Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data
Abstract
1. Introduction
2. Survey Design and Point Estimation
3. Bounded Width Confidence Intervals
Estimation of
4. Sequential Methodology
4.1. Purely Sequential Procedure
4.2. Two-Stage Procedure
4.3. Pilot Cluster Size
5. Characteristics of the Procedures and Simulation Study
5.1. Characteristics
- (i)
- in probability,
- (ii)
- in probability, and
- (iii)
- .
- (i)
- The definition of stopping rule N associated with the purely sequential procedure in (8) yieldsFurthermore, as . Hence, dividing all sides of (14) by C and letting , we prove in probability as .
- (ii)
- Furthermore, as . Now, in probability as . Hence, dividing all sides of (15) by C and letting , we prove in probability as .
- (iii)
5.2. Simulation Study
6. Gini Index Estimation in India
6.1. Application of Purely Sequential Procedure (PSP)
6.2. Application of Two-Stage Procedure
7. Extension: Narrow Confidence Region
8. Discussion
9. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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1 | The survey excluded “(i) Leh (Ladakh) and Kargil districts of Jammu and Kashmir (for central sample), (ii) interior villages of Nagaland situated beyond 5 km of the bus route and (ii) villages of Andaman and Nicobar Islands which remain inaccessible throughout the year.” (National Sample Survey Office 2007). |
Region | H | N | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|---|
Uttar Pradesh | |||||||||
All | 0.2163 | 1262 | 622 | 672 | 0.2116 | 0.2023 | 0.2209 | 0.0186 | 0.2138 |
(0.0042) | (321) | (0.0057) | |||||||
Rural | 0.1997 | 903 | 505 | 523 | 0.2024 | 0.1931 | 0.2117 | 0.0186 | 0.4 |
(0.0041) | (198) | (0.0057) | |||||||
Urban | 0.2229 | 359 | 903 | 359 | 0.2229 | 0.2077 | 0.2381 | 0.0304 | 1.0 |
(0.0092) | (180) | (0.0092) | |||||||
West Bengal | |||||||||
All | 0.2320 | 878 | 587 | 593 | 0.2334 | 0.2239 | 0.2430 | 0.0191 | 0.1282 |
(0.0051) | (190) | (0.0058) | |||||||
Rural | 0.1812 | 551 | 450 | 450 | 0.1816 | 0.1723 | 0.1909 | 0.0186 | 0.2353 |
(0.0048) | (172) | (0.0057) | |||||||
Urban | 0.2609 | 327 | 612 | 327 | 0.2609 | 0.2482 | 0.2736 | 0.0254 | 1.0 |
(0.0077) | (185) | (0.0077) |
Region | H | N | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|---|
Uttar Pradesh | |||||||||
All | 0.2163 | 1262 | 834 | 878 | 0.2117 | 0.2022 | 0.2212 | 0.0190 | 0.2138 |
(0.0042) | (333) | (0.0048) | |||||||
Rural | 0.1997 | 903 | 643 | 667 | 0.2024 | 0.1930 | 0.2117 | 0.0187 | 0.4 |
(0.0041) | (226) | (0.0048) | |||||||
Urban | 0.2229 | 359 | 1282 | 359 | 0.2229 | 0.2048 | 0.2410 | 0.0362 | 1.0 |
(0.0092) | (254) | (0.0092) | |||||||
West Bengal | |||||||||
All | 0.2320 | 878 | 906 | 878 | 0.2320 | 0.2221 | 0.2419 | 0.0198 | 1.0 |
(0.0051) | (223) | (0.0051) | |||||||
Rural | 0.181 | 551 | 552 | 551 | 0.1812 | 0.1719 | 0.1906 | 0.01871 | 1.0 |
(0.0048) | (203) | (0.0048) | |||||||
