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1、June 17, 2020ESTIMATING THE TOP TAIL OF THEFAMILY WEALTH DISTRIBUTION INCANADAPowered by TCPDF (www.tcpdf.org) The Parliamentary Budget Officer (PBO) supports Parliament by providing economic and financial analysis for the purposes of raising the quality of parliamentary debate and promoting greater
2、 budget transparency and accountability. PBO has developed a modelling approach to estimate the top tail of the family wealth distribution in Canada. The modelling approach produces a new micro database of high-net-worth families to undertake analytical and costing work. This report describes the ap
3、proach to constructing the database and showcases its analytical capabilities. PBO wishes to acknowledge Professor Jim Davies, who provided valuable technical clarifications related to estimating the top tail of the family wealth distribution, and officials from Statistics Canadas Survey of Financia
4、l Security (SFS) Team, who answered many questions related to the SFS. Lead Analyst: Nigel Wodrich, Analyst Contributor: Aidan Worswick, Analyst This report was prepared under the direction of: Xiaoyi Yan, Director Nancy Beauchamp, Carol Faucher, Jocelyne Scrim and Rmy Vanherweghem assisted with the
5、 preparation of the report for publication. For further information, please contact pbo-dpbparl.gc.ca Yves Giroux Parliamentary Budget Officer RP-2021-007-S_e Table of Contents Executive Summary 1 1. Introduction 3 2. Measuring family wealth in Canada 4 3. Database construction 7 4. Database capabil
6、ities 8 Modelling approach and assumptions 11 Initial data alignment 11 Rich list data incorporation 12 Pareto interpolation 14 Iterative calibrations 17 Summary statistics 19 Future database development 21 References 22 Notes 25 Estimating the top tail of the family wealth distribution in Canada 1
7、Executive Summary The Parliamentary Budget Officer (PBO) has developed a modelling approach to estimate the top tail of the family wealth distribution in Canada. Its main purpose is to address underreported and missing data of high-net-worth families in the Survey of Financial Security Public Use Mi
8、crodata File (SFS PUMF). Drawing on the National Balance Sheet Accounts (NBSA), the modelling recalibrates the SFS PUMF to add a synthetic dataset of families with wealth over $3 million. This modelling work produced a new analytical resource, the High-net-worth Family Database (HFD). HFD enables PB
9、O to produce cost estimates and analysis of measures affecting Canadian families with wealth in the millions and billions of dollars. Using HFD, PBO finds that Canadas wealthiest families have significantly more wealth than recorded in the SFS PUMF. HFD increases the wealth share of the top 1 per ce
10、nt of families by 12 percentage points compared with the SFS PUMF (Table ES-1). The discrepancy is likely due to sampling and non-sampling errors, especially higher survey non-response among high-net-worth families, in the SFS. Family wealth distribution, SFS PUMF and HFD, by selected quantiles, Can
11、ada, 2016 Family wealth quantile SFS PUMF Share of total wealth HFD Share of total wealth (per cent) (per cent) Top 0.01% 0.4 5.6 Top 0.1% 3.1 12.1 Top 0.5% 9.2 20.5 Top 1% 13.7 25.6 Top 5% 33.0 43.4 Top 10% 47.6 56.4 Top 20% 67.2 73.5 Middle 40% 30.5 25.3 Bottom 40% 2.3 1.2 Sources: PBO calculation
12、s of the SFS PUMF; PBO High-net-worth Family Database This report describes the modelling approach used to produce the synthetic dataset of high-net-worth families, to incorporate it into the SFS PUMF, and to align aggregate values in the combined dataset with those in the NBSA. It will serve as a r
13、eference for future PBO work on the topic as it arises. Table ES-1 Estimating the top tail of the family wealth distribution in Canada 2 HFD was constructed using publicly-available data. Additional documentation is available upon request. Estimating the top tail of the family wealth distribution in
14、 Canada 3 1. Introduction During the 2019 federal election, the Parliamentary Budget Office (PBO) estimated the financial cost of electoral proposals of political parties upon request.1 One such request was made to estimate the fiscal revenues of an annual tax on the net wealth of high-net-worth fam
15、ilies above $20 million.2 PBO faced a key barrier to meet the request: The lack of a publicly available micro database that reliably assesses high-net-worth families in Canada. For example, Statistics Canadas principal family wealth microdata product, the Survey of Financial Security Public Use Micr
16、odata File (SFS PUMF), reports families with wealth up to only $27 million. By contrast, the lowest entry on Canadian Business magazines list of the 100 “Richest People” had a wealth of $875 million. To address the data gap, PBO developed a modelling approach to reliably estimate the top tail of the
17、 family wealth distribution in Canada. This approach consisted of adapting a straight-forward Pareto interpolation technique in Bach et al. (2014) and Saez and Zucman (2019). The technique creates a synthetic dataset bridging wealth microdata from the SFS PUMF and the Canadian Business (CB) magazine
18、s Richest People List. This synthetic dataset enabled PBO to fulfil the electoral costing request with a two-page cost estimate, published in September 2019. Since the federal election, PBO decided to build on that work and develop a functional analytical tool of high-net-worth families. To do so, t
19、he modelling approach used in the election underwent several refinements. The most significant of these was applying a modified ordinary least squares (OLS) regression and iterative calibration procedure developed in Vermeulen (2016) and (2018). The refined approach aligns the aggregate asset, liabi
20、lities, and net worth values in the re-estimated family wealth distribution with those in the National Balance Sheet Accounts (NBSA). As a result of these refinements, what was reported in PBOs electoral proposal cost estimate is not directly comparable with the results in this report. The ultimate
21、product from this modelling work is the High-net-worth Family Database (HFD). HFD was constructed using publicly available data from year-end 2016, the most recent date all sources reported data. It will be used to undertake analytical and costing work on high-net-worth families as it arises. To sho
22、wcase the kind of analytical work that is feasible using HFD, summary statistics from the database are presented in Section 4 and Appendix B of the report. These results are for illustrative purposes and may differ from analysis of a specific measure using HFD. Estimating the top tail of the family
23、wealth distribution in Canada 4 2. Measuring family wealth in Canada For the purposes of this report, PBO measured family wealth in terms of marketable net worth: the amount of money left to a family if it liquidates all its financial and non-financial assets and paid off all its liabilities.3,4Cana
24、dian families collectively hold significant wealth. According to Statistics Canadas National Balance Sheet Accounts (NBSA), which record the stock of assets, liabilities and net worth for each institutional sector, at the end of 2019 Canadas household sector held $11.7 trillion in total net worth. T
25、hat figure is approximately five times larger than Canadas annual GDP.5 Real estate ($5.8 trillion) and mortgages on that real estate ($1.5 trillion) are the single largest asset and liabilities categories, respectively (Figure 2-1). Household assets, liabilities and net worth, Canada, 2019 Q4 Sourc
