IPUMS-International

International Integrated Microdata Access System

A common problem with income data is the use of broad income groups. To compute average incomes for individuals, the mid-point of any "closed" group can be computed. Typically, however, the last group is an open-ended category. In this case, a Pareto estimate can be calculated using the algorithm described on pages 216-217 of the US Bureau of Statistics volume, Income Distribution in the United States, by Herman P. Miller (1966), a 1960 census monograph.

As an example, we use data for full-time workers from the 1986 public use sample for Australia.

Income distribution among persons working 35 hours a week or more, 
		1986 Census of Australia

	Income category	    Number  Percentage
		
	$0 to $1400 p.a.         1029     2.18
	$1401 to $6000           1050     2.23
	$6001 to $9000           2627     5.58
	$9001 to $15000         11158    23.68
	$15001 to $22000        17412    36.96
	$22001 to $32000         9510    20.19
	$32001 to $40000         2433     5.16
	$40001 and over          1894     4.02
	Total                   47113   100.00
		
	Pareto estimate for		
	mean of last category       $54,802 	

The algorithm requires four items of information:

• two frequency counts, one for the second-last, and the other for the last, category; and
  
  
• the lower limits of the last two income categories.

The program also calculates an estimate for the median of the open-ended category, using the algorithm described by Parker and Fenwick in Social Forces, 61, March 1983, page 875.

One of the examples given by Parker and Fenwick (the 1975 Panel Study Bonuses) appears to contain an error. Setting the last count in their appendix table (page 883) to 8 rather than 23 produces results approximating those reported in Table 1 (page 877). Note also that they also recommend using the estimated median for persons in the last (open-ended) income category, rather than the estimated mean.