LINDERT														LINDERT	ROUTH ON "INCOME" DISTRIBUTION FOR "GREAT BRITAIN", 1911/12.																													The Distribution of Income among All Income Recipients															The Distribution of Income among Households, United Kingdom, 1911							The Distribution of Income among the Electorate, United Kingdom, 1911								The Distribution of Income among the Electorate, United Kingdom, 1911
Aug.'88	UK Income Distribution for 1911, after Bowley, Stamp and Routh								Numbers of persons occupied, 1911 and 1913 (1000s)														Estimated Distribution of Pre-tax Income for the United Kingdom, 1911.																The Distribution of Income among All Income Recipients					in the Household Sector, United Kingdom, 1911.							The Distribution of Income among Households, United Kingdom, 1911
											(didn't use 1913:)			Source: Guy Routh. Occupation and Pay in Great Britain 1906-79. London: Macmillan,.																									in the Household Sector, United Kingdom, 1911.																			Class-	Lower limit	Cumulative % shares					Contributions					(£ m.)				Lower limit	Cumulative % shares
Page 1: false start, aimed at 1913:  [See Column X for estimates ->]									1911		(1911 x 1.02628=) 1913			1980. Pp. 47-50, 232-4, 259-60.									Lower limit	Numbers of income earners			Total income (£ millions)			Average income (£)			Lower limit	Notes:										Lower limit	Cumulative % shares													average	of income	above this income limit					to Gini	Lower limit	1000s of	Assumed	1000s of	Income of	Franchise-	Household		of income	above this income limit					Contrib.
First, using the super-tax statistics (Stamp 1922, p. 338) for 1913/14									males	females	males	females											of income		(1000s)								of income						Lower limit					of income	above this lower limit					Contribution	Lower limit	Numbers of households (1000s)			Total income (£ millions)			income of	bracket (£)	Households	Income				coeffic.:	of income	male house-	relative	registered	male-head	weighted	income per		bracket (£)	Franch. men	Income				to Gini
to Pareto-smooth the top ranks:														Routh weaves together the earnings and hours survey of 1906, the agricultural labor									bracket (£)	Males	Females	Both	Males	Females	Both	Males	Females	Both	bracket (£)						of income	1000s of income recip's		Total income (£m.)		bracket (£)	Recipients	Income				to Gini	of income	Male	Female		Male	Female		head alone	100000	0.0005	0.63				2.90487E-06	bracket (£)	hold heads	franchise	male voters	households	income(£m)	man (£)		100000	0.0006	0.70				4.333E-06
				N = cum.no.									(Bowley,'19,	survey of 1907, a study of lower non-wage incomes, the census of 1911, and other										(or both)			(or both)			(or both)			0						bracket (£)	This bracket	Cumulative	This bracket	Cumulative	100000	0.0003	0.63				2.09274E-06	bracket (£)	head	head	Both	head	head	Both	(£)	75000	0.0008	0.88				5.84427E-06	100000	0.068	1	0.068	12.5	12.5	183919.9		75000	0.0011	0.98				8.717E-06
