Testing for output gap convergence using a long memory Markov-Switching model with structural breaks

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The concept of convergence (or lack of it) over time among different indicators of economic or social activity is central in the study of many economic phenomena. For example, one of the main predictions of economic growth theory is that in the long run, all countries with similar technological characteristics would converge to a balanced growth path equilibrium that would equal to labour productivity growth. Hence for economies to grow they would have to increase labour productivity and economies with the same productivity would grow at the same rate and converge to the same equilibrium. This is the so called growth convergence hypothesis, which has been the main focal point ofthe empirical economic growth literature. Another example of convergence is the so called Law of One Price (LOP), where price differential for goods of equalquality but at different locations should vanish over time as consumers would become aware of these differences and act accordingly to eliminate them. Similarly, the Purchasing Power Hypothesis (PPP) looks at foreign exchange rate differentials and analyzes the foreign exchange gaps as simply describing productivity differentials between different countries. Any gap beyond these productivity differentials under the PPP convergence hypothesis would disappear over time. There are many other different examples that describe economic and social activities that can be tested for convergent behavior. In all of these examples mentioned above the time series methodology used to test for the presence of convergence is cast in a dichotomous set up where the relevant gaps (whether measured in terms of incomes, labour productivity, prices or exchange rates or any other measured difference) either follow very fast convergence or very fast divergence without any in between cases. In the current proposal we will use a framework that allows for in between cases of the speed of convergence parameter and also allows for the presence of regime switching events that may change the direction of the convergence process altogether between regimes. We recognize that events that lead to regime changes may not be readily observable or identifiable at the time when they occur and that their influence is likely to affect not only the standard parameters of the process such as the mean function (for example average income gap of over time for the case of growth convergence), but also the speed of convergence. Hence, it is to be expected that there may be different regimes with different convergence speeds, something that may imply that two countries that were on a fast convergence path, may change course and slow down the convergence process or even reverse it. It is the possibility of changes in the speed of convergence that may lead even to possible “reversals” from convergent behaviour to divergent one that the literature has so far ignored and we plan to address in the current proposal.