Joint smoothing of GDP and unemployment with a bivariate HP filter
The problem of jointly estimating unobserved trends and cycles of a bivariate time series considered here appears within the macroeconomic context of Okuns Law when relating output gaps and the unemployment rate. Joint estimation of the output and unemployment trends is carried out by applying a bivariate time series filter that allows for simultaneous estimation of the correlation between cycles. The estimation procedure employed is based on an extension of the univariate Hodrick-Prescott filter and its application in practice is relatively easy. The main contribution of our approach is that we can control the amount of smoothness in the trends by fixing the smoothing parameter. The empirical application uses data on U.S. real gross domestic product and the unemployment rate.
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