Income class:		Total (£K)	Number	of persons	nat. log	nat. log		Over £160					p. 11)	bits.  He adjusts for hours, vacations, and unemployment.									100000	0.068		0.068	12.5		12.5	183911.8		183911.8	100000	Stamp, 1922,					100000	0.068	0.068	12.5	12.5	75000	0.0006	0.88				4.21048E-06	100000	0.068		0.068	12.5		12.5	183911.8	65000	0.0011	1.01				4.6164E-06	75000	0.057	1	0.057	5.0	5.0	87867.8		65000	0.0015	1.12				6.886E-06
> lower	≤ upper	income	of persons	this class	of lower	of cum.		employers &							The population of interest seems to be "employees."  The income concept is								75000	0.057		0.057	5.0		5.0	87859.6		87859.6	75000	p. 338, for					75000	0.057	0.125	5.0	17.5	65000	0.0008	1.01				3.32598E-06	75000	0.057		0.057	5.0		5.0	87859.6	55000	0.0015	1.18				8.45128E-06	65000	0.036	1	0.036	2.5	2.5	70091.5		55000	0.0020	1.30				1.26E-05
limit (£)	limit	assessed	assessed	and up	Y-limit	N		indep.workers	500	30	513.1	30.8		earnings, excluding property income and income from self-employment.  I should therefore									65000	0.036		0.036	2.5		2.5	70083.3		70083.3	65000	1911/12.					65000	0.036	0.161	2.5	20.0	55000	0.0011	1.17				6.0891E-06	65000	0.036		0.036	2.5		2.5	70083.3	45000	0.0022	1.45				1.94239E-05	55000	0.057	1	0.057	3.4	3.4	58780.1		45000	0.0030	1.60				2.897E-05
5000	10000	57713	8388	13231	8.517	9.490		salaried:	385	0	395.1	0.0		use his materials only for the bottom part of the distribution, where income from the									55000	0.057		0.057	3.4		3.4	58771.9		58771.9	55000						55000	0.057	0.218	3.4	23.4	45000	0.0016	1.45				1.39955E-05	55000	0.057		0.057	3.4		3.4	58771.9	35000	0.0035	1.83				4.25048E-05	45000	0.109	1	0.109	5.4	5.4	49806.3		35000	0.0047	2.03				6.339E-05
10000	15000	28224	2339	4843	9.210	8.485								excluded sources was negligible.  I propose using Routh to distribute two income ranges by									45000	0.109		0.109	5.4		5.4	49798.2		49798.2	45000						45000	0.109	0.327	5.4	28.8	35000	0.0025	1.83				3.06283E-05	45000	0.109		0.109	5.4		5.4	49798.2	25000	0.0062	2.41				0.0001	35000	0.191	1	0.191	7.6	7.6	39699.2		25000	0.0083	2.67				0.0001686
15000	20000	16572	965	2504	9.616	7.826		Under £160						size.  The first is the range £160-400, which he divides into three classes.  The second is									35000	0.191		0.191	7.6		7.6	39691.1		39691.1	35000						35000	0.191	0.518	7.6	36.4	25000	0.0045	2.41				8.14849E-05	35000	0.191		0.191	7.6		7.6	39691.1	20000	0.0092	2.90				0.0002	25000	0.393	1	0.393	11.6	11.6	29417.8		20000	0.0124	3.21				0.0002374
20000	25000	11070	496	1539	9.903	7.339		employers &						the broad range £0-160, which he divides into nine classes.  In the latter, his distribution									25000	0.393		0.393	11.6		11.6	29409.7		29409.7	25000						25000	0.393	0.911	11.6	48.0	20000	0.0066	2.90				0.000114767	25000	0.393		0.393	11.6		11.6	29409.7	15000	0.0147	3.61		Quantile	Cumulative	0.0004	20000	0.442	1	0.442	9.8	9.8	22112.2		15000	0.02	3.99				0.0005343
25000	35000	13260	454	1043	10.127	6.950		indep.workers	1680	620	1724.2	636.3		is applied only to employees, not to the "employers and independent workers" of Bowley.									20000	0.442		0.442	9.8		9.8	22104.1		22104.1	20000						20000	0.442	1.353	9.8	57.7	15000	0.01	3.60				0.000258408	20000	0.442		0.442	9.8		9.8	22104.1	10000	0.0289	4.87		income	income	0.0012	15000	0.813	1	0.813	14.0	14.0	17212.3		10000	0.04	5.40				0.0017864
