1. Comparing register and survey wealth data Fredrik Johansson and Anders Klevmarken Department of Economics Uppsala University

2. An ideal measure? The measure on which the decision maker acts! Is the survey response such a measure? – Probably not! What about the market value of an asset? – Yes, perhaps if there is a well defined market value. But, what is the market value of a house which is not put on the market?

3. Less of nonresponse and measurement errors in register data? Complete enumeration – but not always of the target population Register data are collected for administrative purposes and not for statistical purposes Self-interest in underreporting assets and over reporting liabilities But in Sweden: Banks, insurance companies, brokers and housing associations report to the tax authorities for each single individual. The market value of real estate is an estimate produced by Statistics Sweden

4. The estimates of market values of real property in register data Error=estimate – true market value

5. Table 2. Descriptive statistics for true and estimated market values by property, sales data 2003 VariableMedian*Mean*Std dev*SkewnessKurtosisN Home equity Estimate 962.21 240.5963.91.995.8754.253 True 942.41 222.6950.91.885.5754.253 Error 27.017.9316.8-0.7414.7454.253 Corr(True, Error) -0.125 (<0.001)

6. What is a measurement error? Survey response – ”ideal” value We will use the market value as of the last of December 2003 as the ideal value of a financial asset assuming that register data have no measurement errors. For real property we recognize that there are measurement errors both in the survey and in the register measures. We will account for the measurement error in register data when ever possible.

7. Assets included Home equity (owner occupied house or condominium) Other real estate Bank holdings Bonds Stocks and shares Mutual funds Debts

8. Data sources Register data: LINDA 2002 sample size approx. 1.1 million individuals Survey data: UU_RAND 2002, sample size 1431 individuals (households) aged 50+, response 893, subsample from LINDA SHARE_SE 2003, sample size 4700 households, response 2208, at least one household member 50+

9. Table 3. Descriptive statistics for SHARE_SE and corresponding register data VariableMedianMeanStd DevN Home equity Survey885 9811 166 7581 015 6171,398 Register808 7501 022 380922 0351,398 Difference42 943144 377771 5021,398 Other real property Survey492 212889 1401 452 201645 Register327 570711 9101 542 788645 Difference98 442177 2301 103 324645 Bank Survey49 221130 524224 0291,511 Register49 773130 198223 4801,511 Difference984326139 2021,511 Bonds Survey49 22184 537127 470307 Register26 02574 517145 690307 Difference-16610 02091 416307

10. VariableMedianMeanStd DevN Stocks Survey49 221191 236344 467685 Register34 100153 676382 360685 Difference4 38437 560293 909685 Mutual funds Survey98 442181 519266 968934 Register109 631219 918301 978934 Difference-5 322-38 399229 176934 Total debt Survey246 106409 761837 956731 Register300 000440 240731 472731 Difference-21 746-30 479549 625731 Total net worth Survey821 9931 251 1621 530 6601,515 Register613 8651 007 8391 432 0511,515 Difference70 404243 3231 095 5641,515

11. The very rich UU-RAND compared to LINDA 2002 SHARE_SE compared to LINDA 2003

12. Measurement errors and the variance (inequality) of wealth

13. ρ(W*,u)ρ(W*,u) S(u)/S(W*)S(u)/S(W*) Ow n h o m e, c o r r e c t e d 1.03E+121.03E+12 9.04E+119.04E+11 4.95E+114.95E+11 -0.275-0.275 0.7400.740 Ba n k a c c o u n t s 5.02E+105.02E+10 4.99E+104.99E+10 1.94E+101.94E+10 -0.307-0.307 0.6230.623 Bo n d s 1.62E+101.62E+10 2.12E+102.12E+10 8.36E+098.36E+09 -0.501-0.501 0.6270.627 Sto c k s 1.19E+111.19E+11 1.46E+111.46E+11 8.64E+108.64E+10 -0.507-0.507 0.7690.769 Mu t u a l f u n d s 7.13E+107.13E+10 9.12E+109.12E+10 5.25E+105.25E+10 -0.523-0.523 0.7590.759 De b t s 7.02E+117.02E+11 5.35E+115.35E+11 3.02E+113.02E+11 -0.168-0.168 0.7510.751 AssetVar(W)Var(W*)Var(u)ρ(W*,u)S(u)/S(W*) Own home, corrected 1.03E+129.04E+114.95E+11-0.2750.740 Bank accounts 5.02E+104.99E+101.94E+10-0.3070.623 Bonds 1.62E+102.12E+108.36E+09-0.5010.627 Stocks 1.19E+111.46E+118.64E+10-0.5070.769 Mutual funds7.13E+109.12E+105.25E+10-0.5230.759 Debts 7.02E+115.35E+113.02E+11-0.1680.751 Table 4. The relative importance of measurement errors in estimating the variance of an asset, by type of asset

