Note on the Interpretation of Convergence Speed in the Dynamic Panel Model

Studies using the dynamic panel regression approach have found the speed of income convergence among the world and regional economies to be high. For example, Lee et al. (1997, 1998) report the income convergence speed to be 30% per annum. This note argues that their estimates may be seriously overstated. Using a factor model, we show that the coefficient of the lagged income in their specification may not be the long-run convergence speed, but the adjustment speed of the short-run deviation from the long-run equilibrium path. We give an example of an empirical analysis, where the short-run adjustment speed is about 40%.Convergence speed, Dynamic panel regression, Factor model

Absolute and Conditional Convergence: Its Speed for Selected Countries for 1961--2001

The study gives the theoretical justification for the per capita growth equations using Solovian model(1956) and its factor accumulation assumptions. The different forms of the per capita growth equation is used to test for 'absolute convergence' and 'conditional convergence' hypotheses and also work out the speed of absolute and conditional convergence for selected countries from 1961-2001.Only EU and East Asian countries together have shown uniform evidence of absolute convergence in all periods. While EU as a region has shown significant evidence of absolute convergence in two periods, 1961-2001 and 1970-2001, there is no convincing statistical evidence in favor of absolute convergence in the last two periods: 1980-2001 and 1990-2001. The speed of absolute convergence in the four periods range between 0.99-2.56 % p.a. (2% for the EU was worked out by Barro and Xavier Sala-i-Martin, 1995, for European regions) for EU while it ranges between 0.57-1.16 % p.a. for the countries in East Asia and EU regions together. However, there is no evidence of convergence among the South Asian countries in all periods and some major CIS republics since 1966.There is however tendency for absolute convergence among countries of South Asia, East Asia and European Union together particularly after the 1980s. Conditional convergence is prevalent among almost all pairs of regions in our sample except East Asian and South Asian nations together. Speed of conditional convergence ranges from 0.2 % in an year to 22%.In the European nations, the speed of conditional convergence works out be nearly 20 % unlike the speed of absolute convergence which hovered around 2 %.Such results would mean that countries in Europe are converging very quickly to their own potential level of incomes per capita but not so quickly to a common potential level of income per capita.Growth equation; absolute convergence; conditional convergence; speed of absolute and conditional convergence; elasticity of output with respect to capital; half life of convergence

On the Convergence Speed of Spatially Coupled LDPC Ensembles

Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemble, with a wave-like convergence propagating through the spatial dimension of the graph, allowing to approach the MAP threshold. We focus on this particularly interesting regime in between the BP and MAP thresholds. On the binary erasure channel, it has been proved that the information propagates with a constant speed toward the successful decoding solution. We derive an upper bound on the propagation speed, only depending on the basic parameters of the spatially coupled code ensemble such as degree distribution and the coupling factor $w$. We illustrate the convergence speed of different code ensembles by simulation results, and show how optimizing degree profiles helps to speed up the convergence.Comment: 11 pages, 6 figure

European Regional Convergence in a Human Capital Augmented Solow Model

In this paper, the process of productivity convergence is investigated for the enlarged European Union using regional (NUTS-2) data. The Solow model extended by human capital is employed as a workhorse. Alternative strategies are proposed to control for spatial effects. All specifications confirm the presence of convergence with an annual speed between 3 and 3.5 percent towards regional steady states. Furthermore, a geographically weighted regression approach indicates a wide variation in the speed of convergence across the regions, where a higher speed is striking in particular in France and the UK. Clusters of convergence can be identified, where regions with high convergence also have high initial income levels.Solow model, regional convergence, spatial lags, spatial filtering

REPEATED GAMES WITH PROBABILISTIC HORIZON

Repeated games with probabilistic horizon are defined as those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, they assign a probability pt to the event that "the game ends in period t". In this framework we analyze Generalized Prisoners' Dilemma games in both finite stage and differentiable stage games. Our construction shows that it is possible to reach cooperative equilibria under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite. More precisely, we completely characterize the existence of sub-game perfect cooperative equilibria in finite stage games by the (first order) convergence speed: the behavior in the limit of the ratio between the ending probabilities of two consecutive periods. Cooperation in differentiable stage games is determined by the second order convergence speed, which gives a finer analysis of the probability convergence process when the first convergence speed is zero.Leptokurtic distributions are defined as those distributions for which the (first order) convergence speed is zero and they preclude cooperation in finite stage games with probabilistic horizon. However, this negative result is obtained in differential stage games only for a subset of these distributions.repeated games, probabilistic horizon, cooperation