Looking for the missing rich: tracing the top tail of the wealth distribution

Bach, Stefan; Thiemann, Andreas; Zucco, Aline Article — Published Version Looking for the missing rich: tracing the top tail of the wealth distribution International Tax and Public Finance Provided in Cooperation with: German Institute for Economic Research (DIW Berlin) Suggested Citation: Bach, Stefan; Thiemann, Andreas; Zucco, Aline (2019) : Looking for the missing rich: tracing the top tail of the wealth distribution, International Tax and Public Finance, ISSN 0927-5940, Springer, Berlin, Vol. 26, Iss. 6, pp. 1234-1258, https://doi.org/10.1007/s10797-019-09578-1 , https://link.springer.com/article/10.1007/s10797-019-09578-1 This Version is available at: https://hdl.handle.net/10419/215786 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Online Appendix: Looking for the missing rich: Tracing the top tail of the wealth distribution October, 2019 Contents 1 Tail wealth distributions by rich list and minimum wealth 2 2 Adjusted tail wealth distributions 8 3 Wealth distribution: Distributional tables 11 4 Aggregate statistics on assets and liabilities 15 5 Construction of an adjusted micro data base for the wealth top tail 21 1 1 Tail wealth distributions by rich list and minimum wealth Figure 1: Tail wealth distribution by rich list and minimum wealth, Germany, first wave of the HFCS 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Manager Magazin 200 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Manager Magazin 100 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Forbes HFCS Manager Magazin/Forbes Regression(HFCS and rich list) Source: HFCS (first wave), Manager magazin (2011) and Forbes (2011); own calculations. 2 Figure 2: Tail wealth distribution by rich list and minimum wealth, Germany, second wave of the HFCS 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Manager Magazin 200 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Manager Magazin 100 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Forbes HFCS Manager Magazin/Forbes Regression(HFCS and rich list) Source: HFCS (second wave), Manager magazin (2014) and Forbes (2014); own calculations. 3 Figure 3: Tail wealth distribution by rich list and minimum wealth, France, first wave of the HFCS 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Challenges 200 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Challenges 100 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Forbes HFCS Manager Magazin/Forbes Regression(HFCS and rich list) Source: HFCS (first wave), Challenges (2010) and Forbes (2010); own calculations. 4 Figure 4: Tail wealth distribution by rich list and minimum wealth, France, second wave of the HFCS 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Challenges 200 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Challenges 100 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Forbes HFCS Manager Magazin/Forbes Regression(HFCS and rich list) Source: HFCS (second wave), Challenges (2015) and Forbes (2015); own calculations. 5 Figure 5: Tail wealth distribution by rich list and minimum wealth, Spain, first wave of the HFCS 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) El Mundo 74 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Forbes HFCS Manager Magazin/Forbes Regression(HFCS and rich list) Source: HFCS (first wave), El Mundo (2009) and Forbes (2009); own calculations. 6 Figure 6: Tail wealth distribution by rich list and minimum wealth, Spain, second wave of the HFCS 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) El Mundo 117 richest HH 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: .5 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 1 million Euro) 1 P(X>=x) 10 100 1000 10000 Net wealth in million Euro (wmin: 2 million Euro) Forbes HFCS Manager Magazin/Forbes Regression(HFCS and rich list) Source: HFCS (second wave), El Mundo (2012) and Forbes (2012); own calculations. 