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Standardization and Decomposition of Rates: a User's Manual

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Standardization and Decomposition of Rates: a User's Manual Current Population Reports Special Studies P23-186 Standardization and Decomposition of Rates: A User's Manual by Prithwis Das Gupta U.S. Department of Commerce Economics and Statistics Administration BUREAU OF THE CENSUS ...) Acknowledgments This report was prepared in the Population Division, under the general direction of J. Gregory Robinson, Chief, Population Analysis and Evaluation Staff. Donald J. Hernandez and Jorge del Pinal reviewed the draft of the report. Rheta D. Pemberton typed the manuscript, and Tecora B. Jimason provided statistical assistance. Michael J. Roebuck of the Demographic Statistical Methods Division conducted the statistical reView. The staff of the Administrative and Publications Services Division, Walter C. Odom, Chief, provided publication planning, design, composition, editorial review, and printing planning and procurement. Linda H. Ambill edited and coordinated the publication; Shirley A. Clark designed the cover. - Current Population Reports Special Studies P23-186 Standardization and Decomposition of Rates: A User’s Manual by Prithwis Das Gupta Issuedfº October 1993 \{*/•º of * U.S. Department of Commerce Ronald H. Brown, Secretary Economics and Statistics Administration Paul A. London, Acting Under Secretary for Economic Affairs BUREAU OF THE CENSUS Harry A. Scarr, Acting Director sº/ Economics and Statistics BUREAU O F THE CENSUS Administration Harry A. Scarr, Acting Director .Paul A London, Acting Under Secretary for Economic Affairs William P . Butz, Associate Director for Demographic Programs POPULATION D IVISION Arthur J. Norton, Chief SUGGESTED C ITATION Manual, Das G upta, Prithwis, Standardization and Decomposition of Rates: A User's U.S. Bureau of the Census, Current Population Reports, Series P23-186, U.S. Government Printing Office, Washington, DC, 1993. Office, Washington, DC 20402. For s ale by Superintendent of Documents, U.S. Government Printing Contents Page C hapter 1. Introduction ........................................................................................ 1 Chapter 2. Rate as the Product of Factors................................................................... 5 2.1 Introduction................................................................................. 5 2.2 The Case of Two Factors ................................................................. 6 2.3 The Case of Three Factors ............................................................... 7 2.4 The Case of Four Factors ................................................................ 9 2.5 The Case of Five Factors ................................................................. 11 2.6 The Case of Six Factors .................................................................. 14 2.7 The Case of P Factors .................................................................... 15 2.8 The General Program ..................................................................... 16 Chapter 3. Rate as a Function of Factors ................................................................... 19 3.1 Introduction ................................................................................ 19 3.2 The Case of Two Factors ................................................................. 19 3.3 The Case of Three Factors ............................................................... 20 3.4 The Case of Four Factors ................................................................ 24 3.5 The Case of Five Factors ................................................................. 26 3.6 The Case of Six Factors .................................................................. 27 3.7 The Case of P Factors .................................................................... 32 3.8 The General Program ..................................................................... 32 3.9 Example 3.7 (Ten Factors)................................................................ 33 Chapter 4. Rate as a Function of Vector-Factors ........................................................... 37 4.1 Introduction ................................................................................ 37 4.2 The Case of Two Vector-Factors ......................................................... 37 ( ) 4.3 The Case of Three Vector-Factors ....................................................... 42 4.4 The Case of Four Vector-Factors ........................................................ 44 4.5 The Case of Five Vector-Factors ......................................................... 46 4.6 The Case of Six Vector-Factors .......................................................... 49 4.7 PVector-Factors and the General Program ............................................. 53 Chapter 5 . Rate f rom Cross-Classified Data ................................................................. 55 5.1 Introduction ................................................................................ 55 5.2 The Case of One Factor .................................................................. 55 5.3 The Case of Two Factors ................................................................. 59 5.4 The Case of Three Factors ............................................................... 63 5.5 The Case of Four Factors ................................................................ 70 5.6 The Case of Five Factors ................................................................. 75 5.7 The Case of Six Factors .................................................................. 79 5.8 The Case of P Factors .................................................................... 82 5.9 The General Program ..................................................................... 91 Chapter 6. Three or More Populations ....................................................................... 97 6.1 introduction ................................................................................ 97 6.2 The Case of Three Populations .......................................................... 98 6.3 The Case of Four Populations ............................................................ 99 6.4 The Case of Five Populations ............................................................ 104 6.5 The Combined Program ................................................................... 105 6.6 The General Case of N Populations (Including Time Series)........................... 105 TABLES 2.1 Mean Earnings as the Product of Two Factors for Black Males and White Males, 18 Years and Over: United States, 1980 ............................................... 7 2.2 Standardization and Decomposition of Mean Earnings in Table 2.1 ................... 7 2.3 Crude Birth Rates as the Product of Three Factors: Austria and Chile, 1981 ......... 9 2.4 Standardization and Decomposition of Crude Birth Rates in Table 2.3 ................ 9 2.5 Percentage Having Nonmarital Live Births as the Product of Four Factors for White Women Aged 15 to 19: United States, 1971 and 1979 ............................... 11 2.6 Standardization and Decomposition of Percentages Having Nonmarital Live Births in Table 2.5 ............................................................................... 11 2.7 Total Fertility Rate as the Product of Five Factors: South Korea, 1960 and 1970.... 14 2.8 Standardization and Decomposition of Total Fertility Rates in Table 2.7 .............. 14 3.1 Crude Rate of Natural Increase as a Function of Crude Birth Rate and Crude Death Rate: United States, 1940 and 1960 ................................................... 20 3.2 Standardization and Decomposition of Crude Rates of Natural Increase in Table 3.1 ................................................................................. 20 3.3 Illegitimacy Ratio for Whites as a Function of Three Factors: United States, 1963 and 1983 ................................................................................. 22 3.4 Standardization and Decomposition of Illegitimacy Ratios in Table 3.3 ............... 22 3.5 Crude Birth Rate as a Function of Four Factors: Austria and Chile, 1981 ............ 25 3.6 Standardization and Decomposition of Crude Birth Rates in Table 3.5 ................ 25 3.7 Crude Birth Rate as a Function of Five Factors: Austria and Chile, 1981 ............. 27 3.8 Standardization and Decomposition of Crude Birth Rates in Table 3.7 ................ 27 3.9 Family Headship Rate for Mothers, 18 to 59 Years, as a Function of Six Factors: United States, White, 1950 and 1980 .................................................. 30 3.10 Standardization and Decomposition of Family Headship Rates in Table 3.9 .......... 30 3.11 Percentage Having Live Births as a Function of Six Factors, for White Women Aged 15 to 19: United States, 1971 and 1979 ......................................... 31 3.12 Standardization and Decomposition of Percentages Having Live Births in Table 1 3.11 ....................................................................................... 3 3.13 M ean Parity of a Cohort as a Function of Ten Factors (Parity Progression Ratios), for White Women: United States, 1908 and 1933 Cohorts ........................... 34 3.14 Standardization and Decomposition of Mean Parities in Table 3.13 ................... 3 4 4.1 F emale Intrinsic Growth Rate per Person as a Function of Two Vector-Factors: United States, 1960 and 1965 .......................................................... 39 4.2 Standardization and Decomposition of Female Intrinsic Growth Rates per Person in Table 4.1 ................................................................................
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