Relevant and even prescient commentary on news, politics and the economy.

Optimal Taxation of Capital Income 2019 (let them Bern).

I wrote a post about optimal taxation of capital income which (the web is sometimes wonderful) was made legible by the blessed [person who choses to remain anonymous].

But that was back in Obama center left 2008. I want to update given what I learned since then and given the appearance of socialist US citizens.

First, what I should have known already is that the standard Judd 85/86 result that the optimal rate of taxation of capital income goes to zero as time goes to infinity is what mathematicians call a boo boo (oopsie). The asserted theorem is false as explained by Ludwig Straub and Ivan Werning.

This is an interesting event in the history of thought and the sociology of economics — a standard mathematical result which is simply wrong. It is especially interesting as the proof that Judd made a whoopsie was published years ago, yet the false alleged result survives. One might almost suspect that ideology or class interest is involved.

The key issue is that Judd considered tax rates which change over time and their incentive effects and then casually assumed that the public sector budget is always balanced. I guess he guessed this was OK because of Ricardian equivalence which says that. given a long list of implausible assumptions, the timing of *lump sum* taxes doesn’t matter, so the timing of taxes only matters because of incentive effects.

In fact Judd’s alleged proof is completely invalid. It is simply a math mistake.

The model
There are 2 groups workers and investors. The workers consume all of their income which consists of a wage and, possibly, a subsidy from the state. Investors have capital income — interest after tax A_tf'(K_t)-tau_tK where tau_t is the rate of taxation of capital, A_t is their wealth and K_t is total capital (these must be equal under Judd’s assumption that the state neither borrows nor accumulates a sovereign wealth fund).

Investors maximize an intertemporal utility function with rate of imaptience rho. The claim is that if the state wishes to maximize a weighted average of workers’ instantaneous utility and investors’ instantaneous utility and also has rate of time preference rho, then Tau_t goes to zero as t goes to infinity.

Now first note that even if Judd were right it would tell us nothing about what taxes will be optimal for the next million years. Oddly, many people some of whom are economists (one of whom Edward Prescott has won the Nobel memorial prize in economics) conclude that taxes on capital income should be cut to zero right now.

Second allow the state to accumulate wealth and consider the simplest case in which investors maximize the discounted stream of the logarithm of their consumption. This means that they consume (rho)A_t no matter what Tau_t is. Assume that tau_t can’t be greater than some limit taumax or the state will grab capital instantly which is, in effect, a lump sum tax and doesn’t distort.

In this case, Tau_t does go to zero, because the state accumulates until it’s income covers all its expenses plus whatever subsidy it chooses to pay workers and the distribution of income is exactly that which it finds optimal and then ceases to tax as there is no reason to tax anyone. Note that in this case there is no trade off between efficiency and desired redistribution — the distribution converges to that desired as if there were no problems with incentives. This is roughly the opposite of the standard interpretation. In the long run, the distribution of income is exactly as desired. There is no more taxation because there is no more reason to tax.

(More generally if the elasticity of substitution is less than one in the model (as it is in the data) the state will redistribute more until the investors are relatively poorer than is optimal. This is because the income effect of the tax is greater than the substitution effect, so high taxes on capital income promote saving. But I want to mainly stick with logarithmic utility).

Now consider an extreme case in which the state cares only about the welfare of workers. Judd claims the result holds even in this case. He is wrong even if the state is allowed to accumulate a sovereign wealth fund. In that case, there is a loss due to investors consumption equal to (rho)A_t and the state aims to mimimize A_t. If there is an upper limit on Tau, then Tau_t is always at this limit. The optimal policy is to tax capital income at the maximum rate allowed forever.

Now consider Judd’s assumption that the state can’t accumulate a sovereign wealth fund. The fact that it must leave the wealth in the hands of investors who consume it at rate rho means the optimal steady state K=K* is what it would be if there were depreciation at rate rho. This means that f'(K*)=2rho.
For investors to choose this steady state, it must be that the after tax return on capital (f'(K*) – tau) is equal to rho so 2rho -tau = rho and tau=rho.

