How fat is the top tail of the wealth distribution?

Transcription

1 How fat is the top tail of the wealth distribution? Philip Vermeulen European Central Bank DG-Research Household wealth data and Public Policy, London 9/March/2015 Philip Vermeulen How fat is the top tail 9/March/ / 44

2 This slideshow should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the author and do not necessarily reflect those of the ECB. Philip Vermeulen How fat is the top tail 9/March/ / 44

3 Intro Wealth distribution and its tail 30 percent of wealth is held by 1 percent of the population (Kennickell, 2009) Piketty Capital in the Twenty-First Century Stiglitz The Price of Inequality: How Today s Divided Society Endangers Our Future analysis of tax and redistribution policies needs detailed distributional information Philip Vermeulen How fat is the top tail 9/March/ / 44

4 Intro Purpose of the research Philip Vermeulen How fat is the top tail 9/March/ / 44

5 Intro Purpose of the research How much wealth is in the tail? Philip Vermeulen How fat is the top tail 9/March/ / 44

6 Intro Purpose of the research How much wealth is in the tail? Does survey data give a good account of tail wealth? Philip Vermeulen How fat is the top tail 9/March/ / 44

7 Intro Purpose of the research How much wealth is in the tail? Does survey data give a good account of tail wealth? Show the importance of differential unit non-response for tail wealth estimation Philip Vermeulen How fat is the top tail 9/March/ / 44

8 Intro Purpose of the research How much wealth is in the tail? Does survey data give a good account of tail wealth? Show the importance of differential unit non-response for tail wealth estimation Improve on the estimation of tail wealth in the presence of differential unit non-response. Philip Vermeulen How fat is the top tail 9/March/ / 44

9 Intro Purpose of the research How much wealth is in the tail? Does survey data give a good account of tail wealth? Show the importance of differential unit non-response for tail wealth estimation Improve on the estimation of tail wealth in the presence of differential unit non-response. New estimates of tail wealth: US, UK, Germany, France, Spain, Italy, The Netherlands, Belgium, Austria, Finland, Portugal Philip Vermeulen How fat is the top tail 9/March/ / 44

10 Intro Wealth distribution data Household wealth surveys US Survey of consumer finances UK Wealth and Assets survey European Household Finance and Consumption Survey Complex survey designs: stratification, clustering, weighting representative of population Philip Vermeulen How fat is the top tail 9/March/ / 44

11 Intro Literature: Tail wealth estimation Wealth tax records: Roine and Waldenström (2009), Alvaredo and Saez (2009), Dell, Piketty and Saez (2007) estate tax records: Atkinson and Harrison (1978), Atkinson, Gordon and Harrison (1989), Kopczuk and Saez (2004), Piketty, Postel-Vinay and Rosenthal (2006) Capitalization capital income: Atkinson and Harrison (1978), Saez and Zucman (2014) Philip Vermeulen How fat is the top tail 9/March/ / 44

12 Intro Part of the wealth distribution Germany Density 0 2.0e e e wealtheuro Philip Vermeulen How fat is the top tail 9/March/ / 44

13 Intro Part of the wealth distribution France Density 0 1.0e e e e e wealtheuro Philip Vermeulen How fat is the top tail 9/March/ / 44

14 Part of the wealth distribution Italy Intro Density 0 1.0e e e e wealtheuro Philip Vermeulen How fat is the top tail 9/March/ / 44

15 Part of the wealth distribution Spain Intro Density 0 1.0e e e wealtheuro Philip Vermeulen How fat is the top tail 9/March/ / 44

16 Intro The wealth distribution is special Practically all familiar distributions: inflation, bond returns, stock returns, growth rates, mean and variance that makes sense (central tendency and fluctuations around it) wealth distribution in contrast: an astronomically long tail: roughly twenty thousand times larger than the first 95 percent of the distribution Has a mean and variance that don t make sense. NEED to sample especially from the tail to estimate its importance Philip Vermeulen How fat is the top tail 9/March/ / 44

17 Intro Household wealth survey data: two problems - one solution PROBLEM I = Efficiency: a simple random sample yields an inefficient estimate of the distribution of wealth PROBLEM II = BIAS: survey weights that remain uncorrected for differential unit non-response SOLUTION : Oversample the wealthy Philip Vermeulen How fat is the top tail 9/March/ / 44

18 Intro Household wealth survey data: oversampling the rich very different strategies to oversample wealthy households US, UK: income tax files Spain, France: wealth tax files Finland: income register data Germany, Belgium: income of regions Portugal, Austria: metropolitan areas Italy, Netherlands: No oversampling Philip Vermeulen How fat is the top tail 9/March/ / 44