7 2 Adjusted tail wealth distributions Figure 7: Adjusted tail wealth distribution, Germany - first wave of the HFCS 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 Pr(X>=x) 100101102103104105 Net wealth in million Euro xmin: 0.5 million Euro Empirical ccdf (Manager Magazin 2011, top200) ccdf (Imputed Values) Regression (HFCS) Regression (HFCS & Manager Magazin 2011, top200) Source: HFCS (first wave), Manager magazin (2011) and Forbes (2011); own calculations. Figure 8: Adjusted tail wealth distribution, Germany - second wave of the HFCS 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 Pr(X>=x) 100101102103104105 Net wealth in million Euro xmin: 0.5 million Euro Empirical ccdf (Manager Magazin 2014, top200) ccdf (Imputed Values) Regression (HFCS) Regression (HFCS & Manager Magazin 2014, top200) Source: HFCS (second wave), Manager magazin (2014) and Forbes (2014); own calculations. 8 4 Aggregate statistics on assets and liabilities Table 8: Asset and liabilities of households in Germany according to national and financial accounts, 2010 (End-of-year level) ESA 2010 Assets billion Euro % ESA 2010 Liabilities billion Euro % Non-financial assetsa) 6,040 57.8 Loans and other liabilities 1,520 14.5 AN.111 Dwellings 3,483 33.3 AF.41 Short-term loans 75 0.7 AN.112 Other buildings and structures 413 4.0 AF.42 Long-term loans 1,434 13.7 AN.113 Machinery and equipment 134 1.3 AF.8 Other liabilities 11 AN.2111 Land underlying buildings and structures 1,775 17.0 AN.2112-9 Land under cultivation, other land 212 2.0 Other non-financial assetsb) 23 0.2 Financial assets 4,411 42.2 AF.21 Currency 106 1.0 AF.22 Transferable deposits 694 6.6 AF.23 Other deposits 913 8.7 AF.3 Debt securities 219 2.1 AF.511 Listed shares 191 1.8 AF.512 Unlisted shares 46 0.4 AF.519 Other equity 184 1.8 AF.52 Investment fund shares or units 396 3.8 AF.61 Non-life insurance technical reserves 243 2.3 Net wealth 8,932 85.5 AF.62 Life insurance and annuity entitlements 765 7.3 Net wealth less currency, AF.63 Pension entitlements 614 5.9 non-life insurance technical reserves, AF.8 Other financial assets 39 0.4 pension entitlements 7,969 76.2 Total 10,451 100.0 Total 10,451 100.0 Note: a) Including non-profit institutions serving households (NPISH). b) Cultivated assets and other natural resources, intellectual property products, inventories. Source: Federal Statistical Office, national accounts; Deutsche Bundesbank, financial accounts. 15 Table 9: Asset and liabilities of households in Germany according to national and financial accounts, 2014 (End-of-year level) ESA 2010 Assets billion Euro % ESA 2010 Liabilities billion Euro % Non-financial assetsa) 7,037 58.0 Loans and other liabilities 1,587 13.1 AN.111 Dwellings 4,047 33.4 AF.41 Short-term loans 65 0.5 AN.112 Other buildings and structures 436 3.6 AF.42 Long-term loans 1,506 12.4 AN.113 Machinery and equipment 141 1.2 AF.8 Other liabilities 17 AN.2111 Land underlying buildings and structures 2,100 17.3 AN.2112-9 Land under cultivation, other land 286 2.4 Other non-financial assetsb) 27 0.2 Financial assets 5,093 42.0 AF.21 Currency 128 1.1 AF.22 Transferable deposits 981 8.1 AF.23 Other deposits 889 7.3 AF.3 Debt securities 162 1.3 AF.511 Listed shares 234 1.9 AF.512 Unlisted shares 69 0.6 AF.519 Other equity 206 1.7 AF.52 Investment fund shares or units 443 3.6 AF.61 Non-life insurance technical reserves 307 2.5 Net wealth 10,542 86.9 AF.62 Life insurance and annuity entitlements 886 7.3 Net wealth less currency, AF.63 Pension entitlements 752 6.2 non-life insurance technical reserves, AF.8 Other financial assets 36 0.3 and pension entitlements 9,355 77.1 Total 12,129 100.0 Total 12,129 100.0 Note: a) Including non-profit institutions serving households (NPISH). b) Cultivated assets and other natural resources, intellectual property products, inventories. Source: Federal Statistical Office, national accounts; Deutsche Bundesbank, financial accounts. 