter, the Hodrick-Prescott filter, and a method incorporating structural determinants of unemployment are included in a Phillips curve in order to generate a forecast of one-period-ahead inflation. Despite earlier results regarding the Livingston survey information, the analysis does not indicate that the Livingston survey information can aid policymakers in forecasting inflation. Further, even though the most common method of estimating natural rates is via a Phillips curve, the Phillips curve method of estimating the natural rate of unemployment does not appear superior—in terms of its forecasting power—to other methods of estimating the natural rate when the Phillips curve is utilized as the forecasting equation. Slight evidence is provided in support of the Hodrick-Prescott filter as an estimator of the natural rate of unemployment. Both the Kalman and Hodrick-Prescott filters feature the benefit of requiring only one series of data, and the Kalman approach is quite parsimonious.