Figures and tables in Comparing Register and Survey Wealth Data | International Journal of Microsimulation

Abstract

Survey measures of wealth are error prone with a relatively large error variance. The errors are not uncorrelated with the true values but tend to have a negative correlation, which implies that wealthy people tend to underreport and less wealthy to over report. There is no general tendency of survey data to underestimate mean wealth with the exception of the last percentile. The underestimate of the wealth of the very rich is however not due to underreporting but rather to selective nonresponse. Using simple models this paper discusses consequences of error prone wealth data.

This article contains 4 figures and 8 tables.

Figures

**Figure 1.** The distribution of the difference between total gross wealth from the SHARE-SE survey and the corresponding register measure from LINDA.

**Figure 2.** The distribution of the difference between total net worth from the SHARE-SE survey and the corresponding register measure from LINDA.

**Figure 3.** Ratios of total net worth means from the RAND-UU survey to means from LINDA, by total net worth percentiles

**Figure 4.** Ratios of total net worth means from the SHARE_SE survey to means from LINDA, by total net worth percentiles

Tables

Table 1. Correspondence between survey questions and register definitions for assets included in total net worth

Asset	UU-RAND	SHARE_SE	Register
Own home	What is the market value of your home, i.e., what would you get for it if you sold it today?	In your opinion, how much would you receive if you sold your property today?	FFSTEGM: Market value of residential home. FBORMH; Market value of tenant owned apartment.
Other real property	What is the market value of your property? Refers to holiday homes or time-share apartments for leisure purposes.	In your opinion, how much would you receive if you sold your property today? Includes secondary homes, holiday homes, other real estate, land or forestry.	FFSTFRM: Market value of holiday home The following variables are only included for SHARE_SE: FFSTHYM: Market value of owned apartment houses. FFSTINM: Market value of owned industrial premises. FFSTJBM: Market value of owned farm property. FFSTEJM: Market value of buildings on farm property. FFSTUM: Market value of real estates abroad.
Bank holdings	If you added up the balances of these accounts how much would they amount to? Includes checking account, bank or postal giro account, savings account, capital account or other account, such as an ICA account or OK account.	About how much did you have in bank accounts, transaction accounts or saving accounts?	FKUBANK: The total amount on bank accounts.
Bonds	If you had sold these bonds at the end of 2002, how much would you have received for them? Includes Swedish and foreign bonds, national, municipal and business bonds, as well as premiums and savings bonds.	About how much did you have in government or corporate bonds?	FKUPREM: Market value of premium bonds. FKUVPR: Market value of interest-bearing securities.
Stocks and shares	If you had sold these stocks how much would you have received from their sale? Includes both Swedish and foreign stocks and both listed and unlisted stocks.	About how much did you have in stocks or shares (listed or unlisted)?	FOTCMV: Market value of stocks on the OTC or O list. FAKTIBMV: Market value of stocks on the A list. FAALMV: Market value of stocks on the lists “nya marknader” and aktietorget.*
Mutual funds	If you had sold these funds, how much would you have received for them? Includes stock funds, bond funds or mixed funds	About how much did you have in mutual funds or managed investments accounts?	FRFONMV: Market value of interest funds. FOFOMV: Market value of other funds than interest funds.
Total debt	This variable is the sum of the following three survey questions; (i) How much of a loan did you have all together on your dwelling at the end of 2002? (ii) How much did these loans amount to all together on the last day of December 2002? (Refers to weekend homes or time-share apartments for leisure purposes). (iii) How much did your total debt amount to on the last day of December 2002? (The respondents are asked to exclude the debts defined in (i) and (ii) above.	How much did you owe in total?	FKURTA: Is equal to total debt to financial institutions. FKUSKOP: Is equal to issued option contracts (debts) FSKURST: Other debt.

The latter two lists include small companies that are not yet qualified for the “official” lists.

Table 2. Descriptive statistics for true and estimated market values by property, sales data 2003