16 Table 10: Asset and liabilities of households in France according to national and financial accounts, 2010 (End- of-year level) ESA2010 Assets billion Euro % ESA2010 Liabilities billion Euro % Non-financial assets 7,042 63.5 Loans and other liabilities 1,323 11.9 AN.111 Dwellings 3,076 27.7 AF.4 Loans 1,057 9.5 AN.112 Other buildings and structures 150 1.4 AF.8 Other liabilities 266 2.4 AN.113 Machinery and equipment 43 0.4 AN.2111 Land underlying buildings and structures 3,164 28.5 AN.2112-9 Land under cultivation, other land 430 3.9 Other non-financial assetsa) 179 1.6 Financial assets 4,043 36.5 AF.21 Currency 49 0.4 AF.22 Transferable deposits 288 2.6 AF.29 Other deposits 773 7.0 AF.3 Debt securities 77 0.7 AF.4 Loans 25 0.2 AF.511 Listed shares 160 1.4 AF.512 Unlisted shares 330 3.0 AF.519 Other equity 306 2.8 AF.52 Investment fund shares or units 257 2.3 AF.61 Non-life insurance technical reserves 87 0.8 Net wealth 9,763 88.1 AF.62 Life insurance and annuity entitlements 1,249 11.3 Net wealth less currency, AF.63 Pension entitlements 164 1.5 non-life insurance technical reserves, AF.8 Other financial assets 277 2.5 and pension entitlements 9,463 85.4 Total 11,085 100.0 Total 11,085 100.0 Note: a) Cultivated assets and other natural resources, intellectual property products, inventories. Source: INSEE, national accounts; Banque de France and European Central Bank, financial accounts. 17 Table 11: Asset and liabilities of households in France according to national and financial accounts, 2014 (End- of-year level) ESA2010 Assets billion Euro % ESA2010 Liabilities billion Euro % Non-financial assets 7,141 61.1 Loans and other liabilities 1,354 11.6 AN.111 Dwellings 3,435 29.4 AF.4 Loans 1,178 10.1 AN.112 Other buildings and structures 147 1.3 AF.8 Other liabilities 176 1.5 AN.113 Machinery and equipment 37 0.3 AN.2111 Land underlying buildings and structures 2,907 24.9 AN.2112-9 Land under cultivation, other land 441 3.8 Other non-financial assetsa) 175 1.5 Financial assets 4,538 38.9 AF.21 Currency 65 0.6 AF.22 Transferable deposits 319 2.7 AF.29 Other deposits 888 7.6 AF.3 Debt securities 77 0.7 AF.4 Loans 31 0.3 AF.511 Listed shares 189 1.6 AF.512 Unlisted shares 373 3.2 AF.519 Other equity 366 3.1 AF.52 Investment fund shares or units 291 2.5 AF.61 Non-life insurance technical reserves 109 0.9 Net wealth 10,326 88.4 AF.62 Life insurance and annuity entitlements 1,415 12.1 Net wealth less currency, AF.63 Pension entitlements 188 1.6 non-life insurance technical reserves, AF.8 Other financial assets 228 2.0 and pension entitlements 9,964 85.3 Total 11,680 100.0 Total 11,680 100.0 Note: a) Cultivated assets and other natural resources, intellectual property products, inventories. Source: INSEE, national accounts; Banque de France and European Central Bank, financial accounts. 18 Table 12: Asset and liabilities of households in Spain according to national and financial accounts, 2009 (End- of-year level) ESA 2010 Assets billion Euro % ESA 2010 Liabilities billion Euro % Non-financial assetsa) 5,884 77.5 Loans and other liabilities 942 12.4 Financial assets 1,711 22.5 AF.4 Loans 901 11.9 AF.21 Currency 92 1.2 AF.8 Other liabilities 41 0.5 AF.22 Transferable deposits 300 3.9 AF.29 Other deposits 408 5.4 AF.3 Debt securities 39 0.5 AF.511 Listed shares 104 1.4 AF.512 Unlisted shares 253 3.3 AF.519 Other equity 45 0.6 AF.52 Investment fund shares or units 151 2.0 AF.61 Non-life insurance technical reserves 24 0.3 Net wealth 6,653 87.6 AF.62 Life insurance and annuity entitlements 110 1.4 Net wealth less currency, non-life AF.63 Pension entitlements 143 1.9 insurance technical reserves, AF.8 Other financial assets 42 0.6 and pension entitlements 6,394 84.2 Total 7,595 100.0 Total 7,595 100.0 Note: a) Only real estate assets. Including non-profit institutions serving households (NPISH). Source: Banco de Espa˜ na and European Central Bank, financial accounts; estimation on real estate assets by Banco de Espa˜ na. 19 Table 13: Asset and liabilities of households in Spain according to national and financial accounts, 2011 (End- of-year level) ESA 2010 Assets billion Euro % ESA 2010 Liabilities billion Euro % Non-financial assetsa) 5,208 74.7 Loans and other liabilities 918 13.2 Financial assets 1,761 25.3 AF.4 Loans 868 12.5 AF.21 Currency 89 1.3 AF.8 Other liabilities 50 0.7 AF.22 Transferable deposits 299 4.3 AF.29 Other deposits 434 6.2 AF.3 Debt securities 82 1.2 AF.511 Listed shares 90 1.3 AF.512 Unlisted shares 237 3.4 AF.519 Other equity 83 1.2 AF.52 Investment fund shares or units 121 1.7 AF.61 Non-life insurance technical reserves 19 0.3 Net wealth 6,051 86.8 AF.62 Life insurance and