## wp18171 - Appendix can be found here ## Source details **Canonical URL:** [wp18171 - Appendix can be found here](https://www.imf.org/-/media/files/publications/wp/2018/wp18171.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2018/wp18171.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2018/wp18171.pdf.json) --- ### I. Introduction — purpose and motivation - Goal: provide a systematic characterization of whether returns to wealth have an individual component, whether that component persists over time, whether it correlates with wealth, and whether it shows intergenerational persistence. - Data: administrative tax records of capital income and wealth stocks for all taxpayers in Norway for 2004-2015 (with 2004 used as initial conditions). - Motivation from literature: - Heterogeneity in returns to wealth can generate a thick right tail in the wealth distribution (Benhabib et al., 2011; Gabaix et al., 2016). - Need for long, well-measured panel data covering whole wealth distribution and multiple generations. ### II. Data sources, coverage, and variable definition - Longitudinal administrative coverage: - Every Norwegian resident from 1967 to 2015 with demographics and geographic identifiers; linked detailed registries for 2004-2015: tax records, shareholder registry, private business balance sheets, housing transaction registry, deposit and loan account data. - Asset and liability values measured as of December 31 each year. - Advantages: - Universal coverage including very top of distribution; most components third-party reported without top-/bottom-coding; long panel (2004-2015) enabling within-person persistence and parent-child matching; inclusion of private business holdings. - Shortcomings: - (a) assets and liabilities valued at an annual frequency; (b) market value of private businesses may be mismeasured; (c) private pension wealth data absent. - Sample selection and cleaning: - Dropped people with less than USD 500 in financial wealth (about NOK 3000). - Trimmed returns at top and bottom 0.5% each year; focus on ages 20–75; leverage above 99th percentile winsorized. - Asset grouping: - Safe assets w_s: cash/bank deposits and money market/bond funds and bonds. - Risky assets w_m: listed stocks (direct w_m,l,d or mutual fund w_m,l,i), unlisted shares w_m,u, risky assets abroad w_m,x. - Housing w_h: principal and secondary homes (imputed via hedonic model). - Definitions: - Financial wealth F_it = w_s_it + w_m_it. - Net worth N_it = G_it − b_it where G_it = F_it + w_h_it. ### III. Measures of returns and key descriptive statistics - Two return measures: - Return to financial wealth (average): ̃r_F_it = y_F_it / F_it where y_F_it sums income from safe and risky assets (explicitly including dividends, capital gains, mutual fund yields, private business distributed dividends and retained profits). - Return to net worth: ̃r_N_it = (y_F_it + y_h_it − y_b_it) / G_it; y_h_it = d_h_it + g_h_it with imputed rent fraction 2.88%. - Baseline (annual average-of-beginning-and-end stocks): - r_F_it = y_F_it / ((F_it + F_it+1)/2). - r_N_it = (y_F_it + y_h_it − y_b_it) / ((G_it + G_it+1)/2). - Real, cross-sectional realized return summary (value-weighted, pooled 2005–15): - Financial wealth: average real return 4.2%, standard deviation 14.4% (value-weighted mean 0.0419; St.dev. 0.1435). - Net worth: average real return 4.1%, standard deviation 8.3% (value-weighted mean 0.0406; St.dev. 0.0825). - After-tax mean return to net worth: 0.0366; St.dev.: 0.0746. - Percentile differences and patterns: - Return to financial wealth increases with financial wealth percentile; 90th–10th percentile difference roughly 260 basis points. - Return to net worth negative for households with negative net worth; for positive net worth returns rise with position but more slowly due to cost of debt. - Difference between average return at 90th and 10th percentiles of net worth roughly 17 percentage points. ### IV. Decomposition of heterogeneity and empirical model - Sources of heterogeneity in a given year: - Observables (risk exposure, scale), idiosyncratic transitory variations, persistent unobservable component. - Empirical model: - Panel regression r^x_{i(g)t} = X'_{i(g)t} β^x + u^x_{i(g)t} with u^x_{i(g)t} = f^x_{i(g)} + e^x_{i(g)t}. - Controls: lagged wealth percentiles (scale), portfolio shares, stock-portfolio average β, time effects, demographics, education, homeownership, employment, county dummies. - Individual fixed effect f^x_{i(g)} captures persistent unobserved heterogeneity. - Explained variability: - Observables alone explain roughly one-third of variability in returns to financial wealth or net worth. - Adding individual fixed effects increases explained variability by 23% for financial wealth and by 49% for net worth. - Distribution of fixed effects (balanced panel, demeaned): - Financial wealth fixed effects: standard deviation 3.6%, 90th–10th percentile difference 5.1 percentage points, skewness 3.66, kurtosis 24.78. - Net worth fixed effects: standard deviation 5.4%, 90th–10th percentile difference 5.5 percentage points, skewness -6.31, kurtosis 101.59. ### V. Estimation results — asset premia, demographics, and fixed effects - Returns to financial wealth (pooled OLS, ~31 million observations): - Estimated excess returns (relative to deposits/cash): - Private businesses: premium 8 percentage points. - Directly held listed stocks: premium 2 percentage points. - Mutual funds: premium 1.7 percent. - Bonds: premium 1.3 percent. - Portfolio magnitudes: - Increasing listed stocks share by 30 percentage points → increase in return ≈ 63 basis points. - Increasing private businesses share by 30 percentage points → increase in return ≈ 248 basis points. - Stock-portfolio β: one standard deviation increase in β increases returns by 4.5 basis points; β significant but adds little to explained variation. - Education effects: - An additional year of schooling raises returns by 1.6 basis points. - Completing college: 6.4 basis points higher average return versus high school. - Economics/business education: 10 basis points higher returns. - Combined: economics college graduates enjoy systematic difference of 16 basis points, which compounds to 4.3% more wealth at retirement for one dollar saved every year over 40 years (conditioning on similar wealth and portfolio composition). - Adding individual fixed effects raises adjusted R2 to 0.394 (23% increase over specification without fixed effects). - Returns to net worth: - Housing share strongly positive: investing with deposits a house worth 50% of initial gross assets increases average return on net worth by 360 basis points (0.5×7.2%). - Leverage effects negative and highly significant: - If house purchase fully financed with debt (leverage increase 0→0.33), average return on net worth increases by 82.5 basis points (0.33×7.2% − 0.33×4.7%). - Adding β has small effect; interacting asset shares with time dummies increases fit slightly (adjusted R2 up to 0.36). - Adding individual fixed effects increases adjusted R2 by 49% (implies important persistent component). - Strong positive Spearman rank correlation 38% between fixed effects for financial wealth and net worth. - Persistent heterogeneity summary: - Fixed-effect dispersion accounts for roughly 29% of variance in unobserved component of returns (var(f)/var(u) ≈ 0.29 in baseline). ### VI. Stylized facts, scale dependence, and robustness - Scale dependence: - Returns and heterogeneity rise monotonically with wealth percentile and accelerate in top decile; top decile dominated by private equity heterogeneity. - Scale dependence persists within asset classes (safe vs risky; private equity and direct stockholding). - Individual Sharpe ratio (2005–15) rises monotonically with 2004 wealth percentile; definition: - S_i = (∑_{t=1}^T r̂_it / T) / sqrt( (∑_{t=1}^T r̂_it^2 / T) − (∑_{t=1}^T r̂_it / T)^2 ) where r̂_it = ω^a_it (r^F_it − r^s_t). - Returns to net worth pattern (pooled 2005–15): - Below 20th percentile: net worth negative, returns non-monotonic; very bottom can have return around -20% due to high leverage. - Above 20th percentile: returns grow with wealth, concave then convex above roughly 80th percentile. - Compared to 10th percentile, the top 90th percentile average return on net worth is 17 percentage points higher. - Robustness checks and measurement concerns: - Snapshot timing addressed by averaging beginning and end-of-year wealth. - Private business valuation: - Dropping private equity holders yields virtually no differences in net worth returns; moderate differences in financial wealth returns at very top. - Applying market-to-book multipliers (industry-specific; average 1.24) adjusts top returns by ≈100 basis points downward for financial wealth; negligible elsewhere. - Unobserved pension wealth: occupational pensions ~12% of aggregate household gross wealth in 2015; extended measures discussed in OA. - Saving-rate bias: propensity to save out of wealth declines with wealth; rank correlation (s_it/w_it, w_it) = -0.19 (p-value <1%); if bias exists, likely downward. - Before-tax vs after-tax: - Taxes smooth returns: bottom benefit from interest deductibility; top pay more wealth tax. - Wealth tax rates over sample: 2005–08 progressive (0.9% and 1.1% brackets); after 2008 flat 1.1% (reduced to 1% in 2014 and 0.85% in 2015) above rising cutoff. - Capital income tax: 28% in 2006–12, 27% in 2013, 25% in 2014. ### VII. Micro evidence on ability, deposits, and Sharpe ratios - Sharpe ratio regressions (Table 7; N = 1,663,694 whole sample; N = 1,247,940 excluding private equity owners): - Wealth