Variable	Median*	Mean*	Std dev*	Skewness	Kurtosis	N
Own home
Estimate	962.2	1 240.5	963.9	1.99	5.87	54.253
True	942.4	1 222.6	950.9	1.88	5.57	54.253
Difference	27.0	17.9	316.8	-0.74	14.74	54.253
Corr(True. Difference) -0.125 (<0.001)
Holiday homes
Estimate	585.8	791.2	697.6	3.68	22.42	9.231
True	553.8	792.5	757.3	3.45	19.07	9.231
Difference	32.4	-1.2	350.6	-1.97	25.84	9.231
Corr(True. Difference) - 0.395 (<0.001)
Apartment Houses
Estimate	2.577.3	10 932.2	31 675.6	8.82	103.47	2.009
True	2.502.0	9 749.4	25 229.6	7.47	76.35	2.009
Difference	133.8	1 182.8	9 742.6	15.25	287.69	2.009
Corr(True. Difference) 0.553 (<0.001)
Farm property
Estimate	830.4	1 147.8	1 140.8	2.73	11.05	3.064
True	753.1	1 081.8	1 114.5	2.77	11.61	3.064
Difference	34.6	66.0	562.1	1.15	14.13	3.064
Corr(True. Difference) -0.205 (<0.001)

Note: p-values within parenthesis.

Expressed in 1.000 SEK.

Table 3. Descriptive statistics for SHARE_SE and corresponding register data

Variable	Median	Mean	Std Dev	N
Own home
Survey	885 981	1 166 758	1 015 617	1,398
Register	808 750	1 022 380	922 035	1,398
Difference	42 943	144 377	771 502	1,398
Other real property
Survey	492 212	889 140	1 513 275	645
Register	327 570	711 910	1 652 271	645
Difference	98 442	177 230	1 244 990	645
Bank
Survey	49 221	130 524	224 029	1,511
Register	49 773	130 198	223 480	1,511
Difference	984	326	139 202	1,511
Bonds
Survey	49 221	84 537	127 470	307
Register	26 025	74 517	145 690	307
Difference	-166	10 020	91 416	307
Stocks
Survey	49 221	191 236	344 467	685
Register	34 100	153 676	382 360	685
Difference	4 384	37 560	293 909	685
Mutual funds
Survey	98 442	181 519	266 968	934
Register	109 631	219 918	301 978	934
Difference	-5 322	-38 399	229 176	934
Total debt
Survey	246 106	409 761	837 956	731
Register	300 987	448 269	738 448	731
Difference	-22 885	-38 508	551 117	731
Total gross wealth
Survey	984 423	1 406 966	1 701 859	1,531
Register	838 014	1 282 001	1 697 605	1,531
Difference	15 555	124 964	1 020 692	1,531
Total net worth
Survey	821 993	1 251 162	1 530 660	1,515
Register	613 865	1 007 839	1 432 051	1,515
Difference	70 404	243 323	1 095 564	1,515

Table 4. The relative importance of measurement errors in estimating the variance of an asset, by type of asset

Asset	Var(W)	Var(W*)	$V a r (\tilde{W})$	Var(u)	$V a r (W - \tilde{W})$	A = ρ(W,u*)	B = S(u)/S(W*)	1+2(A/B)
Own home	1.03E+12		8.50E+11		5.95E+11
Own home, corrected	1.03E+12	9.04E+11		4.95E+11		-0.275	0.740	0.257
Other real estate	2.29E+12		2.73E+12		1.55E+12
Bank accounts	5.02E+10	4.99E+10		1.94E+10		-0.307	0.623	0.013
Bonds	1.62E+10	2.12E+10		8.36E+09		-0.501	0.627	-0.596
Stocks	1.19E+11	1.46E+11		8.64E+10		-0.507	0.769	-0.319
Mutual funds	7.13E+10	9.12E+10		5.25E+10		-0.523	0.759	-0.379
Debts	7.02E+11	5.45E+11		3.04E+11		-0.180	0.746	0.517
Gross wealth	2.90E+12		2.88E+12		1.04E+12
Net wealth	2.34E+12		2.05E+12		1.20E+12

Table 5. Variances and correlation coefficients of asset components

	True components						Error components
	Own home	Bank	Bonds	Stocks	Mutual Funds	Debts	Own home	Bank	Bonds	Stocks	Mutual Funds	Debts
Own home	9.04E+11						-0.275
Bank		4.99E+10	0.081	0.244	0.406	0.100		-0.307	0.264	-0.078	-0.091	-0.019
Bonds			2.12E+10	-0.005	0.104	-0.050		-0.013	-0.501	-0.027	-0.090	-0.050
Stocks				1.46E+11	0.265	0.096		-0.222	0.072	-0.507	0.218	0.026
Mutual Funds					9.12E+10	0.025		-0.084	0.181	-0.100	-0.523	0.015
Debts						5.45E+11		-0.160	0.049	0.035	-0.001	-0.180
Own home							4.95E+11
Bank								1.94E+10	0.064	0.128	0.049	0.035
Bonds									8.36E+09	0.109	0.084	0.076
Stocks										8.64E+10	-0.104	0.070
Mutual Funds											5.25E+10	0.022
Debts												3.04E+11