26、e: PBO calculations of Statistics Canada Table 36-10-0580-01 (National Balance Sheet Accounts for the household sector, 2019 Q4) The distribution of wealth among households is heavily skewed toward the wealthiest families.6 In Canada, a small proportion of families at the top of the distribution pos
27、sess net worth that is orders of magnitude higher than the countrys median net worth (Figure 2-2). The high concentration of wealth among a small number of families makes it difficult to reliably measure wealth at the very top of the distribution. This difficulty is evident in Figure 2-1 Financial a
28、ssets($7.5T)Non-financial assets($6.5T)Total liabilities($2.3T)Net worth($11.7T)Currency & Deposits($1.6T)Real estate($5.8T)Mortgages($1.5T)Net worth($11.7T)Listed & Unlisted Shares($1.2T)Consumer durables ($0.7T)Consumer credit ($0.7T)Mutual Funds($1.5T)Life insurance & pensions($2.8T)+-=Estimating
29、 the top tail of the family wealth distribution in Canada 5 the Survey of Financial Security Public Use Microdata File (SFS PUMF), Statistics Canadas national survey to measure Canadians net worth. The wealthiest family observed in the 2016 SFS PUMF had a net worth of only $27 million;7 the survey d
30、id not report any wealthier families, for several potential reasons (Box 2-1). Distribution of family net worth, Survey of Financial Security Public Use Microdata File, 2016 Source: PBO calculations using the 2016 SFS PUMF There are at least four general approaches that can be taken to improve estim
31、ates of the top tail of the family wealth distribution. The first involves compiling dossiers on each high-net-worth family, much like the Forbes Worlds Billionaires list. The second uses individual income tax returns to capitalize the incomes reported by taxpayers. The third uses estate tax records
32、 to back out the wealth recorded by the deceased and makes certain assumptions about how the recorded wealth of the deceased relates to the actual wealth of the living. The fourth consists of adjusting the family wealth distribution in national surveys like the SFS PUMF using data from other sources
33、. This last approach is PBOs preferred approach and is further developed in the next section. -5051015202530 - 20 40 60 80 100$ millionsFamily PercentileMedian net worth($0.3 million)Top net worth($27.3 million)Figure 2-2 Estimating the top tail of the family wealth distribution in Canada 6 Box 2-1
34、Limitations of national wealth surveys in measuring high-net-worth families There are several plausible reasons national wealth surveys, like Canadas SFS, are limited in measuring and analyzing high-net-worth families. Surveys may be subject to sampling errors if the surveyed sample is not represent
35、ative of the population, including at the top of the family wealth distribution. Response errors, where families inaccurately report, willingly or not, the value of their assets and liabilities, may bias estimates for high-net-worth families. Certain large asset and liabilities values in the SFS PUM
36、F are also subject to top-coding, where they are replaced with a maximum value. While this procedure ensures the confidentiality of released data, it also reduces top wealth shares (see Appendix A.3). The most impactful limitation may be differential unit non-response, the tendency of high-net-worth
37、 families to be less likely to participate in surveys. If high-net-worth families are undersampled and the survey weights of those that are sampled are not adequately scaled upwards, top wealth shares will be underestimated. While Statistics Canada reports the overall response rate (70.3 per cent fo
38、r the 2016 SFS), little is publicly-known about the incidence of differential unit non-response in the SFS. There is evidence from the U.S. of a positive correlation between wealth and the rate of unit non-response in its main wealth survey, the Survey of Consumer Finances (Kennickell & Woodburn, 19
39、97) Statistics Canada attempts to address differential unit non-response among high-net-worth families by oversampling geographic areas known to have higher income and believed to have higher wealth (Statistics Canada, 2018a). However, similar approaches to oversample high-net-worth families using g
40、eographic or income-stratified geographic information in several European countries have been shown to be of limited effectiveness in accurately measuring the wealth of high-net-worth families (Vermeulen, 2018). Estimating the top tail of the family wealth distribution in Canada 7 3. Database constr
41、uction PBOs High-net-worth Family Database (HFD) was constructed using data from three sources: 1. The Survey of Financial Security Public Use Microdata File.8 The SFS PUMF is Canadas national net worth survey. Statistics Canada surveys a representative sample of over 12,000 resident economic famili
42、es on their major financial and non-financial assets and debts.9 HFD uses the most recently-published iteration of the SFS PUMF, from 2016. 2. The National Balance Sheet Accounts. The NBSA aggregate the individual balance sheets of households across the economy and reports their aggregate financial
43、assets, non-financial assets, liabilities, and ultimately net worth.10 HFD uses NBSA data from 2016 Q4, the date that aligns most closely with the vintages of the SFS PUMF and CBs Richest People List used in the database.11 3. Canadian Business magazines Richest People List. CB conducts journalistic
44、 and market research to compile a list of the 100 wealthiest Canadian citizens.12 HFD uses CBs 2017 Richest People List, which was published in December 2016 and corresponds most closely with the 2016 SFS PUMF. PBO followed Vermeulens (2016) elegant approach to address missing and underreported data
45、 of high-net-worth families in the SFS PUMF and build HFD. First, the aggregate values of financial assets, non-financial assets, and total liabilities in the SFS PUMF were adjusted to align with the corresponding totals by category in the NBSA. Second, data from CBs Richest People List were added t
46、o the SFS PUMF. Third, the resulting joint dataset was used to run a modified OLS regression that would determine the shape of the wealth distribution for the missing and underreporting families and bridge the top of the SFS PUMF and the bottom of the CB Richest People List. Fourth, the results from
47、 the modified OLS regression were applied to create a new synthetic dataset of high-net-worth families. Fifth, the synthetic dataset was merged with the joint dataset from the second step. The addition of the synthetic dataset generally creates more assets and liabilities than there are in the NBSA,
48、 which leads to sixth step: to reduce (or increase) each of the financial assets, non-financial assets, and total liabilities in the SFS PUMF by an adjustment factor and returning to the second step to repeat the procedure iteratively until the value of the financial assets, non-financial assets, an
49、d total liabilities in the final, integrated dataset (combining NBSA-adjusted SFS PUMF, the synthetic dataset, and CBs Richest People List) are equal to those in the NBSA. Estimating the top tail of the family wealth distribution in Canada 8 The modelling approach used to construct HFD is described
50、in greater detail in Appendix A. 4. Database capabilities PBO generated summary statistics of HFD to showcase its analytical capabilities. Using HFD, PBO finds that Canadas wealthiest families have significantly more wealth than recorded in the SFS PUMF. The wealth share of the top 1 per cent of fam
51、ilies increases by 12 percentage points in HFD compared with the SFS PUMF (Table 4-1). Family wealth distribution, SFS PUMF and HFD, by selected quantiles, Canada, 2016 Family wealth quantile SFS PUMF Share of total wealth HFD Share of total wealth (per cent) (per cent) Top 0.01% 0.4 5.6 Top 0.1% 3.