Urban | 0.2609 | 327 | 869 | 327 | 0.2609 | 0.2458 | 0.2761 | 0.0303 | 1.0 |
(0.0077) | (207) | (0.0077) |
Region | H | N | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|---|
Uttar Pradesh | |||||||||
All | 0.2163 | 1262 | 401 | 540 | 0.2138 | 0.2035 | 0.2242 | 0.0207 | 0.0 |
(0.0042) | (302) | (0.0063) | |||||||
Rural | 0.1997 | 903 | 386 | 400 | 0.2014 | 0.1899 | 0.2130 | 0.0231 | 0.1714 |
(0.0041) | (168) | (0.0070) | |||||||
Urban | 0.2229 | 359 | 578 | 359 | 0.2229 | 0.2077 | 0.2381 | 0.0304 | 1.0 |
(0.0092) | (168) | (0.0092) | |||||||
West Bengal | |||||||||
All | 0.2320 | 878 | 324 | 319 | 0.2288 | 0.2175 | 0.2401 | 0.0226 | 0.1795 |
(0.0051) | (158) | (0.0069) | |||||||
Rural | 0.1812 | 551 | 276 | 289 | 0.1829 | 0.1721 | 0.1937 | 0.0216 | 0.2353 |
(0.00477) | (138) | (0.0066) | |||||||
Urban | 0.2609 | 327 | 392 | 327 | 0.2609 | 0.2482 | 0.2736 | 0.0254 | 1.0 |
(0.0077) | (142) | (0.0077) |
Region | H | N | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|---|
Uttar Pradesh | |||||||||
All | 0.2163 | 1262 | 572 | 653 | 0.2123 | 0.2010 | 0.2236 | 0.0226 | 0.2138 |
(0.0042) | (728) | (0.0058) | |||||||
Rural | 0.1997 | 903 | 496 | 510 | 0.2010 | 0.1893 | 0.2128 | 0.0234 | 0.1714 |
(0.0041) | (197) | (0.0060) | |||||||
Urban | 0.2229 | 359 | 821 | 359 | 0.2229 | 0.2048 | 0.2410 | 0.0362 | 1.0 |
(0.0092) | (717) | (0.0092) | |||||||
West Bengal | |||||||||
All | 0.2320 | 878 | 517 | 519 | 0.2318 | 0.2199 | 0.2437 | 0.0238 | 0.1538 |
(0.0051) | (186) | (0.0061) | |||||||
Rural | 0.1812 | 551 | 351 | 352 | 0.1815 | 0.1703 | 0.1927 | 0.0223 | 0.2353 |
(0.0048) | (163) | (0.0057) | |||||||
Urban | 0.2609 | 327 | 556 | 327 | 0.2609 | 0.2458 | 0.2761 | 0.0303 | 1.0 |
(0.0077) | (162) | (0.0077) |
Region | H | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|
Uttar Pradesh | ||||||||
All | 1262 | 1146 | 1171 | 0.2163 | 0.2137 | 0.2072 | 0.2202 | 0.0131 |
(321) | (1146) | (0.0042) | (0.0040) | |||||
Rural | 903 | 398 | 406 | 0.1997 | 0.2027 | 0.1940 | 0.2114 | 0.0174 |
(198) | (398) | (0.0041) | (0.0053) | |||||
Urban | 359 | 1177 | 359 | 0.2229 | 0.2229 | 0.2077 | 0.2381 | 0.0304 |
(180) | (359) | (0.0092) | (0.0092) | |||||
West Bengal | ||||||||
All | 878 | 624 | 626 | 0.2320 | 0.2307 | 0.2216 | 0.2398 | 0.0182 |
(190) | (624) | (0.0051) | (0.0055) | |||||
Rural | 551 | 422 | 420 | 0.1812 | 0.1785 | 0.1707 | 0.1862 | 0.0155 |
(173) | (422) | (0.0048) | (0.0047) | |||||
Urban | 327 | 857 | 327 | 0.2609 | 0.2609 | 0.2482 | 0.2736 | 0.0254 |
(185) | (327) | (0.0077) | (0.0077) |
Region | H | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|
Uttar Pradesh | ||||||||
All | 1262 | 1665 | 1262 | 0.2163 | 0.2163 | 0.2081 | 0.2245 | 0.0164 |
(333) | (1262) | (0.0042) | (0.0042) | |||||
Rural | 903 | 593 | 595 | 0.2000 | 0.2000 | 0.1914 | 0.2085 | 0.0171 |
(226) | (593) | (0.0041) | (0.0044) | |||||
