Kiel Institute of World Economics
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Kiel Working Paper No. 1086
Markov or Not Markov –
This Should Be a Question
Frank Bickenbach and Eckhardt Bode
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Markov or Not Markov – This Should Be a Question
Although it is well known that Markov process ...view middle of the document...
Depending on the underlying
concept of convergence (unconditional or conditional β-convergence, σconvergence, stochastic convergence), the statistical method employed
(descriptive statistics, econometric approaches for cross-section, time-series, or
panel data, Markov chain, or stochastic kernel estimations), and the geographic
scope of analysis (countries, regions in single or groups of countries), the
conclusions vary widely, ranging from rapid convergence to club convergence,
and divergence. De la Fuente (1997), Durlauf and Quah (1999), and Temple
(1999) have provided excellent reviews of the vast literature.
Most empirical approaches are based on hypotheses about the processes of
interest rather than just describing them in a positive analysis. Often, some sort
of a law (a ‘law of convergence’, a ’law of motion’) is postulated to be valid
even beyond the respective time period under consideration. The supposed relevance for future developments certainly has contributed to the popularity of
respective approaches in the scientific as well as in the public sphere, as compared to simple descriptive statistics like the coefficient of variation. A politician,
e.g., worrying about whether poor regions within his country, or poor countries
in the world, may actually run the risk of being caught in a poverty trap will be
strongly interested in a prediction for the future rather than just a description of
In standard convergence regressions, as proposed by Barro and Sala-i-Martin
(1991), and Mankiw et al. (1992), neoclassical growth theory is used to derive the
hypothesis that income levels tend to converge. Having identified empirically a
tendency towards (β-) convergence in the past, the underlying theoretical model
suggests that convergence will continue until all regions will have the same percapita income level (unconditional β-convergence) or, at least, an income level
representing their specific behavioral and technical conditions (conditional βconvergence).
In Markov-chain approaches, as proposed by Quah (1993a; 1993b), the ‘law of
motion’ driving the evolution of the income distribution is usually assumed to be
memoryless and time-invariant. Having estimated probabilities of moving up or
down the income hierarchy during a transition period of given length a stationary
income distribution is calculated which characterizes the distribution the whole
system tends to converge to over time. Although several authors (such as Quah
himself, or Rey 2001b) emphasize that the stationary distribution represents
merely a thought experiment it is often necessary to clarify the direction of the
evolution since the estimated transition probability matrix by itself is not really
informative about the evolution of the income distribution.1
The power of convergence regressions with respect to both describing comparative income growth processes in the period of analysis, and assessing the
validity of neoclassical...