52、1 12.1 Top 0.5% 9.2 20.5 Top 1% 13.7 25.6 Top 5% 33.0 43.4 Top 10% 47.6 56.4 Top 20% 67.2 73.5 Middle 40% 30.5 25.3 Bottom 40% 2.3 1.2 Sources: PBO calculations of the SFS PUMF; PBO High-net-worth Family Database Appendix B presents additional summary statistics for year-end 2016, HFDs base period w
53、hen each of its sources most recently reported data. Analyzing high-net-worth families in subsequent periods requires making certain assumptions about the evolution of families and their wealth since the end of 2016. To illustrate the kinds of assumptions required to bring HFD forward, PBO also gene
54、rated summary statistics on high-net-worth families for year-end 2019. PBO assumed that, since 2016: - The composition of families (number of people, age, etc.) has remained constant across the wealth distribution;13 Table 4-1 Estimating the top tail of the family wealth distribution in Canada 9 - T
55、he number of families has grown at the same rate as the number of individuals, and this growth has been uniform across the wealth distribution;14 - Aggregate financial assets, non-financial assets, and total liabilities have grown at the same rate as indicated in the NBSA, and this growth has been p
56、roportional across the family wealth distribution. Following these assumptions, PBO applied two adjustments to HFD. First, the weight of each observation was increased by growth rate of Canadas population between 2016 Q4 and 2019 Q4. Second, the financial assets, non-financial assets, and total liab
57、ilities of each observation was increased proportionally, until their aggregate totals matched those in the NBSA in 2019 Q4. The resulting summary statistics are presented in Tables 4-2 and 4-3. Both tables highlight the strong concentration of wealth among Canadas high-net-worth families. Family we
58、alth distribution, by selected quantiles, Canada, 2019 Family wealth quantile Wealth threshold Number of families Total wealth Share of total wealth ($ millions) (thousands) ($ billions) (per cent) Top 0.01% 143.1 1.6 654 5.6 Top 0.1% 29.3 16.0 1,427 12.2 Top 0.5% 9.7 79.7 2,410 20.6 Top 1% 6.1 159.
59、3 3,010 25.7 Top 5% 2.3 796.7 5,107 43.7 Top 10% 1.6 1,593.5 6,629 56.7 Top 20% 1.0 3,186.9 8,633 73.8 Middle 40% 0.1-1.0 6,373.8 2,932 25.1 Bottom 40% under 0.1 6,373.8 132 1.1 Source: PBO High-net-worth Family Database; PBO calculations based on Statistics Canadas Quarterly Demographic Estimates a
60、nd the NBSA Table 4-2 Estimating the top tail of the family wealth distribution in Canada 10 Wealth distribution, by selected wealth thresholds, Canada, 2019 Family wealth threshold Families with wealth above: Number of families Total wealth Share of total wealth (thousands) ($ billions) (per cent)
61、$1 billion 0.1 221 1.9 $500 million 0.2 333 2.8 $250 million 0.7 488 4.2 $100 million 2.7 785 6.7 $50 million 7.2 1,097 9.4 $25 million 19.4 1,525 13.0 $10 million 76.3 2,377 20.3 $5 million 206.6 3,271 28.0 $2.5 million 699.1 4,871 41.6 $1 million 3,123.7 8,570 73.3 Source: PBO High-net-worth Famil
62、y Database; PBO calculations based on Statistics Canadas Quarterly Demographic Estimates and the NBSA Table 4-3 Estimating the top tail of the family wealth distribution in Canada 11 Modelling approach and assumptions Initial data alignment PBO performed an initial adjustment to the SFS PUMF microda
63、ta so that the aggregate values of assets, liabilities, and net worth aligned with the corresponding totals by category for the household sector in the NBSA. While the SFS PUMF and the NBSA both estimate household net worth, there are procedural and conceptual distinctions between the two sources th
64、at lead to slightly different estimates.15 Most obviously, the SFS PUMF is derived from a survey with confidence intervals on its estimates; the NBSA measure stocks and flows in capital and financial accounts but because certain household categories are calculated as residuals from other sectors, th
65、e NBSA have a margin of error of their own. The SFS does not sample the territories and certain population groups representing two per cent of the population. Certain assets and liabilities are also measured differently. For example, the NBSA do not record the value of collectibles such as art work;
66、 the two sources measure credit card debt differently, the main reason Statistics Canada (2019a) identifies for under-coverage of total liabilities in the SFS PUMF (Table A1-1). Concordance between the SFS PUMF and the NBSA Household Sector, 2016 SFS PUMF NBSA Coverage ($ billions) ($ billions) (SFS
67、/NBSA) Financial assets 5,845 6,468 0.904 Non-financial assets 6,193 5,934 1.043 Total liabilities 1,751 2,062 0.850 Net worth 10,287 10,339 0.995 Sources: PBO calculations of the 2016 SFS and Statistics Canada Table 36-10-0580-01 Notes: NBSA totals reflect results for 2016 Q4. Business equity was c
68、ounted as a financial asset. Totals may not add due to rounding. Nevertheless, there are several reasons for which it is desirable to bring the SFS PUMF into alignment with the NBSA. Alignment can compensate for underreporting in national wealth surveys (Vermeulen, 2016). Unlike the SFS and its pred
69、ecessor, the Survey of Consumer Finances (SCF), the NBSA have Table A1-1 Estimating the top tail of the family wealth distribution in Canada 12 been estimated on a consistent basis over time (Davies and Di Matteo, 2020). This consistency allows for better comparison of the family wealth distribution
70、 estimates going back in time. The NBSA are also estimated and released more frequently (quarterly) than the SFS (triennially). The higher frequency provides opportunities to update estimates in non-survey years of the SFS. Finally, alignment with the household sector of the NBSA permits analyses of
71、 the overall position of households relative to other economic sectors included in the NBSA (Statistics Canada, 2019a). For some of these same reasons, Statistics Canada also performs alignment between the SFS and the NBSA in its Distributions of Household Economic Accounts (DHEA) dataset. To bring
72、the SFS PUMF into alignment with the NBSA, PBO first classified each asset and debt variable from the SFS PUMF into three large categories: financial assets;16 non-financial assets; and total liabilities.17 For each category, PBO calculated an adjustment factor as the inverse of the “coverage” calcu
73、lation in Table A1-1. We increased (decreased) the financial assets, non-financial assets, and total liabilities values for each family in the SFS PUMF by the relevant adjustment factor. Since each family has a unique portfolio of assets and liabilities, their net worth varies differently with this
74、adjustment procedure.18 Rich list data incorporation The next procedure consisted of adding wealth data from a rich list to the NBSA-adjusted SFS PUMF. The motivation to augment the SFS PUMF with rich list data is to improve the accuracy of the subsequent regression analysis that estimates Pareto pa
75、rameters used in the imputation of the missing and underreported high-net-worth families.19 Vermeulen (2018) demonstrates that the addition of even a small number of entries from a rich list significantly improves the accuracy of interpolated top tail estimates, enough that there is almost no estima
76、tion bias.20 In Canada there are two prominent, publicly available rich lists: the Forbes list of the worlds billionaires, which includes Canadian entries; and Canadian Business (CB) magazines Richest People List. PBO elected the latter for HFD, following Davies and Di Matteo (2020). They note that