35000	45000	8628	217	589	10.463	6.378		salaried:	735	550	754.3	564.5											15000	0.813		0.813	14.0		14.0	17204.2		17204.2	15000						15000	0.813	2.166	14.0	71.7	10000	0.02	4.86				0.000864437	15000	0.813		0.813	14.0		14.0	17204.2	5000	0.08	7.64		shares:	shares:	0.0069	10000	2.090	1	2.09	25.2	25.2	12060.8		5000	0.11	8.46				0.01
45000	55000	6265	126	372	10.714	5.919		("int'rmed"?)						Routh's "annual income" distribution for  "Great Britain" in 1911/12:									10000	2.090		2.090	25.2		25.2	12052.6		12052.6	10000						10000	2.090	4.256	25.2	96.9	5000	0.06	7.62				0.004956677	10000	2.090		2.090	25.2		25.2	12052.6	700	1.44	28.59	Top 1%:	21.75		0.4719	5000	8.143	1	8.143	55.1	55.1	6768.4		700	2.03	32.76	Top 1%:	19.68		0.75
55000	65000	3803	64	246	10.915	5.505												Numbers in class					5000	8.143		8.143	55.0		55.0	6760.3		6760.3	5000						5000	8.143	12.4	55.0	152.0	700	1.04	28.44	Top 1%:	27.59		0.3432	5000	8.143		8.143	55.1		55.1	6760.3	600	1.64	29.60				0.1098	700	200.0	1.0476	209.5	416.6	436.5	2083.1		600	2.30	33.91				0.17
65000	75000	2997	43	182	11.082	5.204								Getting				with this lower bound					700	200.00		200.0	415.0		415.0	2075.0		2075.0	700	1910. Bowley, 1920, p. 22, and 1914, p. 261.					700	200.0	212.4	415.0	567.0	600	1.19	29.38				0.0799	700	200.0		200.0	416.6		416.6	2075.0	500	1.97	31.04				0.1887	600	28.3	1.0476	29.6	19.8	20.7	698.2		500	2.76	35.56				0.30
75000	100000	5621	64	139	11.225	4.934		Wage earners						more than	male	female	total	male	female	total			600	28.3	1.0	29.3	18.0	0.6	18.6	635	635	635	600	Census totals were allocated across the three classes between					600	29.3	241.7	18.6	585.6	500	1.43	30.70				0.1393	600	28.3	0.5	29.3	19.8	0.3	20.1	635.0	400	2.51	32.98				0.3210	500	47.8	1.0476	50.1	28.2	29.5	589.5		400	3.51	37.77				0.50
100000	and up	13435	75	75	11.513	4.317		all:	11000	4650	11289.1	4772.2		£0	11665	4993	16658	44	109	153			500	47.8	1.6	49.4	25.6	0.9	26.4	535	535	535	500	£400 and £700 according to abatement proportions given in					500	49.4	291.1	26.4	612.0	400	1.82	32.48				0.2368	500	47.8	0.9	48.7	28.2	0.5	28.6	535.0	300	3.23	35.04				0.4482	400	77.9	1.0476	81.6	37.9	39.7	486.3		300	4.51	40.12				0.70
								Of which,					(Subtract	10	11621	4884	16505	637	331	968			400	77.9	2.6	80.5	34.3	1.1	35.4	440	440	440	400	Bowley, 1914, p. 62. Bracket means assumed.					400	80.5	371.6	35.4	647.4	300	2.35	34.37				0.3306	400	77.9	1.4	79.3	37.9	0.6	38.5	440.0	200	5.30	39.30	Top 5%:	38.69		1.3586	300	104.0	1.0476	109.0	40.4	42.3	388.5		200	7.37	44.99	Top 5%:	40.96		2.10
Printed totals:		167589	13231	Pareto slopes of lnN = lnA - a lnY as inferred				occupied					Bowley's un-	20	10984	4553	15537	1177	1456	2633			300	104.0	3.5	107.5	36.4	1.2	37.6	350	350	350	300	Census numbers of salaried plus independent and self-employed					300	107.5	479.1	37.6	685.0	200	3.86	38.23				1.0042	300	104.0	1.9	105.9	40.4	0.7	41.1	350.0	160	7.66	42.95				1.6376	200	298.3	1.0476	312.5	83.5	87.4	279.8		160	10.65	49.15	Top decile:	48.33		2.49
