ABSTRACT
In order to make statistical analysis, we must discretize the United Nations model so that it transform from differential equations into difference expressions, i.e., a 2-dimension map. Then the analysis of continuous dynamics changes to that of discrete dynamics. If 10=Δt as taken, then dx/dt∝∆x/∆t. Let r(t), u(t) and r(t)*u(t)/[r(t)+u(t)] be independent variables, and ∆u(t)/∆t and ∆r(t)/∆t be dependent variables. A multivariate stepwise regression analysis based on the least squares computation gives the following model
. (15)
This is a pair of difference equations of which all kinds of statistics including F statistic, P value (or t statistic), variance infl ation factor (VIF) value and Durbin-Watson (DW) value can pass the tests at the signifi cance level of 01.0=α (Appendix 1). In this model, c=0. Although we should have b=d in theory, they are not equal in the empirical results. There might be two reasons for this. One is that the US is not a truly closed system because of mass foreign migration; the other is that the natural growth of the urban population is dependent on the urban-rural interaction. The second reason might be more important. But on the whole, the equations as a special case of the United Nations model can better describe the American urban and rural population migration process in the recent 200 years.