77、CBs list contains billionaires missing in the Forbes list and includes entries below Forbes US$1 billion cut-off.21 Before they could be added to the NBSA-adjusted SFS PUMF, data from CBs Richest People List required adjustment.22 Estimating the top tail of the family wealth distribution in Canada 1
78、3 Unlike the SFS PUMF, CB includes non-resident Canadians in its accounting of the 100 Richest Canadians. As a result, PBO dropped non-resident Canadians from the CB dataset, similar to MacDonald (2018). In addition, several CB entries refer to extended families comprising multiple family units. The
79、se include entries entitled “family”, “brothers”, and “estate”, or that otherwise listed multiple people who were not married. By contrast, the SFS PUMF family unit consists of economic families and persons not in an economic family (unattached individuals). PBO developed an approach to split extend
80、ed families in the CB into constituent economic families. We used public sources to identify the generation(s) controlling the family wealth. Each sibling (and cousin, if applicable) within the controlling generation(s), as well as their living parent(s) (and uncles and aunts, if applicable), was tr
81、eated as a unique economic family. We assumed that the extended familys reported wealth resides exclusively and entirely within the identified constituent economic families. We also assumed that the extended familys wealth is divided evenly among its constituent economic families. Finally, we droppe
82、d all split entries that fell below the lowest entry ($875 million) on the CB list. This final procedure ensured that the top of the wealth tail, above $875 million, comprised of a complete population of families above that level to avoid bias in the subsequent regression analysis to estimate Pareto
83、 parameters. Following this splitting procedure, the cleaned CB dataset included 80 resident economic families. Each held a wealth of at least $875 million, and collectively they held $197 billion in wealth. PBO added the cleaned CB data to the NBSA-adjusted SFS PUMF, creating a joint dataset (see F
84、igure A2-1). Each CB observation was assigned a weight of 1, reflecting that each observation represents a one family unit. Estimating the top tail of the family wealth distribution in Canada 14 Family wealth distribution in the joint dataset,23 2016 Sources: PBO calculations of the 2016 SFS PUMF an
85、d Canadian Business Richest People List, 2017 Pareto interpolation PBO used the joint dataset to impute the missing and underreported high-net-worth families. To do so, PBO referred to the modified OLS regression approach for complex survey designs in Vermeulen (2018). The resulting estimated Pareto
86、 parameters were then used to interpolate the missing and underreported high-net-worth families. A key assumption for this imputation procedure is that the top of the family wealth tail exhibits a Pareto distribution. This assumption has been widely applied in the literature on wealth distributions,
87、 including in Canada. Davies and Shorrocks (1999) characterize the notion that the top wealth tail follows a Pareto distribution as an “enduring feature” of the wealth distribution. Brzozowski et al. (2010) assume that the top decile of the SFS is Pareto-distributed in their comparison of different
88、statistical methods to impute top-coded observations into the SFS PUMF. Ogwang (2011) finds that CBs Richest People List from 1999 to 2008 displays Pareto power law24 behaviour using modified OLS and MLE estimation methods. Davies and Di Matteo (2020) assume that the top wealth tail follows a Pareto
89、 distribution in their analysis of the evolution of top family wealth shares in Canada between 1892 and 2016. Vermeulen (2018) notes another key assumption: that the national wealth survey and rich list datasets “are consistent with the same Pareto 1 10 100 1,000 10,000 100,000 1,000,000 10,000,0000
90、1101001,00010,000Economic familiesWealth ($ millions)Number of economic families within each one-million-dollar wealth bracketSFS PUMFsCanadian BusinessFigure A2-1 Estimating the top tail of the family wealth distribution in Canada 15 distribution”. PBO makes that assumption, but its a cautious one
91、for two reasons. The first is due to the reliability and substance of documentation available on CBs methodology. The most recent CB methodology that PBO could locate dates from 2006.25 The methodology provides useful information about CBs approach, at least for that year. The methodology indicates
92、that at least certain debts (privately-owned companies, real estate) are ascertained or estimated, and deducted from total assets. However, the methodology also states that “intentionally conservative estimates” are used to valuate private investments and that “its safe to assume the Rich 100 are wo
93、rth more than the stated amount” (Canadian Business, 2006). Davies and Di Matteo (2020) note that the problems of rich list data compilation are reduced by the scrutiny the lists attract and the refinements the lists undergo as they are repeated annually (CB has been compiling a rich list since 1999
94、). While its reasonable to assume that CB approximates the wealth of the highest-net-worth Canadians, its unclear what, if any, bias there may be in its dataset. The second note of caution in assuming the joint dataset lies on the same Pareto distribution is due to top-coding in the SFS PUMF. The SF
95、S PUMF is top-coded such that a certain number of the largest values on some of the assets and debts are replaced with a maximum value to ensure the confidentiality of each observation disclosed in public use files. However, it also reduces the wealth of the top families in the SFS PUMF relative to
96、SFS data available at a Research Data Centre (RDC), which is not top-coded.26 Brzozowski et al. (2010) reported that the wealth share of the top 1 percent of families was approximately 1.5 percentage points lower in the 1999 SFS PUMF (13.2 percent) than in the 1999 SFS RDC data (15.7 percent). The d
97、egree of top-coding in the 2016 SFS PUMF is not reported publicly, and PBO has not analyzed the extent of top-coding or its potential bias on the Pareto estimates. In theory, this potential bias is reduced by estimating the Pareto parameters over a sufficiently large segment of the top tail of the j
98、oint dataset; a larger segment should include, proportionally, fewer top-coded families, reducing the potential bias those families could introduce. To apply Vermeulens (2018) regression approach, PBO first isolated a subset of observations the joint dataset with wealth over which the regression wou
99、ld be run. The choice of an appropriate or even a best-fit is unclear and often determined case by case.27 In Vermeulens (2018) re-estimation of top wealth shares in 10 European countries and the U.S., the choice of depends, in part, on the method used in each countrys national wealth survey to over
100、sample high-net-worth families, who are less likely to respond to such surveys. Countries that oversample using individual information, such as income tax information (the U.S.) or taxable wealth information (Spain, France), were each tested with ranging from 500,000 to 10 million. By contrast, coun
