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

*在研究许多经济现象时，不同经济或社会活动指标之间随着时间的推移而趋同(或不趋同)的概念是核心。例如，经济增长理论的主要预测之一是，从长远来看，所有具有类似技术特征的国家都将收敛到与劳动生产率增长相等的均衡增长路径均衡。因此，经济要增长，就必须提高劳动生产率，生产率相同的经济体将以同样的速度增长，并向同样的均衡收敛。这就是所谓的增长收敛假说，它一直是经验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)，即相同质量但不同地点的商品的价格差异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，并采取相应的行动来消除这些差异。同样，购买力假说(PPP)着眼于汇率差异，并将外汇缺口分析为简单地描述不同国家之间的生产率差异。在购买力平价趋同假说下，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来描述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，用于检验是否存在趋同的时间序列方法都是在一个二分的设置中进行的，在这种设置中，相关差距(无论是以收入、劳动生产率、价格、汇率或任何其他衡量的差异衡量)要么遵循非常快的收敛，要么遵循非常快的背离，而在两种情况下没有任何差异。在目前的提案中，我们将使用一个框架，该框架允许在两种情况之间使用收敛速度参数，并且还允许存在可能完全改变不同制度之间收敛过程方向的制度转换事件。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，其影响不仅可能影响进程的标准参数，如平均函数(例如，在增长趋同的情况下，随着时间的推移平均收入差距)，而且还会影响收敛的速度。因此，可以预期的是，可能会有不同的制度和不同的融合速度，这可能意味着两个处于快速融合道路上的国家可能改变路线，减缓融合进程，甚至逆转融合进程。正是趋同速度发生变化的可能性，甚至可能导致从趋同行为到发散行为的“逆转”，这是文献迄今所忽视的，我们计划在当前的提案中加以解决。

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