percentile in 2004: coefficient 0.0052 (Whole sample), 0.0059 (No P.E. owners). - Year of schooling: 0.0403 (Whole); quadratic term negative (-0.0009). - Economics/Business degree: 0.0401 (Whole), 0.0543 (No P.E. owners). - Adjusted R^2: 0.125 (Whole), 0.0869 (No P.E. owners). - Interpretation: higher education, economics/business degree, and wealth percentile predict higher risk-adjusted returns; correlation between Sharpe ratio and individual fixed effect = 0.52. - Deposits evidence (2005–15 universe of deposit accounts): - Deposits up to 2 million NOK insured; returns bear no risk. - Returns on deposits positively correlated with years of education and economics/business degree; increase with deposit size; decrease with account experience. - Controls explain 53% of variation; adding individual fixed effects increases fit by 14%. - Standard deviation of individual-level deposit returns 2.6%; bank fixed effects SD 0.9%. - High-education/high-fixed-effect individuals deposit at higher-return banks, consistent with persistent ability to obtain better returns even on risk-free instruments. ### VIII. Persistent heterogeneity — subgroup patterns and taxation effects - Subgroup fixed-effect dispersion: - Business owners: fixed-effect SD 6.4 vs non-owners SD 1.6 (financial-wealth returns). - Persistent component of returns increases with wealth percentile; sharper for financial wealth. - Debt-holders: distribution shifts left with longer left tail. - Participants in risky asset markets: higher and more dispersed fixed effects. - Individuals with economics/business degree: less volatile fixed-effect distribution. - Taxation: - After-tax returns on net worth reduce persistent heterogeneity: SD falls from 5.4% to 3.6%. - Relation between persistent component and wealth is flatter for net-of-tax returns. - Interpretation of fixed effects: - Possible components: persistent risk tolerance, scale effects, financial sophistication/access. - Evidence supports coexistence: returns respond to portfolio risk exposure and β; scale matters; education matters conditional on risk and wealth; fixed effects materially increase explained variation. ### IX. Intergenerational persistence and mobility - Parent-child linkage (over 11 million father-child pairs): - Estimated persistence f_x_i(g) = ρ f_x_i(g−1) + η_x_i(g). - Intergenerational rank correlations (regressions): - Financial wealth percentile regression slope ≈ 0.3; return to financial wealth percentile slope ≈ 0.11. - Net worth wealth slope ≈ 0.16; return slope ≈ 0.15. - Fixed-effect persistence: - Estimated f_i(g) = const + 0.14 f_i(g−1) (example characterization). - Corr(f_i(g), f_i(g−1)) reported: 0.142 (financial wealth), 0.058 (net worth), 0.064 (after-tax net worth). - Controls (wealth, education) reduce slopes for financial-wealth returns but positive and significant correlations remain. - Summary: substantial within-generation persistence and heterogeneity; milder but positive intergenerational persistence in returns, especially via the permanent (fixed-effect) component. ### X. Implications for measurement, modeling, and taxation - Measurement: - Capitalizing capital income using average rates may overstate wealth concentration when returns heterogeneous and correlated with wealth. - Modeling wealth inequality: - Evidence supports models where heterogeneity in returns, intergenerational persistence (type dependence), and scale dependence are important determinants of thick right tail of wealth distribution. - Comparisons: Benhabib et al. (2017) calibration average return 3.0%, cross-sectional SD 2.7%, intergenerational persistence 0.17; slope of relation between wealth percentile and average fixed effect ~0.01 in Benhabib et al., comparable to 0.012 estimated here. - Tax policy: - In presence of heterogeneous returns, switching capital income tax to wealth tax widens after-tax heterogeneity in returns: capital income tax disproportionately reduces after-tax return for high-return individuals, whereas wealth tax spreads burden differently. - Variance decomposition of persistent vs transitory heterogeneity provides empirical inputs for assessing optimal capital income taxation. - Amplifying mechanisms: - Assortative mating by returns and intra-household wealth management can amplify heterogeneity and wealth concentration. - Life-cycle heterogeneous-return models allowing heterogeneity in human and non-human capital and preferences required to quantify relative importance of inequality sources. *Source: wp18171 - Appendix can be found here (IMF Working Paper PDF content provided).* ### Appendix can be found here ### wp18171 - Appendix can be found here ### I. Introduction — purpose and motivation - Goal: provide a systematic characterization of whether returns to wealth have an individual component, whether that component persists over time, whether it correlates with wealth, and whether it shows intergenerational persistence. - The study uses administrative tax records of capital income and wealth stocks for all taxpayers in Norway for 2004-2015 (with 2004 used as initial conditions). - Key motivations from the literature: - Heterogeneity in returns to wealth can generate a thick right tail in the wealth distribution (Benhabib et al., 2011; Gabaix et al., 2016). - Need for long, well-measured panel data covering the whole wealth distribution and multiple generations to document persistence and scale dependence. ### II. Data sources and variable definition - Data coverage and linkages: - A longitudinal database covering every Norwegian resident from 1967 to 2015 with demographics (gender, age, marital status, educational attainment) and geographic identifiers. - For 2004-2015, linked registries include: (a) tax records with detailed income, assets, liabilities; (b) shareholder registry for listed and unlisted shares; (c) balance sheet data for private businesses; (d) housing transaction registry; (e) deposit and loan account data with bank identifier, amount, and interests received/paid. - Asset and liability values measured as of December 31 each year. - Advantages emphasized: - Universal coverage including individuals at the very top of the wealth distribution. - Most income and wealth components reported by third parties and recorded without top- or bottom-coding. - Long panel dimension (2004-2015) allowing within-person persistence analysis and matching parents to children for intergenerational study. - Inclusion of private business holdings as well as listed stocks and housing. - Shortcomings noted: - (a) assets and liabilities valued at an annual frequency; - (b) the market value of private businesses may be mismeasured; - (c) private pension wealth data is absent. - Additional detail: mapping between capital income tax components and specific asset categories is provided in the Online Appendix (OA). ### III. Measures of returns and key descriptive statistics - Two broad return measures considered: - Return to financial assets (reflects portfolio composition and risk/return considerations). - Return to net worth (dominated by housing, more consumption-oriented). - Sample period(s) referenced: - Data span 2004-2015 with analysis focusing on 2005-15. - Cross-sectional realized return summary (value-weighted averages and dispersion): - Financial wealth: average real return 4.2%, standard deviation 14.4%. - Net worth: average real return 4.1%, standard deviation 8.3%. - Percentile differences and patterns: - Return to financial wealth increases steadily with position in the financial wealth distribution; the return difference between the 90th and the 10th percentile is roughly 260 basis points. - Return to net worth is negative for households with negative net worth (reflecting the cost of debt); for households with positive net worth, average returns rise with net worth position at a slower pace than for financial wealth due to the counteracting effect of the cost of debt. - The difference between the average return at the 90th and 10th percentiles of net worth is roughly 17 percentage points. ### IV. Decomposition of heterogeneity and estimation approach - Sources of heterogeneity in returns in any given year: - Differences in observables (e.g., risk exposure, wealth/scale). - Idiosyncratic transitory variations (good or bad luck). - Persistent unobservable component (critical for theories of wealth concentration). - Empirical model features: - Panel data statistical model for returns to wealth including an individual fixed effect. - Controls: lagged wealth (“scale”), shares invested in various asset types, degree of stock portfolio diversification (“risk exposure”), time effects, and demographics. - Individual fixed effect captures unobserved persistent heterogeneity in returns controlling for scale and risk-taking. - Explained variability results: - Observable characteristics alone explain roughly one-third of the variability in returns to financial wealth or net worth. - Adding individual fixed effects increases explained variability in returns to financial wealth by 23% and in returns to net worth by 49%. - Distribution of individual fixed effects: - Standard deviation of fixed effects: 3.6% for financial wealth; 5.4% for net worth. - Robustness and interpretation: - Persistent heterogeneity remains statistically significant and quantitatively large even for deposit accounts with universal deposit insurance (where risk considerations should not matter). - Interpretation: persistent traits (financial sophistication, ability to process and use financial information, entrepreneurial managerial ability) can generate persistent differences in