{"slug": "errors-in-the-research-of-emmanuel-saez-and-gabriel-zucman", "title": "Errors in the Research of Emmanuel Saez and Gabriel Zucman", "summary": "An audit of 138 papers by economists Emmanuel Saez and Gabriel Zucman found 2,035 problems, of which 147 were serious enough to change a headline number, with 69% of the papers containing at least one problem and 97% of major and moderate errors with a clear direction overstating the paper's claim. The audit was run as two independent reviews per paper by Claude Opus 5.5 and OpenAI's GPT-6 Astra, followed by a third adjudicating agent that re-verified, attempted to refute and graded each claimed problem. Among the flagged findings, the auditors estimated that roughly a fifth to a third of the measured fall in the top 1% tax rate after 1950 comes from the papers' choice to count all corporate tax as paid by shareholders rather than partly by workers and other investors.", "body_md": "Errors in the research of Emmanuel Saez and Gabriel Zucman\n\n138papers audited\n\n2,035problems found\n\n147serious enough to change a headline number\n\n69%of papers have at least one\n\n97%of major and moderate errors with a clear direction overstate the paper's claim\n\nHow this was done\n\nTwo independent audits of each paper. One by Claude Opus 5.5, one by OpenAI's GPT-6 Astra, neither seeing the other's work. Each obtained the paper, its appendices and its replication data, recomputed the headline numbers from the authors' own files and, where possible, from the original sources (tax statistics, national accounts, Federal Reserve and survey data), checked that cited sources say what is claimed, and probed every assumption the conclusions rest on.\n\nThen an adjudicator. A third agent re-verified every claimed problem, tried to refute each one, discarded those that did not survive, searched for problems both auditors missed, and graded what remained by how far it undermines the paper's own headline claim: major changes a core number materially, moderate affects secondary results or a core result modestly, minor is a presentation or arithmetic slip. Confidence is graded separately.\n\nThe papers · newest first\n\n202614 papers\n\nJohannesen, Sæverud, Saez · American Economic Review: Insights 8(2): 247-264\n\nThe savings limit studied in the paper governs two benefits at once: the yearly cash payment and a health subsidy for medicine, dental care and glasses. The paper credits the whole savings response to the cash payment, and the 2003 and 2010 rule changes it uses as tests also changed the health subsidy. The response is real, but how much of it is due to the cash payment alone is not known.\n\nmoderateThe 20% figure compares savings on 31 December, the day the government checks them, which is also when these pensioners' bank balances are lowest because the yearly payment arrives in January and is spent over the year.\n\nmoderateTo estimate the effect, the paper compares the same people at ages 60-64 and at 70-74, assuming their savings would otherwise have looked the same ten years later.\n\nminorThe same comparison that shows lower savings near the limit also shows 10-17% higher savings among the poorer half of these pensioners.\n\nminorAn earlier version of the paper used a different method and found an effect about half as large, though over a shorter period and when the payment was smaller.\n\nThe paper counts every dollar of corporate tax as paid by the companies' shareholders. Government agencies instead assume part of it is paid by workers and by other investors. Under the agencies' rules the top 1%'s tax rate still falls a lot after 1950, but by about 8-10 points instead of 13. So roughly a fifth to a third of the measured fall comes from this accounting choice.\n\nmoderateThe paper says the agencies' method would show the top 1%'s tax rate falling by only 7 points instead of 13.\n\nmoderateThe paper's 2021 figures were not computed from 2021 tax records.\n\nmoderateWe could not rebuild the paper's numbers from the public data files.\n\nmoderateThe paper says taxes like sales taxes are counted against the people who buy the goods.\n\nWhen the authors actually published 'real-time' numbers during the pandemic, those numbers showed income inequality before taxes and benefits barely changing. Once tax data arrived, it turned out that the top 1% had gained a lot and the bottom half had lost ground. The paper reports its method as accurate in recessions without showing this record, so it overstates how much one can trust its real-time numbers on who gains from growth, although its real-time numbers on the effect of government aid were accurate.\n\nmoderateThe test the authors use to show their method works lets the method peek at some of the very answers it is supposed to predict.\n\nmoderateThe paper's accuracy scores look impressive partly because they give the method credit for getting overall economic growth right, which it simply takes from official statistics.\n\nmoderateSome of the paper's headline numbers on how fast the wealth of the richest grew during Covid are a few points higher than what the authors' own published data show.\n\nmoderateThe paper's month-by-month wealth series shows the March 2020 stock-market crash happening in January, before it actually happened, and much milder than it was.\n\nThe paper says Swedish holding companies explain about half of why top incomes seem to have grown much less in Sweden than in the US, where tax rules discourage such companies. But the US figure it relies on uses a narrower legal definition than the one applied to Sweden, so the US side was assumed to need no correction. The best-known US correction would probably strengthen the paper's point, so its direction holds, but 'half' is a rough number.\n\nmoderateThe paper has Swedish holding-company data only from 2000.\n\nmoderateThe middle class in Norway and Sweden pays a lot of sales tax (VAT) and payroll tax.\n\nmoderateThe headline that the very richest pay about 15-20% in total taxes comes from one three-year window and from groups of only about 12 Norwegian and 24 Swedish households.\n\nmoderateOver 18 years the richest families took out only about a fifth (Sweden) or an eighth (Norway) of their companies' profits.\n\nThe tax only charges the gap between 2% of a household's wealth and the income tax it already pays. The paper assumes everyone worth over GBP100m already pays very little (0.2% of their wealth). But the study it cites assumes that people worth GBP100m-1bn pay six times as much (1.2%), and the paper itself says they pay 'considerably' more. Using the cited study's own figures, the tax would raise about GBP8bn, not GBP10bn.\n\nmajorRich people usually respond to a new wealth tax by moving abroad, hiding or undervaluing assets, or shuffling wealth around.\n\nmoderateThe paper claims the tax would raise a growing share of national income each year, and that top fortunes would keep outgrowing the economy even with the tax.\n\nmoderateThe summary says the standard objections to wealth taxes 'do not hold', but the paper never actually examines some of them, such as whether people can pay a yearly tax on assets that produce little cash.\n\nmoderateThe paper says Britain's richest pay less than a quarter of their income in tax, far below ordinary people.\n\nThe paper's first finding is that, after 2013, getting rich stopped being linked to sending money to tax havens. But the paper never checks whether the before/after gap is bigger than chance alone could produce, and its own numbers show it is not. The pattern points the same way in every version of the analysis, but the evidence is too noisy to say how large the change was, or even to be sure there was one.\n\nmajorTo show the change is specific to tax havens, the paper compares haven transfers with transfers to ordinary countries and says the latter did not change.\n\nmajorBefore 2013, when someone hid money abroad, their officially reported wealth fell afterwards.\n\nmoderateAfter 2013, the estimated effect of haven transfers on taxes and reported wealth is close to zero, but it is measured so imprecisely that sizeable remaining effects cannot be ruled out.\n\nmoderateThe paper says rich people did not start routing money to tax havens through their companies instead of their personal accounts.\n\nThe paper measures how much faster declared wealth grew in tax havens than in ordinary countries. It then applies that extra growth to the money in the ordinary countries too, even though they were the comparison group. Done consistently, the paper's own method gives about a quarter of the increase rather than 38%.\n\nmajorIn 2017 Colombia did several things at once: it began exchanging bank information internationally, ran the last round of a tax amnesty, and made hiding assets abroad a crime.\n\nmajorFATCA only tells Colombia how much interest and dividends a US account paid.\n\nmajorThe paper adds up the wealth people disclosed after the tax office's letters and counts it as part of the growth in wealth held abroad.\n\nmoderateThe 38% comes from a single, statistically weak estimate.\n\nThe paper argues Forbes misses hundreds of smaller billionaires, which would push the tax take up to $115-128 billion. That estimate comes from a curve-fitting exercise that gives wildly different answers depending on the year and on whether the very richest people are included. A reconstruction from state tax data finds far fewer missing billionaires, adding about $5 billion rather than $24 billion.\n\nmoderateThe '25 times richer since 1982' figure starts in a year when stock prices were unusually low and California's top fortunes were measured from a very small group; starting a year later gives about 15 times.\n\nmoderateThe $100 billion figure is 5% of what Forbes says California's billionaires own, minus a 10% allowance for avoidance and departures.\n\nmoderateThe paper's claim that a yearly wealth tax would lose little revenue to billionaires moving away depends on how mobile billionaires are, and it uses an estimate drawn from European millionaires.\n\nminorThe paper says billionaires who left to dodge a one-time tax would not stay away for good, but people who have already paid the cost of moving often do not move back.\n\nThe paper says US companies moved 1-5 percentage points of their profits back home after the 2017 reform, but it measures this only against 2017, an unusually good year for profits abroad. Compared with the average of the years just before the reform, the share booked abroad in 2018-2019 was about the same or higher. After allowing for ups and downs in the economy, the fall is about 1-2 points and could be chance. The paper's broader point, that the reform changed little, is if anything strengthened.\n\nmoderateIn 2020 the government paid companies hundreds of billions of dollars through the pandemic Paycheck Protection Program, and the official statistics count this money as US corporate profit.\n\nmoderateFor listed companies, the authors trimmed the biggest losses before adding up profits, but they described a different, two-sided trimming.\n\nmoderateOne of the four data sources was adjusted to match another, so it cannot independently confirm it.\n\nmoderateThe paper's estimate of how much profit six big companies brought back home is roughly right but somewhat too high, mainly because Microsoft changed its accounting rules partway through the period.\n\nThe USD 24bn assumes that every very rich family pays in full and that nobody moves abroad, reorganises their holdings or gets their companies valued low. The authors' own earlier work and the studies they cite expect a fifth or more of such revenue to be lost, so on this count alone a realistic figure is nearer USD 19-20bn.\n\nmajorThe report says the new tax would push the super-rich's tax rate to 50% in Brazil and 34% in Chile, above what ordinary people pay.\n\nmajorFor four of the seven countries, nearly all the fortunes being taxed are not observed in any data.\n\nmoderateIn different places the report says the new tax would subtract income taxes only, income and wealth taxes, or even company taxes already paid.\n\nmoderateThe report's '0.6% of the region's GDP' is really a simple average of seven country percentages, computed with GDP from different years between 2017 and 2022.\n\nBillionaires pay very little personal income tax, but the companies they own pay corporate tax, which the author himself counts when he says billionaires pay less than everyone else. Counted that way, they already pay roughly 2% of their wealth in tax each year, not 'almost nothing'. The proposed 2% would come on top of that, which the article does not explain. The numbers are right, but the 'almost untaxed' message overstates the case.\n\nmoderateThe EUR 220 billion assumes that nobody avoids the tax and that every country with billionaires takes part.\n\nmoderateThe article says the practical hurdles are small and support is building.\n\nminorThe French numbers (about 150 billionaires with EUR 750 billion) don't come from the same list as the world numbers and don't match either of the two usual rich lists.\n\nminorThe claim that billionaires pay 'about 0.3% of their wealth' in income tax comes from studies of just three countries (the US, France and the Netherlands) and is assumed to hold everywhere.\n\nThe paper argues that trade raised taxes on capital by moving activity from small family businesses into corporations. But for most developing countries that split is not measured; it is estimated with a formula based on average income, so the data cannot show that trade, rather than ordinary economic growth, caused the shift. The separate finding that corporations paid higher effective tax rates holds up better.\n\nmoderateChina's official statistics started counting the income taxes of private and foreign-owned firms only in 2001.\n\nmoderateThe paper measures the rise from 1989, a low year when Brazil and Argentina had hyperinflation and when the data for many countries switch from old archives to modern statistics.\n\nmoderateTo show its explanation is believable, the paper borrows numbers from a published trade model and concludes the explanation accounts for about 75% of the estimated effect.\n\nmoderateThe 2022 versions say capital taxes fell 5 points worldwide.\n\nThe note says it makes no sense to count lost income taxes forever while counting the new tax only once. That logic works against the critics' guess about extra unannounced departures, which assumed the tax would be charged every year. It does not settle the case of people who genuinely moved to dodge the one-time tax. Moving back is costly, so they may stay away and their California income tax may be lost for good, and the note gives no evidence that they will return. This does not overturn its conclusion, because the people reported to have left pay relatively little California income tax.\n\nmoderateThe note repeats that the tax would raise $100 billion and says there is no real evidence that billionaires have escaped it.\n\nminorThe note mainly blames the critics' negative result on a very low discount rate that multiplies yearly losses 67 times.\n\nminorThe note says the state's nonpartisan Legislative Analyst's Office concluded the tax would raise tens of billions of dollars on net.\n\nminorThe note says the three richest people reported to be leaving paid only $269 million in California income tax in 2025.\n\nThe memo says anyone who thinks the default formula overvalues their stake can hand in an appraisal and pay tax on that number. The law is stricter. The owner must prove with 'clear and convincing evidence' that the formula 'substantially' overstates the value, and the tax agency can use the same route to push values up. Small overvaluations would stick, and private-business owners could find the escape hatch harder to use than the memo suggests.\n\nmajorThe law gives market-price treatment to 'publicly traded assets', and founders' special voting shares are not themselves traded on any exchange.\n\nmoderateThe law blocks the usual discounts for owning a small, hard-to-sell slice of a business.\n\nmoderateMark Zuckerberg holds almost all of his special Meta shares through private holding companies, not in his own name.\n\nminorA few weeks before the memo, the same authors had written that founders' special shares might fall under the private-company rules.\n\nThe brief says a French study found that a one-point tax rise drives out only 0.003-0.03% of rich taxpayers a year, and puts this next to a Scandinavian figure of about 2%. The two numbers measure different things (a yearly flow per point of income tax versus a long-run total per point of wealth tax), and the French study itself says French reactions are about as strong as the Scandinavian ones. The conclusion that emigration was not the main problem survives, but the French evidence is made to look far more reassuring than it is.\n\nmoderateThe studies the brief relies on do say that the rich moving abroad matters less than their other reactions.\n\nmoderateThe brief says, citing the OECD, that wealth-tax revenues did not grow even as household wealth grew.\n\nmoderateThe brief says a tax on fortunes above about EUR 100 million would fix the problem of the rich paying lower tax rates.\n\nmoderateThe brief says old wealth taxes failed partly because they started at too low a level, which supposedly pushed governments to add loopholes.\n\nTwo people, Google's founders, hold about a quarter of all the wealth the tax would hit. Both bought homes and moved business entities out of California in the weeks before the January 1, 2026 cutoff. One of the report's own authors wrote in a companion paper that Page might be able to show he had already left. If they don't owe the tax, $100 billion becomes about $78 billion, but the report dismisses the risk instead of showing it.\n\nmoderateThe report says California's independent budget office agreed that lost income taxes would be tiny next to $100 billion.\n\nmoderateThe report says very rich people rarely move to avoid taxes.\n\nmoderateThe report says its estimate is probably too low because Forbes misses some billionaires.\n\nmoderateThe report assumes only 10% of the money will be lost to avoidance and evasion, but gives no evidence for that number and no range.\n\nThe book says billionaires pay half the overall tax rate of the average French person, but the two figures do not count the same taxes: the billionaires' figure leaves out several taxes that are counted for everyone else, such as VAT on spending, some business and property taxes, and inheritance taxes. Measured the same way, billionaires in 2016 paid roughly half to two-thirds of the average rate, so the gap is real and large but probably smaller than 'half'. Cuts to company taxes since 2016 would lower billionaires' rate today, which partly offsets this.