How To Prevarication Amongst Statistics
Along amongst David Leonhardt's interesting article "Taxmageddon," terminal weekend's New York Times Lord's Day Review included this twosome of graphs. These belong high upward inwards the pantheon of "How to prevarication amongst statistics" (one of my favorite books) examples.
These graphs are paired left in addition to right inwards the original. (I made them large in addition to split them upward hence you lot could run into them. They're fifty-fifty clearer on the Times' website) On the left, is this graph:
Right side past times side to it, is this one
(The graphs had piffling to make amongst the article, hence I presume they are the operate of the Times staff, non Leonhardt.)
It's damning, right? The rich got huge revenue enhancement cuts (top graph) in addition to hence made a ton of coin courtesy of the regime (+528% alter inwards income, numbers to the right of the get-go graph). The rich are also feeding at the trough of revenue enhancement breaks (bottom graph). Outrage!
***
Now hold off a infinitesimal here...The transcend graph is a revenue enhancement rate, the per centum of income paid, spell the bottom graph is total dollars. To say this is comparison apples in addition to oranges is an insult to fruits.
In fact, wealthier people pay nearly all Federal income taxes. So it's non surprising that they make goodness to a greater extent than inwards dollar terms from revenue enhancement deductions -- except credits, which is coin the regime pays you lot fifty-fifty if you lot pay no taxes.
If nosotros expressed the bottom graph every bit a per centum of taxes, or a per centum of income -- the same units every bit the transcend graph -- you'd run into a dramatic reversal of the implication. Since the lower percentiles receive got hence much less income in addition to pay hence much less taxes, the graph would advise those amongst less income larn the largest (percent) benefits.
***
The transcend graph is fifty-fifty to a greater extent than misleading, at to the lowest degree for the Times' destination which is to dorsum a heighten inwards Federal income taxes for the wealthy.
Where does this lx in addition to 71% revenue enhancement charge per unit of measurement inwards the 1960s come upward from? The basic fact of the Federal taxation is that it raises nearly 20% of gross domestic product despite wild variation inwards the statutory revenue enhancement rates. In 1960 Federal revenue enhancement receipts (NIPA tabular array 3.2) divided past times national income (NIPA 1.12) were 93.9/2013.9 = 19.8%. In 2004 this ratio was 2013.9/10534.0 = 19.1%.
Statutory revenue enhancement rates inwards the 1960s were every bit much every bit 90% marginal rates on the highest incomes. (Remember George Harrison's "Taxman?" "One for you, nineteen for me." He wasn't kidding.) But the revenue enhancement code was hence shot total of loopholes that the Federal regime didn't collect nearly that fraction of income from anyone.
So where does the 71% come upward from? At to the lowest degree the Times gives their source, hence you lot tin larn dorsum in addition to run into what the heck the seat out means. These are estimates past times Emmanuel Saez in addition to Thomas Piketty of total Federal taxes -- private income, corporate income, payroll (Social Security, etc.), in addition to estate taxes -- divided past times an approximate of income, which excludes Government transfers. (The newspaper is here in addition to a longer working newspaper version here.)
To what extent is this the statutory charge per unit of measurement in addition to to what extent is it actual coin paid? I'm all the same tracking this down, but it appears to hold out some of each. For example, "We work the TAXSIM estimator developed at the National Bureau of Economic Research ... to compute federal private income taxes." That seems to imply this is taxes the NBER thinks they should receive got paid, non what people truly paid. But they make receive got private marker IRS data, hence inwards theory know what people truly paid. On the other hand, it doesn't add together up: Total revenue enhancement recepits are 20% of income. So how tin everybody's charge per unit of measurement come upward downwardly yet the total charge per unit of measurement rest stuck at 20%? How tin the charge per unit of measurement of everybody who has whatever coin inwards 1960 hold out higher upward 20%, yet the average is all the same 20%?
But let's non brand it to the depths of the sausage factory, as it does non affair for the request here. (And my caput starts to wound anytime I delve inwards to the details of this variety of calculation.)
The of import point, for the Times is that graph has basically nix to make amongst Federal income taxes. All of the activeness comes from Saez in addition to Piketty's assigment of corporate taxes in addition to estate taxes. They assume all corporate taxes are paid past times stockholders in addition to bondholders. This is conceptually right -- it is non truthful that "corporations" acquit whatever revenue enhancement burden. Someone is paying, through higher prices, lower salaries, or lower returns to investors. Saez in addition to Piketty assume it's all the latter.
Here is Saez in addition to Piketty's breakdown of how taxes changed betwixt 1960 in addition to 2004 (source):
The actual private income revenue enhancement describe has non changed much at all, other than to autumn slightly for all income groups. Almost all of the Times' fabled taxes the rich were happily paying inwards 1960 comes from Saez in addition to Piketty's assignment of corporate taxes to wealthy people in addition to their calculations of estate taxes! (Estate taxes are notorious for the games the rich pay to avoid them.)
