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

不同的经济或社会活动指标在一段时间内趋同（或不趋同）的概念是研究许多经济现象的核心。例如，经济增长理论的一个主要预测是，从长远来看，所有具有类似技术特征的国家都将趋同于一个均衡的增长路径均衡，这将等于劳动生产率的增长。因此，各经济体要实现增长，就必须提高劳动生产率，而生产率相同的经济体将以相同的速度增长，并趋于相同的均衡。这就是所谓的增长趋同假说，这一直是主要的焦点， 实证经济增长文献。趋同的另一个例子是所谓的一价定律（LOP），即相同价格的商品的价格差异。 但在不同地点的质量应该随着时间的推移而消失，因为消费者会意识到这些差异，并采取相应行动消除它们。同样，购买力平价假说（PPP）也将汇率差异作为单纯的生产率差异来分析。在购买力平价趋同假设下，超过这些生产率差异的任何差距都会随着时间的推移而消失。还有许多其他不同的例子描述了可以测试收敛行为的经济和社会活动。在上述所有这些例子中，用于检验是否存在趋同的时间序列方法被置于一种二分法中，其中相关差距（无论是以收入、劳动生产率、价格或汇率或任何其他衡量的差异来衡量）要么遵循非常快的趋同，要么遵循非常快的背离，而没有任何中间情况。在目前的建议中，我们将使用一个框架，允许在收敛速度参数的情况下，也允许政权切换事件的存在，可能会改变收敛过程的方向完全政权之间。我们认识到，导致制度变化的事件在发生时可能不容易观察或识别，它们的影响可能不仅影响过程的标准参数，如均值函数（例如，在增长收敛的情况下，随着时间的推移平均收入差距），而且收敛的速度。因此，可以预期，可能会有不同的制度，具有不同的趋同速度，这可能意味着两个走在快速趋同道路上的国家，可能会改变方向，减慢收敛过程，甚至使收敛过程逆转，而收敛速度的变化甚至可能导致“逆转”从收敛行为到发散行为，这是文献迄今为止忽略的，我们计划在当前的提案中解决。

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 of the empirical economic growth literature. Another example of convergence is the so called Law of One Price (LOP), where price differential for goods of equal quality 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.