14. Wealth as a dependent variable

15. Estimated regression slopes with measurement errors in the dependent variable; independent variable is age Own home -12,654-8,821-3,833 Other real estate-5,323-1,845-3,478 Bank accounts 1,8362,007-171 Bonds 557931-374 Stocks 1,5562,779-1,223 Mutual funds 2,1713,203-1,031 Debts -15,877-10,968-4,910 Gross wealth 27,12921,2925,837 Net wealth 43,00632,26010,747

16. Estimated regression slopes with measurement errors in the dependent variable; independent variable if ”healthy” Own home 71591105627-34035 Other real estate15017512432525850 Bank accounts 2450825349-841 Bonds 1299154897501 Stocks -6888-7140253 Mutual funds 5041250437-24 Debts 4049-4125645305 Gross wealth 474173188870285303 Net wealth 470124230126239998

17. Wealth as explanatory variable

19. If Y is error prone with the additive error ν then,

20. Estimated regression slopes with measurement errors in the independent variable (gross wealth) / Dep. Var. Own home 0.277 (0.013) 0.310 (0.011)-0.1591.20E+123.32E+120,360 Other real estate 0.521 (0.028) 0.634 (0.018)-0.5442.01E+125.72E+120,352 Bank accounts 0.045 (0.003) 0.047 (0.003)-0.0029.70E+112.95E+120,328 Bonds 0.000 (0.004) 0.002 (0.004)-0.0071.69E+126.80E+120,249 Stocks 0.039 (0.006) 0.047 (0.006)-0.0281.76E+124.70E+120,376 Mutual funds 0.057 (0.005) 0.055 (0.005)0.0001.31E+123.89E+120,336 Debts 0.264 (0.013) 0.254 ( 0.011 )-0.1011.24E+124.50E+120,275 Health 1,55E-08 (9,15E-09) 1,68E-08 (1,03E-08)-1,19E-011,1E+122,14E+120,505

21. Multivariate regression with one error prone variable (gross wealth)

22. Regressions of assets (y) on error prone gross wealth (W) and age (X) Own home 0.268 (0.012) -4682 (2271) 0.361 (0.012) -5161 (2013) Other real estate 0.431 (0.025) 3012 (6070) 0.636 (0.018) 4203 (4259) Bank accounts 0.021 (0.002) 2439 ( 377) 0.023 (0.002) 2329 ( 374) Bonds 0.000 (0.003) 1035 ( 580) 0.000 (0.002) 1036 ( 578) Stocks 0.051 (0.007) 7172 (1516) 0.063 (0.007) 6685 (1475) Mutual funds 0.054 (0.005) 4904 ( 949) 0.062 (0.005) 4499 (926) Debts 0.056 (0.005) -8244 (1157) 0.053 (0.005) -8698 (1162)

23. Conclusions With the exception of the top 1% SHARE_SE does not underestimate the average level of wealth. The survey has rather a tendency to over estimate wealth. At the top 1% the underestimate is due to selective nonresponse. Very, very rich people do not participate, while there is no tendency for those who participate to underreport. The main problem in the survey is the large error variance and the negative correlation between errors and true values. In our data the error variance ranges from almost 40% of the true variance (bank holdings) to almost 60% (stocks). The correlation ranges from -0.17 (debts) to -0.52 (mutual funds)

24. Conclusions cont. The consequences are: 1.No severe overestimates of inequality. 2.In regressions with error prone gross wealth as an explanatory variable the negative bias from the error variance is to a large extent compensated by the negative correlation between error and true value. The survey estimate of the marginal effect of gross wealth appears to have little bias. 3.In regressions with wealth as a dependent variable the correlation between the measurement errors and explanatory variables will bias the slope estimates. The sign of the bias depends on asset and explanatory variable.

25. Conclusions cont. Measurement errors in (our) wealth surveys do not have classical properties. Compensating error properties give decent estimates of the inequality of wealth and of the marginal effect of wealth, But approximately the right estimates for the wrong reason is a poor consolation! We need to learn more to be able to compensate for the effects of errors in survey wealth measures and if possible design surveys such that measurement errors are in controle.

26. SHARE_SE compared to LINDA 2003