(It also appears to me that Saez in addition to Piketty are a fleck off here: If you lot accuse corporate income revenue enhancement against the rich, don't you lot receive got to split that revenue enhancement past times an income mensurate that includes corporate income? In general, you lot receive got to split taxes past times pre-tax income non post-tax income. Dividing corporate taxes past times private income, in addition to non including corporate income, tin make "rates" higher upward 100%. On the other hand, if their "income" seat out attributes all corporate income every bit private income to the wealthy, hence the distribution of income is grossly overstated. Ok, we're non going inwards to the sausage factory, perchance for some other ship service someday, but I'm all the same scratching my head.)
As Piketty in addition to Saez seat the matter:
Now, when nosotros utter nearly the "Buffet rule," that is nearly raising the individual Federal income revenue enhancement rate. If nosotros calculate Warren Buffet's taxes this way -- including all corporate taxes paid past times all Berkshire Hathaway companies (and why non belongings taxes, concern taxes, concern contributions to social insurance, in addition to all other business-paid taxes), Buffet's revenue enhancement rates would hold out correctly measured, in addition to a lot to a greater extent than than his secretary's revenue enhancement rate!
This assignment of corporate taxes takes us into the night territory of who bears the burden of taxes rather than who truly pays them. Saez in addition to Piketty are assuming that rates of render on investments are reduced because corporations pay taxes, hence rich people larn less render than they would otherwise. Hence, it's "like" paying to a greater extent than taxes. Ok, that's how economists shout out back nearly things, but why halt here? Who truly bears the burden of the much larger wedge betwixt what employers pay in addition to what employees get? And all the other taxes, that distorts prices in addition to reward all over the place. And spell we're at it, why non "who bears the burden of regulation?" through higher prices or lower returns?
Bottom line: It may hold out fine for Saez in addition to Piketty's purpose, but I doubtfulness whatever New York Times reader had the faintest thought they were looking at a graph that primarily said "rich people were wound past times taxes inwards the 1960s non because they truly paid to a greater extent than taxes but because nosotros assume corporate income taxes drove downwardly the rates of render on their investments!"
And, inwards instance you lot shout out back this all means nosotros should larn dorsum to the days of "Mad Men" taxation, Saez in addition to Piketty warn:
***
Now, hold off at the nefarious pairing of the turn down inwards (statutory) revenue enhancement charge per unit of measurement amongst the alter inwards income on the right paw side of the transcend graph. We cutting rich people's taxes in addition to hold off how they got richer!
Here, the Times got besides clever past times half. The crusade in addition to trial insinuation hither is truly a provide sider's dream, if you lot tin read in addition to add. The insinuation is, the rich got richer because they got to continue all that income that they're non paying to the government. Even that doesn't add together up: a 528% ascent is much to a greater extent than than (1-0.34)/(1-0.71) = 2.28 = 128% ascent inwards after-tax income.
But the tabulated ascent is inwards pretax income. (At to the lowest degree the labels are honest.) As revenue enhancement rates came down, people went out in addition to made an enormous amount to a greater extent than income inwards the get-go place.
H5N1 528% increase inwards income is a lot. 71% x $100 = $71.00. 34% x $100 x (1+5.28) = $213.52. So, using the New York Times' numbers, nosotros would infer that lowering the revenue enhancement rate on the transcend earners corresponded to tripling the revenue enhancement revenue earned from that group! The rich are, apparently, paying much to a greater extent than inwards taxes than before.
If you lot receive got the Times' numbers seriously, Art Laffer's wildest dreams came true.
***
Update: Abel Winn notes it's worse than I said:
These graphs are paired left in addition to right inwards the original. (I made them large in addition to split them upward hence you lot could run into them. They're fifty-fifty clearer on the Times' website) On the left, is this graph:
Right side past times side to it, is this one
(The graphs had piffling to make amongst the article, hence I presume they are the operate of the Times staff, non Leonhardt.)
It's damning, right? The rich got huge revenue enhancement cuts (top graph) in addition to hence made a ton of coin courtesy of the regime (+528% alter inwards income, numbers to the right of the get-go graph). The rich are also feeding at the trough of revenue enhancement breaks (bottom graph). Outrage!
***
Now hold off a infinitesimal here...The transcend graph is a revenue enhancement rate, the per centum of income paid, spell the bottom graph is total dollars. To say this is comparison apples in addition to oranges is an insult to fruits.
In fact, wealthier people pay nearly all Federal income taxes. So it's non surprising that they make goodness to a greater extent than inwards dollar terms from revenue enhancement deductions -- except credits, which is coin the regime pays you lot fifty-fifty if you lot pay no taxes.