\n\nmoderateThe book expects the tax to raise about €20 billion a year in France, but that figure simply applies the tax rate to a magazine's rich list and assumes that no one would move abroad, hide wealth or have their fortune valued below the rich-list figure.\n\nmoderateThe book says a 2% yearly tax on large fortunes is exactly the rate at which billionaires would pay the same overall share of their income in tax as the average person, but that only works if their fortunes produce income equal to about 6% of their value each year.\n\nminorA section heading in the book says billionaires contribute only 13% of their income to French public finances, but the calculation leaves out the taxes their companies pay abroad while still counting the money used to pay those taxes as part of their income.\n\nminorIn one sentence the English translation says billionaires provide 0.3% of France's tax revenue, when the French original, and the English edition's own introduction, say 0.03%, ten times less.\n\nThe paper's statistical case that equality itself raises productivity, beyond education and health spending, comes from comparing whole world regions: rich, equal Europe against poorer, unequal regions. Comparing countries within the same region, or the same country over time, the link vanishes or reverses. The data show that equality and prosperity can coexist, but they cannot show that equality caused the prosperity, and they cannot 'rule out' that equality had some cost.\n\nmajorWhen the paper's regression code is re-run on the data the authors published, the numbers printed in the paper do not come out.\n\nmajorThe US spends much more than Europe on education and health, but mostly on private health care.\n\nmajorThe paper's figures make Scandinavia and the Netherlands look 20-40% more productive per hour than the US.\n\nmajorTo show that US productivity growth slowed as inequality rose, the authors' spreadsheet averaged the World War II years into the 1950 starting point, for the US only and without saying so.\n\nThe 30% average includes Social Security and Medicare payroll taxes, a large part of what ordinary workers pay, which fund benefits that come back to them; those benefits are not counted as their income, and billionaires pay almost none of these taxes. Counting the benefits as income, as the Congressional Budget Office does, lowers the average to about 27%, so billionaires' 24% is still lower but the gap halves; with other common choices the two rates are within a point or two.\n\nmoderateThe paper counts part of billionaires' stock-market gains as income, which makes their tax rate look lower, but counts no such gains as income for everyone else.\n\nmoderateThe paper says its main 2018-2020 numbers do not rely on Forbes magazine's estimates of what billionaires' private companies are worth, but its main tables do: private-company income is set at Forbes's value times the return earned on their public stocks.\n\nmoderateFor the corporate taxes of billionaire-owned companies, the paper uses accounting tax charges rather than the cash the companies actually paid, even though one table says 'cash'.\n\nmoderateTo check its results over a decade, the paper looks at the people who were richest at the end of the decade, who are by definition those whose fortunes grew most, which makes their tax rate look lower.\n\nThe paper's headline average tax rate of 42.5% includes some payments that are not taxes, such as contributions to private pension funds and bookkeeping entries for civil servants' pensions. On the official figures the paper itself cites, the average is about 38-39%. The rich still pay far less than average, but the gap is smaller than the headline suggests.\n\nmoderateMost of the difference between what the rich and everyone else pay comes from sales taxes and payroll contributions, which ordinary workers pay heavily and the rich pay little of relative to their income.\n\nmoderateThe paper's poorest half includes some business owners whose companies lost money that year, which pulls the bottom half's income share down.\n\nmoderateTwo of the paper's own tables give numbers for income as reported on tax returns that cannot both be right.\n\nmoderateThe paper's estimate of company profits kept inside firms on behalf of their owners is about a quarter higher than the national statistics the authors themselves use as a check.\n\nTo claim that a 2% levy brings billionaires up to, but not above, what ordinary people pay, the author has to assume how much income billionaires earn each year relative to their fortunes. The lecture does not say what it assumed (9%), and the author's own tax-record studies point to 5.6-7.4%. At those levels a 2% levy would take 43-50% of billionaires' income, more than any other group pays. The tax would raise the same money, but it would not be the 'minimal' fix the lecture describes.\n\nmoderateThe lecture says the fortunes of the world's richest one-in-a-million households grew 7.1% a year after inflation.\n\nmoderateThe $200-250 billion is what the tax would bring in during its first year if every country adopted it, fortunes were valued at magazine rich-list prices, and at most a fifth of the money were lost to avoidance.\n\nmoderateThe claim that French billionaires pay 'about half' the rate of everyone else counts pension contributions and VAT as taxes paid by ordinary people.\n\nmoderateThe lecture says billionaires can easily afford 2% a year because their wealth has grown about 7.5% a year.\n\nThe note says a 2% tax on fortunes above EUR 100 million would end the situation in which Europe's richest pay lower tax rates than ordinary people. Its own source says this is true only on a rough average dominated by the United States. It also warns that in the Netherlands and Italy people far below EUR 100 million already pay less than the middle class, which this tax would not change. The money estimates are not affected, but this fairness claim is overstated.\n\nmoderateThe note counts every billionaire with an EU passport as taxable in their home country.\n\nmoderateThe note presents its totals as what the tax 'would raise'.\n\nmoderateTo include people worth EUR 100 million to EUR 1 billion, the note multiplies each country's billionaire figure by one worldwide factor.\n\nminorFor France the note mixes two rich lists and adds $150 billion, apparently the Hermes family that Forbes leaves out, without explaining how.\n\nThe paper credits all of the 1996-1997 rise in reported wealth taxpayers to pre-filled returns, assuming nothing else would have changed. But the number of taxpayers was rising by roughly 5-10% a year anyway, so the true effect is probably about 12-16% more taxpayers rather than 'almost 20%'. The effect is still large; it is overstated by roughly a quarter.\n\nmoderateThe paper says the number of reported wealth taxpayers between the threshold and twice the threshold fell by one-third in 1994.\n\nmoderateThe paper treats 1994 as a clean experiment in which only the rule about who must report wealth changed.\n\nmoderateThe paper says shares were taxed at 80% of their value throughout; in fact the rule changed several times, including in 1987 and 1997, years used in the comparisons.\n\nmoderateThe paper argues that people dislike writing outright falsehoods on a tax form, which is why filing rules and pre-filled forms worked.\n\nThe '$1 trillion' assumes the gains would be taxed at about 40%. Yet the paper says they would be taxed like ordinary capital gains, whose top US rate is about 24%. At that rate the same calculation gives roughly half a trillion dollars. That is still a lot of money, but the headline depends on a rate rise that was proposed and never passed, and the paper does not say so.\n\nmoderateThe paper says Europe's past wealth taxes relied on people declaring their own wealth, while today governments could use information from banks.\n\nmoderateThe estimate assumes billionaires would report their wealth at exactly the values Forbes publishes, with no undervaluation or avoidance.\n\nminorThe paper puts the combined economic output of the G20 at $100 trillion.\n\nminorThe revenue figures are simple multiplications that assume nothing changes once the tax exists.\n\nThe 70% comes from dividing by a number that is the difference between two large, uncertain estimates. Using the paper's own uncertainty, the true share could plausibly be anything from about 40% to over 100%, far wider than the 56-95% range it reports, and a 10% change in the assumed interest rate alone moves it between 64% and 96%.\n\nmajorThe 70% figure divides the hidden wealth brought into compliance by an estimate of how much would have stayed hidden without the policy.\n\nmoderateThe paper says the money flows it compares moved in step before 2013, but its own chart shows a clear jump in 2009.\n\nmoderateThe 70% was calculated only for wealth people held in their own names, about half of Danish offshore wealth, but the summary applies it to all offshore wealth.\n\nmoderateTo scale up 26 audits of holding companies, the paper uses a formula that corrects for company size twice, which can make the estimated hidden wealth in such companies too small.\n\nThe report says the wealth of the richest one-in-a-million households grew about 7% a year after inflation, which it reads as a 7.5% annual return on their money. But that 7% is how fast the group's combined wealth grew while the group itself kept getting bigger as the world's population grew. Per household the growth was about 5.3%, implying a return of roughly 5.8%, no higher than the average return the report cites for everyone. The revenue estimates are unaffected, but the claim that billionaires earn unusually high returns, and the reassurance built on it, are much weaker.\n\nmoderateThe report says 2% is exactly the rate at which billionaires would pay the same share of their income in tax as middle-class people.\n\nmoderateThe finding that the very richest pay a smaller share of their income in taxes than other groups is backed by government data in France and the Netherlands.\n\nmoderateThe summary says billionaires' 'effective tax rate' is 0.3% of their wealth.\n\nmoderateThe report concludes the tax could be enforced even if some countries refuse to join.\n\nMost people who live in Dubai are foreigners, so many 'foreign-owned' homes are simply homes that expatriates live in. The note compares its figure with other cities where only owners living abroad are counted. Counted the same way in Dubai, as the authors later did, the share is about 30% instead of 43%. That is still far higher than anywhere else, but about a third less 'offshore' wealth than the note implies.\n\nmoderateThe note did not observe Russian purchases directly after the invasion.\n\nmoderateThe note says Russian buying rose about ten- to sixteen-fold.\n\nmoderateThe data behind the note are leaked or confidential, so no one outside the team can check the numbers, and several of the steps that turn raw records into the headline figures are not fully explained.\n\nmoderateThe note argues that because so much foreign and Russian money flowed into Dubai property, the UAE cannot have improved its anti-money-laundering controls.\n\nThe essay quotes a 2021 draft saying the richest 1% fail to report over 20% of their income, against 7% for the bottom half. Before the essay was published the same authors revised this to roughly 16% against 10%. The rich still under-report more, but the gap is about half as large as the essay says.\n\nmoderateThe chart of US companies' profits in tax havens credits the wrong source, and its last point (57%) is a projection drawn as if it were data.\n\nmoderateThe essay says it is reasonable to assume hidden wealth everywhere is as concentrated among the ultra-rich as in Scandinavia, citing one supporting study.\n\nmoderateThe essay says the Federal Reserve's own wealth data confirm that the richest 1% of Americans hold almost 40% of all wealth, after 'small adjustments'.\n\nmoderateThe essay says the share of national income going to the top 1% of Americans doubled since the 1970s.\n\nThe paper's single biggest item is a large, fast-growing block of untaxed partnership income. The paper assigns it to the rich by assuming it is spread like the partnership income people report on their tax returns. The rival authors later traced who actually owns the partnerships that claim this depreciation, and found it much less concentrated at the top. The paper does not discuss that evidence. If the evidence is right, this item explains a small part of the disagreement rather than its largest part.\n\nmoderateHow much of the gap is credited to each disagreement depends on a bookkeeping choice, and the paper makes that choice in the way most favourable to its 'three-quarters' figure.\n\nmoderateWhat the paper calls 'consumption taxes' also includes items that are not taxes, such as income of charities and payments from the Federal Reserve.\n\nmoderateThe paper says the rival study hands investment income to public employees whose pensions have no assets behind them.\n\nmoderateThe paper argues that the rival study's capital-income numbers cannot be right because wealth became more concentrated.\n\nThe paper's eye-catching claim that Danish tax audits actually lower multinationals' total worldwide tax bills depends on valuing Denmark's extra revenue at a 22% tax rate, but Denmark's rate in the years studied was 23.5-25%. With the correct rate the effect is roughly zero or slightly positive, so the claim that enforcement lowers global taxes is not supported, although the broader point that most of what Denmark gains is simply taken from other high-tax countries still holds.\n\nmoderateThe paper's model assumes that a tax-dodging firm always keeps its profit shifting just small enough to avoid an audit.\n\nmoderateThe paper uses European and OECD dispute statistics to show that tax havens rarely appear in tax disputes, but it misreads how these statistics are compiled: each dispute is counted once by each of the two countries involved, which makes havens look about half as common as they are, and one haven (Switzerland) was left out of the count.\n\nmoderateThe paper's description of an international survey says only two tax havens are ever named as targets, but its own chart shows six more havens being named and the two it mentions ranked third and fourth overall.\n\nmoderateThe paper's appendix table splitting corrections between Danish-owned and foreign-owned multinationals has its two halves labelled the wrong way round in the journal's version, which reverses one of the paper's main findings; the authors corrected it by hand on their own website copy.\n\nThe report says profit shifting costs governments nearly 10% of the world's corporate tax revenue and has not declined. For 2021-22 these numbers were largely assumed rather than measured, and the same team's later, more complete estimates put the cost at about 7% and show a modest fall after 2018. The central fact, that roughly $1 trillion of profits is booked in tax havens each year, still stands.\n\nmajorThe report says the global minimum tax on companies was weakened 'by a factor of two' after the 2021 deal by a growing list of loopholes.\n\nmajorThe 'three-fold fall' in offshore tax evasion comes from measurements made in Denmark, which has an unusually effective tax administration, applied to the whole world.\n\nmoderateOne step in the report's chart subtracts revenue for 'exempting US companies' that its own starting calculation had never counted, so the same thing is taken off twice.\n\nmoderatePart of the claimed weakening comes from a rule that lets some company tax credits count as income rather than as tax cuts.\n\nThe chart says it compares tax burdens measured the same way in all three countries, but the French line measures something different: only working-age people with jobs, with pension contributions counted as taxes. That choice makes French taxes look flat. Measured the way the chart's note describes, the same French study finds that tax rates rise clearly with income, from about 27% to about 50%, and fall only slightly at the very top.\n\nmoderateWhether US taxes look 'flat' depends on accounting choices the paper does not mention, chiefly whether Social Security contributions, which buy future pension rights, count as taxes, and whether tax credits paid to low earners count as tax cuts.\n\nmoderateThe paper says the very rich paid much higher tax rates in the 1950s-60s, mostly through the tax on corporate profits.\n\nmoderateThe paper says the tax rate on billionaires' wealth that would raise the most money is high, around 6-12% a year.\n\nminorThe chart's notes do not accurately say who and which years are included: the US 'poorest tenth' leaves out the very lowest earners, and the Dutch figures are from 2016, not 2018.\n\nThe essay says household wealth in the US, Western Europe and China grew from about two times the nation's yearly income in the 1950s to six times today. For the US, the essay's own sources put the 1950s level at about three and a half times, so the US increase was only about 60% as large as stated, and those sources give no 1950s figure for China at all. The tripling is right for France and Germany, and the broader point that wealth has grown much faster than incomes still stands.\n\nmoderateThe essay's Dubai figures were copied correctly from a 2022 study, but the same research team, including the essay's author, revised it in 2025: property owned by people living outside the United Arab Emirates is now put at about $68 billion, not $146 billion, with country figures cut by a third to two-thirds.\n\nmoderateThe essay says past wealth taxes failed partly because people reported their own wealth instead of getting forms pre-filled from bank and property records.\n\nmoderateThe essay says property taxes barely touch the rich, since the very wealthy hold little of their wealth in homes.\n\nmoderateThe essay says good design can cut the extent to which the rich escape a wealth tax (by hiding, moving or reshuffling assets) to very low levels, but gives no evidence, and the best studies, including one of Denmark co-written by the essay's author, find that the wealth people report still shifts substantially with the tax even under well-run systems.\n\nWhen France raised the wealth-tax entry point to EUR 1.3 million in 2011, anyone just above it suddenly owed EUR 1,250-2,750 while anyone just below owed nothing. That jump alone is a strong reason to report wealth just under the line, so the evidence at this threshold cannot show that paperwork rather than tax drove the response. The paper's main evidence, at EUR 2.57 million, is not affected.