Methods of restoring the per-capita income distribution in large samples to generalized population levels

This paper provides an analysis of popular methods for correcting sample distribution of income per-capita and proposes a methodology for evaluating the parameters of a lognormal income distribution, taking into account unequal response rates between individuals with different income levels, income deciles - a result of survey design and the survey non-response rate. The authors propose the fitting of a lognormal distribution on the basis of comparing mean and boundary income levels for defined population intervals between the sample and general distribution, instead of the more common approach of frequency analysis between the two. The mean income value of a given interval, with enough observations, is less volatile than the individual frequencies on the interval. This is especially important in situations where individual frequencies in the sample distribution significantly differ from the population distribution itself. The authors examine two different criteria for estimating the optimal lognormal distribution parameters. The first method is similar to the methodology used in Russian statistics, and does not require preliminary information on the share of the poor population. The parameters are estimated using the condition of equality between the sample and population mean income, and the right-income boundary of the first income deciles. The second criterion is based on minimizing the squared sum of deviations between the mean income levels for the middle eight income deciles of the sample and population mean values. Neither of the two criteria uses the hypothesis of non-response rates increasing with households’ income growth, which allows one to assess the representative-value of the sample survey. The results of the calculations show that the method achieves the highest parity between sample and population distributions in the middle-part of the lognormal distribution, but suffers from underrepresentation in the lower part of the distribution, i.e. for poor households and individuals.

логнормальное распределение, оценка параметров, выборочное обследование, отказы от участия в опросе, средний душевой денежный доход, генеральная совокупность, децильные интервалы денежных доходов населения, lognormal distribution, parameter estimation, sample survey, non-response rate, mean income, general equilibrium, income deciles

1. Айвазян С.А., Калеников С.О. Качество жизни, уровень бедности и дифференциации по расходам населения России. Промежуточный отчет по гранту РПЭИ, декабрь, 1999.

2. Балансы доходов и потребления населения. Вопросы методологии и статистического анализа / под ред. А.Х. Карапетяна и Н.М. Римашевской. - М.: Статистика,1969.

3. Колмаков И.Б. Методы и модели прогнозирования показателей дифференциации и поляризации денежных доходов населения: дисс.. д-ра экон. наук. М., 2008.

4. Поманский А.Б. Анализ модели стимулирования и логарифмически нормальное распределение доходов // Экономика и математические методы. 1985. T. XXI. Вып. 3.

5. Суворов А.В. Проблемы оценки дифференциации доходов населения в современной России / / Проблемы прогнозирования. 2008. № 2.

6. Шевяков А.Ю., Кирута А.Я. Измерение экономического неравенства и бедности. - М.: Лето, 2002.

7. Шевяков А.Ю., Кирута А.Я. Неравенство, экономический рост и демография: неисследованные взаимосвязи. - М.: М-студия, 2009.

8. Шевяков А.Ю., Кирута А.Я. Экономическое неравенство, уровень жизни и бедность населения России и ее регионов в процессе реформ; методы измерения и анализ причинных зависимостей. Заключительный отчет по гранту РПЭИ. - М.: ЭПИКОН, 1999.

9. Banerjee A., Yakovenko V.M., Di Matteo T. A study of the personal income distribution in Australia // Physica A: statistical mechanics and its applications. 2006. Vol. 370.

10. Bilkova D. Lognormal distribution and using L-moment method for estimating its parameters // International journal of mathematical models and methods in applied sciences. 2012. Issue 1. Vol. 6.

11. Clementi F., Gallegati M. Power law tails in the Italian personal income distribution // Physica A: statistical mechanics and its applications. 2005. Vol. 350.

12. Dagum C. A systemic approach to the generation of income distribution models // Journal of Income Distribution. 1997. Vol. 6. No 1.

13. Deville J.-C. Generalized calibration and application to waiting for non-response // COMPSTAT: Proceedings in Computational Statistics 14th Symposium held in Utrecht, The Netherlands, 2000. - Heidelberg: Physica-Verl., 2000.

14. Vanderhoeft C. Generalised Calibration at Statistics Belgium: SPSS Module g-CALIB-S and Current Practices // Statistics Belgium Working Paper. 2001. No 3.

15. Vinderhoeft с., Museux J.-M., Wkeytens E. g-DESIGN and g-CALIB-S: SPSS modules for Generalized Calibration // The Survey Statistician. IASS Newsletter, 2000. No. 43.