19 Intro The effect of different oversampling strategies Number of wealthy households in the samples > 2 million euro Absolute Number vs Pct in sample Sample size Absolute number Pct of sample USA Spain UK France Germany Italy Netherlands Philip Vermeulen How fat is the top tail 9/March/ / 44

20 The data The extreme tail The forbes list (billion euro) Individuals Total wealth Pct country wealth USA Germany UK Italy Spain France Austria Netherlands Portugal Belgium Finland Philip Vermeulen How fat is the top tail 9/March/ / 44

21 The data The Household data: the missing end of the tail MIND THE GAP Max wealth Survey vs Min wealth at Forbes Million euros Max wealth SCF/WAS/HFCS Min wealth Forbes USA Spain France UK Finland Germany Belgium Portugal Austria Italy Netherlands Philip Vermeulen How fat is the top tail 9/March/ / 44

22 The data Some observations large gap between the highest wealth household in HFCS sample and the poorest household in Forbes suggest combination of non-response and lack of effective oversampling suggest to estimate the tail of the distribution survey + Forbes data Philip Vermeulen How fat is the top tail 9/March/ / 44

23 Tail distributions How to estimate tail wealth Survey Sample only Directly from the observations in the survey samples Assume tail is Pareto:(pseudo) maximum likelihood Assume tail is Pareto: Regression method on survey sample Survey sample + Forbes Assuming tail is Pareto: Regression method on survey sample+forbes data Philip Vermeulen How fat is the top tail 9/March/ / 44

24 Tail distributions A candidate distribution for the tail Pareto distribution (Power law) complementary CDF or tail function defined on the interval [w min, [ and α > 0 P(W > w) = ( w min w )α (1) α tail index determines the fatness of the tail. The lower α, the fatter the tail. Philip Vermeulen How fat is the top tail 9/March/ / 44

25 Tail distributions Method 1: Pseudo maximum likelihood Maximum likelihood is impossible, cannot write the likelihood function Pseudo maximum likelihood act as if the data were a census L(α,w min W) = f(w i ) sw i Does not deal with the differential non-response problem Philip Vermeulen How fat is the top tail 9/March/ / 44

26 Tail distributions An interesting property of the Pareto complementary CDF or tail function P(W > w) = ( w min w )α (2) n(w i ) the number of households that have wealth above w i (rank of the household) log(n(w i )) = log(n)+αlog(w min ) αlog(w i ) n(w i ) N = (w min w i ) α (3) log of the rank of the household and log of its wealth are on a straigth line. Philip Vermeulen How fat is the top tail 9/March/ / 44

27 Tail distributions Method 2: Regression method log(n(w i )) = constant αlog(w i ) log of the rank of the household and log of its wealth are on a straight line. use survey data to construct n(w i ) also use Forbes data to construct n(w i ) α RH ˆ : survey data only α RHF ˆ : survey data + Forbes data Philip Vermeulen How fat is the top tail 9/March/ / 44

28 Tail distributions Log rank of the household and log wealth (USA) USA lnwealtheuro g_lnr f_lnr Graphs by country Philip Vermeulen How fat is the top tail 9/March/ / 44

29 Tail distributions Log rank of the household and log wealth (Germany) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

30 Tail distributions Log rank of the household and log wealth (UK) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

31 Tail distributions Log rank of the household and log wealth (France) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

32 Tail distributions Log rank of the household and log wealth (Italy) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

33 Tail distributions Log rank of the household and log wealth (Spain) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

34 Tail distributions Log rank of the household and log wealth (Netherlands) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

35 Tail distributions Log rank of the household and log wealth (Belgium) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

36 Tail distributions Log rank of the household and log wealth (Austria) lnwealtheuro ln_rank_hfcs ln_rank_forbes Philip Vermeulen How fat is the top tail 9/March/ / 44

37 Tail distributions The effect of differential unit non-response: Monte Carlo 1 million households draw wealth from Pareto distribution with tail index α rich list (households more than 740 million euro) A survey sample is drawn for 750 households: 1) No oversampling: simple random sample 2) Oversampling (4 strata: 75, 150, 225, 300) non-response probability follows *ln(Wealth) Estimate tail index using pseudo maximum likelihood, regression method survey, regression method survey + rich list twenty thousand Monte Carlo iterations Philip Vermeulen How fat is the top tail 9/March/ / 44