\n\nmoderateIn the first year, reported wealth growth was about a fifth lower for households just under the new cut-off.\n\nmoderateThe paper measures how long the under-reporting lasted with two methods, and they disagree: one says the effect kept adding up every year, the other that it grew only slowly.\n\nmoderateThe '22.5%' means that the households who gamed the threshold had, by 2017, avoided about a fifth of their own wealth tax.\n\nmoderateThe paper uses a second episode, a EUR 3 million cut-off in 2012, to confirm that paperwork rather than tax rates drove the response.\n\nThe paper checks what happens if one trusts tax havens' own (incomplete) statistics instead of the authors' corrections, and reports that the estimate would fall by only 18%. Because of a units mistake in the spreadsheet, the correct fall is about half, and the paper's stated minimum of 22% becomes roughly 10-12%. The main 36% figure is unchanged, but it leans on the authors' data corrections far more than readers are told.\n\nmajorThe paper claims that, once profit shifting is accounted for, the share of output going to corporate profits rose in Germany, France and Italy.\n\nmajorThe paper says US companies shift about twice as much profit as other multinationals, relative to their foreign earnings.\n\nmoderateThe authors say a second, completely separate method gives the same answer, which is meant to reassure readers.\n\nmoderateThe summary says profits would rise about 20% in high-tax EU countries and 10% in the US if shifting stopped.\n\nTo fill a gap in official statistics, the authors assume that three-quarters of the stock-market value of all companies registered in the Cayman Islands (mostly large Chinese tech firms) is owned from abroad in a way that ends up counted as hidden household wealth. This guess is not tested, yet it explains most of the increase in offshore wealth since about 2016 and roughly $1.7-1.9 trillion of the $13 trillion figure for 2023. Without it the series is flatter, which still fits the paper's 'stable' story but makes the 2023 total smaller.\n\nmoderateThe authors do not measure offshore bank deposits directly; they assume deposits always make up the same 18% slice of the total.\n\nmoderateApart from Switzerland, the statistics do not reliably show how much of the money held in each financial centre belongs to rich individuals, so the authors assign each centre an assumed 'household share' (20% for the UK, 70% for Hong Kong, and so on).\n\nmoderateTo go back to 1980 the authors convert unexplained gaps in world income statistics into a wealth estimate, but they add bank deposits that the source figures already include, inflating the pre-2001 numbers by about 19%.\n\nmoderateThe paper says its estimate for Americans is close to what US tax authorities now see through FATCA reports.\n\nThe report assigns the emissions from building factories, machines and buildings to the people who own the wealth that pays for them, not to the people who buy what is produced. That is a defensible choice but not the usual one, and the report never shows what happens if it is changed. Counted the more usual way, the richest 1% produce about 8-11% of emissions rather than 17%. The claim that they added more to emissions growth than the poorer half of humanity then no longer holds, although emissions remain very unequally spread.\n\nmoderateThe report's own figures for how many millionaires there are, how much they own and what tax rates apply do not add up to the revenue it reports.\n\nmoderateThe richest 1% held about 38% of the world's wealth in 1995 and still about 38% in 2021, so receiving 38% of the new wealth simply means their slice stayed the same size.\n\nmoderateFor many middle-income countries, such as Thailand, Indonesia or Turkey, the report's figure for household wealth is far below its own figure for total private wealth, though by its definition the two should be almost the same.\n\nmoderateFor many countries, including China and India, the report's '2021' figures reuse income distributions last measured in 2014-2015, with only average incomes updated.\n\nThe paper says profit shifting peaked just before the 2017 US tax reform and fell afterwards. Its own numbers show the share of profits sent to tax havens was about the same in 2023 as in 2018, and higher in 2019-2020 than in 2017-2018. Shifting did dip, but only in 2021-2022, and it partly bounced back in 2023.\n\nmoderateA programming step treats years in which Ireland reports more income than the US as if Ireland were hiding income, and adds that amount.\n\nmoderateThe 8% figure counts the tax that high-tax countries lose but ignores the tax that tax havens collect on the same profits.\n\nmoderateThe paper describes one method for estimating shifting before 2015 but uses another.\n\nmoderateHow low profit shifting was in 1975 depends on choices the paper does not explain, especially how oil companies' profits are treated.\n\nAbout two-fifths of the EU's EUR 55 billion comes from supposedly low-taxed profits that big European companies record in their home countries. Those profits look low-taxed mainly because they include dividends passed between companies of the same group, and similar income the new rules ignore. Correcting for this alone brings the EU figure down to about EUR 42 billion or less.\n\nmoderateFor Poland and a few smaller countries, the model applies the minimum tax to the profits of every locally owned company, small firms included.\n\nmoderateWhere two data sources disagree, the model always picks the one that yields more revenue.\n\nmoderateThe US already has its own minimum tax on foreign profits, in force since 2018.\n\nmoderateThe figures rest on the first, admittedly imperfect years of company data, projected forward with economic growth, and are presented as single numbers with no margin of error.\n\nThe study shows convincingly that people did not simply swap illegal hiding for legal tax tricks one-for-one: their taxes went up and stayed up. But the paper goes further and says it can rule out any significant shift to legal tax avoidance. Its tests are not sharp enough for that. Some avoidance routes are measured imprecisely, moving abroad is barely measured at all, and the one clear response, setting up holding companies, is played down.\n\nmoderateAbout half of the roughly 1,500 people who came forward did so after 2013, when the data stop, so the study never sees what they did afterwards.\n\nmoderateThe paper's main number, taxes rising about 30%, compares taxes after people came forward with what they 'claimed' before.\n\nmoderateThe paper says the crackdown raised each person's yearly taxes by about 2% of everything they own.\n\nTo work out how much of a non-European company's gain the EU could tax, the paper assumes that almost every such company makes 10% of its sales in the EU. Many of them, such as Indian and American electricity companies, sell almost nothing in Europe. Using realistic figures removes roughly EUR 6-17 billion from the EUR 65 billion estimate.\n\nmajorMost of the money would have to come from companies based outside the EU, such as Saudi Aramco, Exxon or Shell.\n\nmoderateShell's stock-market value rose by about EUR 43-47 billion in this period, not the EUR 114 billion the paper uses.\n\nmoderateWhen a company pays for an acquisition with new shares, its total stock-market value rises even though its owners gained nothing.\n\nmoderateThe first version of the paper and the authors' widely read column said EUR 80 billion.\n\nThe essay says the richest 1% get 'almost 20%' of income and own 'almost 40%' of wealth. The wealth number counts people in a way (tax-filing units) that gives a higher figure than the way the income number counts them. On the same basis the authors' own figure is about 35%. Other researchers estimate roughly 31-34% for wealth and about 14% for income, though those estimates are disputed. The top 1% clearly hold a very large share, but readers are not told that these exact numbers are contested.\n\nmoderateWhen the essay lists the hard problems in measuring the very rich, it mentions only missing data that would, if fixed, probably show even more inequality.\n\nmoderateThe essay's charts show US inequality falling steeply during World War II.\n\nminorThe billionaire chart has no published data file.\n\nminorThe 1913 point in the billionaire chart cannot be reproduced from the method the caption describes: standard stock-price data give about 0.95% rather than 0.85%.\n\nGovernments, especially China's and Saudi Arabia's, own a big slice of the companies that would pay this tax. When a state-owned company pays the tax to its own government, no new money is raised: the government is paying itself. Taking this into account cuts the real yield by about one-seventh, although it stays roughly the same size.\n\nmoderateThe paper simply multiplies the tax rate by today's stock-market value.\n\nminorThe paper puts the size of the G20 economies in 2019 at $100 trillion; the true figure is about $76 trillion.\n\nminorFor the US, the paper's method understates what the tax would raise.\n\nminorBecause the tax is a share of stock-market value, its yield rises and falls with share prices.\n\nThe study finds no clear rise in multinationals' tax payments, but its measurement is too imprecise to rule out a sizeable rise, perhaps enough to recover about half of the tax the paper says Chile was losing. 'We could not detect an effect' is not the same as 'there was no effect'.\n\nmajorThe paper's strongest evidence that the reform did nothing compares how readily firms paid their related companies in low-tax countries before and after the reform, and it is precise only when it counts whether payments happen at all.\n\nmoderateThe paper's headline number for how strongly payments respond to tax rates shrinks by 60% simply by counting money in thousands of dollars instead of dollars, so it should not be read as 'payments are 5% higher'.\n\nmoderateThe paper checks several routes firms could use to move profits, but some are not observed at all (money coming into Chile), and the goods check covers only about a tenth to a sixth of multinationals' trade, using affiliation defined from data collected after the reform.\n\nmoderateSeveral other careful studies find that rules like Chile's do reduce profit shifting and raise revenue.\n\nThe paper's main table compares what each country's wealth tax raised with what a simple 1% tax on the richest 1% would have raised. Using the data source the paper names, the 'would have raised' numbers come out much lower than printed for Norway, Spain and Switzerland; only France matches. Corrected, Norway's tax raised about as much as the simple tax would, so the table no longer shows Norway's or Switzerland's taxes leaking, although other evidence suggests they did.\n\nmoderateThe paper judges every country's tax against the same imaginary tax instead of against its own rules.\n\nmoderateThe paper says Europe's wealth taxes failed partly because people reported their own wealth with no checks.\n\nmoderateThe paper says Europe's wealth taxes failed because politicians chose to weaken them, not because of economics, but it does not test this.\n\nmoderateThe claim that a Warren-style tax would raise about 1% of national output, and nearly double the tax rate of the 400 richest, assumes the very rich would hide only 15% of their wealth.\n\nTo decide whether a foreign owner lives abroad, the paper mostly relies on a rule of thumb: an owner whose address is unknown but who rents out all their Dubai flats is assumed to live abroad, and that pattern is then extended to everyone else. The rule is sensible but untested, so the $68 billion could plausibly be somewhat lower or higher (roughly $50-75 billion). Dubai would still stand far above the other cities compared.\n\nmoderateThe raw data support the paper's finding that richer Norwegians are more likely to own Dubai property.\n\nmoderateThe first version of the paper (2022) said foreigners held at least $146 billion of Dubai property, twice as much as in London.\n\nmoderateNorway's tax office confirms that about four in five Norwegian owners of Dubai property did not report it, so the paper's main tax point is sound.\n\nmoderateThe paper's $2.7 billion a year of hidden income assumes that owners everywhere comply as poorly as Norwegians, including Gulf owners whose home countries do not tax income at all, and it counts rents before costs.\n\nThe note says about half of all Russian household wealth is held abroad. The study it cites says about half of Russians' financial savings (bank deposits, shares, bonds) are abroad. Once homes, land and businesses are counted, the share held abroad is about a quarter. Russians' offshore wealth is still very large, but the note doubles its share.\n\nmoderateNo survey measures household wealth in Russia.\n\nmoderateThe note says about 20,000 Russians had more than EUR 10 million and about 50,000 more than EUR 5 million.\n\nmoderateThe database version the note used divided the fortunes of the richest Russians by a national total that left out money held offshore and business assets.\n\nmoderateThe figure that Russia's richest keep 60% of their wealth offshore is not measured from Russian data.\n\nThe paper says that after its fixes the two studies agree, but it never re-runs the numbers with all the fixes together. Adding up the fixes that have actually been calculated closes about half of the gap. The rest closes only if every uncertain assumption is set the way that favours the authors.\n\nmajorThe paper says the rival study underestimates the very rich's bonds and other interest-paying assets by 60%.\n\nmoderateA footnote that supports the 60% figure uses arithmetic that cannot work at the interest rate the text says was used.\n\nmoderateThe paper argues the rival study undervalues large private businesses, especially those owned through chains of holding companies.\n\nmoderateThe paper says the two studies agree everywhere except for the richest 0.01%.\n\nThe authors said their estimate of how much hidden income raises the top 1%'s share was, if anything, too low. Their own later work cut it by about a third, from 1.5 to about 1 percentage point, and their new range runs down to zero. The main reason is that redoing the total amount of hidden income with the IRS's newer method gave about a quarter less, the kind of downward revision the reply had dismissed.\n\nmoderateWhen an auditor simply moves income from one line of a tax form to another, nothing was really hidden.\n\nmoderateThe reply says it answers every point the critics made, but it skips several.\n\nmoderateTo answer the critics, the authors re-ran their correction for hidden income several ways and said their original method was, if anything, slightly too low for the top 1%.\n\nminorThe reply argued intuitively that the original method would, if anything, understate evasion at the top.\n\nFor 13 EU countries without detailed multinational data, the note uses the profits of all domestically owned companies, including small, purely domestic firms that the minimum tax would never cover. This inflates the figures for countries such as Poland and Germany and slightly enlarges the estimated carve-out loss. Even removing this component entirely still leaves a loss of 13-17%.\n\nmoderateThe note counts goods held in stock (inventories) as 'substance' that shields profits from the minimum tax, but the rules eventually adopted do not count them.\n\nmoderateA few suspicious entries in the 2016 data, such as one Belgian entry showing almost 90 cents of profit per euro of sales, inflate the euro amounts the note reports.\n\nmoderateAbout half of the EU-wide loss comes from countries whose carve-out effect is not measured directly but borrowed from averages over other countries, an average heavily influenced by Chinese companies with huge domestic asset holdings.\n\nminorPart of what the note calls 'non-haven' income is really unidentified income, some of it taxed almost nothing and probably sitting in tax havens.\n\nFor 13 EU countries, including Germany, Spain and Poland, the 'home-country' part of the estimate is calculated from the profits of all domestic companies, not just multinationals. For Poland this makes the figure at least four times too big; for Germany it may even be too small, so the EU total is probably somewhat too high, but by an uncertain amount.\n\nmoderateThe official company statistics sometimes count dividends paid inside a corporate group as extra 'profit' at headquarters, where they are barely taxed.\n\nmoderateThe authors present EUR 170 billion as a cautious minimum.\n\nmoderateWhen two data sources disagree about profits in tax havens, the report always takes the larger number.\n\nmoderateThe report says one of its sources measures the profits that each country's companies book in tax havens.\n\nThe estimate assumes the government could tax billionaires on the full value Forbes magazine puts on their fortunes, losing nothing to disputes over what private companies are worth or to tax dodging. In 2019 and early 2021 the same authors assumed about 15% would be lost. Using their own assumption brings the yield down to roughly $0.77-0.87 trillion, so '$1 trillion' sits near the top of the plausible range rather than in the middle.\n\nmoderateThe trillion-dollar figure only holds if Congress first raised the top tax rate on capital gains to 39.6%, as President Biden proposed, and that never happened.\n\nmoderateThe proposal has built-in features that the revenue estimate leaves out: a cap for people just over $1 billion, a promise to adjust the tax down if asset values later fall, and interest on the ten yearly payments.\n\nmoderateA one-time tax on gains already made does not change people's incentives, but only if they believe it will never happen again.\n\nmoderateThe trillion-dollar figure assumes Biden's capital-gains plan but counts only half of it.\n\nThe chapter's key number, that the 400 richest Americans paid 23% of their income in taxes in 2018, less than anyone else, was an early estimate made before full data existed. When the authors later updated their own figures (in 2020, before the chapter appeared, and again in 2022 and 2026), the same group came out at 27-29%, about what the average American pays. A separate 2025 study by the authors using actual tax records for the 400 wealthiest finds about 24%, so the claim may still hold, but the chapter gives no warning that its number was this uncertain.\n\nmoderateTo get 23%, the authors divide the taxes of the 400 by their income plus part of the stock-market profits they cashed in, although the chart's own axis says 'percentage of pretax income'.