F. HASHEMI

36

evolving, corresponding to our theoretical predictions.

2). The value for the income adjustment rate

is

positive as expected.

3). The value for the diffusion parameter

is small

and positive as expected.

4). The diffusive limit, i.e., the limit as of the

variance is:

t

2

lim t

t

The results predict that if we

start with a normal distribution and let the model drive the

distribution, the distribution variance will tend toward a

constant

and concentrated around a mean u.

5. Final Remarks

A methodology has been proposed which is a more

transparent way to quantify the dynamics of income, as it

avoids the complications associated with dynamic infer-

ence and statistical regression fallacy inherent in stan-

dard cross-section tests [20-22]. The present study is in

the spirit of probabilistic models of Krugman [23] who

studies city sizes, Axtell [24] and Hashemi [25,26] who

study firm sizes, and Hashemi [27,28] who studies in-

come and rate of unemployment. Our suggestion is that

these models could provide interesting insights as well, if

applied to spatial dynamics of personal income.

One fruitful extension of the present study would be to

relax the homogeneity assumptions of the model pa-

rameters. Another interesting extension would be to ex-

amine if the driving forces of convergence and diver-

gence are the same for other components of income such

as profit, interest and rent. We hope the present study

illustrates that the endeavor is promising.

6. Acknowledgments

The author has benefited from discussions with Minimax

consulting on the statistical analysis in this paper.

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