Table 6. Estimated regression slopes with measurement errors in the dependent variable

Dep. var	${\overset{⌢}{α}}_{1}$	$\tilde{α_{1}}$	$b_{u X}$	${\overset{⌢}{α}}_{1}$	$\tilde{α_{1}}$	$b_{u X}$
Indep. var	Age			Gender
Own home	-12,654	-8,821	-3,833	-95,289	-45,449	-49,840
Other real estate	-5,323	-1,845	-3,478	-130,307	-210,552	80,245
Bank accounts	1,836	2,007	-171	-568	1,685	-2,252
Bonds	557	931	-374	-1,783	-2,369	586
Stocks	1,556	2,779	-1,223	-29,007	-11,176	-17,831
Mutual funds	2,171	3,203	-1,031	-8,444	-1,653	-6,791
Debts	-15,877	-10,968	-4,910	-105,990	-122,514	16,525
Gross wealth	27,129	21,292	5,837	-113,586	-153,823	40,236
Net wealth	43,006	32,260	10,747	-7,597	-31,308	23,711
	Schooling			Health
Own home	64,900	57,997	6,903	71,591	105,627	-34,035
Other real estate	40,892	21,286	19,606	150,175	124,325	25,850
Bank accounts	1,330	561	769	24,508	25,349	-841
Bonds	-805	-2,747	1,942	12,991	5,489	7,501
Stocks	3,210	3,791	-581	-6,888	-7,140	253
Mutual funds	6,056	3,677	2,379	50,412	50,437	-24
Debts	91,571	35,350	56,221	4,049	-41,256	45,305
Gross wealth	152,642	108,158	44,484	474,173	188,870	285,303
Net wealth	61,071	72,808	-11,737	470,124	230,126	239,998

Table 7. Estimated regression slopes with measurement errors in the independent variable (gross wealth)

Dep. Var.	${\hat{α}}_{1}$	${\tilde{α}}_{1}$	$b_{u W^{}}$	$S_{u}^{2}$ *	$S_{W^{}}^{2}$	$S_{u}^{2}$ / $S_{W^{}}^{2}$
Own home	0.277 (0.013)	0.310 (0.011)	-0.159	1.20E+12	3.32E+12	0,360
Other real estate	0.521 (0.028)	0.634 (0.018)	-0.544	2.01E+12	5.72E+12	0,352
Bank accounts	0.045 (0.003)	0.047 (0.003)	-0.002	9.70E+11	2.95E+12	0,328
Bonds	0.000 (0.004)	0.002 (0.004)	-0.007	1.69E+12	6.80E+12	0,249
Stocks	0.039 (0.006)	0.047 (0.006)	-0.028	1.76E+12	4.70E+12	0,376
Mutual funds	0.057 (0.005)	0.055 (0.005)	0.000	1.31E+12	3.89E+12	0,336
Debts	0.263 (0.012)	0.272 (0.011)	-0.001	1.91E+12	6.27E+12	0,304
Health	1,55E-08 (9,15E-09)	1,68E-08 (1,03E-08)	-1,19E-01	1,1E+12	2,14E+12	0,505

Computed as if there were no errors in register data.

Table 8. Multivariate regressions with errors in one explanatory variable and decomposition of the estimates.