annuity entitlements 116 1.7 Net wealth less currency, AF.63 Pension entitlements 139 2.0 non-life insurance technical reserves AF.8 Other financial assets 52 0.8 and pension entitlements 5,805 83.3 Total 6,969 100.0 Total 6,969 100.0 Note: a) Only real estate assets. Including non-profit institutions serving households (NPISH). Source: Banco de Espa˜ na and European Central Bank, financial accounts; estimation on real estate assets by Banco de Espa˜ na. 20 5 Construction of an adjusted micro data base for the wealth top tail In our paper, we replace the HFCS wealth top tail by imputed households that follow the Pareto distribution. The very end of the top tail we replace by observations from rich lists, given that these lists provide an empirical estimate for the very top. In this section, we describe the different steps of how we constructed this adjusted top tail. First of all, it is helpful to recall the characteristics of the Pareto distribution: The probability density function of the Pareto distribution is defined on the wealth interval [wmin;∞[as f(w) = αwα min wα+1;α>0, (1) αbeing the slope parameter and wmin the minimum wealth which determines the lower bound of the top tail. When representing the top tail of the wealth distribution by the Pareto distribution, we can calculate total tail wealth as Z∞ wmin f(w)w Ntt dw =Z∞ wmin αNtt (wmin w)αdw (2) Ntt being the top tail population, measured by the sum of weighted households in the HFCS with a net worth of wmin or higher. In the following, we outline the different steps to derive the adjusted wealth top tail based on actual micro data. 1. Create a dataset with zobservations (households) whose net wealth increases on a logarithm scale up to ’∞’, where the first household has net wealth higher than wmin. In this paper, we approximate ∞by 200 billion Euros which is equivalent to wz, net wealth of observation z.1 2. For each interval between two observations in the wealth distribution [wi−1,wi], calculate the number of households, IHi, which falls into that interval as IHi=Zwi wi−1 Ntt f(w)dw;i=1, ..., z and w0=wmin. (3) We index IH by i, as it will serve as weight for household iin the adjusted top tail. 3. For each interval between two observations in the wealth distribution [wi−1,wi], calculate total net wealth, IWi, according to the Pareto distribution: IWi=Zwi wi−1 f(w)w Ntt dw =Zwi wi−1 αNtt (wmin w)αdw;i=1, ..., z and w0=wmin. (4) 4. Calculate the final net wealth of each household,w∗i, which falls in the wealth interval [wi−1,wi]such that w∗iIHi=IWi(5) and w∗i=IWi IHi (6) where w∗i>wiand w∗i<wi+1. As a result, the weighted sum of top tail household net wealth, w∗i, matches the sum calculated according to formula 2, given that ’∞’ is approximated by the same number, here 200 billion Euros. 1The choice of the proxy for ’∞’, e.g. 200 billion Euros, has an impact on the estimate of total net wealth. Increasing the proxy for ∞ for any given α,wmin, and Ntt shrinks the difference between total tail wealth - calculated according to equation 2 and replacing ∞by the proxy - and its theoretical expected value (calculated as Ntt wmin α α−1(Vermeulen, 2016, p.15)). For instance, when setting ∞to 5 trillion Euros the two calculations yield almost the same result. However, given that in reality, there is no household with net wealth of infinity, we are confident that approximating ∞by a lower net wealth value, based on the rich list, is the appropriate approach. 21 5. Finally, replace the very end of this new discrete top tail Pareto distribution by the rich list, where each entry has a weight of one. Accordingly, we calculate total top tail wealth in our micro data as Total tail wealth = m ∑ i w∗iIHi+ R ∑ j=1 wj;i=1, ..., m j =1, ..., R, (7) where mis the richest household in the imputed top tail which has net wealth below the net wealth of the poorest rich list entry and Ris the number of rich list entries. 22 References Challenges (2010). Les 500 plus grandes fortunes professionnelles de France. Challenges 220. Challenges (2015). Les 500 plus grandes fortunes professionnelles de France. Challenges 441. El Mundo (2009). 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