Abstract

This article develops and evaluates a method for deriving postcensal estimates of household income distributions for counties. A modified lognormal probability curve is used as a model of income distribution. The function is closely related to the classical lognormal model, but it contains a nonlinear component in its derivation. Simulated postcensal estimates of household income distributions are compared with 1980 census data for the counties in California. The results indicate that the modified lognormal curve approximates observed income distributions well and produces reliable postcensal estimates for areas with a wide variety of median income levels and numbers of households.

The text of this article is only available as a PDF.

References

Aitchison, J., & Brown, J. (
1957
).
The Lognormal Distribution
.
Cambridge, U.K.
:
Cambridge University Press
.
Anscombe, F., & Tukey, J. (
1963
).
The examination and analysis of residuals
.
Technometrics
,
5
,
141
160
. 10.2307/1266059
Belsley, D., Kuh, E., & Welsch, R. (
1980
).
Regression Diagnosis: Identifying Influential Data and Sources of Collinearity
.
New York
:
Wiley
.
Blaylock, J., & Smallwood, D. (
1982
).
Analysis of income and food expenditure distributions: A flexible approach
.
Review of Economics and Statistics
,
64
,
104
109
. 10.2307/1937949
April 1, 1980, Estimates of the Number of Households by County
. (
1981
).
Sacramento
:
California State Dept. of Finance
.
Champernowne, D. (
1953
).
A model of income distribution
.
Economic Journal
,
63
,
318
351
. 10.2307/2227127
Chatterjee, S., & Price, B. (
1977
).
Regression Analysis by Example
.
Toronto
:
Wiley
.
Duncan, D., Cuzzort, R., & Duncan, B. (
1961
).
Statistical Geography: Problems in Analyzing Areal Data
.
Glencoe, Ill.
:
Free Press
.
Fay, R., & Herriot, R. (
1979
).
Estimates of income for small places: An application of James Stein procedures to census data
.
Journal of the American Statistical Association
,
74
,
269
277
. 10.2307/2286322
Gillaspy, T., and M. McMurry. 1986. Estimating Income Distributions of Counties in Minnesota. Paper presented at the Annual Meeting of the Population Association of America, San Francisco.
Garofalo, G., & Fogarty, M. (
1979
).
Urban income distribution and the urban hierarchy-equality hypotheses
.
Review of Economics and Statistics
,
61
,
381
388
. 10.2307/1926067
Gastwirth, J. (
1972
).
The estimation of the Lorenz curve and Gini index
.
Review of Economics and Statistics
,
54
,
306
316
. 10.2307/1937992
Gupta, M. (
1984
).
Functional form for estimating the Lorenz curve
.
Econometrica
,
52
,
1313
1314
. 10.2307/1911001
Hoover, E. (
1941
).
Measurement of industrial location
.
Review of Economics and Statistics
,
23
,
162
171
.
Jahn, J. (
1950
).
Measurement of ecological segregation
.
American Sociological Review
,
15
,
100
104
. 10.2307/2086407
Johnson, N. (
1949
).
Systems of frequency curves generated by methods of translation
.
Biometrika
,
36
,
149
176
.
Johnson, N., & Kotz, S. (
1970
).
Continuous Univariate Distributions
.
New York
:
Houghton Mifflin
.
Kakwani, N., & Podder, N. (
1976
).
Efficient estimation of the Lorenz curve and association inequality measures from grouped observations
.
Econometrica
,
44
,
137
148
. 10.2307/1911387
Kalecki, M. (
1945
).
On the Gibrat distribution
.
Econometrica
,
13
,
161
170
. 10.2307/1907013
Krishnaji, N. (
1970
).
Characterization of the Pareto distribution through a model of underreported incomes
.
Econometrica
,
38
,
251
255
. 10.2307/1913007
Marschak, J. (
1942
).
Income inequality and demand studies
.
Econometrica
,
11
,
163
166
. 10.2307/1909266
Estimating Population and Income for Small Areas
. (
1980
).
Washington, D.C.
:
National Academy Press
.
Roy, A. (
1950
).
A further note on the distribution of individual output
.
Economic Journal
,
60
,
831
836
. 10.2307/2226739
Smith, G. (
1947
).
Lorenz curve analysis of industrial decentralization
.
Journal of the American Statistical Association
,
42
,
591
596
. 10.2307/2280015
Spar, M., and J. Martin. 1979. Refinements to regression-based estimates of postcensal population characteristics. Review of Public Data Use 7(5/6).
Stiglitz, J. (
1969
).
Distribution of income and wealth among individuals
.
Econometrica
,
37
,
382
397
. 10.2307/1912788
Summers, A., & Wolfe, B. (
1978
).
Estimating household income from location
.
Journal of the American Statistical Association
,
73
,
288
292
. 10.2307/2286654
Swanson, D. (
1978
).
An evaluation of ratio and difference regression models for estimating small highly concentrated populations: The case of ethnic groups
.
Review of Public Data Use
,
6
,
18
27
.
Swanson, D. (
1981
).
Allocation accuracy in population estimates: An overlooked criterion with fiscal implications
Small Area Population Estimates, Methods and Their Accuracy and New Metropolitan Area Def-initions and Their Impact on the Private and Public Sector
(pp.
13
21
).
Washington, D.C.
:
U.S. Government Printing Office
.
Tayman, J., & Schäfer, E. (
1985
).
The impact of coefficient drift and measurement error on the accuracy of ratio-correlation population estimates
.
Review of Regional Studies
,
15
(
2
),
3
10
.
. Census of Population, Household Income in 1969 for States, SMSA’s, Cities and Counties: 1970
. (
1973
).
Washington, D.C.
:
U.S. Government Printing Office
.
1970 Census of Population, Characteristics of the Population
. (
1973
).
California
:
Washington, D.C.: U.S. Government Printing Office
.
Money Income Estimates for Local Areas: Detailed Methodology and Evaluation
. (
1980
).
Washington, D.C.
:
U.S. Government Printing Office
.
Census of Population: 1980, General Social and Economic Characteristics, PC80-J-C6
. (
1983
).
California. Washington, D.C.
:
U.S. Government Printing Office
.
Estimates of Per Capita Income: Regional Information System
. (
1986
).
Washington, D.C.
:
U.S. Government Printing Office
.
Vining, R. (
1945
).
Regional variation in cyclical fluctuations viewed as a frequency distribution
.
Econometrica
,
13
,
183
213
. 10.2307/1907184
Wilson, A. (
1974
).
Urban and Regional Models in Geography and Planning
.
New York
:
Wiley
.