The production function approach to the Belgian output gap, estimation of a multivariate structural time series model

A multivariate structural time series model is applied to the factor inputs of a production function (or components thereof) to estimate the Belgian output gap. The usefulness of capacity utilization is also investigated but the variable is not given a prominent status. The number of independent cycles - there may be more than one - and the frequencies retained in the cycles are not restricted a priori. To allow for leads and lags between variables, phase shifts à la Rünstler are introduced at a later stage. Additivity of leads and lags is not imposed. Over 1983-2004, a 3.5 years periodicity is found in the cycles. At that periodicity, the cycles in the participation and unemployment rates are negligible. Two independent cycles hide behind the cycles of the other variables: hours, TFP and capacity utilization. A common cycle restriction is rejected, even allowing for idiosyncratic cycles. The cycles present in the whole data set cannot be subsumed in a single measure such as capacity utilization. Phase shifts are significant, with hours leading by as much as 3 quarters and capacity utilization lagging but additivity of leads and lags is rejected. The resulting output gap has much in common with the NBB business survey indicator.