(vs. sum of above:)		167588	13231	from the log graph:  (i) don't bother applying				minors:	370	240	379.7	246.3	occ's from	40	9807	3097	12904	2928	2430	5358			200	298.3	9.9	308.2	74.6	2.5	77.1	250	250	250	200	were allocated between £160 and £400 according to Routh's					200	308.2	787.3	77.1	762.1	160	5.60	41.51	Top 5%:	40.38		1.2170	200	298.3	5.4	303.6	83.5	1.3	84.8	250.0	140	9.21	44.89				1.1028	160	341.4	1.0476	357.7	71.4	74.8	209.2		140	12.73	51.29				1.60
				the Pareto curve above £75,000; (ii) between				occupied					Feinstein	60	6879	667	7546	2524	492	3016			160	341.4	11.4	352.8	63.2	2.1	65.3	185	185	185	160	earnings shares for Great Britain males.					160	352.8	1140.1	65.3	827.3	140	6.72	43.21				0.8159	160	341.4	6.1	347.6	71.4	1.1	72.6	185.0	120	13.67	49.74	Top decile:	45.75		3.1960	140	227.3	1	227.3	38.4	38.4	169.0		120	18.69	56.63	2nd decile:	9.29	57.62	4.56
				£45,000 and £75,000, the alpha slope is:				adults:	10630	4410	10909.4	4525.9	pop. 0-14	80	4355	175	4530	1753	110	1863			140	227.3	2.3	229.6	33.6	0.3	34.0	148	148	148	140	The 13,415,000 males and 5,820,000 females under £160 (Bowley,					140	229.6	1369.7	34.0	861.3	120	9.96	47.44				2.3923	140	227.3	1.3	228.5	38.4	0.2	38.6	148.0	100	25.43	60.63	2nd decile:	9.43	55.18	8.3834	120	650.8	1	650.8	95.8	95.8	147.2		100	34.22	68.47	3rd decile:	7.63	65.25	11.21
					1.927								('72,p.T123)	100	2602	65	2667	1417	56	1473			120	650.8	8.2	658.9	83.3	1.0	84.3	128	128	128	120	1919, p. 11 and Feinstein, 1972, p. T123) were allocated over					120	658.9	2028.7	84.3	945.7	100	18.60	56.98	Top decile:	47.49		6.5550	120	650.8	4.4	655.2	95.8	0.6	96.4	128.0	80	40.07	71.81	3rd decile:	8.93	64.12	9.7967	100	1695.1	1	1695.1	212.7	212.7	125.5		80	50.31	78.61	4th decile:	6.86	72.11	10.06
	2.078614			(iii) between £10,000 and £45,000, the				Total occupied	14300	5850	14675.8	6003.7		120	1185	9	1194	544	7	551			100	1695.1	65.3	1760.4	183.1	7.0	190.1	108	108	108	100	nine classes in proportion to Routh's GB earnings distribution.					100	1760.4	3789.1	190.1	1135.8	80	29.52	66.80	2nd decile:	10.76	58.24	8.2642	100	1695.1	35.2	1730.3	212.7	3.8	216.5	108.0	60	62.33	85.32	4th decile:	7.64	71.76	12.1842	80	2097.1	0.8375	1756.3	217.6	182.2	103.8		60	73.47	90.31	5th decile:	6.31	78.42	10.46
	2.415844			alpha slope is:		1.706	; and (iv)		(Bowley's 1919 totals)					140	641	2	643	190	2	192			80	2097.1	128.2	2225.3	184.5	11.3	195.8	88	88	88	80	Bracket means were assumed.					80	2225.3	6014.3	195.8	1331.6	60	47.15	79.24	3rd decile:	8.90	67.14	12.2332	80	2097.1	55.6	2152.7	217.6	4.9	222.5	88.0	40	94.68	98.92	5th decile:	6.08	77.84	8.8080	60	3019.4	0.8375	2528.7	251.0	210.2	83.1		40	99.83	99.97	6th decile:	5.09	83.51	4.48
				don't use the Pareto slope below £10,000.										160	451		451	174	0	174			60	3019.4	573.5	3592.9	208.3	39.6	247.9	69	69	69	60						60	3592.9	9607.2	247.9	1579.5	40	78.24	94.50	4th decile:	7.05	74.20	15.0302	60	3019.4	255.1	3274.5	251.0	17.6	268.6	69.0	20	99.40	99.96	6th decile:	6.07	83.90	0.2261	40	3434.7	0.8375	2876.5	207.1	173.5	60.3		20	99.89	99.99	7th decile:	5.05	88.56	0.0001488