If nosotros expressed the bottom graph every bit a per centum of taxes, or a per centum of income -- the same units every bit the transcend graph -- you'd run into a dramatic reversal of the implication. Since the lower percentiles receive got hence much less income in addition to pay hence much less taxes, the graph would advise those amongst less income larn the largest (percent) benefits.
***
The transcend graph is fifty-fifty to a greater extent than misleading, at to the lowest degree for the Times' destination which is to dorsum a heighten inwards Federal income taxes for the wealthy.
Where does this lx in addition to 71% revenue enhancement charge per unit of measurement inwards the 1960s come upward from? The basic fact of the Federal taxation is that it raises nearly 20% of gross domestic product despite wild variation inwards the statutory revenue enhancement rates. In 1960 Federal revenue enhancement receipts (NIPA tabular array 3.2) divided past times national income (NIPA 1.12) were 93.9/2013.9 = 19.8%. In 2004 this ratio was 2013.9/10534.0 = 19.1%.
Statutory revenue enhancement rates inwards the 1960s were every bit much every bit 90% marginal rates on the highest incomes. (Remember George Harrison's "Taxman?" "One for you, nineteen for me." He wasn't kidding.) But the revenue enhancement code was hence shot total of loopholes that the Federal regime didn't collect nearly that fraction of income from anyone.
So where does the 71% come upward from? At to the lowest degree the Times gives their source, hence you lot tin larn dorsum in addition to run into what the heck the seat out means. These are estimates past times Emmanuel Saez in addition to Thomas Piketty of total Federal taxes -- private income, corporate income, payroll (Social Security, etc.), in addition to estate taxes -- divided past times an approximate of income, which excludes Government transfers. (The newspaper is here in addition to a longer working newspaper version here.)
To what extent is this the statutory charge per unit of measurement in addition to to what extent is it actual coin paid? I'm all the same tracking this down, but it appears to hold out some of each. For example, "We work the TAXSIM estimator developed at the National Bureau of Economic Research ... to compute federal private income taxes." That seems to imply this is taxes the NBER thinks they should receive got paid, non what people truly paid. But they make receive got private marker IRS data, hence inwards theory know what people truly paid. On the other hand, it doesn't add together up: Total revenue enhancement recepits are 20% of income. So how tin everybody's charge per unit of measurement come upward downwardly yet the total charge per unit of measurement rest stuck at 20%? How tin the charge per unit of measurement of everybody who has whatever coin inwards 1960 hold out higher upward 20%, yet the average is all the same 20%?
But let's non brand it to the depths of the sausage factory, as it does non affair for the request here. (And my caput starts to wound anytime I delve inwards to the details of this variety of calculation.)
The of import point, for the Times is that graph has basically nix to make amongst Federal income taxes. All of the activeness comes from Saez in addition to Piketty's assigment of corporate taxes in addition to estate taxes. They assume all corporate taxes are paid past times stockholders in addition to bondholders. This is conceptually right -- it is non truthful that "corporations" acquit whatever revenue enhancement burden. Someone is paying, through higher prices, lower salaries, or lower returns to investors. Saez in addition to Piketty assume it's all the latter.
Here is Saez in addition to Piketty's breakdown of how taxes changed betwixt 1960 in addition to 2004 (source):
(It also appears to me that Saez in addition to Piketty are a fleck off here: If you lot accuse corporate income revenue enhancement against the rich, don't you lot receive got to split that revenue enhancement past times an income mensurate that includes corporate income? In general, you lot receive got to split taxes past times pre-tax income non post-tax income. Dividing corporate taxes past times private income, in addition to non including corporate income, tin make "rates" higher upward 100%. On the other hand, if their "income" seat out attributes all corporate income every bit private income to the wealthy, hence the distribution of income is grossly overstated. Ok, we're non going inwards to the sausage factory, perchance for some other ship service someday, but I'm all the same scratching my head.)
As Piketty in addition to Saez seat the matter:
The larger progressivity inwards 1960 is non mainly due to the private income tax. The average private income revenue enhancement charge per unit of measurement inwards 1960 reached an average charge per unit of measurement of 31 percent at the really top, exclusively slightly higher upward the 25 percent average charge per unit of measurement at the really transcend inwards 2004. Within the 1960 version of the private income tax, lower rates on realized majuscule gains, every bit good every bit deductions for involvement payments in addition to charitable contributions, reduced dramatically what otherwise looked similar an extremely progressive revenue enhancement schedule, amongst a transcend marginal revenue enhancement charge per unit of measurement on private income of 91 percent.Note the tiny percentages of total income involved. These are non going to residual anyone's budget.