101、tries that oversample using income-stratified geographic information (Germany, Belgium), geographic information only (Austria, Portugal), or no oversampling at all (Italy, Estimating the top tail of the family wealth distribution in Canada 16 Netherlands) were each tested with ranging from 500,000 t
102、o only 2 million. In those countries, there were too few observations above thresholds higher than 2 million to accurately estimate Pareto parameters. Canadas SFS does not appear to use individual information to oversample high-net-worth families. The survey stratifies each province into rural and u
103、rban areas. In rural areas, the SFS uses geographic information from the Labour Force Survey area frame to select a multi-stage sample. In urban areas, the SFS uses information from the Socioeconomic indicators File (SEF) T1 Family File (T1FF), such as age and income, to stratify the Address Registe
104、r into groups of dwellings predicted to have similar wealth (Statistics Canada, 2018b). The urban stratum for the highest wealth represents the top 5 percent of each province.28 PBO thus narrowed the range of appropriate in the Canadian context to between $750,000 and $3 million, an approximate conv
105、ersion of the euro values of used in Vermeulen (2018) for countries that also use geographic and income-stratified geographic information to oversample high-net-worth families. Vermeulen (2018) and Chakraborty et al. (2019) highlight a trade-off when selecting a specific : A lower threshold will inc
106、rease the sample size for the regression leading to a more reliable Pareto estimation, but at the risk of potentially including observations that do not follow Pareto tail behaviour. Ultimately, PBO chose the upper-bound of the range of appropriate : $3 million. Compared with national wealth surveys
107、 in European countries that oversampled using geographic or income-stratified geographic information, Canadas SFS PUMF has comparatively many more observations at the 2 million / $3 million threshold.29 The choice of a higher permits more observations from the NBSA-adjusted SFS PUMF to be retained p
108、ost-interpolation while maintaining a robust sample size to undertake the regression estimate of Pareto parameters. Having chosen a , PBO ranked all observations with wealth , = 1, | from the joint dataset in descending order of their wealth. Each observation with wealth and weight was defined in te
109、rms of , the average weight of all observations with wealth equal or greater than , and , the average weight of the wealthiest observations (=1). Vermeulen (2018) proposes one final specification to the regression. Gabaix and Ibragimov (2011) found that log-rank-log-size OLS regressions were systema
110、tically, strongly biased in small samples. Vermeulen (2018) therefore reduces the rank of each observation in the regression by . The modification reduces the bias to a leading order. Estimating the top tail of the family wealth distribution in Canada 17 The resulting modified OLS regression is desc
111、ribed by: ln ( 0.5) = ln() + (ln() ln () The estimated coefficient from the above regression is the Pareto parameter, which determines the shape of re-estimated top tail of the family wealth distribution. In general, a higher results in a fatter top tail and a higher concentration of wealth. The est
112、imated coefficient was applied to a standard Pareto cumulative distribution function over a given wealth interval , | : (,) = 1 1 The above cumulative distribution function (,) yields estimates between 0 and 1 for the probability that a family in the top tail will have wealth between and . Following
113、 Chakraborty et al. (2019), cumulative distribution estimates were converted into the number of synthetic families within the wealth interval , by multiplying the distribution function (,) by , the sum of the weights of all observations with wealth , = 1, | . Like Davies and Di Matteo (2020), PBO re
114、tained the cleaned CB entries without interpolation. The resulting synthetic dataset consists of families with wealth between ($3 million) and , the wealth of the lowest entry from the cleaned CB dataset ($875 million). After replacing observations from the joint dataset with wealth , =1, | with the
115、 synthetic dataset, PBO created an integrated dataset. The integrated dataset combines families from the NBSA-adjusted SFS PUMF with wealth under ; families from the synthetic dataset with wealth between and ; and families from the cleaned CB with wealth equal or higher than . Iterative calibrations
116、 Substituting high-net-worth families in the NBSA-adjusted SFS PUMF with the interpolated synthetic and cleaned CB datasets creates a problem: Families in the new integrated dataset possess more aggregate wealth than the household sector in the NBSA. PBO followed Vermeulen (2016) to implement an ite
117、rative calibration procedure that aligns aggregate asset, liabilities, and net worth values in the integrated dataset with those in the NBSA. The first step requires returning to the NBSA-adjusted SFS PUMF (the product of Appendix A.1). For families with wealth in the NBSA-adjusted SFS PUMF, PBO cal
118、culated three ratios: aggregate financial assets to aggregate net worth; aggregate non-financial assets to aggregate net worth; Estimating the top tail of the family wealth distribution in Canada 18 and aggregate total liabilities to aggregate net worth. The ratios were then applied uniformly to syn
119、thetic and CB families in the integrated dataset to divide their wealth into constituent asset and liabilities values. In the next step, PBO calculated aggregate values for financial assets, non-financial assets, and total liabilities across the entire integrated dataset. The aggregate values in the
120、 integrated dataset were compared with their corresponding values in the NBSA. To the extent that integrated dataset aggregate values were higher (lower) than the NBSA, PBO applied a downward (upward) revision to the adjustment factors applied to the original SFS PUMF data in Appendix A.1. From ther
121、e, PBO re-estimated the Pareto parameters in Appendix A.3 and repeated this adjustment and re-estimation procedure iteratively until the aggregate values of financial assets, non-financial assets, and total liabilities were aligned to their corresponding values in the NBSA. This procedure typically
122、required several repetitions to produce NBSA-calibrated values for all assets and liabilities. The final, calibrated value of the parameter, which determines the shape of the family wealth distribution, was 1.45.30 The final adjustment factors applied to SFS PUMF data to bring the integrated dataset
123、 into alignment with the NBSA are presented in Table A4-1. Altogether, financial and non-financial assets were reduced by 5.8 percent and 13.0 percent, respectively. Total liabilities were adjusted up by 12.8 per cent, reflecting the significantly lower reported liabilities in the SFS PUMF compared
124、with the NBSA. Estimating the top tail of the family wealth distribution in Canada 19 Adjustment factors applied to the SFS PUMF to align aggregate asset and liabilities values in the integrated dataset with the NBSA Initial alignment Iterative calibrations Overall Appendix A.1 Appendix A.4 (A.1*A.4
125、) Financial assets 1.106 0.852 0.942 Non-financial assets 0.959 0.907 0.870 Total liabilities 1.176 0.959 1.128 Source: PBO calculations The iterative calibration procedure was repeated until aggregate values for assets and debts were within 0.00001 per cent of the corresponding values in the NBSA.
