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

******经济或社会活动的不同指标之间随时间的趋同（或缺乏趋同）的概念是许多经济现象研究的核心。例如，经济增长理论的主要预测之一是，从长期来看，所有具有类似技术特征的国家将趋同于一个平衡的增长路径均衡，这将等于劳动生产率的增长。因此，要实现经济增长，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。这就是所谓的增长收敛假设，它一直是实证经济增长文献的主要焦点。另一个趋同的例子是所谓的一价定律（LOP），即相同质量的商品在不同地点的价格差异会随着时间的推移而消失，因为消费者会意识到这些差异，并采取相应的行动来消除它们。同样，购买力假设（PPP）着眼于外汇汇率差异，并将外汇缺口简单地描述为不同国家之间的生产率差异。在购买力平价趋同假设下，超出这些生产率差异的任何差距都将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趋同行为的经济和社会活动。在上面提到的所有这些例子中，用于测试是否存在收敛的时间序列方法是在一个二分设置中进行的，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测量差异来衡量）要么遵循非常快的收敛，要么遵循非常快的发散，而没有任何中间情况。在当前的建议中，我们将使用一个框架，该框架允许在收敛速度参数之间的情况下，也允许存在可能在不同状态之间改变收敛过程方向的状态切换事件。我们认识到，导致制度变化的事件在发生时可能不易观察或识别，而且它们的影响可能不仅影响平均函数等过程的标准参数（例如，在增长收敛的情况下，随着时间的平均收入差距），而且还影响收敛的速度。因此，可以预期的是，可能会有不同的制度具有不同的趋同速度，这可能意味着两个在快速趋同道路上的国家可能会改变方向，减缓趋同进程，甚至逆转趋同进程。收敛速度变化的可能性甚至可能导致从收敛行为到发散行为的可能“逆转”，这是文献迄今为止所忽略的，我们计划在当前提案中解决。*****

******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.*****