\n\nmoderateWhether lower-income groups pay 'the same' rate as everyone depends on bookkeeping choices: the authors count tax credits for low-wage workers as government spending rather than tax refunds, count workers' Social Security contributions as taxes but leave them out of income, and drop the lowest-income tenth of adults from the chart.\n\nmoderateThe claim that a wealth tax would double the richest Americans' tax rate assumes that only 15% of their wealth would escape it, an assumption the chapter does not mention.\n\nmoderateThe chapter suggests Europe's wealth taxes were scrapped mainly by conservatives and because rich people could move abroad, but several were abolished by left-of-centre governments, and international experts also blamed high running costs and economic side-effects.\n\nThe chapter's most quoted claim, that in 2018 the 400 richest Americans paid a lower tax rate than any other group, depends on a gap of half a percentage point. That gap disappears or reverses with the authors' own updated figures, released before the chapter came out, or with the standard way of counting tax credits for low-income workers. What does hold is that the very richest pay noticeably less than the merely rich just below them.\n\nmoderateThe chapter's figures for how much wealth the very richest hold, and so how much a wealth tax could raise, come from the high end of the available estimates.\n\nmoderateHow much a wealth tax raises depends on how much wealth the rich manage to hide or shelter.\n\nminorThe chart showing how much a wealth tax would have shrunk the biggest fortunes assumes nobody avoids the tax, while the rest of the chapter assumes 15% avoidance.\n\nminorThe chapter says one group's tax rate would rise 'by 14%' when it means 14 percentage points, a much bigger increase (from about 30% to 44%).\n\nAbout a fifth of the '$2 trillion from withholding' in the abstract comes from another part of the package: taxing gains when people die or give assets to charity. Some of that is paid by people well below the $50 million line. In a billionaires-only version, withholding itself raises about $440 billion, not $925 billion.\n\nmoderateWithholding mostly collects, early and in one burst, taxes on gains the very rich have already built up.\n\nmoderateThe $2 trillion figure comes from a budget model whose workings were never published.\n\nmoderateThe authors back up the outside $2.2 trillion estimate with their own $2.4 trillion.\n\nmoderateThe paper promises that nobody will end up paying too much if their assets later lose value.\n\nThe chart says it compares the same tax measure in both countries, but the French line comes from a different calculation (working-age people only, measured against a broader income concept). When the same source's comparable numbers are used, richer people pay a clearly larger share of income in tax in both countries, so the claim that the tax systems are 'approximately proportional' does not hold as stated. The lecture's wider point that public spending does much of the equalising is not overturned, but this piece of support for it is weaker than presented.\n\nmoderateThe chart dates Indonesia's compulsory-schooling law to the late 1970s, but the national programme began in 1984; the big jump in enrollment came earlier, when the government built tens of thousands of schools.\n\nmoderateOther researchers using the same tax records find that the rise in the top 10%'s share of US income since 1980 is about 40% smaller than in the figures the lecture uses.\n\nminorFor the US, the 'flat' tax picture depends on choices: counting Social Security payroll taxes as taxes, counting tax credits for low-wage workers as spending rather than tax cuts, and leaving out the lowest-income ninth of adults.\n\nminorThe 'over 50 percent by 1880' figure for Black children's school enrollment is not a measured number: it comes from scaling Census figures in a way the paper does not explain, and direct census-based estimates are much lower (roughly a quarter to a third).\n\nThe article's striking claim that the 400 richest Americans paid a lower tax rate in 2018 than the average American comes from an early version of the authors' data. In the updated version that the article uses for its income and wealth charts, the difference almost vanishes (27.2% against 28.3%), and in a 2022 update the richest 400 pay slightly more than average. A later study that matched the richest Americans to their actual tax records does support the claim, so it is not disproved, but the article's own evidence for it is fragile.\n\nmajorAbout 40% of the nation's income does not appear on individual tax returns, so the authors have to estimate who receives it, and several of their choices are debated.\n\nmoderateThe article's figures for the poorer half of Americans, such as income before taxes rising from about $17,500 per adult in 1980 to $18,500 in 2018, come from an older version of the data than the one shown in its own charts.\n\nmoderateTo show how much each group would have gained or lost if everyone's income had grown at the same rate since 1980, the article's spreadsheet averages percentage changes in a way that does not give the change in each group's average income.\n\nmoderateThe article says the Federal Reserve's wealth figures 'paint the same picture' as the authors' own.\n\nThe paper says one group of critics mishandles income that never appears on tax returns, and that this explains about half of why their numbers differ. Checked against the government's accounts and the IRS audit study it relies on, the effect more plausibly explains a quarter to a third of the difference. The critics' method does still seem to understate the top 1%'s income somewhat, so the rebuttal points the right way but is roughly twice as strong as the evidence allows.\n\nmoderateTo estimate how much the richest own in bonds and deposits, researchers divide their interest income by an assumed interest rate, so the answer depends heavily on that rate.\n\nmoderateThe paper checks a rival's numbers against Federal Reserve survey data and finds them far off.\n\nmoderateA key number in the paper is that about half of private-business profits are a return on the business's machines, buildings and other assets rather than pay for the owner's work.\n\nmoderateThe paper treats its own revised figures as precise, and as if they could only be too low, while rejecting its critics' figures.\n\nThe memo says the IRS gets no balance sheets from foreign companies owned by Americans. In fact, Americans who control a foreign company or partnership must already send the IRS its balance sheet. The real gap is foreign firms that Americans own without controlling them, so the problem is smaller than the memo says, though it is real.\n\nmoderateThe memo assumes that the central stock depository knows who owns company shares.\n\nmoderateThe memo suggests the IRS could measure racial gaps by borrowing race information from Social Security.\n\nmoderateReporting bank, brokerage and 401(k) balances, home values and debts would capture most of what ordinary families own.\n\nminorThe memo says the IRS lacks information on who owns ordinary corporations.\n\nThe note says its revised numbers now match the Federal Reserve's own wealth statistics almost exactly. The authors' own spreadsheet shows they still differ: in 2018 the richest 1% hold about 25% of their wealth in bonds and deposits in the authors' series versus 22% in the Fed's, and the two estimates of the top 1%'s share of all wealth differ by about 2 percentage points in most years before 2017. The series are close, but 'almost identical' and 'fully consistent' overstate the match.\n\nmoderateThe note lists each change but never says what all the changes together did to the main results.\n\nmoderateIn October 2019 the authors changed how they assign corporate taxes, putting all of them on owners of corporate shares; the note calls this 'the only meaningful way', although official agencies and many economists split the tax differently.\n\nmoderateFor years before 1962 the authors estimate tax rates for each income group separately, and the pieces do not add up: the groups together pay up to about 5% more or less tax than the national total, and in the 1930s the rate shown for the top 0.1% is about 7 points higher than its two sub-groups imply because a cap applied to the very top was not carried through.\n\nmoderateTo turn reported interest income into an estimate of bonds and savings, the authors must assume what interest rate the rich earn.\n\nThe bill limits how much of a billionaire's gains can be taxed in one year to a quarter of their wealth above $1 billion, but the report read the limit as applying to the tax bill instead. As written, the bill would have raised about $9-10 billion for 2020, not $23 billion. Most of the rest would come due in 2021-22, and only from billionaires still living in New York, which undercuts the report's claim that the tax gives them no new reason to leave.\n\nmoderateThe report put the 120 New York billionaires' combined wealth at $530 billion, but Forbes's own figures for the same 120 people that day add up to about $586 billion.\n\nmoderateThe report says research shows state taxes on the very rich are always below the point where they start to lose money.\n\nmoderateThe report says the tax is clearly constitutional.\n\nmoderateThe estimate assumes New York would value billionaires' mostly private companies at Forbes's figures.\n\nThe authors say they knocked 20% off their estimate to allow for tax dodging. In their table, though, that cut is not applied to California's 99 billionaires, who hold more than a third of the taxable wealth. Correcting this trims the headline only a little, to about $6.9 billion. It does make the figures for a billionaires-only version of the tax roughly a fifth to a quarter too high.\n\nmoderateThe authors did not publish how they built their numbers, which can be rebuilt only by working out several hidden choices.\n\nmoderateThe report says the tax was built to avoid constitutional problems, but it never discusses the part most likely to be challenged in court: taxing people for up to ten years after they move away.\n\nmoderateThe report says the tax would bring in the same share of the economy every year, starting right away.\n\nmoderateThe report argues the rich will not leave, because California's share of millionaires kept rising after a 2012 tax increase.\n\nThe paper says the US could tax foreign tax-haven companies in proportion to their US sales, using reports that already exist. But those reports show where a company's subsidiaries are based, not where its customers are, and the agreements for sharing them between governments forbid using them to set tax bills. New reporting would be needed, so this part of the plan is harder to carry out than the paper suggests.\n\nmoderateSome of the low-taxed foreign profits the paper counts are already taxed by the US today under older anti-avoidance rules.\n\nmoderateThe paper assumes the US would keep two-thirds of the extra tax.\n\nmoderateThe paper's favourite estimate uses tax rates taken from profitable companies only, and in some countries these rates look too low, because internal dividends and past losses may make companies appear to pay less tax than they really do.\n\nmoderateThe paper's first sentence says the world's average corporate tax rate fell from 49% to 23%.\n\nThe 'about 25%' figure is not measured; it is simulated by assuming that 80% of the extra earnings of graduates of better colleges is caused by the colleges rather than by the kind of students they admit. Other research finds anything from almost no such effect to a large one. The simulated gain moves almost one-for-one with that assumption, and more than half of it comes from assuming that richer students who lose their places would earn less, so the true figure could easily be 10-20% rather than 25%.\n\nmoderateThe paper says colleges are about as divided by family income as neighborhoods.\n\nmoderateAbout a quarter of college students never took the SAT or ACT, so the authors filled in plausible scores for them, and the check they offer is weaker than the paper says.\n\nminorSome colleges look like 'mobility engines' partly because they sit in very unequal places such as New York, Los Angeles and the Texas border, with many poor families and some very high wages.\n\nminorAn appendix claims the paper's numbers agree closely with a well-known earlier study.\n\nThe paper's headline says world inequality went up after 1980. In the authors' own numbers that is true only if you look at the share going to the very richest. By the most common overall yardstick (the Gini coefficient) world inequality was flat, and the poorer half of the world increased its share of income by about a fifth. So 'the top pulled away' is supported, but 'inequality rose' as a general statement is not.\n\nmajorHidden in the authors' computer code is a line that, without explanation, assumes Middle Eastern incomes in the early 1980s were a third lower than in 1985, when the authors' own data say they were about a fifth higher (the oil boom was ending).\n\nmoderateThe paper says that neither the rise of emerging economies after 2000 nor the 2008 financial crisis stopped global inequality from rising.\n\nmoderateThe authors' own database now reports much smaller gains for the world's richest over 1980-2016 than this paper does: for example 72% instead of 101% for the top 1%, and 120% instead of 235% for the top 0.001%.\n\nmoderateChina's spectacular growth figure (831%) depends on the authors adjusting China's official inflation numbers downward to its growth.\n\nEconomists agree that US income inequality has risen since about 1980 but disagree about how much. A leading alternative estimate finds a rise only about half as large as the author's, partly because a 1986 tax reform changed how income was reported. The essay doesn't mention this debate. Most data sets, including the critics' own, still show today's inequality back near its level of the early 1900s, so the essay's basic message stands.\n\nminorThe essay says inequality began rising again with Reagan's election in 1980.\n\nminorBefore taxes, the richest 1% of Americans now get about as large a share of national income as a century ago.\n\nminorThe essay implies that Reagan-era, pro-market policies caused the rise in inequality.\n\nThe essay blames rising inequality on a list of free-market policies, as if that were settled, without giving evidence. Research, including a study printed in the same journal issue, finds that changes in technology and in the demand for educated workers explain a large part of the growing wage gaps. The policies on the list did play a role, so the claim is incomplete rather than wrong, and the essay's main argument does not rest on it.\n\nmoderateThe essay says flatly that minimum wages do not cost jobs.\n\nminorThe essay says that freeing up financial markets brings crises instead of growth.\n\nminorThe essay lists the 'dismantling of the welfare state' among the causes of rising inequality.\n\nminorThe essay treats the stagnation of working-class incomes as an established fact.\n\nThe column says its revenue figure already allows for wealthy people dodging the tax. In fact the calculation multiplies the tax rates by today's wealth and assumes nobody changes behaviour. Suppose the rich shield only 15% of their wealth, the figure the same authors assumed for a US proposal a year earlier. The tax then raises about 0.9% of GDP instead of 1.05%, and repaying the debt takes about 11 years rather than 10. With larger but plausible responses it takes 13-16 years. The tax would still raise a lot of money, but the precise promise is not backed by the calculation.\n\nmoderateThe authors say a temporary wealth tax only hits wealth people already have, so it does not discourage new investment.\n\nmoderateTo justify the plan, the column says post-war Germany paid off its war debts with highly progressive, temporary wealth taxes instead of inflation, and that this launched its 'economic miracle'.\n\nminorThe estimate is built from a few round numbers, such as how large European wealth is relative to the economy and what share the top 1% hold.\n\nminorIn the printed book, the footnote that should explain how tax evasion was handled is blank, so book readers get the claim with no explanation.\n\nTo project 30 years ahead, the model needs to know how much people value leaving wealth at death, and eight years of data cannot tell. The paper fills the gap by assuming that the tax cut does not change how fast people's wealth grows in their 80s. The evidence it cites for that assumption fits any value equally well, so the long-run numbers could easily be half as large, or somewhat larger.\n\nmajorEarlier drafts of this same study, using what the authors then called their preferred methods, found much smaller effects.\n\nmajorThe comparison group for the very wealthy was supposed to be households whose tax did not change.\n\nmajorBefore the reform, the 'treated' rich households were already falling behind the comparison group, and the paper assumes that gap would have kept widening.\n\nmoderateThe abstract says the very richest respond more than the merely wealthy.\n\nWhen the paper's own most cautious assumptions are used together, counting hidden income slightly lowers the top 1%'s share of income (about 19.7% instead of 20.3%) rather than raising it. The paper shows its cautious assumptions only one at a time, so its flat statement that evasion makes measured inequality higher goes beyond its evidence. Its central estimate (about +1 point) is still a reasonable best guess.\n\nmoderateThe headline '9 to 33 points' compares the new estimates with what auditors directly found.\n\nmoderateTo spread the hidden business income the audits missed, the main scenario assumes the richest owners under-report at the same rate as everyone else.\n\nmoderateIn the widely cited 2021 version, the IRS's standard correction on its own raised the top 1%'s income share by 0.6 points.\n\nmoderateThe estimate of income hidden offshore borrows the share of undeclared money from Swiss bank cases.\n\nThe headline, that reshuffling students could cut the rich-child advantage by about a quarter, holds only if 80% of the earnings edge of graduates of better colleges comes from the college itself rather than from whom it admits. The paper’s test of that assumption is indirect. Later studies disagree: some find colleges matter about that much, others (in Texas) find far less. With more cautious assumptions the effect would be roughly 10–20% instead of 25%: still positive, but smaller.