38 Tail distributions Pareto tail index estimates under differential unit non-response Monte Carlo estimates of Pareto tail index TRUE MAX REGR REGR Resp Rich list α LIK +LIST obs obs (1) (2) (3) (4) (5) (6) No Oversampling Oversampling the rich Philip Vermeulen How fat is the top tail 9/March/ / 44

39 Tail distributions Tail wealth estimates under differential unit non-response Monte Carlo estimates of tail wealth as a proportion of true tail wealth (1) (2) (3) (4) (5) TRUE survey est. MAX REGR REGR α LIK + LIST No Oversampling Oversampling the rich Philip Vermeulen How fat is the top tail 9/March/ / 44

40 Tail distributions TAIL WEALTH DISTRIBUTION (MONTE CARLO EXAMPLE) 10 0 Monte Carlo: Tail of the wealth distribution P(X>=x) Empirical ccdf (Sample) Empirical ccdf (Rich list) Regression (SAmple) Regression (Sample and Rich list) TRUE power law Wealth (in million euro) Philip Vermeulen How fat is the top tail 9/March/ / 44

41 Estimation results TAIL WEALTH DISTRIBUTION (Germany) 10 0 Tail of the wealth distribution P(X>=x) Empirical ccdf (Survey) Empirical ccdf (Forbes) Regression (survey) Regression (survey and Forbes) Pseudo Maxlik(survey) Wealth (in million euro) Philip Vermeulen How fat is the top tail 9/March/ / 44

42 Estimation results TAIL WEALTH DISTRIBUTION (USA) 10 0 Tail of the wealth distribution P(X>=x) Empirical ccdf (Survey) Empirical ccdf (Forbes) Regression (survey) Regression (survey and Forbes) Pseudo Maxlik(survey) Wealth (in million euro) Philip Vermeulen How fat is the top tail 9/March/ / 44

43 Estimation results TAIL WEALTH DISTRIBUTION (USA) 10 0 Tail of the wealth distribution P(X>=x) Empirical ccdf (Survey) Empirical ccdf (Forbes) Regression (survey) Regression (survey and Forbes) Pseudo Maxlik(survey) Wealth (in million euro) Philip Vermeulen How fat is the top tail 9/March/ / 44

44 Estimation results TAIL WEALTH DISTRIBUTION (UK) 10 0 Tail of the wealth distribution P(X>=x) Empirical ccdf (Survey) Empirical ccdf (Forbes) Regression (survey) Regression (survey and Forbes) Pseudo Maxlik(survey) Wealth (in million euro) Philip Vermeulen How fat is the top tail 9/March/ / 44

45 Estimation results TAIL WEALTH DISTRIBUTION (UK) 10 0 Tail of the wealth distribution P(X>=x) Empirical ccdf (Survey) Empirical ccdf (Forbes) Regression (survey) Regression (survey and Forbes) Pseudo Maxlik(survey) Wealth (in million euro) Philip Vermeulen How fat is the top tail 9/March/ / 44

46 Average Pareto tail index Estimation results Regres Regres excl Forbes incl Forbes countries using tax/income records to oversample USA UK France Spain Finland other or no oversampling Germany Austria Belgium Portugal Italy Netherlands Philip Vermeulen How fat is the top tail 9/March/ / 44

47 Estimation results Percentage wealth share of top 1 pct of households Regres SURVEY incl Forbes countries using tax/income records to oversample USA to +3 UK to +5 France to +3 Spain to +2 Finland to +3 other or no oversampling Germany to +10 Austria to +9 Belgium to +4 Portugal to +6 Italy to +7 Netherlands to +10 Philip Vermeulen How fat is the top tail 9/March/ / 44

48 Estimation results Percentage wealth share of top 5 pct of households Regres SURVEY incl Forbes countries using tax/income records to oversample USA to +2 UK to +5 France to +2 Spain to +2 Finland to +2 other or no oversampling Germany to +8 Austria to +6 Belgium to +3 Portugal to +4 Italy to +6 Netherlands to +10 Philip Vermeulen How fat is the top tail 9/March/ / 44

49 Conclusion Conclusion unobserved differential non-response creates substantially downward biased estimates of tail wealth oversampling (using tax records) allows to observe and address (partially) differential non-response combining Forbes/rich lists tail wealth individuals with survey data improves tail wealth estimates Germany, Austria, The Netherlands, Italy have substantially higher tail wealth than can be derived from the HFCS data only Philip Vermeulen How fat is the top tail 9/March/ / 44