returns to wealth that are as relevant as differences in risk exposure or scale. ### V. Stylized facts and empirical patterns emphasized - Returns to wealth are heterogeneous across individuals. - Returns covary with the level of wealth: - Positive correlation between financial wealth and its return, with substantial acceleration in the top decile. - Net worth returns show a different profile due to debt costs and housing composition. - Persistence: - There exists a persistent unobserved component in individual returns that contributes materially to cross-sectional dispersion. - Intergenerational patterns (overview previewed here; detailed results in later sections): - Returns to wealth are correlated across generations, though there is evidence of mean reversion at the top. - Some intergenerational correlation is explained by scale dependence, but a positive and significant correlation remains after controlling for wealth or education. ### VI. Contribution relative to prior work - Distinctions relative to Bach et al. (2015) and other literature: - Focus on actual, realized returns to wealth rather than expected returns from standard finance models. - Analysis spans the entire wealth distribution (including those with negative net worth) rather than focusing only on the top 60%. - Use of long panel data to study within-person persistence and intergenerational persistence — the paper is the first to provide systematic evidence of persistence in returns within and across generations. - Implication for modeling wealth inequality: - Evidence supports models where heterogeneity in returns and intergenerational persistence (type dependence) and scale dependence (positive correlation of returns with wealth) are important determinants of the thick right tail of the wealth distribution. *Source: wp18171 - Appendix can be found here (IMF Working Paper PDF content provided).* ### 2.1 Administrative wealth and capital incomerecords ### 2.1 Administrative wealth and capital income records ### Data sources, coverage, and taxation - Norwegian households are subject to both an income tax and a wealth tax. - Annual tax record data are available since 1993; the analysis uses data starting in 2004 because the shareholder registry and other registries are only available since 2004. The typical sample period is 2005–2015, with 2004 used as initial condition. - The collection of tax information is mostly done through third parties: employers report earned labor income; financial intermediaries (banks, stock brokers, insurance companies, etc.) report the value of assets and income earned on these assets. - For traded assets, the value reported is the market value. - Net wealth in excess of an exemption threshold is taxed at a flat rate of around 1% during the sample period. The exemption threshold increased over time and was in the later years around NOK 1.5 million for a married couple (and half that for a single person). Household assets are reported and recorded even if they fall short of this threshold. - Certain assets were valued at a discount in certain years when calculating taxable wealth (example: stocks were valued at 85% of market value in 2007). Discounted values are adjusted back to market values before constructing household wealth. - Individuals in a household are taxed jointly for wealth taxation (i.e., married couples) and separately for income tax purposes. - The fact that financial institutions supply information directly to the tax authority greatly reduces the scope for tax evasion. ### Sample selection and data cleaning - Dropped people with less than USD 500 in financial wealth (about NOK 3000) to reduce errors from highly volatile reported stocks. - Trimmed the distribution of returns in each year at the top and bottom 0.5% and dropped observations with trimmed returns. - Focus on Norwegian population aged between 20 and 75 (results robust to including younger or older samples). - For legibility, leverage levels above the 99th percentile in each year are winsorized. ### Wealth aggregates: asset grouping and measurement - Assets grouped into three broad categories: safe assets (w_s), risky assets (w_m), and housing (w_h). - Safe assets (w_s) = (a) cash/bank deposits (domestic or foreign), and (b) money market funds, bond mutual funds, and bonds (government and corporate). - Risky assets (w_m) = (a) market value of listed stocks w_m,l (held directly w_m,l,d or indirectly through mutual funds w_m,l,i), (b) value of shares in private businesses and other unlisted shares w_m,u, and (c) value of risky assets held abroad and outstanding claims and receivables w_m,x. - Listed stocks are reported at market value. The market value of directly held stocks w_m,l,d_t is defined as w_m,l,d_t = ∑_k p_k,12/31,t s_k_it, where s_k_it are shares held at 12/31 of year t and p_k,12/31,t the price at the same date. The market value of mutual funds w_m,l,i is directly available from tax records. - Value of unlisted stocks is obtained as the product of the equity share held in the firm and the “assessed value” of the firm reported by the private business to the tax authority. - The (log) assessed value is strongly correlated with the firm (log) book value (correlation 0.88). - In more than 50% of cases, the assessed value exceeds the book value. - Medium- to large-sized firms (turnover above NOK 5 million, or USD 500k) are required to have audited balance sheets. - Housing stock w_h includes principal residence and secondary homes. House values are imputed by merging transaction data from the Norwegian Mapping Authority (Kartverket), land registration, and the population Census, and using a hedonic model for price per square meter (house characteristics, time dummies, location dummies and interactions). - Outstanding debt from tax records equals the sum of student debt, consumer debt, and long-term debt (mortgages and personal loans). Separation of debt types uses an administrative registry on loan and deposit accounts with lender ID, loan balances, and interests paid. - Student debt identified by Norwegian State Education Loan Fund lender ID. - Consumer loans estimated as sum of loans from intermediaries specializing in consumer lending and loans with interest rates persistently above 10% (an observed lower bound of interest-bearing loans in the consumer lending sector over the sample period). - Excluded assets: vehicles, boats, cabins, and real estate abroad (these represent roughly 5% of total household assets). Other unobserved assets include collectibles, art, wine, jewelry, etc., when not reported. ### Definitions of wealth measures and composition findings - Financial wealth F_it = w_s_it + w_m_it. - Net worth N_it = G_it − b_it where G_it = (F_it + w_h_it) is gross wealth and b_it is outstanding debt. - Composition findings (Panel A/B of Table 1; descriptive highlights): - Safe assets dominate the portfolio of people below median wealth. - Public equity (especially through mutual funds) gains weight among people above the median and below the top 1%. - The share in private businesses strongly increases above the 95th percentile and is close to 90% for the top 0.01%. - Bottom 20% of the net worth distribution has negative net worth on average due to debt exceeding assets. - Housing is the largest asset for most people; only at the very top of the net worth distribution do risky financial assets replace housing as preeminent. - Average leverage (debt scaled by gross assets) reported by selected fractiles, distinguishing consumption debt, student debt, and long-term debt. ### Measuring returns to wealth: definitions and computation - Two return measures: - Return to financial wealth (average): - ̃r_F_it = (y_s_it + y_x_it + y_l,i_it + (d_l,d_it + g_l,d_it) + (d_u_it + g_u_it)) / F_it = y_F_it / F_it (equation (1) in source) - Denominator is financial wealth measured at the beginning of year t. Numerator sums income from safe and risky assets accrued in year t: - y_s_it: income on safe assets (interest income on domestic and foreign deposits and bond yields). - y_x_it: yields from risky assets held abroad and outstanding claims and receivables. - y_l,i_it: yields from mutual funds. - d_l,d_it: dividends on directly held listed shares (available from the Shareholder Registry). - g_l,d_it: accrued capital gains and losses on directly held listed shares. - d_u_it: distributed dividends from private equity (available from the Shareholder Registry). - g_u_it: individual share of the private business’ retained profits. - Return to net worth: - ̃r_N_it = (y_F_it + y_h_it − y_b_it) / G_it (equation (2) in source) - Compared with return to financial wealth, numerator adds yield on housing y_h_it and subtracts interest payments on debt y_b_it. Dollar yield on net worth is expressed as share of gross wealth G_it (also known as ROA in accounting literature). - Yield on housing y_h_it = d_h_it + g_h_it where: - d_h_it is imputed rent net of ownership and maintenance cost. - g_h_it = Δw_h_it is capital gain/loss on housing. - Imputed rent assumed to be a constant fraction of house value estimated to be 2.88% (following Eika et al. (2017)). - Baseline measures adjust for intra-year purchases/sales by using average of beginning and end-of-year stocks: - r_F_it = y_F_it / ((F_it + F_it+1)/2) (equation (3)) - r_N_it = (y_F_it + y_h_it − y_b_it) / ((G_it + G_it+1)/2) (equation (4)) - These are the baseline measures of returns; results are similar if beginning and end-of-period wealth are weighted differently. - Returns are net of inflation (using the 2011 CPI) and gross of taxes/subsidies. Section 3.3.1 extends analysis to after-tax returns. ### Addressing measurement limitations and robustness checks - Three main limitations and approaches: 1. Snapshot timing: assets observed at end of each period while income flows occur throughout the period. - Addressed by using average of beginning and end-of-year wealth in denominator (equations (3) and (4)). - Sample selection (dropping people with less than USD 500 in financial wealth) attenuates the issue where beginning-of-period wealth is zero but capital income positive due to saving during the year. 2. Private business tax value vs market value: - Tax-assessed values may understate market values, potentially overstating measured returns and exaggerating the slope of wealth–return relationship. - Two approaches to check sensitivity: - (a) obtain measures of returns that exclude private equity owners; - (b) apply industry-specific multipliers estimated from cases where private equity firms become public, or publicly listed firms return private (market-to-book multipliers). 