Hanihara's Conundrum Revisited. Theoretical Estimates of the Immigration into Japan during the 1,000 Year Period from 300 B.C. to A.D. 700.

Abstract

Prehistoric Japanese population is believed to have increased from 75, 800 in 300 B.C. to 5, 399, 800 in A.D. 700-a 70-fold increase in 1, 000 years. The rate of natural increase-hereafter called the annual growth rate-likely averaged 0.1% during this period. A closed population growing at this rate would have experienced only a 2.7-fold increase, so that the deficit must have been balanced by immigration, and the question is how much? Hanihara (1987), who assumed constant growth and immigration rates, arrived at an estimate of over 3, 000 immigrants per year-an “unacceptably” high level of immigration. In this paper, we modify Hanihara's original model to permit the annual growth rate to vary around the long term average of 0.1%. Specifically, we model the annual growth rate as an autoregressive time-series with normally distributed random shocks. When the autoregressive coefficient, b, and the standard deviation of the random shocks, h, are large, the requisite level of immigration may be substantially reduced. In particular, with b=0.9 and h=0.1, 50 immigrants per year may suffice. Time-series data on crude birth and death rates are available from historical-demographic studies. Unfortunately, the parameters b and h estimated from these data may not be large enough for the predicted reductions to occur.