1996; Pesaran, 2007). However, evidence is found for convergence in per capita income growth rates in the cointegration testing framework, suggesting that income gaps do not increase over time. More recently, a factor model-framework for club convergence testing has been proposed which is less liable to make false rejections of the formation of convergence clubs than previous time-series approaches. In a dataset spanning 1970-2003 for income per capita in 152 economies, evidence was found for the existence of 5 convergence clubs, with the first dominated by advanced economies (Phillips and Sul, 2007, 2009).

# **4.1 Convergence clubs: Commonalities in productivity** **_levels_**

The first strand of the literature can identify clubs of economies well in an ex-post sense: those economies who have converged over time towards common attraction points will have similar productivity levels and thus be found to have been in a convergence club. Updating the distributional analysis literature to the post-2000 period, when EMDE productivity growth has picked up substantially relative to earlier decades, results in a similar number of clubs relative to earlier estimates (4 in the most recent period). However, relative to earlier studies, 10 faster-growing EMDEs have separated from the lowest productivity club over the past decade to join a convergence club consisting of many middle-income EMDEs (Annex D). The period of faster productivity growth in EMDEs has resulted in new convergence club dynamics—a more comprehensive examination in the following section of both the level of productivity and the trajectory of productivity over time provides greater clarity over the development of convergence clubs in recent decades.

# **4.2 Convergence clubs: Commonalities in productivity** **_trajectories_**

Common productivity trajectories. The clubs identified above capture common productivity levels at different points in time. However, these same productivity levels can be achieved along very different trajectories— a low-productivity economy may be on a growth path that is convergent with high-productivity economies in the future but may not be considered to be in a similar convergence club based on a snapshot of productivity levels alone. This section identifies commonalities in the trajectories of productivity over time: countries in the same convergence club are on paths that converge towards similar productivity levels, even if productivity differentials are high in the period under examination.

**Methodology** . Labor productivity (in logs) is modeled as a country-specific weighting on a common factor _μt_ , which reflects the common productivity attraction point that club members are drawn to (Phillips and Sul 2009):

Countries in the same convergence club will initially feature different coefficients _bit_ , reflecting their varying distance from a common attraction point. For a group of economies to form a convergence “club”, their deviations from the common attraction point should fall over time. Using an iterative procedure, the methodology tests combinations of economies for common convergence dynamics; economies that do not display falling productivity gaps are discarded until groups are found that do (Annex E). Data are available for 29 advanced economies and 68 EMDEs for 12