3. Unobserved wealth components: - Pension wealth (state pensions, occupational pensions, individual pensions): occupational pensions represented roughly 12% of aggregate household gross wealth in 2015, but administrative data on occupational or individual pension plans and individual investment choices are not available. - An “extended” measure of return can be constructed as a weighted average of return to social security wealth and the return to (financial or net) wealth; methods discussed in OA, Section OA.1. - Assets held abroad but not reported are not observed; imputing returns is difficult without portfolio composition information. - Excluded assets with hard-to-measure returns (cars, vehicles, collectibles, art, wine, jewelry, etc.)—some are taxed and reported, others not, depending on conditions. *Source: wp18171 - 2.1 Administrative wealth and capital income records (excerpt).* ### 2.4 Some conceptual remarks ### 2.4 Some conceptual remarks ### Offshore wealth and top percentiles - Alstadsæter et al. (2017) estimate that only people above the 99th percentile have assets offshore. - For the authors' purposes, the key issue is whether offshore wealth distorts measures of gross (of tax) returns on wealth. - If wealth is held abroad mostly to profit from more rewarding investment opportunities not available at home (as argued by Zucman, 2013), then the authors' estimates are conservative for heterogeneity in returns and their correlation with wealth. - Dropping people in the top 0.5% or 1% of the wealth distribution does not affect the results (the authors note that all wealth offshore seems to be sitting in these top fractions according to Alstadsæter et al., 2017). ### Government Pension Fund Global (GPFG) as national wealth - The GPFG market value (2017) is 8,400 billion NOK ($1,100 billion). - At face value, this corresponds to 1.6 million NOK per person ($203k). - Institutional features: - The fund is “owned by the Norwegian people” and no-one receives direct payments from the GPFG. - Each year the expected real return of the fund (formerly around 4% and recently revised to 3%) may be allocated to the government budget, yielding lower taxes or more spending and benefiting taxpayers indirectly. - If returns are used to reduce taxes, beneficiaries are mainly at the top of the wealth distribution due to high tax progressivity. - If returns fund programs for the poor, beneficiaries are mainly at the bottom. ### Unit of analysis and marital treatment - All returns statistics reported are at the individual, not the household, level. - When individuals are married, spouses are assumed to share household wealth and capital income equally (consistent with Norwegian law on equal splitting of family assets at divorce). - Implementation: per-capita household wealth and capital income are assigned to each spouse, then the return to individual wealth is computed. ### Choice of ex-post realized returns (model-free) over model-implied expected returns - The authors use ex-post realized returns to measure average returns to wealth. - Contrast with asset pricing model approach (e.g., CAPM, as used by Bach et al. (2015)): - Advantage of model approach: increased precision by relying on long time series of market returns—valuable with short individual realized-return series. - Drawbacks of model approach: - Imposes a pricing model (e.g., CAPM) and its assumptions (ability to borrow at a risk free rate, absence of trading frictions, etc.). - Expected returns attributed to an individual in a given year are affected by returns realized in future years. - Individuals holding a given asset are imputed the same average return regardless of holding period, so differences due to market timing or financial sophistication are not captured; method is biased toward attributing differences to exposure to systematic risk. - What matters for wealth accumulation (and for explaining concentration/inequality via the return heterogeneity channel) are actual, realized returns, not expected returns. - Conclusion: The ex-post realized returns approach is model-free, reflects all sources of heterogeneity across individuals relevant for generating returns to wealth, and is more appropriate for the research question linking wealth and returns. ### Pecuniary vs non-pecuniary components of returns - Ownership of assets may provide both pecuniary and non-pecuniary benefits: - Example: “socially responsible investments” provide a “consumption” return besides pecuniary return (Bollen, 2007). - Example: holding a checking account yields liquidity services (access to ATM facilities, check-writing) as non-pecuniary returns. - The paper focuses on the pecuniary component of returns for two reasons: - Estimation of non-pecuniary returns is challenging and often subjective. - Wealth accumulates over time due to pecuniary returns, and the goal is to show empirical properties of returns relevant for the relation between inequality and returns to wealth. - Caveat: some heterogeneity in pecuniary returns may reflect heterogeneity in preferences for non-pecuniary components (investors accepting lower pecuniary returns because of higher non-pecuniary returns). Even if total return is equalized in equilibrium, observable heterogeneity in the pecuniary component may persist. *Source: wp18171 - 2.4 Some conceptual remarks (PDF chapter/section).* ### Section 4, we discuss in detail various channels of influence. One simple explanation is that ### Section 4, we discuss in detail various channels of influence. One simple explanation is that ### Scale dependence of returns on financial wealth - Wealthier households have higher exposure to risk; heterogeneity in returns rises almost monotonically with wealth and accelerates in the top decile, where it is dominated by heterogeneity in the return to private equity (see Figure OA.9 in the OA). - Positive correlation between returns and wealth holds within broad asset classes: - Panel B of Figure 2 reports average returns on safe assets and risky assets separately, showing scale dependence is pervasive. - Figures OA.11 and OA.12 show scale dependence even within narrower risky asset categories (private equity and direct stockholding). - This evidence rules out that the correlation arises only because of participation costs in risky asset markets. - Individual Sharpe ratio (risk-adjusted return) for 2005-15 rises monotonically with individual wealth percentile in 2004: - Individual Sharpe ratio definition used: - S_i = (∑_{t=1}^T r̂_it / T) / sqrt( (∑_{t=1}^T r̂_it^2 / T) − (∑_{t=1}^T r̂_it / T)^2 ) - where r̂_it = ω^a_it (r^F_it − r^s_t), and (r^F_it − r^s_t) is the deviation of individual return to financial wealth from the 3-month T-bill; ω^a_it is the weight of individual assets in period t relative to the entire 2005-15 period. - Data restricted to individuals present for the entire 2005-2015 period to increase precision. - Plotting Sharpe ratio against 2004 wealth percentile eliminates reverse causality concerns (results similar if percentile averaged over 2000-2004). ### Scale dependence of returns to net worth - Panel A of Figure 4 (pooled 2005-15) shows average and median return to net worth by net worth percentiles: - Below the 20th percentile: return has a non-monotonic shape and net worth is negative. - Above the 20th percentile: return grows with wealth, first at a decreasing rate then convexly in the top two deciles. - Return to net worth decomposed as: - r^N_it = (r^f_it α + r^h_it (1−α)) − (r^{b,l}_it θ_l + r^{b,c}_it θ_c + r^{b,s}_it (1−θ_l − θ_c)) L_it - where r^f, r^h, r^{b,j} are returns to financial wealth, housing, and cost of debt of type j (long-term debtl, consumer debt c, student debts), α is share of financial wealth out of total assets, θ_j is share of type-j debt out of total debt, and L is overall leverage. - Bottom 20%: liabilities exceed assets; composition of debt shifts from long-term collateralized debt at the very bottom to uncollateralized consumer debt higher in the bottom 20%: - At the very bottom leverage is highest, implying a large negative return to overall net worth (around -20% at the very bottom). - Presence of substantial private equity wealth partly compensates via relatively high return to financial wealth. - Entrepreneurs are concentrated at the bottom: as many entrepreneurs at the bottom 1% as at the top 3% (around 50%). - Average age of entrepreneurs: bottom 20% = 39; top 20% = 53. - Transition moving up distribution: - As leverage declines, return to net worth becomes less negative. - Around the 10th-15th percentile returns to net worth decline