126、PBO applied a very small, proportional adjustment to the financial assets, non-financial assets, and total liabilities of all families in the integrated dataset to fully align their aggregate values with those in the NBSA. The resulting dataset is the High-net-worth Family Database (HFD). Summary st
127、atistics Tables B-1 and B-2 present summary statistics from HFD for its base year 2016. The HFDs results are comparable to other precedents in the literature: wealth shares in Table B-1 are comparable to Davies and Di Matteo (2020); the number and wealth of families in Table B-2 are similar to Wealt
128、h-X (2017); and the HFDs overall finding of significant upward revisions to top wealth shares relative to national wealth surveys dovetails results in Bach et al. (2015), Vermeulen (2016) and (2018), and Davies and Di Matteo (2020). For reference in interpreting the summary statistics, the calibrate
129、d HFD represents approximately 15,349,000 families that collectively possess $10.3 trillion in wealth. Table A4-1 Estimating the top tail of the family wealth distribution in Canada 20 Family wealth distribution, by selected quantiles, Canada, 2016 Family wealth quantile Wealth threshold Number of f
130、amilies Total wealth Share of total wealth ($ millions) (thousands) ($ billions) (per cent) Top 0.01% 130.5 1.5 574 5.6 Top 0.1% 26.7 15.3 1,254 12.1 Top 0.5% 8.9 76.7 2,117 20.5 Top 1% 5.5 153.4 2,644 25.6 Top 5% 2.1 767.5 4,488 43.4 Top 10% 1.4 1,534.9 5,829 56.4 Top 20% 0.9 3,069.9 7,599 73.5 Mid
131、dle 40% 0.1-0.9 6,139.7 2,613 25.3 Bottom 40% under 0.1 6,139.7 128 1.2 Source: PBO High-net-worth Family Database Family wealth distribution, by selected wealth thresholds, Canada, 2016 Wealth threshold Families with wealth above: Number of families Total wealth Share of total wealth (thousands) ($
132、 billions) (per cent) $1 billion 0.1 184 1.8 $500 million 0.2 277 2.7 $250 million 0.6 408 3.9 $100 million 2.2 656 6.3 $50 million 6.2 925 8.9 $25 million 16.7 1,287 12.5 $10 million 63.7 1,994 19.3 $5 million 173.8 2,751 26.6 $2.5 million 549.5 3,983 38.5 $1 million 2,699.0 7,246 70.1 Source: PBO
133、High-net-worth Family Database Table B-1 Table B-2 Estimating the top tail of the family wealth distribution in Canada 21 Future database development Future work on HFD will be guided by topics of relevance to parliamentarians, the availability of new data sources, and the evolution of the academic
134、literature on measuring top wealth shares. PBO wishes to verify whether top-coding in the SFS PUMF introduces bias to the estimation of Pareto parameters. This analysis can be done by constructing HFD using SFS data from a Statistics Canada Research Data Centre (RDC), where observations are not top-
135、coded, and comparing the SFS PUMF and SFS RDC versions of HFD. Statistics Canada collected data for its next iteration of the SFS between September and December 2019 (Statistics Canada, 2019b). Its unclear when the new public use microdata file will be available. PBO plans to adapt HFD to the most r
136、ecent publicly available version of the SFS, which will be conducted triennially going forward. Future database development may also have to contend with the potential loss of an existing data source. The rich list used to construct HFD came from CBs Richest People 2017, which corresponds to data fr
137、om 2016. While CB published a list for 2018 (corresponding to data from 2017), PBO has not been able to locate a 2019 publication of this list. If CB has discontinued publication of an annual rich list, PBO will consider alternative rich lists, such as the Forbes Worlds Billionaires List, to update
138、HFD. Finally, there is the potential for future research to offer opportunities to refine the modelling approach used to construct HFD. Topics of interest include the identification of a best-fit , the wealth threshold at which Pareto interpolation begins; a more refined approach to divide the wealt
139、h of synthetic high-net-worth families into constituent asset and liabilities categories; the possibility to estimate more granular categories of assets and liabilities of high-net-worth families; and the consideration of incorporating non-marketable forms of wealth in estimates of the top tail of t
140、he family wealth distribution. PBO plans to monitor the academic literature for new theories and methodologies that could refine or enhance HFD. Estimating the top tail of the family wealth distribution in Canada 22 References Auten, G., & Splinter, D. (2019). Income Inequality in the United States:
141、 Using Tax Data to Measure Long-term Trends (Working paper). Retrieved from http:/ Bach, S., Beznoska, M., & Steiner, V. (2014). A Wealth Tax on the Rich to Bring Down Public Debt? Revenue and Distributional Effects of a Capital Levy in Germany. Fiscal Studies, 35(1), 67-89. Bach, S., Thiemann, A.,
142、& Zucco, A. (2015). The Top Tail of the Wealth Distribution in Germany, France, Spain, and Greece. Retrieved from Deutsches Institut fr Wirtschaftsforschung website: https:/www.diw.de/documents/publikationen/73/diw_01.c.513261.de/dp1502.pdf Brzozowski, M., Gervais, M., Klein, P., & Suzuki, M. (2010)
143、. Consumption, income, and wealth inequality in Canada. Review of Economic Dynamics, 13(1), 52-75. Canadian Business (2006). Rich 100 Methodology. Retrieved from Internet Archive website: https:/web.archive.org/web/20060318021430/http:/ Canadian Business (2016). Canadas Richest People: The Complete
144、Top 100 Ranking (2017). Retrieved from https:/ Catherine, S., Miller, M., & Sarin, N. (2020). Social Security and Trends in Inequality. Manuscript in progress. Retrieved from the SSRN website: https:/ Chakraborty, R., Kavonius, I. K., Prez-Duarte, S., & Vermeulen, P. (2019). Is the Top Tail of the W
145、ealth Distribution the Missing Link between the Household Finance and Consumption Survey and National Accounts?. Journal of Official Statistics, 35(1), 31-65. Davies, J. (1993). The Distribution of Wealth in Canada. Research in Economic Inequality, 4(1), 159-180. Davies, J., & Shorrocks, A. (1999).