\n\nmoderateThe paper says its test shows ‘at least 80%’ of the college earnings advantage is caused by colleges and that this matches earlier research.\n\nmoderateAbout a quarter of students, including almost half of low-income students, had no test score, so the authors filled one in from similar students with similar adult earnings.\n\nmoderateTo put ACT and SAT takers on one scale, the authors used a conversion table made for the new SAT introduced in 2016, but their SAT scores come from the old test of 1996–2004.\n\nmoderateIn the simulation, every gain for a low-income student moving to a better college is matched by a loss for a richer student moving down, and colleges are assumed not to change when their student bodies are transformed.\n\nThe interview says the richest 1% of Americans went from owning 20% of all private wealth in the early 1980s to 40% today, a doubling. The authors' own published figures say it was about 24% then and about 39% recently: a big increase, but about 60% rather than 100%. The direction is right, but the size of the change is exaggerated by roughly a quarter or more.\n\nmoderate'About 40% of multinational profits are moved to tax havens' sounds like 40% of everything big companies earn.\n\nmoderateThe 40% figure is backed by the Federal Reserve's own household survey (about 38-39% in 2016), so the level is fine.\n\nmoderateThe 40% figure comes from one well-known study by Zucman and co-authors.\n\nminorThe interview says an economic rule, the 'Ramsey rule', tells us not to tax things that react strongly to taxes.\n\nThe authors say a 6% tax on all income would by itself pay for health insurance for everyone. Their own spreadsheets show it raises roughly two-thirds to four-fifths of the cost they assign to it. Their overall plan still balances, but only because other new taxes chip in, or because of extra income tax on higher wages that the authors never count.\n\nmoderateToday, health premiums paid by employers are not taxed.\n\nmoderateThe book says its plan uses a 6% tax.\n\nmoderateThe paper the book cites for 'complete details' has never been made public, and the code that computes who would pay the tax has not been released.\n\nmoderateThe plan only adds up if public insurance costs about $8,000 per insured worker, against about $13,000 for today's employer plans.\n\nThe famous 'billionaires pay less than the working class' result rests on a gap of about one percentage point. Count the tax credits that low-income workers receive through the tax system as reducing their taxes, as government agencies do and as the authors themselves did in a later version of their online calculator, and the working class pays less than billionaires. Other reasonable choices push the other way, so the honest conclusion is that the two groups pay roughly similar rates, not that billionaires clearly pay less.\n\nmajorThe 2018 figures were estimates made before that year's tax data existed, and they used early numbers that later proved to understate corporate taxes.\n\nmajorThe book says taxes on the rich have collapsed since the 1950s.\n\nmoderateFor working people, the study first subtracts Social Security payroll taxes from their income and then counts those same payroll taxes as taxes paid, even though the book tells readers their income figure includes payroll taxes.\n\nmoderateFor the richest, the authors add part of their stock-market gains to their income before computing tax rates, and the book does not tell readers this.\n\nOne of the paper's two main sources, leaked client records from HSBC's Swiss private bank, suggests that more than half of all hidden wealth belongs to the richest 0.01% of households, but that result rests largely on a single Norwegian family with about $288 million at the bank, which the paper never mentions. Leaving that one family out lowers the paper's headline estimate of the share of taxes the very richest evade from about 24% to 21%, and undercuts the paper's claims that its different sources confirm one another. The main conclusion survives because the other main source, records of people who came forward in tax amnesties, does not involve this family and on its own gives 23%.\n\nmoderateBesides the data work, the paper offers a theory of why the banks that help people hide money mostly serve the very rich.\n\nmoderateThe richest 0.01% are estimated to hide about 12% of their wealth offshore yet evade about 24% of their taxes, because the paper assumes the hidden money earns a fully taxable 4.5% a year, about twice the rate at which their declared fortunes generate taxable income (about 2.2% a year); a footnote describes this inaccurately.\n\nmoderateThe paper suggests that its Scandinavian findings may, if anything, understate evasion by the rich elsewhere, and its pattern has been applied to other countries, including the United States.\n\nmoderateThe earlier, widely circulated 2017 working-paper version claimed that counting hidden wealth substantially changes the long-run story of inequality: for instance, that it cancels out half of the fall since the 1930s in the share of wealth held by Norway's richest 0.1%, and lifts the richest 0.01% above their 1940s level.\n\nThe note says the tax would completely close the gap between how fast billionaires' fortunes grow and how fast ordinary families' wealth grows. The authors' own simulation of the tax - the one drawn in the note's figure - shows the richest 400 still pulling ahead, only more slowly: about a third of the gap remains, and more if some evasion is allowed. The tax would shrink the gap a lot, but not eliminate it.\n\nmajorThe note assumes every rich family hides the same 16% of its wealth whether it pays a 1% or an 8% tax.\n\nmoderateThe ten-year figure simply multiplies the first year's revenue by 13, as if the tax would not shrink the fortunes it taxes.\n\nmoderateThe note's dramatic 'what if the tax had existed since 1982' numbers assume nobody evades, while its revenue estimate assumes everyone hides 16%.\n\nmoderateThe estimate relies partly on a wealth dataset that shows more wealth at the very top than other sources - including a revised version the same authors published the same month.\n\nThe $212 billion figure depends on a guess that the very rich would hide or shelter only 15% of their wealth. That guess came from averaging four foreign studies in a way that leaned toward small responses; for example, it used the small Danish estimate for the moderately rich rather than the much larger one the same study (co-written by Zucman) found for the very rich. Reasonable alternative assumptions give about a quarter less money in the first year, so the estimate is better described as optimistic than as middle-of-the-road.\n\nmoderateThe note says the rich escape about half of the estate tax, citing two studies.\n\nmoderateThe note says audits of big estates collapsed from 65% to under 9%.\n\nmoderateThe note answers the critics' lowest number ($25 billion) as if it were their forecast, even though the critics had said it was probably too low and had offered $75 billion as an optimistic alternative.\n\nmoderateThe note's striking claim that just 15 people would pay more than the critics' total for all 75,000 families mixes two different taxes: the critics' number was for the basic 2% tax, while the note's number adds the extra 1% charged on billionaires and assumes no avoidance at all.\n\nThe paper's summary says multinationals pay lower tax rates than local firms, but the paper never measures tax as a share of profit. Its own chart implies multinationals pay roughly the same tax per peso of reported profit (about 11% versus 10%). They pay less relative to their wage bill only because they report less profit relative to it. So this paper does not show the 'lower tax rate' claim, though it might hold in other data.\n\nmoderateThe paper says tax-planning advisers at Chile's four biggest consulting firms grew about 15 times after the reform.\n\nmoderateThe finding that multinationals report lower profits and pay less tax comes from one particular statistical comparison that outsiders cannot check.\n\nminorThe paper's key chart is based on confidential tax records, and the published description leaves out basic facts.\n\nminorThe summary says multinationals make up a large share of Chile's GDP, but the paper actually measures their share of company sales (40%), which is a different thing; company sales add up to almost three times GDP.\n\nThe paper says the richest tenth's share of Chinese wealth jumped from 40% to 67% in twenty years. But the early years come from one survey and the later years from a different one, and the correction applied to the surveys was quietly changed from year to year, which made the rise look smooth. Wealth very likely did become more concentrated; how much and when is far less certain than the paper suggests.\n\nmoderateThe paper says high saving explains over half of why Chinese wealth grew so much faster than income.\n\nmoderateIn 1978 more than half of China's measured wealth is farmland that could not be bought or sold, so its value had to be assumed.\n\nmoderateThe paper offers a market-to-book ratio of about 1 for Chinese companies as evidence that its valuations are sound, and even as a sign of strong shareholder rights.\n\nmoderateThe published tables were produced from a later, never-posted version of the data.\n\nThe paper's model says billionaires' fortunes could be taxed at about 6% a year before the tax starts bringing in less money, but the model assumes billionaires do nothing to shrink or hide their taxable wealth. Using the authors' own estimate of how much the rich hide, the best rate for revenue falls to about 4%, and lower if they also save less. So the claim that an 8-10% billionaire tax is about the best for revenue does not hold up, although taxes of a few percent would still raise substantial money.\n\nmoderateThe paper assumes the rich would hide only 15% of their wealth from the tax, whatever the rate.\n\nmoderateThe paper's striking claim that the 400 richest Americans pay a lower total tax rate than middle-class families rests on gaps of only half a point to two and a half points.\n\nmoderateEstate-tax records suggest wealth is much less concentrated than other sources show.\n\nmoderateHow much the richest 0.1% own depends heavily on an assumption about the interest rate they earn on bonds and deposits.\n\nThe paper's 'world' wealth figures treat hundreds of millions of people in Eastern Europe and the former Soviet Union as if they were as rich as people in Britain, France and Spain, and convert currencies in a way the paper never mentions. With reasonable alternatives, the rise in the richest 1%'s share shrinks from about 5 points to between about 1 and 4 points, and the poorer three-quarters' share rises instead of staying flat. The richest 1%'s share still goes up in every version.\n\nmoderateThe tax-based US estimate assumes that rich and ordinary families earn the same interest rate on their savings.\n\nmoderateTo defend its tax-based numbers, the paper cites studies as saying things they do not say - for example, that the richest earn lower interest rates, or that the two US data sources agree within statistical error - and leaves out evidence, including the author's own earlier finding, that the richest earn higher interest rates.\n\nmoderateThe paper says the survey and the tax records give 'virtually identical' figures, but it compares a group of 1.26 million households with a group of 1.7 million tax-filing units.\n\nmoderateThe paper says the Forbes rich list and the tax-based estimate move together 'strikingly' from year to year; in the paper's own data they move in opposite directions about half the time.\n\nThe authors' own method says people hide more wealth when the tax rate is higher, but they applied the same 15% to billionaires facing 3% or 6% rates. Applied consistently, most of the extra $0.9 trillion promised from the higher billionaire rate disappears; the effect on the main estimates is only a few percent.\n\nmajorThe estimates assume the very rich would hide or shelter only 15% of their wealth.\n\nmoderateIn 2019 the authors averaged two data sources; one of them was later revised by the authors themselves and now shows about a quarter less wealth above $50 million.\n\nmoderateThe estimates come as precise numbers, but the survey behind them includes only a handful of super-rich families; one family alone accounts for about an eighth of the survey's taxable wealth.\n\nmoderateRecords from the existing estate tax show the very rich reporting far less wealth at death than surveys and Forbes lists suggest, and the letters do not explain this gap.\n\nThe shortcut gets about the right total for the top 1% for partly the wrong reasons. It gives the richest group too large a share of the income that never shows up on tax returns, and it ignores that the people at the top of the full national-income ranking are not the same people as those at the top of the tax-return ranking. In the US data these two mistakes roughly cancel, so the match does not show that the authors' complex method boils down to two simple rules.\n\nmajorTo argue that a rival study (Auten and Splinter) is unrealistic, the paper adjusts its two rules until it reproduces the rival's numbers, then says the adjustment needed -- capital income becoming very equal -- contradicts the evidence that wealth became more concentrated.\n\nmoderateOne of the shortcut's two rules quietly folds in capital gains (profits from selling assets), computed in a slightly inconsistent way, although the paper describes it as using ordinary taxable capital income.\n\nmoderateThe paper cites an IRS audit study as backing its own way of assigning unreported income to the rich and contradicting the rival's.\n\nminorThe paper converts the rival's percentage into dollars using the wrong total, which makes the rival's top 1% look as if it gets less money than the top 1% in raw tax data.\n\nThe authors' computer code quietly replaced the Middle East's average income for 1980-84 with a much lower number, and that number is contradicted by the data they were using. This makes the world's richest 1% look as if they started from a lower point in 1980, so the rise in their share of world income looks about a quarter larger than the data support. The headline 'twice as much' comparison barely changes.\n\nmoderateThe report's 'global' wealth estimate silently treats about 150 million people in Russia, Ukraine and neighbouring countries as if they were as wealthy as typical people in Britain, France and Spain.\n\nmoderateFor about a third of the world's adults, including Japan, Korea and Indonesia, the report has no income-distribution data and borrows other countries' patterns.\n\nmoderateThe database behind the report has been revised many times since 2017.\n\nmoderateThe report's estimate of how fast America's richest gained wealth used a method that assumed the rich earn the same interest rate on their savings as everyone else.\n\nAbout two-fifths of national income never appears on anyone's tax return, so the authors had to decide who receives it, and their choices tend to give more of it to the richest. With other reasonable choices, the rise in the top 1%'s share since 1980 ranges from about half as large to nearly as large as reported. Under the main critics' choices, the top 1% never overtakes the bottom half. The paper gives single numbers with no ranges, so figures like '81 times' are one estimate among several, even though the overall direction is not in doubt.\n\nmoderateThe spreadsheet formula that computes government transfers to the middle class leaves out a needed weight and overstates them by about a quarter.\n\nmoderateThe authors used records of tax-free retirement payouts to work out who owns retirement savings.\n\nmoderateSpending on schools, roads and defence has to be assigned to someone.\n\nmoderateThe paper says that since 2000 the richest 1% have gained mainly from owning capital, especially from profits kept inside corporations, and that capital provides over half their income.\n\nTo estimate who gets the income that never shows up on tax forms, the authors had to make assumptions, and other researchers using different assumptions find that the rise in the share going to the richest 1% was only about half as big. Who is right is still debated; either way, the gap between the top and the bottom in the US widened.\n\nmoderateThe authors later found and fixed a mistake in how they assigned retirement income, and with that and other updates their own current figures show the richest 1% gaining a little less and the poorer half gaining a little (about 7% over 37 years) rather than nothing.\n\nmoderateTo turn China's money incomes into 'real' growth, the authors used their own estimate of price increases instead of the official one, without saying so in the chapter; with the official figure China's growth would look almost twice as large, and with another respected estimate about a third smaller.\n\nmoderateThe chapter says its new estimate for China's top 1% (about 13% of income) is a minimum, but the underlying study itself points to reasons it could be too high as well as too low, and the tax data behind the correction exist only for 2006-2010 and were stretched to cover 1978 and 2015.\n\nmoderateThe table gives growth figures for tiny groups at the very top (a few hundred to a few thousand people) as if they were precise, but these numbers are mostly modelled rather than observed and have changed a great deal between versions, for France from +158% to +47%.\n\nThe paper assumes that in every country the richest 0.01% of households own about half of all hidden offshore wealth, because that is what Scandinavian data showed. It says it checked that other assumptions make little difference, but those checks are not in its published appendix or data. With a plausible lower figure, the extra inequality it reports for France, Britain and Spain shrinks by half or more, and France no longer overtakes Scandinavia.\n\nmajorThe claim that most of the Russian super-rich's wealth is hidden abroad is not measured.\n\nmajorVenezuela is the paper's only Latin American example of offshore wealth near 60% of GDP.\n\nmoderateTo decide which country owns the money in each tax haven, the paper uses several rules of thumb.\n\nmoderateTo extend its estimates back to the 1950s, the paper says it assumed offshore wealth grew like the wealth held in Swiss banks, but the spreadsheet actually uses a faster-growing series covering all tax havens.