sharply due to shift to high-rate consumer debt, shrinking housing wealth, and dominance of liquid low-return investments. - Once net worth is positive, return increases with wealth, initially concave then convex above roughly the 80th percentile. - Housing returns are more homogeneous and driven by time and location; returns to financial wealth increase with wealth. - Comparison statistic: - Compared to people in the 10th percentile of net worth, people in the top 90-th percentile have an average return on net worth that is 17 percentage points higher. ### Robustness checks - Before-tax vs. after-tax returns: - After-tax return to net worth defined as: - r^N_it = y^F_it + y^h_it − y^b_it − T_y − T_w (G_it + G_{it+1})/2 - where T_y are taxes on capital income net of deductions on debt interest, and T_w are taxes on net worth. - Taxes smooth returns: - At the bottom of the distribution after-tax return exceeds before-tax due to deductibility of interest on debt (especially mortgages). - At the top the opposite occurs due to lower incidence of debt and higher incidence of the wealth tax. - Wealth tax details over sample: - 2005-08: progressive; 0.9% on every NOK of net worth between first cutoff (150k, 200k or 350k depending on year) and second cutoff (540k), and 1.1% for every NOK above second cutoff. - After 2008: flat 1.1% (reduced to 1% in 2014 and 0.85% in 2015) on every NOK of net worth above a cutoff (rising over time from 470k to 1250k). - In computation of net worth, different components assessed at different face values (i.e., bonds at 100%, housing at 25%, etc.). - Capital income taxed at a flat rate (28% in 2006-12, reduced to 27% in 2013, and 25% in 2014). - Saving rates and potential measurement bias: - Concern: higher propensity to save out of wealth (s_it/w_it) among wealthy could mechanically inflate measured returns. - Constructed savings measure: s_it = w_{it+1} − w_it − y_it. - Empirical finding: no evidence that propensity to save out of wealth rises with wealth; evidence it declines. - Rank correlation between (s_it/w_it) and w_it is -0.19 (p-value <1%). - If any bias exists, likely downward. - Similar result present in Bach et al. (2017). - Mismeasurement of private equity wealth: - Two concerns: understatement of private business value and rising fraction of private equity holders with wealth percentile. - Exercise 1: drop private equity holders — virtually no differences in net worth returns (minor differences at very top); moderate differences for financial wealth; qualitative message unchanged. - Exercise 2: adjust book value of private equity using market-to-book multipliers from “sometimes listed” firms: - Estimated multipliers range from 0.6 (“Utilities and Construction”) to 2.9 (“Retail Trade”), average 1.24. - Inflating/deflating book value by multipliers yields a downward correction of about 100 basis point in return to financial wealth at the very top; negligible elsewhere. - Effect on return to net worth even less pronounced. - Results virtually identical if using multipliers estimated only using private firms that go public. - Conclusion: adjustments do not change qualitative finding of substantial scale dependence in wealth returns. ### Modeling and estimation of returns to wealth - Goal: determine whether heterogeneity in returns is due to observables and transitory shocks or persistent unobserved factors (permanent component). - Persistence in returns is essential for heterogeneity to explain fat tail of wealth distribution and fast transitions in wealth concentration. - Linear panel regression model for returns: - r^x_{i(g)t} = X'_{i(g)t} β^x + u^x_{i(g)t} - r^x_{i(g)t} denotes return to wealth type x (financial wealth or net worth) for individual i in generation g in year t. - X_{i(g)t} is vector of controls capturing predictable variation due to observables. - Four specifications considered: 1. Baseline controls: - Age dummies, years of education, study concentration in economics or business, gender, marital status, county dummies, homeownership status, employment status, time dummies, full set of dummies for individual wealth percentiles (computed using lagged wealth values). - Lagged composition of portfolio (shares invested in different asset and liability types). - Rationale: capture life-cycle effects, financial knowledge/sophistication, scale effects, fixed entry costs, economies of scale, and compensation for riskier allocations and leverage. 2. Add average β of individual stock portfolio to better control for risk exposure. 3. Refine risk controls by adding interaction of time dummies and individual risky assets share ω^j_{i(g)t}: - Portfolio return benchmark: r^F_{i(g)t} = r^s_t + ∑_j ω^j_{i(g)t} (r^j_t − r^s_t). - If individuals had identical access to menu of instruments, these controls would absorb all existing variation in returns (useful benchmark). 4. Add individual fixed effects: - Error decomposition: u^x_{i(g)t} = f^x_{i(g)} + e^x_{i(g)t}. - f^x_{i(g)} captures persistent differences across people in average returns (ability to manage portfolio/private business, identify opportunities, persistent risk tolerance, persistent scale). - e^x_{i(g)t} measures unsystematic idiosyncratic variation ("good or bad luck"). - Allows decomposition: var(u^x_{i(g)t}) = var(f^x_{i(g)}) + var(e^x_{i(g)t}). - Further considerations: - Possibility that individual fixed effects are correlated across generations is considered later. *Source: wp18171 - Section 4 (excerpt) from the provided PDF content* ### 4.2 Estimation results ### 4.2 Estimation results ### Returns to financial wealth - Specification: pooled OLS regression of the baseline measure of returns to financial wealth in year t (equation (3), expressed in percentage points). Main sample comprises close to 31 million observations. - Portfolio-share interpretation: coefficients on portfolio shares of asset j interpreted as average excess returns of that asset relative to cash and deposits (excluded share). - Estimated excess returns (relative to deposits/cash): - Private businesses: average premium of 8 percentage points over deposits and cash. - Directly held listed stocks: average premium of 2 percentage points. - Mutual funds: premium 1.7 percent (lower than directly held stocks). - Bonds: premium 1.3 percent (lower than mutual funds). - Foreign/outstanding claims: premium larger than bonds (exact coefficient reported in table). - Magnitudes for portfolio changes: - Increasing the share in listed stocks by 30 percentage points increases return to wealth by roughly 63 basis points. - Increasing the share in private businesses by 30 percentage points is associated with an increase in returns on wealth of 248 basis points. - Risk exposure control: - Adding the individual stock-portfolio average beta (β) yields a positive and significant effect on returns to wealth. - One standard deviation increase in β increases returns on financial wealth by 4.5 basis points. - Addition of average β is statistically significant but has no impact on explained variation in returns. - Time interactions: - Replacing portfolio shares with their interaction with time dummies improves fit: adjusted R2 increases from 0.10 to 0.32. - Size and significance of most effects remain largely unchanged. - Demographics and education: - Gender: economically negligible and noisy in richer specifications. - General education: an additional year of formal schooling raises returns by 1.6 basis points. - Completing a college degree results in a 6.4 basis points higher average return compared to holding a high school diploma. - Economics or business education: associated with 10 basis points higher returns. - Combined effect: a systematic difference of 16 basis points enjoyed by economics college graduates (sum of completing college and majoring in economics/business) can produce a difference in wealth at retirement of 4.3% compared to holders of high school diplomas for one dollar saved every year over a working life of 40 years—conditioning on similar wealth and portfolio composition. - Fixed effects (column 4): - Adding individual fixed effects to the time-interacted specification increases adjusted R2 to 0.394 (a 23% increase over column (3)). - Implies returns have an important persistent individual component. - Serial correlation check: - Auto-covariances of first-differenced residuals (Δu_f i(g)t Δu_f i(g)t−s) for s≥2 are minuscule and economically indistinguishable from zero, consistent with e_F i(g)t being serially uncorrelated. ### Returns to net worth - Specification notes: asset shares relative to gross wealth; include housing/gross wealth ratio and leverage for long-term debt, consumer debt, and student debt. Controls include dummies for lagged net worth percentiles. Baseline OLS shown in columns (1)-(3). - Asset premium pattern: - Investments in private equity carry a larger premium than investments in listed stocks and mutual funds; mutual funds’ premium exceeds that of bonds and outstanding claims. - Housing and leverage effects: - Share invested in housing has a strong positive effect on returns to net worth. - Financing with deposits the purchase of a house worth 50% of initial gross assets increases ceteris paribus the average return on net worth by 360 basis points (0.5×7.2%). - Leverage has a negative and highly significant effect on returns. - If house purchase fully financed with debt (leverage increases from 0 to 0.33), the average return on net worth would increase by only 82.5 basis points (0.33×7.2%−0.33×4.7%). - Time dummies: strong explanatory power because imputed rents contain an important