So where did Judd go wrong ? His alleged proof included the assumption that the economy would converge to a steady state. He assumed that A = K, but also considered only the social budget constraint and concluded that, in the optimal steady state f'(K) = rho (as would be true if the state had access to optimal non distortionary taxation or if it could accumulate a sovereign wealth fund). But the restriction A=K is binding & it has a non zero shadow price. That shadow price is not constant even if all observables K, A, w, R consumption of capitalists and consumption of workers are constant.

Given the problem as stated, the economy can’t reach a steady state. The gain to the social planner of being able to accumulate wealth becomes constant. It’s current value grows at rate rho.

The impressive thing is that the alleged result is still accepted even though the proof that it is a math mistake was published over a decade ago.

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The Price of Naltrexone

In The New York Times Abby Goodnough wrote
” she got a Vivitrol (naltrexone) shot but it was so expensive — her co-payment was $600 — that she never got another” !!!

This is insane. Naltrexone is an opioid antagonist. It prevents opioids from causing a high (and relieving pain and suppressing coughing and breathing). In no way is it conceivably a drug of abuse. But opioid addicts who wish to cut off all effects of opioids have to pay for their Naltrexone.

Also (as explained in the excellent article) some of the same people who oppose the use of methadone and buprenorphine oppose naltrexone too. I have never understood their logic. I am sure it is based on a moralistic belief that there are no simple easy solutions. It isn’t even “no pain no gain” as cold turkey withdrawal while using naltexone is just as horrible as any other cold turkey withdrawal. Pointless speculation after the jummp.

But for now two practical proposals. Everyone who wants naltrexone for any reason should be given naltrexone (given no co-pay). I think this is obvious. Now somehow a drug which has been around practically forever is expensive, but the cost of paying off the pharmaceutical company whatever they demand for such a program (which will be great for them) is trivial compared to the costs of the opioid epidemic.

I should have provided a link to the Wiki on Naltrexone. Note the cost (retail) of oral Naltrexone is $0.74 a day — providing one a day to every addict and anyone who wanted to pretend to be an addict would cost hundreds of millions a year. This is a completely insignificant sum for the US government, so it should be done immediately. Delayed release Naltrexone is expensive (prescribing it with a $600 copay is bad practice of medicine). Here a technological improvement has made it possible for doctors to give the patients a better, but expensive option, which they don’t take.

I also have an impractical proposal that Naltrexone should be available over the counter — it can’t be abused and the reported side effects are the reported symptoms of being a person. However, I know this proposal is impractical.

My second practical proposal is phased drug assisted therapy. I think it should be
1) whatever you want for a week provided you don’t want a lethal dose (you want heroin — here’s your heorin)
2) second week whatever you want provided you take your methadone under our supervision. All the heroin you want will be none (it doesn’t do anything for someone full of methadone).
3) third week, 50% methadone 50% buprenorphine.
4) fourth week buprenorhine
5) fifth week 50% buprenorphine 50% naltrexone
6) 6th week through death do us part naltrexone.

Why not ?

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Twelve Dimensional Chess

Barack Obama just won Gallup’s man most admired by US adults poll for the 11th straight time.

Also, in spite of the Republicans’ determined efforts including elimination of the mandate, signups are only 4% fewer than last year’s.

Finally, I am thinking about “eleven dimensional chess”. This was a joke about Obama and Obamaniacs who ascribed his amazing luck to brilliantly subtle strategy. To be honest I was thinking of Hillary Clinton (second to Michelle Obama after 16 first place finishes) as someone who managed eleven dimensional fools mate.

And I recall that the original 11 dimensional chessplaying was cleverly promising health care reform could work without an individual mandate. A merely sly politician would promise this, because he knew that reform was popular, mandates are not popular, and it is better to break a promise after being elected than never to be elected at all. But, it was argued, Obama campaigned in the obvious way on an obvious lie exactly, because he knew that reform without a mandate would be a catastrophe and especially catastrophic for the insurance companies. By making a promise which shouldn’t be kept, he scared them and their tame senator Max Baucus into supported reform if and only if there were a mandate. He also 11 dimensionally managed to cede control to the Senate as is necessary to flatter senators (and avoid the blame for the necessary tradeoffs). The Clinton’s sacrificed their king (and hurt the electoral chances of their queen) by setting up a committee and keeping Senators waiting for months.