The greater progressivity of federal taxes inwards 1960, inwards contrast to 2004, stems from the corporate income revenue enhancement in addition to the estate tax. The corporate revenue enhancement collected nearly 6.5 percent of total personal income inwards 1960 in addition to exclusively simply about 2.5 percent of total income today. Because majuscule income is really concentrated, it generated a substantial burden on transcend income groups. The estate revenue enhancement has also decreased from 0.8 percent of total personal income inwards 1960 to nearly 0.35 percent of total income today. As a result, the burden of the estate revenue enhancement relative to income has declined really sharply since 1960 inwards the transcend income groups
Now, when nosotros utter nearly the "Buffet rule," that is nearly raising the individual Federal income revenue enhancement rate. If nosotros calculate Warren Buffet's taxes this way -- including all corporate taxes paid past times all Berkshire Hathaway companies (and why non belongings taxes, concern taxes, concern contributions to social insurance, in addition to all other business-paid taxes), Buffet's revenue enhancement rates would hold out correctly measured, in addition to a lot to a greater extent than than his secretary's revenue enhancement rate!
This assignment of corporate taxes takes us into the night territory of who bears the burden of taxes rather than who truly pays them. Saez in addition to Piketty are assuming that rates of render on investments are reduced because corporations pay taxes, hence rich people larn less render than they would otherwise. Hence, it's "like" paying to a greater extent than taxes. Ok, that's how economists shout out back nearly things, but why halt here? Who truly bears the burden of the much larger wedge betwixt what employers pay in addition to what employees get? And all the other taxes, that distorts prices in addition to reward all over the place. And spell we're at it, why non "who bears the burden of regulation?" through higher prices or lower returns?
Bottom line: It may hold out fine for Saez in addition to Piketty's purpose, but I doubtfulness whatever New York Times reader had the faintest thought they were looking at a graph that primarily said "rich people were wound past times taxes inwards the 1960s non because they truly paid to a greater extent than taxes but because nosotros assume corporate income taxes drove downwardly the rates of render on their investments!"
And, inwards instance you lot shout out back this all means nosotros should larn dorsum to the days of "Mad Men" taxation, Saez in addition to Piketty warn:
The surge inwards transcend incomes since the 1970s has been driven inwards large role past times a steep increase inwards the undertaking income component, due inwards large role to the explosion of executive compensation. As a result, undertaking income at in ane trial represents a substantial fraction of income at the top. This alter inwards composition is of import to continue inwards mind, because the corporate in addition to estate taxes that had such a potent trial on creating progressivity inwards the 1960s would receive got relatively piffling trial on undertaking income.In sum, this graph has nix to make amongst the principal request -- establishing facts nearly who pays Federal income taxes. It would hold out keen if our national news were to broaden upward in addition to consider all taxes -- yes, proper attribution of corporate taxes (all corporate taxes); along amongst estate, excise, terra firma in addition to local income taxes, sales taxes, belongings taxes, in addition to hence on in addition to hence forth. And proper attribution of the burden of taxes. But it isn't.
***
Now, hold off at the nefarious pairing of the turn down inwards (statutory) revenue enhancement charge per unit of measurement amongst the alter inwards income on the right paw side of the transcend graph. We cutting rich people's taxes in addition to hold off how they got richer!
Here, the Times got besides clever past times half. The crusade in addition to trial insinuation hither is truly a provide sider's dream, if you lot tin read in addition to add. The insinuation is, the rich got richer because they got to continue all that income that they're non paying to the government. Even that doesn't add together up: a 528% ascent is much to a greater extent than than (1-0.34)/(1-0.71) = 2.28 = 128% ascent inwards after-tax income.
But the tabulated ascent is inwards pretax income. (At to the lowest degree the labels are honest.) As revenue enhancement rates came down, people went out in addition to made an enormous amount to a greater extent than income inwards the get-go place.
H5N1 528% increase inwards income is a lot. 71% x $100 = $71.00. 34% x $100 x (1+5.28) = $213.52. So, using the New York Times' numbers, nosotros would infer that lowering the revenue enhancement rate on the transcend earners corresponded to tripling the revenue enhancement revenue earned from that group! The rich are, apparently, paying much to a greater extent than inwards taxes than before.
If you lot receive got the Times' numbers seriously, Art Laffer's wildest dreams came true.
***
Update: Abel Winn notes it's worse than I said:
The transcend graph’s y-axis is scaled according to seat inwards the income distribution, spell the bottom graph’s y-axis is scaled according to seat inwards the distribution of taxpayers. Since exclusively nearly one-half of income earners pay income taxes, beingness inwards the transcend x% of the income distribution agency that ane is inwards nearly the transcend 2x% of taxpayers. So when nosotros run into massive benefits going to the transcend 20% of taxpayers, that agency the revenue enhancement code was benefiting the transcend 40% of income earners. But that doesn’t agree really nicely into the 99% rhetoric that we’ve been hearing hence much of late, in addition to that the NYT graphs appear to hold out backing.
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