146、The Distribution of Wealth. In A. B. Atkinson and F. Bourguignon (Eds.), Handbook of Income Distribution: Volume 1 (pp. 605-675). New York, NY: North-Holland. Davies, J., Shorrocks, A., & Lluberas, R. (2018). Global Wealth Databook 2018. Retrieved from the Credit Suisse website: https:/www.credit- D
147、avies, J., & Di Matteo, L. (2020). Long Run Canadian Wealth Inequality in International Context. Review of Income and Wealth. Advance online publication. https:/doi.org/10.1111/roiw.12453 Estimating the top tail of the family wealth distribution in Canada 23 Gabaix, X., & Ibragimov, R. (2011). Rank
148、1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents. Journal of Business & Economic Statistics, 29(1), 24-39. Gu, W., & Wong, A. (2010). Estimates of Human Capital in Canada: The Lifetime Income Approach (Statistics Canada Catalogue no. 11F0027M No. 062). Retrieved from https:/www150.s
149、tatcan.gc.ca/n1/en/pub/11f0027m/11f0027m2010062-eng.pdf?st=5C89HjQP Kennickel, A., & Woodburn, R. L. (1997). Consistent Weight Design for the 1989, 1992 and 1995 SCFs, and the Distribution of Wealth (Working paper). Retrieved from the Federal Reserve website: https:/www.federalreserve.gov/econresdat
150、a/scf/files/wgt95.pdf Kennickel, A., & Woodburn, R. L. (1997). Consistent Weight Design for the 1989, 1992 and 1995 SCFs, and the Distribution of Wealth (Working paper) Supplemental material. Retrieved from the Federal Reserve website: https:/www.federalreserve.gov/econresdata/scf/files/wgt95app.pdf
151、 MacDonald, D. (2018). Born to Win: Wealth concentration in Canada since 1999. Retrieved from the Canadian Centre for Policy Alternatives website: https:/www.policyalternatives.ca/sites/default/files/uploads/publications/National%20Office/2018/07/Born%20to%20Win.pdf Ogwang, T. (2011). Power laws in
152、top wealth distributions: evidence from Canada. Empirical Economics, 41(2), 473-486. Parliamentary Budget Officer (2019a). Cost Estimate of Election Campaign Proposal Net Wealth Tax. Retrieved from https:/www.pbo-dpb.gc.ca/web/default/files/Documents/ElectionProposalCosting/Results/32630202_EN.pdf P
153、arliamentary Budget Officer (2019b). Evaluation of Election Proposal Costing 2019. Retrieved from https:/www.pbo-dpb.gc.ca/web/default/files/Documents/Reports/ADM001/ADM001_en.pdf Saez, E., & Zucman, G. (2019, January 18). Letter to Senator Elizabeth Warren.Retrieved from https:/gabriel-zucman.eu/fi
154、les/saez-zucman-wealthtax-warren.pdf Statistics Canada (2017). Quarterly Demographic Estimates: October to December 2016 (Catalogue no. 91-002-X). Retrieved from https:/www150.statcan.gc.ca/n1/en/pub/91-002-x/91-002-x2016004-eng.pdf?st=6pE9ffng Statistics Canada (2018a). Survey of Financial Security
155、: Detailed information for 2016. Retrieved from https:/www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&SDDS=2620 Statistics Canada (2018b). 2016 Survey of Financial Security: Public Use Microdata User Guide. Retrieved from Statistics Canadas Survey of Financial Security: Public Use Microdata Fil
156、e. Statistics Canada (2018c). User Guide: Canadian System of Macroeconomic Accounts (Catalogue no. 13-606-G). Retrieved from https:/www150.statcan.gc.ca/n1/en/catalogue/13-606-G Estimating the top tail of the family wealth distribution in Canada 24 Statistics Canada (2019a). Distributions of Househo
157、ld Economic Accounts, estimates of asset, liability and net worth distributions, 2010 to 2018, technical methodology and quality report (Catalogue no. 13-604-M2019001). Retrieved from https:/www150.statcan.gc.ca/n1/en/pub/13-604-m/13-604-m2019001-eng.pdf?st=NR7VbCfH Statistics Canada (2019b). Survey
158、 of Financial Security. Retrieved from https:/www.statcan.gc.ca/eng/survey/household/2620 Statistics Canada (2020a, February 28). Gross domestic product, income and expenditure, fourth quarter 2019 Catalogue no. 11-001-X. Retrieved from https:/www150.statcan.gc.ca/n1/en/daily-quotidien/200228/dq2002
159、28a-eng.pdf?st=SjHJHBRW Statistics Canada (2020b). National Balance Sheet Accounts Table: 36-10-0580-01. Retrieved from https:/www150.statcan.gc.ca/t1/tbl1/en/cv.action?pid=3610058001 Statistics Canada (2020c). Quarterly Demographic Estimates: October to December 2019 (Catalogue no. 91-002-X). Retri
160、eved from https:/www150.statcan.gc.ca/n1/en/pub/91-002-x/91-002-x2019004-eng.pdf?st=CxSrE1dx Vermeulen, P. (2016). Estimating the Top Tail of the Wealth Distribution. The American Economic Review, 106(5), 646-650. Vermeulen, P. (2018). How Fat is the Top Tail of the Wealth Distribution?. Review of I
161、ncome and Wealth, 64(2), 357-387. Wealth-X (2017). World Ultra Wealth Report 2017. Retrieved from https:/ Weil, D. (2015). Capital and Wealth in the Twenty-First Century. The American Economic Review, 105(5), 34-37. Estimating the top tail of the family wealth distribution in Canada 25 1 Parliamenta
162、ry Budget Officer (2019b). Over four months leading up to the 2019 federal election, PBO costed over 200 electoral proposal requests from political parties. 2 Parliamentary Budget Officer (2019a). More specifically, PBO was requested to estimate the revenues from “introducing an annual net wealth ta
163、x on Canadian resident economic families equal to 1% of net wealth above $20 million” for which “all asset and liabilities will be included in the net wealth tax base, except wealth won in lotteries”. 3 This definition is the same as that in the Survey of Financial Security (Statistics Canada, 2018b
164、) and forms the statistical foundation of PBOs modelling in this report. For the purposes of this report, the definition applies equally to the terms “net worth” and “wealth”, which are used interchangeably. 4 There is an emerging literature on whether to include non-marketable forms wealth in the e
165、stimation of household wealth and wealth shares and, if so, how. Weil (2015) describes human capital and public transfer wealth as the two most quantitatively important forms of “wealth-like objects” that are not captured by measures of market wealth. Catherine et al. (2020) focus on the public tran
166、sfer wealth; they develop an approach to incorporate Social Security wealth to the measurement of household wealth in the U.S. They find that this addition attenuates increases in wealth inequality since 1989 and reduces top wealth shares compared with other recent literature. Though these other for
167、ms of wealth, due to their non-marketable nature, may be less tangible and difficult to measure, they also represent significant stores of value in Canada. Gu and Wong (2010) produced estimates for human capital wealth in Canada using a lifetime earnings approach; they found that in 2007, the stock
168、of human capital wealth was $16.4 trillion. By comparison, the (marketable) net worth of the household sector in that same year, as recorded by the National Balance Sheet Accounts (NBSA), was only $6.0 trillion (Statistics Canada, 2020b). Social security also represents a significant store of value
169、in Canada. The NBSA includes in its social security funds sub-sector the Canada Pension Plan (CPP) and Quebec Pension Plan (QPP) (Statistics Canada, 2018c). At year-end 2019, the net worth of this sector was valued at $0.5 trillion (Statistics Canada, 2020b). The NBSA does not accord this net worth
