Uma proposta de calibragem do filtro hodrick-prescott baseada na lei de Okun

Abstract

This work proposes a calibration strategy for the smoothing parameter of the Hodrick-Prescott filter based on an empirical criterion such as Okun’s Law in its gap form. Instead of following the standard practice of choosing a pre-established value for the smoothing parameter based on the American economy, we adopt a parametric choice approach grounded in the maximum log-likelihood of the relationship between the cyclical components of output and unemployment for each country. Using seasonally adjusted quarterly series from seven developed economies, the study evaluates how calibration assisted by Okun’s Law affects the cycle-trend decomposition of output, as well as the empirical adherence of these countries to Okun’s Law. The method consists of using the bilateral and unilateral versions of the Hodrick-Prescott filter for a discrete set of smoothing parameter values. After cyclical decomposition, the cycles are standardized and Okun’s Law is estimated. The choice of parameters is based on the maximum log-likelihood of the cyclical regression, generated by the combination of filter and parameter for the pair of series. The results reveal significant heterogeneity, indicating that the choice of a single parameter may imply different serial interpretations regarding the cyclical and structural nature of a series. In summary, economies with a more stable and conventional output-unemployment relationship favor the choice of higher smoothing parameters, while more unstable economies require very low smoothing parameters. A difference in the optimal parameters between the output and unemployment series is also observed, along with the unilateral version of the filter being preferable to the bilateral version according to the adopted criterion.