But wait. Didn’t I just mention that health care reform is actually functioning without a mandate ? Is it possible that it can work with subsidies which prevent an adverse selection death spiral ? As Obama claimed in t008.

Now that, that is 12 dimensional chess. He was so brilliant that he managed to promise something which was possible (and hasn’t hurt the insurance companies) yet terrified them into supporting health care reform. In this way he 12 dimensionally convinced Republicans that they could destroy healthcare reform by eliminating the mandate, so they did, and we ended up with the policy he most slyly proposed.

Either he is a true genius of 12 dimensional chess or he is very very lucky.

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How much did that bailout cost ?

11 years after the huge financial rescue operation, procrastinators look at the cost to the Treasury. The numbers are gigantic. Also the cost was negative. Saving the financial system and preventing a second great depression was, I think, the most profitable trade in human history by far. Crude accounting suggests this, but there are two relatively sophisticated arguments that the rescue didn’t yield profits and was, in fact, costly.

First the notorious TARP was a small part of the rescue. Fed purchases of risky securities at prices far higher than anyone else was willing to pay dwarfed TARP. Also the separate rescue of Fannie Mae and Freddie Mac was very large compared to TARP. This means that the profit earned on TARP (which is small only compared to the huge amount of wealth at risk) is misleading. In fact, the Treasury made a profit on TARP even including the too small program to help mortgagers (HAMP) which was a gift not a loan and the cost of saving the US automobile industry. But focusing on that implies missing the much bigger picture involving federal reserve banks and the government sponsored entities which have become (again) government owned entities. If one considers them, one sees that the rescue was not just profitable, but the most profitable deal ever.

Here is the cash flow. It is huge and the cash is flowing in to the Treasury.

These are large numbers. The dividends largely resulting from the rescue are roughly 10% as large as total dividends paid by corporations.*

The second argument is that crude accounting is vulnerable to extending and pretending — non performing assets appear on balance sheets as if they were worth their face value. The Federal Reserve Banks do not mark their assets to market. It was arguable that their accounts were deceptive and that the profits they weree required to hand over to the Treasury would be more than balanced by losses which the Treasury would have to bear. Now there has never been final proof of anything ever, but I think it is safe to say that this reasonable argument was incorrect. The rescue might end up costing the Treasury if there is a financial crisis which dwarfs 2008. The assets of the Fed, Frannie and Freddie might become worthless, for example if a very large meteor hits the earth. But that’s not the way to bet.

Also, I told you so on September 18 2010

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The Wizard of Odds

Dorothy was in a strange land and had no idea what would happen next. The good witch of the North said she should follow the scientific method to a sound forecast. Unfortunately, neither she (nor anyone else) explained what exactly the scientific method is.

As she wandered down the yellow brick forking path of endless options, Dorothy was surprised by the voice of a heuristic firmly attached to a degenerate prior. She freed the heuristic from the prior and discovered that he was amazingly swift and flexible. She suggested that with his enormous speed he could quickly reach a sound conclusion.
The disconsolate heuristic said that he could “If I only had a brain.”

And they wandered off to find a shiny extremely strong hypothesis test with a razor sharp ax. The hypothesis test was rigidly chopping down the same deadwood. Dorothy said that his great destructive power could help him clear the way to the truth. All he needed to know was a promising direction, and he could eliminate all plausible but false hypotheses leaving only the truth.

The sorrowful hypothesis test explained that he had no idea how to create hypotheses or to decide which ones were worth testing and sang that he could find the truth “If I only had a heart”.

Having heard of the wonderful Wizard of Odds who could solve all of their problems, they made a bee-line for the land of Odds. On the way they stumbled over a cowardly line. The cowardly line said he made no claim about expected values or disturbance terms, because he claimed to be nothing other than what he was, the King of the summary statistics, the OLS regression.