Urban | 359 | 1712 | 359 | 0.2229 | 0.2229 | 0.2048 | 0.2410 | 0.0362 |
(254) | (359) | (0.0092) | (0.0092) | |||||
West Bengal | ||||||||
All | 878 | 874 | 878 | 0.2320 | 0.2320 | 0.2221 | 0.2419 | 0.0198 |
(223) | (874) | (0.0051) | (0.0051) | |||||
Rural | 551 | 535 | 534 | 0.1812 | 0.1814 | 0.1719 | 0.1910 | 0.0191 |
(203) | (535) | (0.0048) | (0.0049) | |||||
Urban | 327 | 1110 | 327 | 0.2609 | 0.2609 | 0.2458 | 0.2761 | 0.0303 |
(207) | (327) | (0.0077) | (0.0077) |
Region | H | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|
Uttar Pradesh | ||||||||
All | 1262 | 688 | 680 | 0.2163 | 0.2104 | 0.2023 | 0.2185 | 0.0162 |
(302) | (688) | (0.0042) | (0.0049) | |||||
Rural | 903 | 299 | 308 | 0.1997 | 0.2026 | 0.1927 | 0.2126 | 0.0199 |
(168) | (299) | (0.0041) | (0.0061) | |||||
Urban | 359 | 1087 | 359 | 0.2229 | 0.2229 | 0.2077 | 0.2381 | 0.0304 |
(168) | (359) | (0.0092) | (0.0092) | |||||
West Bengal | ||||||||
All | 878 | 396 | 396 | 0.2320 | 0.2293 | 0.2171 | 0.2414 | 0.0243 |
(158) | (396) | (0.0051) | (0.0074) | |||||
Rural | 551 | 275 | 275 | 0.1812 | 0.1750 | 0.1660 | 0.1840 | 0.0180 |
(138) | (275) | (0.0048) | (0.0055) | |||||
Urban | 327 | 582 | 327 | 0.2609 | 0.2609 | 0.2482 | 0.2736 | 0.0254 |
(142) | (327) | (0.0077) | (0.0077) |
Region | H | Lower CI | Upper CI | |||||
---|---|---|---|---|---|---|---|---|
Uttar Pradesh | ||||||||
All | 1262 | 976 | 947 | 0.2163 | 0.2124 | 0.2041 | 0.2207 | 0.0166 |
(302) | (946) | (0.0042) | (0.0042) | |||||
Rural | 903 | 364 | 353 | 0.1997 | 0.2032 | 0.1922 | 0.2142 | 0.0220 |
(197) | (364) | (0.0041) | (0.0056) | |||||
Urban | 359 | 1081 | 359 | 0.2229 | 0.2229 | 0.2048 | 0.2410 | 0.0362 |
(177) | (359) | (0.0092) | (0.0092) | |||||
West Bengal | ||||||||
All | 878 | 607 | 608 | 0.2320 | 0.2315 | 0.2204 | 0.2427 | 0.0224 |
(186) | (607) | (0.0051) | (0.0057) | |||||
Rural | 551 | 391 | 392 | 0.1812 | 0.1759 | 0.1670 | 0.1849 | 0.0178 |
(163) | (391) | (0.0048) | (0.0045) | |||||
Urban | 327 | 754 | 327 | 0.2609 | 0.2609 | 0.2458 | 0.2761 | 0.0303 |
(162) | (327) | (0.0077) | (0.0077) |
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Bilson Darku, F.; Konietschke, F.; Chattopadhyay, B. Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data. Econometrics 2020, 8, 26. https://doi.org/10.3390/econometrics8020026
Bilson Darku F, Konietschke F, Chattopadhyay B. Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data. Econometrics. 2020; 8(2):26. https://doi.org/10.3390/econometrics8020026
Chicago/Turabian StyleBilson Darku, Francis, Frank Konietschke, and Bhargab Chattopadhyay. 2020. "Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data" Econometrics 8, no. 2: 26. https://doi.org/10.3390/econometrics8020026
APA StyleBilson Darku, F., Konietschke, F., & Chattopadhyay, B. (2020). Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data. Econometrics, 8(2), 26. https://doi.org/10.3390/econometrics8020026