Dep. Var	${\overset{⌢}{α}}_{y W . X}$	${\overset{⌢}{α}}_{y X . W}$	${\overset{⌢}{α}}_{y \tilde{W} . X}$	${\overset{⌢}{α}}_{y X . \tilde{W}}$	$S_{u}^{2} / S_{\tilde{W}}^{2}$	$b_{y \tilde{W}}$	$b_{y X}$	$b_{X \tilde{W}}$	$b_{X u}$	$b_{u \tilde{W}}$	$b_{\tilde{W} X}$	$b_{u X}$	$b_{y u}$
A. Explanatory variables are gross wealth (W) and age (X)
Own home	0.275 (0.013)	-4,727 (2,335)	0.309 (0.011)	-6,265 (2,129)	0.360	0.310	-8,821	-2.29E-07	-5.08E-07	-0.224	-8,274	-6,608	-0.159
Other real estate	0.524 (0.028)	9,204 (6,906)	0.635 (0.018)	6,545 (4,763)	0.352	0.634	-1,845	-1.87E-07	-3.17E-07	-0.252	-13,219	-7,869	-0.544
Bank accounts	0.048 (0.003)	3,033 (559)	0.048 (0.003)	2,703 (556)	0.328	0.047	2,007	-5.37E-07	-8.16E-07	-0.154	-14,374	-7,173	-0.002
Bonds	4.7E-04 (0.004)	946 (1,013)	2.1E-03 (0.004)	971 (1,007)	0.249	0.002	931	-2.81E-07	-7.00E-07	-0.175	-19,656	-12,194	-0.007
Stocks	0.041 (0.006)	3,857 (1,367)	0.048 (0.006)	3,398 (1,332)	0.376	0.047	2,779	-2.30E-07	-6.40E-07	-0.217	-12,905	-13,479	-0.028
Mutual funds	0.060 (0.005)	4,353 (987)	0.056 (0.005)	3,814 (990)	0.336	0.055	3,203	-2.74E-07	-6.29E-07	-0.188	-10,888	-8,387	0.000
Debts	0.268 (0.012)	-13,469 (3,154)	0.276 (0.011)	-16,554 (2,970)	0.304	0.272	-11,846	2.45E-07	-5.79E-07	-0.173	17,004	-10,959	-0.093
B. Explanatory variables are gross wealth (W) and gender (X, female=1)
Own home	0.277 (0.013)	3,397 (44,761)	0.310 (0.011)	1,396 (40,964)	0.360	0.310	-45,449	-1.14E-08	-5.27E-09	-0.224	-150,951	-25,189	-0.159
Other real estate	0.520 (0.028)	-128,274 (124,484)	0.633 (0.018)	-126,637 (85,960)	0.352	0.634	-210,552	-5.76E-09	-3.17E-09	-0.252	-132,611	-25,710	-0.544
Bank accounts	0.046 (0.003)	16,355 (11,825)	0.047 (0.003)	13,305 (11,761)	0.328	0.047	1,685	-2.08E-08	-1.94E-08	-0.154	-245,958	-75,333	-0.002
Bonds	-6.6E-05 (0.004)	-2,407 (20,194)	1.8E-03 (0.004)	-1,331 (20,176)	0.249	0.002	-2,369	-2.14E-08	1.56E-09	-0.175	-594,537	10,801	-0.007
Stocks	0.039 (0.006)	3,417 (25,094)	0.047 (0.006)	-1,385 (24,489)	0.376	0.047	-11,176	-1.11E-08	-2.36E-08	-0.217	-207,620	-166,465	-0.028
Mutual funds	0.058 (0.005)	11,990 (19,698)	0.055 (0.005)	9,434 (19,756)	0.336	0.055	-1,653	-1.29E-08	-6.85E-09	-0.188	-200,887	-35,733	0.000
Debts	0.266 (0.013)	-37,655 (49,847)	0.272 (0.011)	-80,012 (47,078)	0.304	0.272	-148,691	-1.52E-08	-3.62E-08	-0.173	-252,850	-164,188	-0.093
C. Explanatory variables are gross wealth (W) and year of schooling (X)
Own home	0.260 (0.013)	27,887 (5,737)	0.297 (0.011)	29,504 (5,159)	0.360	0.310	57,997	4.62E-07	2.63E-07	-0.224	96,035	19,657	-0.159
Other real estate	0.539 (0.029)	-43,158 (15,410)	0.645 (0.018)	-40,365 (10,456)	0.352	0.634	21,286	2.81E-07	2.01E-07	-0.252	95,603	24,045	-0.544
Bank accounts	0.049 (0.004)	-5,824 (1,538)	0.049 (0.003)	-4,135 (1,504)	0.328	0.047	561	5.16E-07	5.60E-07	-0.154	95,628	34,094	-0.002
Bonds	0.002 (0.004)	-3,073 (2,584)	0.003 (0.004)	-3,115 (2,493)	0.249	0.002	-2,747	3.20E-07	6.48E-07	-0.175	132,626	66,831	-0.007
Stocks	0.040 (0.006)	-1,698 (3,200)	0.048 (0.006)	-1,112 (3,077)	0.376	0.047	3,791	3.60E-07	3.24E-07	-0.217	103,054	34,823	-0.028
Mutual funds	0.059 (0.005)	-3,609 (2,474)	0.056 (0.005)	-1,431 (2,444)	0.336	0.055	3,677	4.00E-07	3.98E-07	-0.188	91,814	30,697	0.000
Debts	0.268 (0.013)	-1,819 (6,867)	0.271 (0.012)	3,953 (6,444)	0.304	0.272	33,058	3.58E-07	2.79E-07	-0.173	107,231	22,858	-0.093

Note: In computing these statistics u was defined as $u = W - \tilde{W}$ .