They said that with his daring contempt for consistency and lack of any fear of bias, he surely cold provide them with a forecast. The lion explained that he fit but didn’t forecast – that treating an OLS regression as a forecasting model might appeal to the foolish heuristic, and might follow from implausible hypotheses which were easy to test and reject, but he couldn’t do it because he didn’t have the courage.

Finally they arrived at the City of Odds where they met a wonderful wizard of odds named Thomas Bayes, who dramatically provided the probability of any conceivable event based on any conceivable data set. They were in awe until Toto barked. The Wizard boomed that they should pay no attention to the arbitrary prior behind the curtain.

So Dorothy gave up on the effort to solve the problem of induction. And Toto too.

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A Micro Founded Model in Which Trade Causes Higher Productivity Growth

The division of labor is limited by the extent of the market.

The model is a modified version of the simplified Romer 90 model. The modification is that there is a minimum efficient scale for the production of intermediate goods.

Gross output in the growing sector is (sum i = 1 to N of x_i^alpha)L1^(1-alpha) where x_i is the amount of the ith intermediate good used. There is also another way to produce the final product 1 for 1 from labor output = L2. L1+L2 = L which is fixed.

intermediate goods can be made from the final good one for one, but one must make at least one unit.
There is a small closed economy with (alpha)(L^(1-alpha)) <1. So in this economy it is not efficient to use or produce any intermediate goods. So N is fixed at zero and there is no growth. With free trade and no transporation costs, the relevant L is the world labor force, so it makes sense to make intermediate goods. They have to be invented and intellectual property is protected. Except for the minimum efficient scale of 1 unit, this is Barro and Sala i Martin's simplified version of Romer's 1990 model. Well also the number of inventions is a whole number, because making it a continuum is silly. Value added is proportional to N. So is the real wage. Increased N is technological progress and is the engine of growth and increasing produtivity. N only grows if L is large enough. L is world labor supply if there is free trade. Under autarchy small countries have no growth (which costs more than 1% of potential GDP). The model is very simple and actually very old. Here I come to an embarrassing conclusion. I think the minimum efficient scale isn't even needed at all -- it just makes the result extreme. In fact, I think the model as presented in the textbook has the effect high L causes high growth. There is no minimum efficient scale and no backstop no intermediate goods technology. It was decided that the scale effect was unreasonable, so the model was changed to eliminate it. This eliminated the effect of trade on productivity growth. I don't think it was difficulty of finding a model. It was a consensus on what is a reasonable thing for a model to do. In particular, there was a habit in (not so good) empirical work of treating each country as independent. I mean the standard work horse model confronted with data assumed no trade. Then it implied big countries grow faster than small countries. Ooops. So the model was modified. Then removing a counterfactual implication of the counterfactual no trade assumption removed all effects of trade on productivity growth, and at least one very smart person decided that theory suggested that there was no effect of trade on growth. In fact very old simple theory suggested cases where there could be no growth without trade. And I have 12 minutes left. I will not waste your time suggesting you read more just so that I can present the model in 30 minutes.

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I actually really disagree with Paul Krugman this time

Krugman argues that the Bank of Englands worst case scenario for no deal Brexit is implausibly bad. I agree with his conclusion, but strongly disagree with one argument (on a point which he stresses is quantitatively minor)

… the BoE includes some nonstandard effects of trade: they assume that reduced trade (and foreign direct investment) will reduce productivity more than the direct impacts on resource allocation would predict. They cite some statistical evidence, but it’s important to realize that this is black-box, reduced-form stuff: there’s no explicit mechanism through which it’s supposed to happen.

However, these assumed nonstandard effects aren’t what’s driving the really bad scenarios; they only, as I understand it, contribute something like 1 percentage point of GDP to the predicted costs.


On the substance: I’m skeptical about the supposed effects of trade on productivity. I know that there’s some evidence for such effects; trade seems to favor more productive firms. But relying a lot on effects we can’t model seems dubious.

In particular, I have strong memories of the openness-growth debacle of the 1990s.