														200	277		277	152	0	152			40	3502.7	2832.5	6335.2	168.1	136.0	304.1	48	48	48	40						40	6335.2	15942.4	304.1	1883.6	20	93.48	99.09	5th decile:	6.44	80.64	3.3311	40	3434.7	1324.0	4758.7	207.1	63.6	270.7	48.0	10	99.61	99.99	7th decile:	4.64	88.54	0.0020	20	8.0	0.8375	6.7	0.3	0.3	40.2		10	99.98	100.00	8th decile:	4.15	92.71	0.000108
Resulting high-income profile:									But see Page 4's use of 1911 census figures					300	125		125	53	0	53			20	1408.0	1697.2	3105.2	41.5	50.1	91.6	29.5	29.5	29.5	20						20	3105.2	19047.6	91.6	1975.2	10	99.12	99.95	6th decile:	4.91	85.54	0.3630	20	8.0	684.8	692.9	0.3	20.2	20.5	29.5	0	100.00	100.00	8th decile:	4.21	92.75	0.0015	10	12.0	0.8375	10.1	0.3	0.2	24.4		0	100.00	100.00	9th decile:	3.66	96.37	4.03E-06
(i) above £100,000, the total of £13,435,000 can be divided among the top 75 persons									on persons under 20 "engaged in occupations" =>					400	72		72	28	0	28			10	762.0	385.8	1147.8	11.4	5.8	17.2	15	15	15	10						10	1147.8	20195.4	17.2	1992.4	0	100.00	100.00	7th decile:	4.91	90.45	0.0074	10	12.0	19.3	31.3	0.3	0.3	0.6	15.0				9th decile:	4.21	96.95		0	2.6	0.8375	2.2	0.0	0.0	13.6					10 decile:	3.63	100.00
if necessary, using reasonable assumptions.														500	44		44	14	0	14			0	52.6	127.1	179.7	0.3	0.6	0.9	5	5	5	0						0	179.7	20375.1	0.9	1993.3				8th decile:	4.57	95.03		0	2.6	55.0	57.6	0.0	0.3	0.3	5.0				10th decile:	3.05	100.00					10916.1		1796.4
(ii) Above £75,000 use the printed total of £19,056,000 and 139 persons (includes (i)).														600	30		30	8	0	8																							1993.3363				9th decile:	3.02	98.04			12257.1	2450.8	14708.4	1873.1	115.9	1989.0	135.2																			Mean (£):	164.57		Gini (%)
(iii) Between £45,000 and 75,000 add to (i) + (ii), this formula for income between any														700	22		22	5	0	5			Totals:	14525.1	5850.0	20375.1	1733.2	260.2	1993.3	119.3	44.5	97.8	Compare total personal income of £2,012 m. here to Feinstein's														bottom dec.:	1.96	100.00		Changes from distribution among all earners:											Mean (£):	135.23					(my interpre-									Median (£):	80.02		49.39
lower border and 75,000:  2.07861 x (NY-75000N'), where n" is the predicted number														800	17		17	3	0	3													(1972, p. T5) GNP at factor cost of £2,128 m. for 1911, or																	Gini coeff.(%)	(1) Removal of minors and their incomes: Those under 20 years of age who were "engaged											Median (£):	71.08		Gini coeff.(%)			tation of									(but calculated as if it were £88)
with income ≥ 75000.														900	14		14	5	0	5			Occupied	(just census:)									Bowley's (1937, p. 139) total "national" (personal?) income												Median =					52.35	in an occupation" in the 1911 census were assigned average male and female incomes,											(but calculated as if £69)			48.25			Tanner, 1983,
(iv) Between £10,000 and £45,000, add, to (i) through (iii) above, this formula for														1000	9		9	7.2	0	7.2			minors<20:	2268.4	1301.5	3570.0	56.1	45.0	101.1	24.7	34.6	28.3	of £2,220 m.  for 1913.									Mean =	97.83		58.166613		Median = £58.17 (but calculated as if £50)				by combining Bowley's (1937, p. 46) median adult-male wage rate for 50 weeks with																	pp. 216-7.)									Top 20%:	57.62