\n\nThe paper says almost half of the fall in the foreign taxes paid by US multinationals came from moving more profits into tax havens. Redoing the calculation the paper describes, with the authors' own data, gives roughly one-sixth to one-quarter. Lower tax rates in ordinary countries did most of the work. The paper's numbers appear to measure how much profit was sitting in havens in 2015, not how much more was moved there after 2000.\n\nmoderateThe paper says low foreign taxes explain half of why US investments abroad earn more than foreign investments in the US.\n\nmoderateThe paper links the sharp fall in taxes paid by US oil companies abroad to the 1991 Gulf War, and suggests it may have been a reward for US military protection of oil states.\n\nmoderateFrom 1994 the paper switches to a definition of oil-company profits that no longer subtracts the cost of using up oil reserves.\n\nmoderateThe paper says the 2017 US tax law lets it measure, for the first time, the full tax US companies pay on foreign profits: about 20%.\n\nThe brief's best-known number, that 40% of multinationals' foreign profits are moved to tax havens, rounds up an estimate its source puts at 36%. About half of that estimate comes from the authors' own top-ups to tax havens' incomplete statistics. Other reasonable methods give figures nearer a quarter to a third; some company-level studies find even less, and one finds more. Profit shifting is clearly very large, but the 40% is probably too high and much less certain than the brief suggests.\n\nmoderateThe '15%' rounds up an estimate of 14% for 2015, before the 2017 US tax reform.\n\nmoderateIf one country adopts the plan, companies can no longer escape that country's tax by moving profits or factories elsewhere; that part holds.\n\nmoderateThe plan works only if tax authorities can tell where a company's customers really are.\n\nminorThe brief compares two different things: profits estimated to have been artificially moved (worldwide) and all profits recorded in havens (US firms).\n\nThe paper claims that if a tax on wealth were announced far in advance, people would react so strongly that the best tax would be zero. It uses this to argue for its own new method. In the paper's own model the reaction stays limited, and the best tax stays positive. The paper's main tax formulas are unaffected; one of its arguments for preferring its new method falls away.\n\nmoderateThe paper's numbers say income from wealth should be taxed somewhat more heavily at the top than wages, but only if savings and work respond to taxes equally.\n\nmoderateOne of the paper's formulas for taxing different kinds of assets (say, homes versus stocks) leaves out an adjustment for their different rates of return.\n\nminorThe numbers in the text and the curves in the figures don't quite match.\n\nminorIn a side section linking the paper to an older model in which patience depends on consumption, one formula has a plus sign where a minus sign belongs.\n\nRussian tax statistics group people by their gross takings: for a trader, total sales; for someone selling shares or a flat, the full sale price. To turn those takings into income, the authors assume everyone deducts 70% as costs. But most people in the top brackets are business owners and asset sellers who typically deduct 80-95%. With more realistic deductions, the share of income going to the top 1% falls from about 20% to somewhere between 14% and 19%. That is no longer clearly as high as in the US, though still far above what surveys show.\n\nmajorTo estimate wealth hidden abroad, the authors add up money that left Russia unrecorded each year.\n\nmoderateThe appendix says the authors used the deduction rate actually observed in the tax statistics (about 74% in 2015), but the computer code uses 70%.\n\nmoderateThe paper's sensitivity checks never changed the assumption that matters most for the top-1% figure, so the reassuring statement that all variants give similar results is not a real test.\n\nmoderateBetween the draft and the published version the authors changed how they estimate hidden wealth, roughly doubling the money counted as leaving the country.\n\nThe authors' computer code quietly replaced the Middle East's average income for 1980-84 with a figure almost half the size of the official statistics they had loaded, without any explanation. Because the rich of the Gulf oil states were among the world's top earners in 1980, making them poorer in 1980 makes the world's richest look as if their incomes grew much faster afterwards. Undoing the change cuts the reported growth of the world's richest by about a fifth, although the richest 1% still gained about twice the poorer half's share of growth.\n\nmoderateFor about a fifth of the world's adults (Japan, Indonesia, Pakistan, Bangladesh and other Asian countries without good data) the authors simply copied the pattern of inequality from China and India.\n\nmoderateTo project incomes to 2050, the authors assume each income group keeps getting the same slice of growth it got since 1980; where that slice was negative, the code quietly sets it to zero.\n\nmoderateFor several regions the authors have no data on how income was shared out in 1980, so they assume it was shared the same way as in the first year they do have data (2001 for Latin America, 1990 for the Middle East).\n\nmoderateWhen the same calculation is redone with the newer version of the authors' own database, the headline result (the richest 1% got about twice the poorer half's share of growth) comes out the same, but growth for the very richest is much smaller: about 130% rather than 235% for the top 0.001%.\n\nRussian tax records list only people's gross takings, such as total proceeds from selling shares or business turnover, so the authors had to guess how much of that is actual income. They assumed that 30% of the takings at the top are income, more than the tax records themselves imply, even though top filers are largely business owners and share sellers with large costs. With more realistic assumptions the richest 1% of Russians get roughly 16-19% of national income rather than 20%. Russia's lead over China shrinks by a quarter to two-thirds, but Russia stays ahead.\n\nmoderateTo compare billionaire fortunes with the size of each economy, the authors converted Russia's national income into dollars at the 2016 exchange rate, when the ruble was very weak, instead of at each year's actual rate.\n\nmoderateThe paper says the richest 1% of Russians took more than two-thirds of all income growth between 1989 and 2016, but the authors' own source puts it at 56%.\n\nmoderateThe paper suggests that Russia's 'shock therapy' privatization caused its inequality explosion while China's gradual approach held inequality down.\n\nmoderateThere are no Russian tax records for the 1990s, and the authors switch from one household survey to another in 1994.\n\nThe chapter says it measures wages plus benefits plus self-employment pay. Its charts actually use a slightly different measure, which subtracts payroll contributions and gives each wife half of her husband's pension and Social Security. On the chapter's own description, women would earn about 55-56 cents per man's dollar instead of 57, and the typical man's earnings would have grown about 10% over 50 years rather than not at all. The main message (a large gap, slow growth for men) is unchanged.\n\nmoderateThe chapter says women had nearly caught up with men in having jobs by the early 1990s.\n\nminorThe chapter suggests its long-run numbers come from tax forms that report each spouse's wages.\n\nminorWhether business owners' profits count as pay for work or as investment income is a judgment call, and it changes who appears among top earners.\n\nminorThe chapter says young men earn 1.3 times what young women earn and older men almost twice what older women earn.\n\nThe paper's key medium-run number relied on an early projection of 2015 incomes. Once the IRS's complete 2015 data arrived, top incomes turned out about 3% lower than projected. Rerun with those data, the paper's own calculation says about 31% of the expected extra revenue was lost to behavioral responses, not 'at most 20%'. Most of the money was still raised, so the broad message stands, but the headline figure does not.\n\nmajorTo measure the lasting effect, the paper has to guess how fast top incomes would have grown without the tax increase, and that guess rests on just two years of data.\n\nmoderateThe paper supports its key assumption by saying the same forecasting rule worked after two earlier recessions.\n\nmoderateThe paper's revenue arithmetic uses a shortcut that works for small tax changes.\n\nmoderateThe paper measures top incomes as a share of all income, but top incomes are themselves part of that total, which partly hides their own drop.\n\nThe lecture argues that the rich cannot have been hiding much income in the 1960s, because their charitable donations, which lowered their taxes, were not unusually high then. But donations also depend on tax incentives and on changing habits of giving, and the data cover only the US after 1962. They cannot settle how much tax avoidance mattered, let alone over a whole century or in other countries. The finding that inequality rose is not affected; the claim that avoidance has been ruled out is.\n\nmoderateThe figure that the richest 0.1% of families own about 22% of all household wealth, nearly as much as just before the 1929 crash, assumes the very rich earn the same interest rate on their savings as everyone else.\n\nmoderateTo compare how the top 1% and everyone else fared, the lecture uses income reported on tax returns, which it admits leaves out much of ordinary workers' pay, such as employer health and pension benefits.\n\nmoderateThe charts show the top US tax rate at 70% until 1981, but from 1972 the top rate on salaries, which is how executives are paid, was capped by law at 50%.\n\nmoderateThe lecture shows that places and periods with lower top tax rates had a richer top 1%, and that economic growth did not obviously differ.\n\nTaken together, the poorer half of American families owns only about 1% of all wealth, so in that sense the comment is right. But it is not true that half of all families individually have nothing: the typical family had about $81,000 in 2013, and only about one family in eight had zero or negative wealth. The wording is loose, but it does not change the comment's point that wealth is extremely concentrated.\n\nminorTwo small typing mistakes; they change nothing in what the comment says.\n\nThe chapter says that since 1980 the bottom 90% of Americans got only about a third of the growth in average income. That figure is computed correctly from the authors' data, but other credible ways of counting put it between about 36% and 50%. Every method agrees the bottom 90% fell behind after 1980; how far behind is less certain than the chapter suggests.\n\nmoderateThe chapter says government taxes and transfers did essentially nothing to slow the rise in inequality since 1980, because bigger transfers and less progressive taxes cancelled out.\n\nmoderateThe chapter notes that countries that cut top tax rates the most did not grow faster, and concludes that the rich responded to tax cuts by grabbing a bigger slice of the pie rather than by working harder.\n\nmoderateThe chapter says the US grew faster when finance was tightly regulated (1933-1980), so regulating finance does not hurt growth.\n\nmoderateThe chapter cited new estimates showing the richest 1% going from 23% to 42% of US wealth between 1978 and 2012, and raised the possibility that wealth inequality was 'exploding'.\n\nThe studies show clearly that, near the ceilings and in the short run, employers do not push their share of these contributions onto the individual workers concerned. But for several countries the data cannot tell 'exactly the legal split' apart from 'employers pay somewhat more or less than their legal share', and one German period shows employers paying noticeably more. The paper presents the exact legal split as an established result, which overstates how precise the evidence is.\n\nmoderateThe overview says the four country studies found no break in the earnings distribution anywhere.\n\nmoderateNot seeing people adjust their pay around the ceiling does not mean pay is completely insensitive to contribution rates.\n\nmoderateThe studies look at what happens to an individual's pay right around a threshold that moves every year.\n\nminorFor most of the UK years studied, only the worker's contribution stops at the ceiling.\n\nAnother team using the same US tax records, but different assumptions about income that never shows up on tax forms, finds that the top 1%'s share grew only about half as much as this paper says and that the poorer half's pre-tax incomes grew by about 40% rather than not at all. Experts still disagree about who is right, so this is a serious but unsettled doubt about the size of the US numbers, not about whether inequality rose.\n\nmoderateHow fast Chinese incomes really grew depends on how one corrects for price increases, a long-running dispute about Chinese statistics.\n\nmoderateThe US estimates treated some money that wealthy people merely moved from one retirement account to another as if it were retirement income, which made the top look somewhat richer.\n\nmoderateWhen the same researchers updated their data in later years, several of this paper's numbers changed: the US poorer half's growth went from -1% to between +3% and +7%, France's poorer half no longer grows quite as fast as the average, China's top 1% nearly caught up with its poorer half, and Japan's government wealth turned positive.\n\nmoderateChina published the tax statistics needed to correct its household surveys only for 2006-2010.\n\nTo count public services like schools, police and defence in people's incomes, the guidelines share them out in proportion to income and call this 'neutral'. In fact it is the choice that shows the least redistribution. Giving everyone the same amount would cut the top 1%'s US share from about 15% to 12.5% and raise the poorer half's from 20% to 25%, and the 2016 text did not show this alternative.\n\nmoderateFor France before 1970, the guidelines describe one way of converting old tax statistics and say a second way gives nearly the same answer.\n\nmoderateThe guidelines produce very detailed numbers but give no way of saying how uncertain they are.\n\nmoderateTax returns capture only about half to 60% of national income.\n\nmoderateThe guidelines estimate wealth from the interest and dividends people report, assuming everyone earns the same return on each kind of asset.\n\nThe method infers how much each family holds in bank accounts and bonds from the interest it reports, assuming everyone earns the same interest rate. In reality richer families earn noticeably higher rates, because more of their savings are in bonds, which pay more than bank deposits, and the gap widened as deposit rates fell to almost nothing by 2012; as a result the method credits the rich with too much of this wealth and the middle class with too little. Fixing this still leaves a large rise since the late 1970s in the share owned by the richest 0.1%, but puts that share at roughly 16-20% in 2012 rather than 22%, removes most of the increase after 2000, and leaves it clearly below the 1929 peak of about 25%.\n\nmoderateThe paper says its method passed tests against three independent sources of information on wealth, but those tests compare long-run averages or special groups (such as charitable foundations and wealthy people who have died), and the paper's own figures show the method's central assumption failing in the years after 2000 that drive the headline.\n\nmoderateThe authors later acknowledged an error in their 1930s estimates, which made the richest 0.1% look considerably wealthier during the Great Depression than they were (for example, about 22% of all wealth in 1932 instead of about 17%).\n\nmoderateBonds held through investment funds pay 'dividends' rather than 'interest' for tax purposes, but the method counts them among the assets that produce interest, which inflates the wealth it assigns to each dollar of interest reported, and interest goes disproportionately to the rich.\n\nmoderateThe paper says the middle class's share of wealth fell after the mid-1980s mostly because families took on more debt, but its own figures attribute only about a quarter of the fall to debt.\n\nThe paper's main selling point is that fairness ideas such as 'people who already pay a lot of tax deserve more' or 'focus on the poor' can be plugged straight into the standard tax formulas. A later published proof shows that when people's earnings respond to taxes, plugging in these particular ideas can produce circular judgments: policy A beats B, B beats C, and C beats A. The 'best' tax it recommends then reflects no consistent set of values. The method still works for more traditional fairness views, and newer work suggests a fix, but the paper's broadest claim is overstated.\n\nmoderateIn the survey's posted data, the answers to two of the five 'which family deserves the tax break?' questions were matched to the wrong pair of families, so 40% of those answers were effectively scrambled in the published table.\n\nmoderateThe paper turns survey answers into a 'preferred' tax rate of about 73% using a simple statistical shortcut that misbehaves in this kind of data.\n\nmoderateTo illustrate an 'equal opportunity' tax, the paper splits Americans into just two groups (parents below or above the middle of the income ladder) and finds rates about ten points lower than under a traditional benchmark.\n\nminorIn an appendix, the authors argue that a society that wants to tax 'lucky' income could get stuck at a 100% tax rate, because once nobody works, all income looks like luck.\n\nTo make the state figures match the official national figures, every state's numbers were multiplied by the same correction each year. The note calls this correction minor, but for some groups and years it is large: up to 32% for the top 10% in the 1930s, and it more than doubles the top 0.01% in the late 1980s. In those cases much of what looks like each state's own history is really the national trend copied into every state. For the most-used figure, the top 1%, the correction is small.\n\nmoderateIn some years the IRS published state data only up to '$200,000 and above', so the incomes of the very richest had to be estimated by extrapolation.\n\nmoderateA 'top 1% share' needs an estimate of everyone's income in the state.\n\nmoderateFor Alaska before it became a state, some published numbers are mathematically impossible; for example, the richest 10% supposedly receive less than 10% of income.\n\nmoderateIn 1944 the IRS published only each state's totals, not how income was spread within the state, so there was no real information on that year's state top shares.