by Economic convergence and the Markov chain approach In the Markov chain approach to income convergence … the “law of motion” driving the evolution of the income distribution is assumed memory-less and time invariant. Upon having estimated probabilities of moving up or down the income hierarchy during a transition period of a given length, the law is used to calculate a limiting income distribution characterizing a stochastic steady-state income distribution to which the system converges over time. Although several authors emphasize that the limiting distribution merely represents a thought experiment, this distribution is necessary to clarify the direction of the evolution. The estimated transition probability matrix in itself is often rather uninformative with respect to the evolution of the income distribution. Unlike the convergence-regression approach, however, the reliability of the estimated transition probabilities and hence of the limiting income distribution has rarely been questioned. In most empirical studies, the statistical assumptions underlying the Markov chain approach have been taken for granted, although they are quite restrictive … As an illustration, the article shows that the evolution of the income distribution across the forty-eight contiguous U.S.
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Economic convergence and the Markov chain approach
In the Markov chain approach to income convergence … the “law of motion” driving the evolution of the income distribution is assumed memory-less and time invariant. Upon having estimated probabilities of moving up or down the income hierarchy during a transition period of a given length, the law is used to calculate a limiting income distribution characterizing a stochastic steady-state income distribution to which the system converges over time.
Although several authors emphasize that the limiting distribution merely represents a thought experiment, this distribution is necessary to clarify the direction of the evolution. The estimated transition probability matrix in itself is often rather uninformative with respect to the evolution of the income distribution. Unlike the convergence-regression approach, however, the reliability of the estimated transition probabilities and hence of the limiting income distribution has rarely been questioned. In most empirical studies, the statistical assumptions underlying the Markov chain approach have been taken for granted, although they are quite restrictive …
As an illustration, the article shows that the evolution of the income distribution across the forty-eight contiguous U.S. states from 1929 to 2000 does clearly not follow a common first-order stationary Markov process for various reasons. First, there is a structural break in the aftermath ofWorldWar II that significantly affects the evolution of the income distribution; another structural break may have occurred in the late 1990s. Second, certain groups of states … show a development that is different from other states … Third, states with poor neighbors show a different development than states with rich neighbors. Moreover, a choice for annual transition periods is shown to be inconsistent with the Markov property. Ignoring these factors may considerably affect the correctness of inferences about the evolution of the regional income distribution drawn from the limiting distribution.