aggregate component and miss idiosyncratic parts, explaining relatively high fit (adjusted R2 = 0.33). - Stock-portfolio β: - Adding β has a small effect and no impact on overall fit. - Time interactions: - Interacting asset shares and leverage with time dummies increases fit slightly (adjusted R2 = 0.36); estimated coefficients only marginally affected. - Demographics: - Male dummy: positive, small effect (4 basis point difference). - General education: returns to net worth more responsive to general education than returns to financial wealth. - Compared to having just a high school education, an individual with college education and business/economics concentration would have at retirement 18.7% more net worth (saving one dollar every year for 40 years). - Fixed effects (column 4): - Adding individual fixed effects increases adjusted R2 by 49%, implying individual returns to net worth have an important persistent component. - Strong positive rank correlation (Spearman coefficient of 38%) between the fixed effect in the return to financial wealth and that in the return to net worth. - After-tax robustness: - Qualitatively similar results when focusing on an after-tax measure of return to net worth; excess return on private equity declines due to capital income and wealth tax exposure, while excess return to housing does not change much (see OA). ### Persistent heterogeneity - Distribution of individual fixed effects (returns to financial wealth, balanced panel, demeaned): - Long right tail: Pearson’s skewness coefficient 3.66. - Dispersion: standard deviation 3.6% and 90th-10th percentile difference of 5.1 percentage points. - Excess kurtosis: 24.8. - Distribution of fixed effects (returns to net worth): - Larger heterogeneity: standard deviation 5.4% points and 90th-10th percentile difference of 5.5 percentage points. - Kurtosis: 102. - Skewness: Pearson’s skewness coefficient -6.31 (longer left tail). - Left-tail and kurtosis reflect effect of debt pulling distribution left and housing imputation failing to capture idiosyncratic component. - Subgroup distributions (Figure 7 insights): - Business owners vs non-owners: - Business owners: distribution more spread out and shifted right (standard deviation 6.4 vs 1.6 for non-business owners). - Wealth groups: - Persistent component of returns increases with wealth; steeper relation for returns on financial wealth. - Cross-sectional heterogeneity in returns to financial wealth increases with position in wealth distribution. - For returns on net worth, heterogeneity is more pronounced at the bottom than at the top (reflecting heterogeneity in cost of debt and leverage). - Risky-asset participants and education: - Participants in risky asset markets have higher and more dispersed fixed effects. - Individuals with a degree in economics or business have a less volatile distribution of fixed effects (lower coefficient of variation). - Debt-holders: - Distribution of fixed effects for debt-holders shifts left and has a longer left tail. - Taxation effects: - After-tax returns on net worth lower persistent heterogeneity substantially (standard deviation 3.6 vs. 5.4 percent). - Relation between persistent component and wealth is flatter for net-of-tax returns on net worth. - Variance decomposition (Panel C, Table 6): - Error-term decomposition: var(u_x i(g)t) = var(f_x i(g)) + var(e_x i(g)t). - Using baseline specification: var(f_x i(g))/var(u_x i(g)t) = 0.29. - Persistent differences in returns across individuals can account for between 1/3 to 1/4 of the variance of the unobserved component of returns. ### Interpreting persistent heterogeneity - Three broad explanations for fixed effects in returns to wealth: 1. Persistent differences in risk tolerance: - More risk tolerant individuals allocate persistently larger shares to risky assets and are compensated with a return premium (Merton-Samuelson relation ω_it = E(r_m t − r_s t) / (γ_i σ^2_t); ω_it increases linearly with 1/γ_i). 2. Persistent differences in wealth and scale effects: - Positive effect of the scale of wealth on returns (Piketty, 2014); consistent with low wealth mobility (Norway Shorrocks index 0.16 for quartiles of net worth). 3. Financial sophistication and access: - Heterogeneity in financial sophistication, ability to process/use financial information, access costs to investment opportunities, and other persistent traits (e.g., intertemporal discounting) affecting average returns conditional on portfolio risk exposure and scale. - Evidence supporting coexistence of components: - Returns affected by portfolio risk exposure (shares in risky assets) and average β. - Returns affected by scale of wealth. - Education matters for returns controlling for risk exposure and wealth level, suggesting financial sophistication is important. - Introduction of individual fixed effects substantially increases explained variability (adjusted R2 increases by 23% for returns to financial assets and 49% for returns to net worth), indicating factors beyond measured risk exposure and wealth level drive type dependence in returns. - Private equity note: - Variation in returns to private equity may reflect differences in entrepreneurial ability to manage businesses, holding constant share and size of business. - Fixed-effect model for return to private equity: adjusted R2 jumps from 0.0279 (no fixed effects) to 0.1399 (with fixed effects), a five-fold increase in predictability. *Source: wp18171 - 4.2 Estimation results* ### 5.1 Additional evidence ### 5.1 Additional evidence ### Individual-level regressions and Sharpe ratios - Regressions of the individual return Sharpe ratio (computed as in equation (7)) on financial wealth measured in 2004 and other observables: - Sample specifications: Column 1 uses the whole sample; Column 2 excludes private equity owners. - Controls include: linear wealth percentile, quadratic in age, years of schooling, degree in business, and years owning private company equity. - Robustness: Results unchanged with less parametric specification (wealth percentile dummies). - Key empirical findings: - More educated individuals display higher Sharpe ratios; individuals with a business or economics degree also have higher Sharpe ratios, indicating financial sophistication matters. - Risk-adjusted returns are strongly and significantly increasing with the individual initial wealth percentile. - Risk-adjusted returns increase with experience as a private equity owner. - Results for financial wealth percentile are unchanged when restricting to individuals who have never owned private equity. - Interpretation: - Correlation between wealth and the Sharpe ratio, and between Sharpe ratio and education/experience, matches models where individuals differ in the cost or incentives to collect information (cited: Arrow (1987), Peress (2004), Kacperczyk et al. (2014), Best and Dogra (2017)). - Models with equally informed investors but heterogeneous risk tolerance (à la Merton) predict heterogeneity in return levels but not in risk-adjusted returns, and thus would not predict the observed correlation between wealth and risk-adjusted returns. - Numeric note: - The individual Sharpe ratio is highly correlated with the individual fixed effect (correlation coefficient of 0.52). - Top-trimming: returns also trimmed at the top 0.5%. ### Evidence from the universe of deposit accounts (Norway, 2005-15) - Institutional context: - Deposits up to 2 million NOK (approximately $260,000) are fully insured; therefore returns on such deposits bear no risk. - Data selection and measurement: - Use universe of individual bank deposit accounts for 2005-15. - Select individuals with accounts for all years; eliminate accounts with balance above the deposit insurance threshold or below $500. - Compute account-specific return using interest received divided by average of end- and beginning-of-year deposit balances (analog of equation (3)). - Regression controls: - Demographics, number of yearly accounts (overall and with a given bank), account “experience”, bank fixed effects, time dummies, and log deposit balances. - Main findings: - Returns on deposits are positively correlated with years of education and with having an economics/business degree. - Returns on deposits increase with deposit size (consistent with a scale effect). - Returns on deposits decrease with account “experience” (consistent with teasing rates followed by inertial behavior). - These controls jointly explain 53% of the variation; adding individual fixed effects increases fit by 14%. - Heterogeneity statistics: - Standard deviation of individual-level returns on deposits: 2.6%. - Standard deviation of bank fixed effects: 0.9%. - Bank and individual fixed effects are strongly positively correlated: - High-education individuals tend to deposit at high-return banks; high-fixed effects individuals also do so. - Suggests persistently higher individual deposit returns partly reflect ability to spot high-return banks and allocate liquidity accordingly. - Implication: - Because these deposits bear no risk, heterogeneity in returns on insured deposits cannot be attributed to compensation for unobserved risk tolerance. ### Interpretation: ability, information, and persistent heterogeneity - Summary interpretation: - Persistent heterogeneity in returns reflects not only compensation for risk and scale but also differences in ability to generate returns and superior information about investment opportunities. - Supporting observations: - Education, business/economics degrees, and experience predict higher risk-adjusted returns. - Correlations between individual