\n\nThe chapter's best-known inheritance number, that roughly two-thirds to three-quarters of French wealth in 2010 was inherited, comes from a series built by multiplying another estimate by round factors typed into a spreadsheet, not from the micro data the text describes. The authors' own reproducible estimate is closer to one half. The broad pattern (high, then low, then rising) still holds, but the 2010 level is much less certain than presented.\n\nmajorThe chapter says the richest Americans now hold almost as large a share of wealth as on the eve of the 1929 crash.\n\nmajorMuch of the measured rise in French inheritance since the 1980s comes from gifts made during life, and these were measured in years when temporary tax breaks encouraged people to give early.\n\nmoderateFor recent years the chapter's UK figures count only the wealth of people whose estates go through probate and treat everyone else as owning nothing, which makes the richest tenth appear to hold 70% of wealth instead of roughly 55%.\n\nmoderateThe chapter says the share of inherited wealth fell and then rose again in four European countries.\n\nThe chapter says the richest 1% went from owning under a quarter of US household wealth in the late 1970s to 42% in 2012. That figure came from a then-new method that is very sensitive to how much interest rich people earn on their savings; when this is measured better, including by the authors themselves, the rise is roughly a fifth to two-fifths smaller. Wealth did become much more concentrated, but by less than the chapter's figure implies.\n\nmoderateThe chapter's income numbers come from what people report on tax returns.\n\nmoderateThe chapter's saving rates were not measured from household budgets; they were worked out backwards from the wealth estimates, so they cannot confirm those estimates, and any error in the wealth figures passes straight into them.\n\nmoderateTax records from before the Second World War cover only a small, rich slice of the population, so turning them into national shares requires judgment calls.\n\nmoderateThe wealth figures count homes, savings and shares, but not the value of future Social Security pensions, which are a large part of what ordinary families can count on.\n\nThe chapter says poor children's chances of moving up stayed the same, or even improved slightly, for children born between 1971 and 1993. Newer and much larger data, from a team led by the chapter's own lead author, show that for children born between 1978 and 1992 the link between parents' and children's incomes actually got about a tenth stronger. That is a modest fall in mobility, not stability. The forecasts the chapter relied on for the youngest children pointed the wrong way, although the change is still small compared with the differences between places.\n\nmoderateFor children born after 1982, the chapter's 'no change' evidence is not measured adult income.\n\nmoderateThe chapter's list of traits of high-mobility places treats every area equally, so hundreds of small rural areas count as much as big cities.\n\nmoderateThe chapter stretches its finding back to everyone born in the second half of the 20th century.\n\nmoderateThe headline number (0.34) measures children at about age 30 and parents over five years, which can make family background look a little less important than it is over a lifetime.\n\nThe summary box says top earners went from earning 1.6 times as much as a middle earner in 1978 to three times as much in 2013. The briefing's own chart and the official data show the ratio went from about 1.65 to about 2. The gap did widen, but by about a fifth rather than nearly doubling, so the summary overstates the change about four-fold.\n\nmoderateThe briefing says the richest 1% in Britain get as large a share of investment income as the richest 1% in America.\n\nmoderateThe chart of household wealth compared with national income joins two different official data series at 1997 without saying so.\n\nminorThe briefing says two thirds of the rise in the top 1%'s income share came from bankers' bonuses.\n\nminorThe briefing describes a chart of who gained and lost from the coalition's tax and benefit changes, but swaps the top two groups: in fact the richest 5% lost a little and the next 5% broke even.\n\nThe authors tried to show that distrust of government makes people oppose redistribution, by showing some respondents negative material about government. But that material also changed other opinions, for example whether the rich deserve their income. So the experiment measures the effect of the whole package, not of trust alone. A later study that raised and lowered trust found almost no effect on support for redistribution.\n\nmoderateThe paper says learning about inequality made people trust government less.\n\nmoderateThe authors also ran versions of the experiment that showed only the inequality information.\n\nmoderateTwice as many treated as untreated people quit the survey early.\n\nmoderateThe striking 'support doubles' result came from a slide that also argued for raising the tax.\n\nThe paper's famous 83% top tax rate depends on one number: how much top earners' extra income reflects real extra work and output rather than grabbing a bigger slice. The paper's own growth data are far too noisy to pin that number down. They are equally consistent with the conventional answer of about 57%, so the 83% is an illustration of what follows if the authors' guess is right, not a measured result.\n\nmoderateThe paper's error bars for its cross-country regressions are two to four times too narrow, because each country's year-to-year data are treated as if they were independent pieces of evidence.\n\nmoderatePart of the jump in top incomes reported on US tax returns after 1986 came from business owners moving profits from company accounts onto their personal returns, not from earning more.\n\nmoderateTo measure how much CEOs are paid for pure luck, the authors compare each firm with the rest of its industry.\n\nmoderateThe table on CEO pay across countries says it adjusts for company performance and CEO characteristics in all of its main columns, but the program does so only partly in one column and not at all in the others.\n\nThe method turns interest income into wealth by assuming everyone earns the same interest rate. After 2008 ordinary savers earned almost nothing, while the very rich still earned real interest on their bonds. The method therefore credits the rich with far more savings than they probably had. Using the authors' own estate records and their own later revisions, the 2007-2012 jump in the richest families' share of wealth was roughly a quarter to well over half smaller than reported, though it was still a rise.\n\nmoderateThe paper tests its key assumption by showing that rich estates of different sizes earned similar returns.\n\nmoderateThe paper says the rich got a bigger share of capital tax breaks after 2008, but it never works out who gets those breaks.\n\nmoderateMany wealthy people sold assets and paid themselves dividends in 2012 to beat a tax increase scheduled for 2013, so their 2012 incomes were temporarily inflated.\n\nmoderateThe paper says older families went from about twice as wealthy as average to only 40% wealthier.\n\nThe Reporter says tax breaks for foreign footballers pull in stars but push out weaker foreign players and some local players. That result depends on assuming weaker and stronger players are equally attached to their home country, which the data clearly reject, and on the Dutch league. With a more realistic assumption weaker foreign players are attracted too, and without the Netherlands there is no measurable push-out of local players; only the finding that stars respond more holds up.\n\nmajorThe best-known Danish result, that the tax break doubled the number of well-paid foreigners, comes from one way of counting.\n\nmoderateThe Reporter says that without the tax break foreigners would make up 4% of Denmark's top earners instead of 7.5%.\n\nmoderateThe Reporter says Denmark's special rate for foreigners, once sales taxes are counted, is already about at the level that brings in the most tax revenue.\n\nmoderateTo show that Spain's tax break caused an inflow of foreign players, the Reporter says only players who qualified came, with 'no effect' on those who did not.\n\nThe paper says new saving explains about 60% of the rise in wealth relative to income since 1970, and rising prices of existing assets about 40%. That split only works if one credits saving with a large amount of research spending (which official statistics did not then count as saving) - several times what U.S. official figures support - and also counts statistical discrepancies and reclassifications as saving. With realistic figures the split reverses, so most of the rise came from higher prices, mainly for homes and land; this is the most serious problem found, weakening the paper's explanation of why wealth grew but not the finding that it grew.\n\nmoderateThe paper's signature explanation is that when growth slows but people keep saving, wealth piles up to a larger multiple of income.\n\nmoderateThe paper says that from 1870 to 2010 rises and falls in asset prices roughly cancel out, so today's wealth is largely explained by accumulated saving.\n\nmoderateThe paper reports that the share of national income paid to owners of wealth (as profits, rents and interest) rose everywhere after the 1970s, and takes this as tentative evidence that machines and other equipment can easily take the place of workers.\n\nmoderateThe paper's summary illustrates its theory with a simple example: if people save a tenth of their income, halving economic growth doubles wealth relative to income.\n\nThe paper's main story is that evaders moved money from havens that signed treaties to havens that did not. That pattern largely disappears when the authors' own model is made stricter (a version printed in their drafts but cut from the published table). It is also absent in the eight havens whose data are now public. It may hold for a few small havens, but it is not firmly demonstrated.\n\nmajorThe paper argues that money was not brought home because the total held in havens stayed about the same.\n\nmoderateTaken literally, the paper's own numbers say that once money-shifting is allowed for, deposits in treaty havens fell by only about 5%, a fall not clearly different from zero.\n\nmoderateThe '11 percent' is an average over country-haven pairs in which a tiny pair counts as much as a huge one.\n\nmoderateThe claim that money went to the 'least compliant' havens rests on a number that mostly reflects non-European savers in all havens, Switzerland included.\n\nThe paper says about two-thirds of the fall in US companies' tax rate came from shifting profits to tax havens, but it never calculates this: it assumes the other causes explain only a small part. Using the paper's own numbers, the growth of profits booked in tax havens explains only about a quarter of the fall, and a study of company accounts found that purely domestic firms' tax rates fell about as much. Profit shifting mattered, but it was not the main cause the abstract describes.\n\nmajorThe paper measures where profits are 'booked' using statistics that credit a tax haven with all profits passing through a holding company there, even when the money was earned and taxed in, say, Germany.\n\nmajorThe paper concludes that tax havens cut US companies' tax bills by about a fifth.\n\nmajorThe tax rate the paper tracks divides taxes by profits, but the taxes include tax on companies' gains from selling shares and assets, which are left out of profits.\n\nmajorThe $190-200 billion a year that offshore evasion is said to cost depends on generous assumptions: that hidden wealth earns 7% a year and all of it is taxed annually at top rates, that inheritances are taxed at the highest legal rates everywhere (even in countries with no inheritance tax), and that 90% of the money is hidden.\n\nThe paper says the richest tenth's share of European wealth had already fallen from about 90% to under 60% by the 1950s-60s. Its own chart shows the share was still about 75% in the 1950s and 68% in the 1960s, and only dropped below 60% around 1980. Europe's wealth equalization was real, but slower and more of it happened in peacetime than the text says.\n\nmoderateThe paper says the world's very richest grew their fortunes by 6-7% a year after inflation from 1987 to 2013, more than three times faster than average wealth.\n\nmoderateThe paper's chart says that in the 20th century the after-tax return on wealth fell below the economy's growth rate worldwide, and uses this to explain why the rich never regained their pre-1914 share of wealth.\n\nmoderateFor the US before 1960 the paper had no direct data on the richest tenth's share of wealth.\n\nmoderateThe paper's UK figure for the richest tenth's share of wealth (about 70%) comes from estate records covering only about 3 in 10 adults, and effectively treats everyone else as owning nothing.\n\nThe paper's headline is that each 1% rise in the share of pay that foreigners keep after tax raised their number by 1.5-2%. That comes from one way of choosing comparison groups. The paper's own alternative check, built to rule out a general widening of top pay, gives about 1-1.3% and shows the effect fading over time, yet the text describes it as nearly the same. The tax break clearly attracted many foreigners, but probably by less than the headline says.\n\nmoderateThe introduction says that without the tax break foreigners would make up about 4% of Denmark's top 0.5% of earners instead of 7.5%.\n\nmoderateThe paper checks whether the pay jump after the tax break ends could simply reflect which workers chose to stay.\n\nmoderateBetween the draft and the published version, the way the pay effect was measured changed, and the headline size of the effect roughly doubled; the published paper does not say so.\n\nmoderateUntil 2002, a foreign key employee who stayed in Denmark too long (in the end, more than seven years) had to pay back the tax savings from the scheme.\n\nThe paper says that places with more upward mobility have less segregation, less inequality, better schools, stronger community ties and more two-parent families, and that this holds however the data are sliced. That is true when every area counts equally, including many tiny rural ones. When areas are weighted by how many people live there, the links are roughly half as strong and several disappear, and the paper's own appendix shows this. The broad pattern still holds, but it is much weaker in the big cities where most children grow up than the text suggests.\n\nmoderateThe paper splits inequality into 'the bottom 99%' and 'the top 1%' and concludes that only the first matters for children's prospects.\n\nmoderateThe paper says that growing up in a better area is associated with a gain about 60% as large as being born to richer parents.\n\nmoderateLiving costs are much higher in places like San Jose and San Francisco.\n\nmoderateThe local 'inequality' measure the paper calls a Gini coefficient appears to have been computed by ranking each family against the whole country rather than against its own area.\n\nFor children born after 1982 the paper could not yet see adult incomes. For the youngest (born 1987-93) it predicted their future mobility from whether they enrolled in college at 19, assuming the link between college and later income never changes. The headline of 'no change, and at most a tiny one' depends on that prediction: the incomes actually measured are too noisy to rule out even the 20% worsening that some had predicted.\n\nmajorThe lead author and colleagues later measured the same generations with much larger and more complete data.\n\nmoderateThe paper extends its finding back to people born around 1950.\n\nmoderateTo explain why rising inequality did not reduce mobility, the paper says its companion study predicts only a 7.5% change, but that number moves from about 1% to 11% with reasonable choices about how to weight places and how to handle a break in the Census data.\n\nThe paper's most careful statistical test of whether taxes attract foreign footballers essentially relies on one country, the Netherlands, and on an unstated assumption about which foreign players there received a tax break. Remove the Netherlands, or change that assumption, and this test finds little or no effect. Other evidence in the paper still points to a real effect, but its size is much less certain than the headline suggests.\n\nmajorThe paper's figure for how strongly home-grown players react to taxes (0.15) is largely a by-product of the statistical model's design rather than a direct measurement.\n\nmajorThe paper says low taxes pull in star players and push weaker players out.\n\nmajorThe claim that tax breaks for foreigners push home-grown players out of their own league rests mostly on the Dutch case.\n\nmoderateFor the Netherlands, the tax rate entered for foreign players leaves out VAT (sales tax), although VAT is counted for every other country, including in the earlier version of the same paper.\n\nThe chapter suggests the best top income tax rate might be above 80%, because cutting top rates did not seem to boost economic growth across rich countries. But when the authors' own statistical analysis is re-run, the data turn out to be far too noisy to tell. They are about as consistent with a best rate in the mid-60s, close to the conventional view the chapter questions, as with one near 100%. The '80%-plus' figure is a hypothesis, not a finding.\n\nmoderateThe chapter proposes valuing top earners according to how many of them come from poor backgrounds.\n\nmoderateThe authors argue that the surge in top incomes after tax cuts was not just the rich relabelling income to avoid tax, because the same pattern appears when capital gains are counted.\n\nmoderateThe chapter's simple formula for the best top tax rate assumes a single measured response captures everything that matters.\n\nminorThe paragraph describing the chapter's key international chart was copied from an older version of a related paper that used different years.\n\nThe book's $190 billion yearly tax loss assumes hidden money earns 8% a year and that all of that gain is taxed every year at full rates, and it uses the highest inheritance-tax rates as if nobody qualified for exemptions. The author himself used 6%, 7% and 6.5% in other editions. With more realistic assumptions the loss is still large, but more like $110-170 billion than 'at least $200 billion'.