Parameter variation in the 'logt' convergence test

Abstract

log t" convergence test. It documents the economically and statistically significant within-sample variation in the estimated value of the key parameter of that test when applied to data for 18 OECD countries during the 20th century. This variation suggests the substantial waxing and waning of the forces driving convergence, possibly due to low-frequency shocks and changes in the level economic integration.

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“…The local linear log t regression test by Johnson (2020) is not available in any statistical software. Therefore, this paper uses the R function logt to perform this test.…”

“…Third, this method is robust to structural breaks in time series(Antonakakis et al, 2017).The standard log t regression test, however, does not provide information on the intensity of convergence/divergence for each period analysed, but only for the entire period studied. The local linear log t regression test byJohnson (2020) relaxes this constraint by modifying Eq. (1) as follows:…”

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“…Finally, it should be emphasised that, apart from the aforementioned work by Kerner and Wendler (2022), no other studies have used the approaches outlined by Arestis et al (2017), Gozgor et al (2019), Johnson (2020) and Kwak (2022) to identify convergence clubs.…”

“…Johnson (2020) provided another alternative modification of the log t regression that fully accounts for non‐linearities. He proposed a local linear version of the log t regression of the form: $$$$\begin{equation} \log \left(\frac{{H}_{1}}{{H}_{t}}\right)-2\, \log L\left(t\right)=m\left(\log t\right)+{u}_{t} \end{equation}$$$$where m (log t ) is a smooth function.…”

“…Within this framework at time t , 2 > m '(log t ) ≥ 0 denotes growth convergence while m '(log t ) ≥ 2 implies level convergence, where m '(log t ) is the first derivative of m (log t ). In contrast to Arestis et al.’s (2017) modification, the method of Johnson (2020) can provide information on convergence speed at any time t . Details of the estimation of local convergence speed parameters are included in Johnson (2020).…”