170、to the household sector, but rather to the general government sector. Other social protection “pay-as-you-go” programs, such as federal Old Age Security (OAS) and the Guaranteed Income Supplement (GIS), are not included in the NBSAs social security sub-sector because those programs do not hold accum
171、ulated assets; however, even these transfer programs arguably constitute a form of wealth for households (Catherine et al., 2020). 5 Canadas GDP at market prices in the fourth quarter 2019 was $2.3 trillion (Statistics Canada, 2020a). Notes Estimating the top tail of the family wealth distribution i
172、n Canada 26 6 The concept of a “family” in this report is equivalent to the concept of a “family unit” in Statistics Canada (2018b). This includes economic families and or a person not in an economic family (unattached individual). Statistics Canada (2018b) defines an economic family as “a group of
173、two or more persons who live in the same dwelling and are related to each other by blood, marriage, common law or adoption.” It defines a person not in an economic family as “a person living either alone or with others to whom he or she is unrelated, such as roommates or a lodger.” 7 This wealthiest
174、 observation in the 2016 SFS PUMF represents 965 economic families in the general population. 8 This analysis is based on Statistics Canadas Survey of Financial Security Public Use Microdata, 2016, which contains anonymous data collected in the Survey of Financial Security. All computations on these
175、 microdata were prepared by the Parliamentary Budget Officer (PBO). The responsibility for the use and interpretation of these data is entirely that of the PBO. 9 For more information, see the Survey of Financial Security: Public Use Microdata User Guide, 2016 (Statistics Canada, 2018b). 10 For more
176、 information, see the Canadian System of Macroeconomic Accounts User Guide (Statistics Canada, 2018c). 11 2016 Q4 is the quarter corresponding most closely to the 2016 SFS collection period. According to Statistics Canada (2019b), the 2016 SFS was collected between 9 September 2016 and 6 December 20
177、16. In addition, as stated in the main text, CBs Richest People List was also published in 2016 Q4 (December 2016). 12 For more information, see CBs Rich 100 methodology (Canadian Business, 2006). 13 Auten & Splinter (2019) demonstrate the importance of making assumptions regarding the evolution of
178、family composition when estimating top income shares over time. The authors data shows differential changes to family composition across the income distribution (e.g., outside the top of the distribution, there is a declining marriage rate, declining family size, and increasing numbers of single-par
179、ent households). All things being equal, such differential changes to family composition over time can be expected to cause changes in the distribution of income among families. It would not be surprising to find that differential changes to family composition can also affect top wealth shares. 14 G
180、rowth in the number of families was approximated by the growth rate in the population reported in Statistics Canadas Quarterly Demographic Estimates between 2016 Q4 and 2019 Q4. The approximation was necessary because the number of economic families in 2019 Q4 was not available at the publication da
181、te. The annual growth rates of the population and of the number of economic families have been within 0.3 per cent of each other since 2012. 15 Statistics Canada (2019a) provides an excellent exposition of the conceptual differences between the SFS and the NBSA. 16 Financial assets were calculated u
182、sing employer pension plans valued on a termination basis, rather than a going concern basis. Statistics Canada (2018b) provides a helpful description of the distinction between the two valuation methods. Estimating the top tail of the family wealth distribution in Canada 27 17 Variables were placed
183、 according to the mapping presented in Statistics Canada (2019a), except that PBO retained the value of collectibles in the SFS PUMF. 18 Vermeulen (2016) posits that this adjustment procedure tends to disproportionately increase the wealth of wealthier households, since national wealth surveys tend
184、to underreport financial assets and financial assets represent a higher share of richer families portfolios relative to poorer ones. This dynamic also occurs in the Canadian data. 19 An approach that leverages data from household wealth surveys and rich list data to estimate the top tail of the fami
185、ly wealth distribution is used, among others, in Davies (1993), Bach et al. (2014), Bach et al. (2015), Vermeulen (2016), Davies et al. (2017), Vermeulen (2018), Chakraborty et al. (2019), and Davies and Di Matteo (2020). 20 Vermeulen (2018) develops a Monte Carlo study to demonstrate the utility of
186、 adding rich lists when estimating top tail. The results show that the addition of a rich list to survey data in the regression to estimate Pareto parameters causes the interpolated wealth tail to be estimated with an upward or downward bias of only 0.01. 21 Davies and Di Matteo (2020) provide a hel
187、pful discussion on the differences between the Forbes list and Canadian Business Richest People List and present a comparison of the entries from each list. 22 Bach et al. (2014), Bach et al. (2015), and Davies and Di Matteo (2020) similarly undertake rich list cleaning procedures before incorporati
188、ng rich list data into national wealth survey microdata. 23 Economic families with negative net worth in the SFS PUMF are not presented in Figure A2-1. According to the SFS PUMF, there were 878,482 economic families with negative net worth in 2016. 24 In non-formulaic terms, the Pareto power law as
189、applied to the family wealth distribution asserts that the wealth of the th wealthiest family in the population is inversely proportional to its rank. 25 Canadian Business (2006). The methodology was retrieved using the internet archiving website “Wayback Machine”. 26 Though the SFS Master File is n
190、ot top-coded, the weighting procedure of the survey methodology may reduce the weights of some high-net-worth families even in the Master File. Statistics Canada (2018b) discloses, as part of the weighting procedure, that “influential observation are identified, and weights are reduced for a small n
191、umber of extreme observations.” 27 Vermeulen (2018) explains that it is unclear where the Pareto-distributed top tail of the wealth distribution starts. He addresses the uncertainty by presenting estimates using six different thresholds ranging from 500,000 to 10 million. 28 Disclosed to PBO in corr
192、espondence with analysts from the SFS Team at Statistics Canada. 29 The 2016 SFS PUMF includes 638 observations with wealth greater than $3 million. By contrast, no country in Vermeulen (2018) using geographic or income-stratified geographic information to over-sample high-net-worth families had more than 100 observations with wealth greater than 2 million. Estimating the top tail of the family wealth distribution in Canada 28 30 This value of falls within Davies and Di Matteos (2020) range of estimates to perform top tail imputation on historical Canadian wealth survey data.