fixed effects and bank fixed effects indicate search/selection on provider quality. ### Intergenerational persistence in returns to wealth - Data linkage: - Norwegian data contain individual and family identifiers, enabling parent-child linkage. - Over 11 million father-child pairs are used to estimate correlations. - Statistical approach: - Estimate fixed effect persistence via f_x_i(g) = ρ f_x_i(g−1) + η_x_i(g) (equation (12)), where f_x_i(g) is the fixed effect in returns for individual i in generation g. - Rank percentiles computed relative to birth cohort to account for life-cycle timing differences. - Empirical results (rank correlations and regressions): - Intergenerational rank correlation: - Financial wealth percentile: regression slope 0.3. - Return to wealth percentile: regression slope 0.11. - For net worth, slopes are 0.16 (wealth) vs. 0.15 (returns). - Non-linearities: - Higher polarization at the top of the wealth distribution; lower polarization at the top of the returns distribution. - For the very wealthy, intergenerational correlation in returns facilitates social mobility while intergenerational correlation in wealth weakens it. - Persistent component: - Correlation between fixed effect percentiles (Figure OA.17) is stronger than between returns themselves, implying intergenerational correlation in returns is largely driven by the persistent (fixed effect) component. - Regression controls and robustness: - Adding wealth controls, education dummies, age and year effects lowers slopes for financial wealth returns but not for net worth returns; effects remain positive and significant. - Including individual fixed effects leaves slopes unaffected but raises adjusted R^2 substantially, consistent with intergenerational correlation driven primarily by permanent component. - Results confirmed when dropping private business owners and when using net-of-tax returns. - Summary characterization (after-tax returns on net worth, focusing on fixed effects; ignoring moments higher than second): - f_i(g) ∼ (mean=3.7% + 0.012(P_iw − 50), SD=3.6%) - f_i(g) = const + 0.14 f_i(g−1) - Comparison to Benhabib et al. (2017) calibration: - Benhabib et al. (2017) estimate average returns 3.0%, cross-sectional SD 2.7%, intergenerational persistence 0.17. - The slope of the relation between wealth percentile and average fixed effect is about 0.01 in Benhabib et al. (2017), similar to the 0.012 estimated here. - Overall conclusion on intergenerational persistence: - Substantial persistence and heterogeneity within a generation, but milder persistence across generations, particularly for returns to financial wealth. - Data show an economically small but precisely measured degree of intergenerational persistence in returns. ### Implications for measurement, models, and taxation - Wealth measurement and capitalization methods: - Capitalizing capital income components using average rates of return (as in imputation methods) may overstate wealth concentration if returns are heterogeneous within asset classes and correlate with wealth. - Heterogeneity of returns can generate significant deviations between inequality measures based on imputed versus actual wealth. - Cross-country wealth vs. income inequality puzzle: - Countries with low income inequality can still exhibit high wealth inequality; heterogeneity in returns to wealth can help reconcile differing income concentration but similar top wealth shares. - Theorems cited: - Grey (1994): with homogeneous returns and heterogeneous income, wealth distribution inherits income distribution tails. - Kesten (1973): heterogeneity in returns can generate thick-tailed wealth distributions even without skewed return distributions or income heterogeneity. - If return heterogeneity determines the tail and is similar across countries, wealth concentration can be similar despite income differences. - Taxation of capital income and wealth: - In models with heterogeneous returns, replacing a capital income tax with a wealth tax widens after-tax heterogeneity in returns: capital income tax disproportionately reduces after-tax return for high-return individuals; a wealth tax redistributes burden from high- to low-return individuals. - Potential efficiency gains from reallocation of capital to high-return individuals and incentives for further accumulation depend on the persistence and extent of heterogeneity. - Variance decomposition (Table 6, Panel C) provides empirical inputs to assess optimality of capital income taxation and the relative importance of permanent vs. transitory return heterogeneity (relevant to progressivity of capital income taxation). - Other amplifying mechanisms: - Assortative mating by returns to wealth and intra-household allocation of wealth management can amplify heterogeneity and wealth concentration (documented persistence across marital statuses in related work). - Life-cycle heterogeneous-return models that allow heterogeneity in human and non-human capital and preferences are needed to quantify relative importance of inequality sources; ongoing work addresses estimation of such models. *Source: wp18171 - 5.1 Additional evidence* ### References ### References ### Top income and wealth distribution - Aaberge, R., A. B. Atkinson, and J. Modalsli (2016). The ins and outs of top income mobility. Working paper. - Alstadsæter, A., M. Jacob, W. Kopczuk, and K. Telle (2016). Accounting for business income in measuring top income shares: Integrated accrual approach using individual and firm data from norway. NBER Working Paper No. 22888. - Alstadsæter, A., N. Johannesen, and G. Zucman (2017). Who owns the wealth in the tax heavens? Macro evidence and implications for global inequality. NBER Working Paper No. 23805. - Aoki, S. and M. Nirei (2015). Zipf’s law, Pareto’s law, and the evolution of top incomes in the US. American Economic Journal: Macroeconomics, forthcoming. - Benhabib, J. and A. Bisin (2018). Skewed wealth distributions: Theory and empirics. Journal of Economic Literature, forthcoming. - Benhabib, J., A. Bisin, and M. Luo (2017). Wealth distribution and social mobility in the US: A quantitative approach. Working paper. - Benhabib, J., A. Bisin, and S. Zhu (2011). The distribution of wealth and fiscal policy in economies with finitely lived agents. Econometrica 79(1), 123–157. - Bricker, J., A. Henriques, J. Krimmel, and J. Sabelhaus (2016). Measuring income and wealth at the top using administrative and survey data. Brookings Papers on Economic Activity, 261–312. - Fagereng, A., L. Guiso, F. Guvenen, J. Hubmer, and L. Pistaferri (2018). Origins of wealth inequality. Unpublished manuscript. - Fagereng, A., L. Guiso, D. Malacrino, and L. Pistaferri (2016b). Heterogeneity in returns to wealth and the measurement of wealth inequality. The American Economic Review Papers & Proceedings 106(5), 651–655. ### Intergenerational wealth, mobility, and transmission - Best, J. and K. Dogra (2017). Capital Management and Inequality. University of Oxford Working paper. - Black, S. E., P. J. Devereux, P. Lundborg, and K. Majlesi (2015). Poor little rich kids? The determinants of the intergenerational transmission of wealth. Working paper. - Boserup, S. H., W. 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Accounting for business income in measuring top income shares: Integrated accrual approach using individual and firm data from norway. NBER Working Paper No. 22888. - Deaton, A. (1997). The analysis of household surveys: A microeconometric approach to development policy. World Bank Publications. - Fagereng, A., L. Guiso, D. Malacrino, and L. Pistaferri (2016a). Assortative mating in returns to wealth. Unpublished manuscript. - Eika, L., M. Mogstad, and O. Vestad (2017). What can we learn about household consumption from information on income and wealth. Working paper. - Bricker, J., A. Henriques, J. Krimmel, and J. Sabelhaus (2016). Measuring income and wealth at the top using administrative and survey data. Brookings Papers on Economic Activity, 261–312. ### Theoretical and empirical macro/wealth models - Aiyagari, S. R. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics 109(3), 659–84. - Arrow, K. J. (1987). The demand for information and the distribution of income. Probability in the Engineering and Informational Sciences 1(01), 3–13. - Castaneda, A., J. Díaz-Giménez, and J.-V. Ríos-Rull (1998). Exploring the income distribution business cycle dynamics. Journal of Monetary Economics 42(1), 93–130. - Castaneda, A., J. Díaz-Giménez, and J.