The aim of the paper is to provide a recent overview of Kalman filter employment in the non-accelerating inflation rate of unemployment (NAIRU) estimation. The NAIRU plays a key part in an economic system. A certain unemployment rate which is consistent with a stable rate of inflation is one of the conditions for economic system stability. Since the NAIRU cannot be directly observed and measured, it is one of the most fitting problems for the Kalman filter application. The search for original, NAIRU focused and Kalman filter employment studies was performed in three scientific databases: Web of Science, Scopus, and ScienceDirect. A sample of 152 papers was narrowed down to 25 studies, which were described in greater detail regarding the focus, methods, model features, limitations, and other characteristics. A group of studies using a purely statistical approach of decomposing unemployment into a trend and cyclical component was identified. The next group uses the reduced-form approach which is sometimes combined with statistical decomposition. In such cases, the models are usually based on the backward-looking Phillips curve. Nevertheless, the forward-looking, New Keynesian or rarely hybrid New Keynesian variant can also be encountered.
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