income between any lower border and 45,000: 2.41584 x (NY-45000N')														2000	1.8		1.8	1.05	0	1.05			Occupied																								Top 20%	58.24			earnings ratios for age/sex groups from Levi (1885, pp. 17-21).  Next the minors' total											Top 20%:	55.18														Next 40%:	25.89	Middle 20%	11.40
(v) Between £5000 and £10,000 just accept the figures above, I guess.														3000	0.75		0.75	0.35	0	0.35			adults≥20:	12046.2	2450.8	14497.0																					Next 40%	27.30	Middle 20%:	11.35	earnings were spread in humped distributions (one for males, one for females) over the											Next 40%:	28.72	Middle 20%:	12.14												Bottom 40%	16.49	Bottom 20%	7.29
														4000	0.4		0.4	0.2	0	0.2			Adult inc's	12256.7	4548.5	16805.1	1677.0	215.2	1892.2	136.8	47.3	112.6															Bottom 40%	14.46	Bottom 20%:	4.97	£0-100 income brackets, meeting all accounting constraints.  Their income distributions											Bottom 40%:	16.10	Bottom 20%:	7.25													100.00
Other classes:														5000	0.2		0.2	0.2	0	0.2										Assumed distribution of minors' earnings:																					were then subtracted from the overall distribution, leaving an adults-only distribution.
£700 - £5,000 (for 1910, B, 1920, p. 22): 200,000 incomes worth £415 m.																		male	female	total					M≥20	M<20	F≥20	F<20		(1000s)	£0-10	£10-20	£20-40	£40-60	£60-80	£80-100															(2) Their total earnings (£101.1 m. ) were divided among all adult male earners
£160-£700* (for 1910, p. 22 again): 880,000 incomes worth £250 m.														Sums over income ranges:			£0-160	11214	4993	16207			Levi's earnings ratios:		1.000	0.314	0.661	0.439		Males<20:	50	750	1400	68	0	0															("fathers") between £0 and £700 in proportion to their aggregate class incomes.
Intermediate incomes (below £160, I guess): 4,050,000 incomes (in '10) worth £400 m.																£160-400		379	0	379			1911/14 earnings:		78.75	24.74	52.02	34.55	Bowley	Females<20	25	350	426	375	100	25															(3) Of the 4,548,500 adult female earners, only an estimated 2,450,799 were
(in 1913: B 1937, p. 139).																	£160 up	451.0	0.0	451.0										Both<20:	75	1100	1826	443	100	25															household heads.  The non-head female earners were assumed to have the same size
Wages:  worth £797 m. in 1913 (B 1937, p. 139), but how many folks?  See P. 2 =>														Share, (£160-400/£160 up)				0.84035	1	0.84035											Males:	Females:	Mean inc.:	24.72																	distribution as all female earners, and their total income of £99.8 m. was distributed
	(*Can distribute by class using Bowley '14, p. 262.)													Implied UK occupied, £160-400				743.71	0.0	743.71						£0-700:	1166.2			Tot.minors:	2268	1301		34.62																	equally among the adult-male income ranks at £8.14 per adult male earner.
(Bowley in QJE'14 cites same no's for intermed. and £160-700 as 1911/12.)