|Alvaro Domínguez, Hiroshi Sakamoto
We reexamine the convergence hypothesis of economic growth. Traditionally, it was analyzed using econometric methods, although estimating long-term economic fluctuations with a linear model is not always ideal. We thus employ a Markov chain stochastic model that divides the logarithmic value of relative income, comparing each country's GDP per capita with the average, into several ranks in descending order of income. Using the most recent data, we total the time-series changes of the income states in each sample, and represent them through probabilities. We observe the changing ergodic distribution and show that the world economy is not growing monotonously, and proceed to correct the population size of each country for rank changes. The transition probability matrix is re-estimated by applying population weights to changes in the income states of each country. When there is no population weighting, the model shows that the world economy may be divided into two peaks as before. However, when using population weights, the model yields more optimistic results.