\n\nmajorThe statistics the book uses to show where US companies' foreign profits sit count some profits twice and credit the tax havens with profits earned and taxed in other countries, because that is where holding companies are registered.\n\nmoderateThe book's world total of $7.6 trillion was obtained by assuming that the 8% share measured for 2008 still held, not by adding up the new data, so the reported growth of 'about 25%' is just the growth of the estimated world wealth figure.\n\nmoderateThe claim that 80% of hidden wealth escapes tax comes from Swiss data on European savers, adjusted with an assumed interest rate, and is then applied to every country and every tax haven.\n\nmoderateThe book says money in Swiss banks grew 18% after world leaders vowed to end bank secrecy in 2009.\n\nThe 2002 working paper's table said, for example, that a fortune at the top-1% cutoff would be taxed down to the exempt level in about 9 years. The model's own equations make that impossible: it takes at least 43 years, and about 47 when the model is re-solved. Across the table the times are understated by 2 to 8 times. The 2013 journal version dropped the table, so its theorems are unaffected, but no corrected timeline was ever published.\n\nmoderateWhether the paper's main result applies in the real world depends on how strongly people's saving reacts to after-tax returns.\n\nmoderateIn the paper's model the tax shrinks big fortunes only by leading their owners to spend them down, and that is slow: the largest fortunes take one to several centuries to fall to the exempt level.\n\nmoderateIn the model no one can ever build a new large fortune, so once the old ones are taxed down they are gone for good.\n\nminorThe paper says its conclusions do not depend on how high the tax rate is allowed to go.\n\nThe paper says more than 15% of America's national income moved from the bottom 90% to the top 10% over 30 years, but its figures measure only income reported on tax returns, which is about two-thirds of national income. Measured against all national income, including in the authors' own later estimates, the shift was roughly 8-11%: still very large, but a third to a half smaller than claimed, and about twice (not four times) the size of the trade deficit the paper compares it with.\n\nmoderateThe paper suggests top tax rates could be as high as 83% because top pay partly reflects bargaining power rather than productivity, and it supports this by noting that countries that cut top taxes did not grow faster.\n\nmoderateThe chart comparing the US, UK, Germany and France includes several values the authors filled in by hand or built from assumptions, and mixes series that do and do not count capital gains, without telling the reader.\n\nmoderateThe paper says the richest 1% received almost 60% of all US income growth from 1976 to 2007.\n\nmoderateThe paper says ordinary Americans' incomes grew much more slowly than the economy mainly because of rising inequality.\n\nThe paper's figures are correct for the income people report on tax returns, but that measure leaves out a lot of income. When the same authors later counted all national income, the US increase was about a third smaller and France's increase was much bigger. The gap between the US and continental Europe is therefore far less dramatic than the paper's numbers suggest, although the US and other English-speaking countries still saw larger rises.\n\nmoderateAcross 18 countries, those that cut top tax rates most since the early 1960s did see the biggest rises in top income shares, and that pattern is solid.\n\nmoderateThe paper suggests that when taxes fell, top earners got richer mainly by bargaining for a bigger slice rather than by producing more, so top tax rates could be as high as 83%.\n\nmoderateThe chart labelled as an average of France, Germany and the UK quietly adds Italy, where wealth is highest relative to income, from 1970 onward.\n\nmoderateThe paper argues that the rise in top incomes is not mainly an artefact of the rich reporting more income to the tax authorities after tax cuts.\n\nThe 50-60% figure is the tax rate that would best serve people who inherited nothing, and the paper says so. Its supplement adds that a more conventional goal, counting everyone's well-being equally, would give almost the same answer; that shortcut is mathematically wrong, and a later study using the paper's own formula and data finds such a goal can even call for subsidizing inheritances. The headline therefore stands or falls with the value judgment behind it.\n\nmoderateThe 50-60% rests on particular guesses about how fast inherited wealth grows compared with the economy, why people leave bequests, and how much they cut back when taxed.\n\nmoderateThe abstract says the best tax rate is even higher for the largest inheritances.\n\nmoderateThe paper's numbers for people who inherited middling or large amounts depend on spreadsheet choices that are undocumented and differ between its main table and its figure.\n\nmoderateThe paper's 'inheritance tax' is really the total tax on inherited wealth plus everything it earns over a lifetime.\n\nThe paper says that once hidden offshore money is counted, the eurozone stops being a net debtor and becomes a net lender to the rest of the world. That only works if eurozone residents own about half of the hidden money held outside Switzerland. The author's own later estimate is about a quarter. With that estimate the eurozone comes out roughly even, and on the paper's own assumptions it is still a net debtor in 2008. The hidden wealth clearly makes the eurozone look much less indebted, but the switch to net lender is not established.\n\nmajorThe paper suggests that, once hidden offshore money is counted, rich countries as a group are owed more by the rest of the world than they owe.\n\nmajorThe paper counts all the 'missing' securities in world statistics as hidden household money.\n\nmoderateThe '8%' compares hidden offshore assets with households' financial assets after subtracting all their debts, including mortgages.\n\nmoderateTo show that the 'missing' securities really are households' offshore holdings, the paper says they look just like foreigners' portfolios in Swiss banks, about half of which are mutual funds.\n\nThe study shows clearly that low-paid workers were upset to learn what colleagues earn. It also says better-paid workers were not affected at all, and so people mind falling behind more than they enjoy being ahead. The data are too imprecise to show that: they are also consistent with better-paid workers becoming happier by about as much as low-paid workers became unhappy. 'No measurable effect' was treated as 'no effect'.\n\nmoderateThe claim that people care more about their rank among colleagues than about the size of the pay gap rests on estimates that are mostly not statistically reliable.\n\nmoderateThe paper cannot show that telling workers about pay made the workforce as a whole less satisfied, or that it cost employers anything measurable.\n\nmoderateThe finding that workers below the median became 'less satisfied' partly comes from one question: whether their pay is fair compared with colleagues.\n\nmoderateBeing e-mailed made people a little less likely to answer the survey.\n\nThe reply says the tax advantage married one-earner couples get today is small except for the very rich. In fact it is worth about 5% of earnings for a modest earner (about EUR 100 a month at EUR 2,000 gross) and 6-8% higher up. What keeps most of these couples from losing much under the reform is its general tax cut, not a small advantage.\n\nmoderateThe critic calculated that, under the authors' reform, interest on savings could be taxed at more than 100% of its real value.\n\nmoderateThe critic's main objection was that the book counts pension and unemployment contributions as ordinary taxes, although they buy future benefits.\n\nmoderateTo suggest that counting public services might change the picture, the authors cite a 2003 government report as finding that education spending favours the better-off.\n\nmoderateThe authors said their simulations prove that couples living on one income would not be the big losers if spouses were taxed separately.\n\nThe note's figures are right, but the main public database that hosts them now shows a different set of numbers. Those numbers include one-off profits from selling land and shares, yet are labelled as excluding them, and in 2009 they switch to another team's series. Anyone downloading 'Japan's top 1% share' there gets figures up to about a fifth too high in the 2000s, far higher in the late-1980s bubble, and a fake drop in 2009.\n\nmoderateTo strip out one-off profits from selling assets, the method subtracts 80% of them, a rule borrowed from Canada and never tested for Japan.\n\nmoderateIn 2005 the tax office began publishing much more detailed figures on the very richest.\n\nmoderateFor the 1950s and early 1960s, a correction that stops wage earners being counted twice was applied to the main series but not to the companion series that includes asset-sale profits.\n\nmoderateMost Japanese employees never file a tax return, so the method stitches tax returns together with an employer survey of wages.\n\nThe chapter's numbers depend heavily on one input: how much the rich cut the income they report when their tax rate goes up. The authors call their main figure 'midrange' and a higher figure a 'conservative upper bound'. But the studies they cite, including their own, allow noticeably larger responses. With those, the rate that raises the most money would be closer to 45-55% than 73%, and their 49% suggestion would be about right rather than 'far more likely too low'. A higher top rate would still raise revenue; how high it should go is much less certain than the chapter says.\n\nmoderateThe formula assumes the rich respond to taxes in one simple way over a year or two.\n\nminorThe calculation measures how top-heavy incomes are using an income measure that includes investment gains.\n\nminorThe chapter says a 70% top rate was in force from 1965 to 1981, which suggests high earnings were once taxed that heavily for 17 years.\n\nminorThe chapter gives two different figures for the same group's average income, $1.2 million and $1.364 million.\n\nThe paper says that if top earners respond twice as strongly to taxes, the hidden economic cost of raising each extra dollar from them doubles, from about 34 cents to 68 cents. By the paper's own formula it roughly triples, to about $1.03. The paper's main figures are fine, but this one 'what if' check makes higher top tax rates look less costly than the paper's own method implies.\n\nmoderateThe paper's headline example says the top tax rate could go as high as about 73% before revenue starts to fall.\n\nmoderateThe paper concludes that when top earners report less income after tax increases, it is always because they shift income between years or into other forms, not because they actually work or produce less.\n\nminorThe paper says one-third of the 1986-88 surge in top incomes came from business profits moving onto personal tax returns (S-corporations).\n\nminorOne column of a results table, for the group just below the top 1%, was evidently computed with the wrong variable.\n\nThe notes say inequality fell abruptly during World War II and take that as evidence the war itself drove the change. A careful re-estimate from the same old tax records finds that pre-war inequality was lower, and that much of the fall came earlier, during the Great Depression. On that estimate the wartime drop is about a third smaller overall and far less sudden. The long-run 'U' pattern still holds, but the war-shock story is much less certain.\n\nmoderateIn March 2024 the notes said the richest 1% took 81% of income growth from 2019 to 2022 and that everyone else's income grew only 1%.\n\nmoderateThe notes' best-known figure is that the top 1% took 95% of income gains in 2009-2012.\n\nmoderateThe figures count only the cash income people report on tax returns, before taxes and without government benefits or employer-paid health insurance, and they treat each tax-filing unit (a single person or a couple) as a 'family'.\n\nmoderateTo compare incomes across years the notes adjust for inflation with one particular consumer price index.\n\nThe reply says giving the RSA minimum income to each spouse individually would add only 'a few thousand' people. On the authors' own data and rules, between about half a million and three million people would become eligible, most of them women at home. The cost would be roughly EUR 1-8 billion a year, and a government estimate put it near EUR 9 billion. The cost side of the authors' argument is therefore wrong by a factor of hundreds.\n\nmoderateToday, the stay-at-home wife of a man on an ordinary income gets no RSA, so taking a job costs her no benefit.\n\nmoderateThe authors say their computer simulations prove that one-earner families would not be the big losers.\n\nmoderateThe reply says almost every developed country taxes spouses separately, and cites an article in the same issue as saying so.\n\nminorThe reply says joint family taxation is a small corner of the French system because the income tax raises only 3% of national income, against 6% for the CSG and 10% for some social contributions.\n\nThe paper's best-known US numbers measure income as reported on tax returns. On the authors' own later and broader measure, which also counts income that never appears on tax returns, the fall in the richest 1%'s share of income between 1928 and 1949 and its rise between 1976 and 2007 are both roughly 40-45% smaller, and the US rise is about the same as Britain's and Canada's rather than larger. This is the most important problem found, but it scales back the US numbers rather than overturning the story: the US pattern of high, then low, then high again survives, and the big early-century falls in other countries are just as large on the broader measure.\n\nmoderateThe paper's summary says top income shares rose in English-speaking countries but 'not' in continental Europe or Japan.\n\nmoderateThe widely quoted statistic that the richest 1% of US families received 58% of all income growth between 1976 and 2007 depends heavily on how incomes are adjusted for inflation and on what counts as income.\n\nmoderateA major 1986 US tax reform encouraged business owners to report profits on their personal tax returns instead of inside their companies, which makes top incomes on tax returns jump without any real change in who earns what.\n\nmoderateThe paper combines survey and tax data to show that the richest 1% account for a large part of the rise in overall US income inequality, and that broad point stands.\n\nTo show its conclusion is safe, the paper takes the largest figure it reports for how strongly top earners react to tax rises and calls it a cautious upper limit. That figure comes from a single study and is very imprecise. The true reaction could be big enough that the 2011 US top rate was already close to the rate that raises the most money. Higher rates still look justified with typical figures, but calling the conclusion 'robust' goes further than the evidence.\n\nmoderateThe 73% figure depends on one key number: how much the reported income of the very rich falls when their tax rate rises.\n\nmoderateThe paper's highest figure, 80%, assumes that once loopholes and deductions are removed, the rich would barely react to higher rates.\n\nmoderateThe formula only looks at how much the rich cut their reported income in the short to medium run.\n\nmoderateThe 73% relies on how top-heavy US incomes were in 2005-07, when top tax rates were low.\n\nThe book counts pension and unemployment contributions as taxes. Yet they mostly buy workers their own future pensions and benefits, and the very rich pay almost none of them because they are capped and do not apply to investment income. Counted instead as deferred pay, as the authors' own unpublished tables do, they leave the lowest-paid full-time workers paying about 27% of their income, less than the richest (33%). The fall in rates at the very top is then about half as large.\n\nmajorAbout 45% of the measured income of the richest people in the model is company income, and the tax on it, that never shows up on their own tax returns.\n\nmoderateThe book says at least 90-95% of people in every income group below the top would pay less tax under its reform.\n\nmoderateThe book claims its reform would create about 2% more jobs and leave the state 1-2 billion euros better off once people react to it.\n\nmoderateThe book presents its finding as proven beyond appeal and says every assumption it made understates the problem.\n\nCompanies pay corporate tax, and the model has to decide which households ultimately bear it. It spreads the tax over everyone with savings, including holders of tax-free passbook accounts, rather than over shareholders, and it gives no reason for this choice. If shareholders bear it, as the authors themselves have described the tax, the richest group's rate rises from about 33% to 39% and the drop at the top shrinks by about a third. If all owners of capital bear it, homeowners included, the drop grows somewhat.\n\nmajorTo match national statistics, the model adds a large amount of company income that does not appear on tax returns, and it gives most of it to the people who declare dividends, who are mostly the very rich.\n\nmoderatePension and unemployment contributions mostly buy workers their own future benefits, and the richest pay relatively little of them, so whether they count as taxes changes the picture a lot.\n\nmoderateThe model assumes the richest save about half of their income, more than the 40% the guide describes.\n\nmoderateEverything rests on a synthetic population of 821,815 adults built from confidential data, and the recipe was never published.", "url": "https://wpnews.pro/news/errors-in-the-research-of-emmanuel-saez-and-gabriel-zucman", "canonical_source": "https://saez-zucman-audit-replication.vercel.app/", "published_at": "2026-10-28 20:57:48+00:00", "updated_at": "2026-10-28 21:12:13.701333+00:00", "lang": "en", "topics": ["ai-research", "artificial-intelligence", "large-language-models", "ai-agents"], "entities": ["Emmanuel Saez", "Gabriel Zucman", "Claude Opus 5.5", "OpenAI", "GPT-6 Astra", "American Economic Review: Insights", "Johannesen", "Sæverud"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/errors-in-the-research-of-emmanuel-saez-and-gabriel-zucman", "markdown": "https://wpnews.pro/news/errors-in-the-research-of-emmanuel-saez-and-gabriel-zucman.md", "text": "https://wpnews.pro/news/errors-in-the-research-of-emmanuel-saez-and-gabriel-zucman.txt", "jsonld": "https://wpnews.pro/news/errors-in-the-research-of-emmanuel-saez-and-gabriel-zucman.jsonld"}}