Comparing Results from Unobserved Components Model and Hodrick-Prescott Filter of Output-Gap in Barbados

An important macro-economic issue of developed and developing countries is how best to decompose an economic time series into permanent (trend) and transitory (cycle) components. The issue is vital in empirical macroeconomics since, among other things, it relates to how one can estimate the output gap—the deviation of an economy's output from its potential or trend output. This paper considers how well the unobserved components model and the Hodrick Prescott (HP) filter decomposes real gross domestic product (GDP) in a small island developing state, the state of Barbados. The correlated unobserved components model for Barbados studied in the Agbeyegbe (2020) is modified to allow a second-order Markov trend. The effect of this modification is to make it possible to recover the HP trend as a particular case. The paper then compares several methods useful for trend decomposition of real GDP in Barbados. The competing methods are variants of two widely used trend-cycle decompositions of GDP that give markedly different estimates. Namely, methods based on the unobserved components model (UC) and the HP filter. The correlated unobserved components model produces smaller output gaps in amplitude, whereas the HP filter generates significant and persistent cycles. More specifically, the methods are: (i) the HP filter; (ii) an augmented HP filter (HP-AR), that allows for cyclical components to be serially correlated, introduced by Grant and Chan (2017b); (iii) the correlated unobserved components model (UCUR), without a break; (iv) the correlated unobserved components model (UCUR-t), with a break at time t; and (v) a correlated unobserved components model that allows for a second-order Markov trend process UCUR-2M. The result shows that for Barbados, with data covering the period 1967–2017, the correlated unobserved components model that allows for a break in trend fits the data better than the HP specification. These results are significant from a policy perspective. Knowing the correct duration of the business cycle is essential to providing appropriate recommendations; the result argues against the use of HP-filter in analyzing Barbados' business cycle. The result also finds that for Barbados, it is empirically important to correlate permanent and transitory shocks. By ignoring this correlation, researchers risk providing a misleading analysis of how the Barbadian economy works.