In this paper, our main aim is to examine long-term trends of Japanese inter-prefectural migration after the War by using a Markov migration model. In Japan, Statistics Bureau, Management and Coordination Agency has published official statistics for internal migration by sex and month in Annual Report on the Internal Migration in Japan Derived from the Basic Resident Registers. First of all, we have made the orient-destination tables for inter-prefectural migration by sex and year from 1954 to 1993 based on the Annual Report.
Next we observed dependence of in- and out-migration on the size of populations by prefecture. It is observed that at each period a simple log-linear relation holds between the size of prefectural population and the size of in- or out-migration by prefecture. After 1960 parameters of the model for in-migration and out-migration have come closer and closer, so we can see that after 1970 in-migration and out-migration have tended to balance at each prefecture.
Subsequently we converted the OD tables to Markov matrices and calculated their stationary distributions. By observing the time-series of stationary distributions by year, we can see implicit trends and changes of inter-prefectural migration system, because the stationary distribution is determined only by migration probability independent of initial distribution and it is the ultimate distribution for the stationary Markov process generated by the Markov matrix. Although the real migration process is not a stationary stochastic process, the stationary distribution at each period can be seen as the moving target of the migration system.
Major findings based on the time-series observation of stationary distributions by year are as follows: First from 50th to 1970 migrants tended to concentrate to densely populated industrialized prefectures (Tokyo, Osaka and Aichi), but after that during 70th, populations have redistributed to provincial prefectures. Reconcentration of population to Tokyo area again occurred around mid-80th, it ceased at the beginning of 90th in accordance with economic recession. Second the root mean square (RMS) distance by year between stationary distribution and population distribution by prefecture have rapidly decreased from 1960 to 1975, hence after that real population distributions by prefecture have become very similar to stationary distributions. That is, it can be concluded that recent Japanese inter-prefectural migration system has lost its potential power to redistribute populations. Third the stationary distribution and the income distribution by prefecture have always had a similar pattern at each period, which suggests that income differentials could be a main reason for internal migration. However after mid-60th its RMS distance was always larger than RMS distance between the stationary distribution and the population distribution by prefecture. Hence Shimizu's hypothesis (1964) that internal migration is a movement to reduce income differentials among prefectures does not necessarily hold. In reality, the imbalance of per capita income among prefectures has extended through 80th, but it did not lead redistribution of populations, and the population distribution has stayed at the neighborhood of the stationary distribution at each period during the past two decades.