-V. Ríos-Rull (2003). Accounting for the US earnings and wealth inequality. Journal of Political Economy 111(4), 818–857. - De Nardi, M. and G. Fella (2017). Savings and wealth inequality. Review of Economic Dynamics 26(4), 280–300. - Deaton, A. and C. Paxson (1994). Saving, growth, and aging in Taiwan. In D. Wise (Ed.), Studies in the economics of aging, pp. 331–362. University of Chicago Press. - Benhabib, J., A. Bisin, and S. Zhu (2011). The distribution of wealth and fiscal policy in economies with finitely lived agents. Econometrica 79(1), 123–157. *Source: wp18171 - References* ### 2015. Statistics Norway Reports. ### wp18171 - 2015. Statistics Norway Reports. ### Heterogeneity in returns to financial wealth - Cross-sectional standard deviation of individual returns to wealth plotted by share invested in risky financial assets for 2005-15 shows rising dispersion with larger risky shares (Figure 1). - Value-weighted mean return on financial wealth: 0.0419; standard deviation: 0.1435 (Table 3). - Private equity mean return: 0.1152; St.dev.: 0.4343; skewness: 5.652; kurtosis: 57.91 (Table 3). - Listed shares mean return: 0.0273; St.dev.: 0.3021 (Table 3). ### Correlation between wealth and returns - Relation between returns to financial wealth and financial wealth percentiles (2005-15): average and median returns plotted across percentiles (Figure 2). - Return on safe assets and return on risky assets presented separately in Panel B of Figure 2. - Correlation patterns: regressions and local regressions indicate non-linear relations across wealth percentiles (Figure 2 notes). ### Sharpe ratio and portfolio performance - Average Sharpe ratio of individual wealth portfolios by wealth percentile (2005-15), computed using 2004 wealth percentiles, shows higher Sharpe ratios at higher wealth percentiles (Figure 3). - Regression of Sharpe ratio on observables (Table 7): - Age coefficient: -0.0361 (Whole sample), -0.0434 (No P.E. owners). - Age^2 coefficient: 0.0004 (Whole sample), 0.0005 (No P.E. owners). - Year of schooling: 0.0403 (Whole sample), 0.0391 (No P.E. owners). - Year of schooling^2: -0.0009 (Whole sample), -0.0007 (No P.E. owners). - Economics/Business degree: 0.0401 (Whole sample), 0.0543 (No P.E. owners). - Wealth percentile in 2004: 0.0052 (Whole sample), 0.0059 (No P.E. owners). - Sample sizes: N = 1,663,694 (Whole sample), N = 1,247,940 (No P.E. owners). - Adjusted R^2: 0.125 (Whole sample), 0.0869 (No P.E. owners). ### Returns to net worth and decomposition - Value-weighted mean before-tax return to net worth: 0.0406; St.dev.: 0.0825 (Table 3). - After-tax mean return to net worth: 0.0366; St.dev.: 0.0746 (Table 3). - Before-tax vs. after-tax returns plotted across net worth percentiles (Figure 4, Panel B). - Component contributions to return to net worth by percentile (Figure 5, Panel B): - Return to financial wealth, return to housing, and cost of debt (absolute value) are plotted against net worth percentiles. - Leverage and participation rates by net worth percentile (Figure 5, Panel A): - Homeownership rate, entrepreneurship rate, share consumer debt, share long-term debt plotted by percentile. ### Portfolio composition by fractiles (2005-2015) - Financial wealth shares (Panel A, Table 1) by fractile: - 0-20%: Deposit 0.95; Bonds 0.01; Foreign & outstanding claims 0.00; Mutual funds 0.03; Listed stocks 0.00; Private equity 0.00. - 20-50%: Deposit 0.88; Bonds 0.01; Foreign & outstanding claims 0.02; Mutual funds 0.07; Listed stocks 0.01; Private equity 0.01. - 50-90%: Deposit 0.77; Bonds 0.02; Foreign & outstanding claims 0.04; Mutual funds 0.08; Listed stocks 0.03; Private equity 0.06. - 90-95%: Deposit 0.62; Bonds 0.02; Foreign & outstanding claims 0.07; Mutual funds 0.07; Listed stocks 0.04; Private equity 0.18. - 95-99%: Deposit 0.42; Bonds 0.02; Foreign & outstanding claims 0.09; Mutual funds 0.06; Listed stocks 0.04; Private equity 0.36. - 99-99.9%: Deposit 0.15; Bonds 0.02; Foreign & outstanding claims 0.11; Mutual funds 0.03; Listed stocks 0.03; Private equity 0.66. - 99.9-99.99%: Deposit 0.06; Bonds 0.01; Foreign & outstanding claims 0.10; Mutual funds 0.01; Listed stocks 0.01; Private equity 0.80. - Top 0.01%: Deposit 0.03; Bonds 0.01; Foreign & outstanding claims 0.07; Mutual funds 0.00; Listed stocks 0.01; Private equity 0.87. - Net worth composition (Panel B, Table 1) by fractile (Assets / Liabilities; shares): - 0-20%: Safe assets 0.64; Housing 0.30; Risky assets 0.06; Consumer debt 0.44; Student debt 2.74; Long-term debt 5.90. - 20-50%: Safe assets 0.31; Housing 0.66; Risky assets 0.03; Consumer debt 0.01; Student debt 0.05; Long-term debt 0.40. - 50-90%: Safe assets 0.10; Housing 0.86; Risky assets 0.04; Consumer debt 0.00; Student debt 0.01; Long-term debt 0.21. - 90-95%: Safe assets 0.11; Housing 0.81; Risky assets 0.08; Consumer debt 0.00; Student debt 0.00; Long-term debt 0.12. - 95-99%: Safe assets 0.11; Housing 0.73; Risky assets 0.16; Consumer debt 0.00; Student debt 0.00; Long-term debt 0.10. - 99-99.9%: Safe assets 0.10; Housing 0.44; Risky assets 0.46; Consumer debt 0.00; Student debt 0.00; Long-term debt 0.07. - 99.9-99.99%: Safe assets 0.06; Housing 0.11; Risky assets 0.83; Consumer debt 0.00; Student debt 0.00; Long-term debt 0.04. - Top 0.01%: Safe assets 0.03; Housing 0.03; Risky assets 0.94; Consumer debt 0.00; Student debt 0.00; Long-term debt 0.02. - Notes: Debt leverage values are winsorized at the top 1%. Data for 2005-2015 (Table 1 notes). ### Descriptive statistics (pooled 2005-15; 32,665,032 individual-year observations) - Demographics (Table 2, Panel A): - Mean age: 45.66; Std. dev.: 15.00; P10: 24; Median: 45; P90: 67. - Male: mean 0.50; Married: mean 0.50; Family size mean 2.62 (Std. dev. 1.36). - College education share: 0.35; Years of education mean 13.61 (Std. dev. 3.58). - Economics/Business education: mean 0.12. - Wealth and flows (Table 2, Panels B–C): - Mean safe assets: 38,269; St.dev.: 132,123; P10: 1,380; Median: 13,220; P90: 90,910. - Mean risky assets: 59,555; St.dev.: 2,305,447; Median: 43,059. - Mean financial wealth: 97,825; St.dev.: 2,328,873; Median: 18,356. - Mean housing: 302,110; St.dev.: 329,435; Median: 253,247; P90: 630,577. - Mean gross wealth: 399,936; St.dev.: 2,374,998; Median: 294,056; P90: 757,470. - Mean debt: 122,638; St.dev.: 217,228; Median: 74,366; P90: 292,475. - Mean net worth: 277,297; St.dev.: 2,349,119; P10: -31,190; Median: 169,849; P90: 616,581. - Income from safe assets mean: 9284; Income from risky assets mean: 5,185. - Participation and leverage (Table 2, Panel D): - Fraction with risky assets: 0.47. - Fraction with public equity: 0.38; public equity share mean: 0.08; conditional public equity share mean: 0.22. - Fraction with private equity: 0.13; private equity share mean: 0.06; conditional private equity share mean: 0.46. - Fraction with housing: 0.78; Housing/Gross wealth ratio mean: 0.68; Conditional housing/Gross wealth ratio mean: 0.87. - Fraction with debt: 0.89. - Leverage: Consumer debt mean 0.09; Student debt mean 0.53; Long-term debt (homeowners) mean 0.38; Long-term debt (non-homeowners) mean 4.73. ### Regression evidence: explaining returns to wealth - Returns to financial wealth regressions (Table 4): - Years of education coefficients: 0.0129 (col 1), 0.0109 (col 2), 0.0163 (col 3). - Econ/Business education: 0.1386 (col 1), 0.1255 (col 2), 0.1004 (col 3). - Portfolio share coefficients (column 4, with individual fixed effects): Outst. and foreign share 0.1824; Bonds share 1.2908; Mutual fund share 1.6562; Listed stocks share 1.6050; Private equity share 8.2828. - β of stock market portfolio: 0.8197 (col 4). - Observations: 30,781,599; Adjusted R^2: 0.394 (col 4). - Returns to net worth regressions (Table 5): - Years of education coefficients: 0.1261 (col 1), 0.1227 (col 2), 0.1396 (col 3). - Econ/Business education: 0.1112 (col 1), 0.0920 (col 2), 0.1112 (col 3). - Portfolio and asset share coefficients (column 4, with individual fixed effects): Outst. and foreign claims 3.3979; Bonds share 2.9613; Mutual fund share 3.7882; Listed stocks share 3.9733; Private equity share 10.0421; Housing share 7.2209. - Leverage coefficients (column 4): Student debt -0.1834; Long-term debt -4.7250; Consumer debt -6.4130. - β of stock market portfolio: 0.3191 (col 4). - Observations: 30,555,863; Adjusted R^2: 0.535 (col 4). ### Fixed effects, distribution, and persistence - Distribution of estimated fixed effects (Figures 6 and 7; Table 6 Panel A): - Return to financial wealth, whole sample: Mean 0.00; SD 3.59; Skewness 3.66; Kurtosis 24.78; P10 -2.48; P25 -1.68; P50 -0.69; P75 0.48; P90 2.64. - Return to net worth, whole sample: Mean 0.00; SD 5.36; Skewness -6.31; Kurtosis 101.59; P10 -2.25; P25 -1.07; P50 0.13; P75 1.54; P90 3.29. - After-tax return to net worth, whole sample: Mean 0.00; SD 3.63; Skewness -4.79; Kurtosis 87.47; P10 -1.74; P25 -0.88; P50 0.03; P75 1.09; P90 2.38. - Subgroup statistics (Table 6 Panel A): - Ever in the top 10%: Return to financial wealth mean 2.47; SD 5.68; Return to net worth mean 1.37; SD 2.87; After-tax return mean 0.77; SD 2.10. - College graduate or more: Return to financial wealth mean 0.23; SD 3.75. - Persistence and variance decomposition (Table 6 Panel B–C): - Corr(E(f_i(g)), P_2004) for financial wealth: 0.776; for net worth: 0.852; for after-tax net worth: 0.742. - OLS coeff. f_i(g) on P_2004 (s.e.): 0.040 (0.000) for financial wealth; 0.027 (0.000) for net worth; 0.012 (0.000) for after-tax net worth. - Corr(f_i(g), f_i(g−1)): 0.142 (financial wealth); 0.058 (net worth); 0.064 (after-tax net worth). - Variance decomposition (Panel C): Var(f_i(g))/Var(u_i(g)t) = 0.29 (financial wealth), 0.28 (net worth), 0.26 (after-tax net worth). Var(e_i(g)t)/Var(u_i(g)t) = 0.71 (financial wealth), 0.72 (net worth), 0.74 (after-tax net worth). ### Intergenerational patterns - Rank correlations and regressions (Figure 9; Table 8): - Parent-child percentile regressions of returns: - Financial wealth: Father’s wealth percentile coefficient ranges from 0.1082 (col 1) to 0.0790 (col 4) depending on controls. - Net worth: Father’s wealth percentile coefficient ranges from 0.1546 (col 5) to 0.1688 (col 8). - Table 8 notes: - Columns 1-4 for return to financial wealth; columns 5-8 for return to net worth. - Observations: 11,373,294. - Adjusted R^2 values vary from 0.013 to 0.265 (financial wealth panels) and 0.025 to 0.249 (net worth panels). - Figure 9 reports slope values: Financial wealth wealth slope = .3 (left top), return slope = .11 (right top); Net worth wealth slope = .16 (left bottom), return slope = .15 (right bottom). *Source: wp18171 - 2015. Statistics Norway Reports.* --- _Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18171.pdf_