I comment.

To me sentence “But relying a lot on effects we can’t model seems dubious” seems dubious. What do you mean “we” bright man ? I am willing to bet you could whip up a model where trade causes high productivity growth within 15 minutes.I am not willing to bet on you against you as being the guy who bet he couldn’t do it would creat a bit of conflict of interests.

I will attempt to do it in 30 minutes (OK I have begun thinkin already).

Then against data you have an example (one (1)). I can think of many debacles of people who decided not to rely on an effect because they couldn’t model it.
1) we can’t explain why nominal stickiness might be optimal & in our models firms maximize profits. The claim is true. Menu costs don’t do the trick as firms synchronize. Calvo fairies are embarassingly implausible. Akerlof said near rational (not optimizing). So they decide they must assume prices are flexible and we get a RBC debacle.
2) “zero isn’t an especially important number” Paul Krugman 1988 (at 1050 Mass avenue). There is no reason why people should accept constant nominal wages with 2% expectable inflation and not accept a 2% wage decline with 0% expectable inflation. So it can’t be true. But it is.
3) There can’t be a liquidity trap because of the Pigou effect. Also there is Ricardian equivalence. No one noticed that Pigou and Ricardo contradict each other until … *you* remember when — it was in the 1990s (and that example is *not* an elephant).

Over at the New York Times I ran out of allowed space so I will continue here with examples after the jump.

But now I wan’t to start a clock. Trade causes higher productivity growth in the model which I will present in 30 minutes or less.

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McCaskill, Donnelly and the poll correction

Recently, I claimed that is too cautious when correcting polls for house effects. Multiplying their correction by 4/3 gives lower volatility of generic congressional ballot polls (and for the past 100 days multiplying by 3/2 works even better). I think the are conservative, because adjusting or correcting polls is bound to be controversal and so they impose a pseudo prior that all pollsters are unbiased. In any case, I would like to play with the numbers.

I am going to very crudely adjust their adjustments by multiplying by 4/3. The adjustment is very important when attempting to forecast two red state Senatorial elections in Missouri and Indiana, because they have been polled almost exclusively by pollsters with strong Republican house effects. This means that the fivethirtyeight correction actually flips the lead — the fivethirtyeight corrected polls give a polls only “light” estimate that the Democrat McCaskill is ahead by 0.9% while the simpler average with no adjustment at realclearpolitics shows the Republican Hawley ahead by 2%. That’s not a huge difference.

Looking at the 10 most recent polls I see an average adjusment of 2.98 %. This means my adjustment to the adjustment gives McCaskill an additional 0.99% slightly more than doubling her estimated lead. Interestingly, the adjusted adjusted polls only estimate of 1.89% is almost exactly equal to the fivethirtyeight “classic” estimate of 1.7% which is based on polls and “fundamentals” including fund raising and incumbency.

Up in Indiana, fivethirtyeight gives Joe Donnelly a adjusted polls only estimated lead of 2.6%. the average adjustment of the most recent 10 polls is 1.76% so my adjustment to the adjustment gives him an additional 0.58% and a lead of 3.18%. The classic estimate with fundamentals gives him a lead of 3.2%.

In both cases, the adjusted adjustment makes the light estimate strikingly similar to the fivethirtyeight classic estimate.

With adjusted adjusted polls and fundamentals I get a not so classic estimate of a 2.7% lead for McCaskill and 3.8% for Donnelly.

Very crudely this seems to imply a roughly 70% estimated probability that McCaskill will be re-elected (I just read the probability corresponding to Donnelly’s light 538 adjusted 2.6 %).

update: Arizona too. Harris interactive is running a tracking poll of the Arizona senate race. This means it has a big effect on the forecast. This is important, because fivethirtyeight estimates that Harris interactive has a 2.3% Republican house effect, and there is evidence that the fivethirtyeight estimated house effects are cautious, conservative and therefoer 0.75 times the optimal estimates .

Based on their adjusted polls, they estimate that Synema is 1.6% ahead of McSally. The average adjustment of the past 10 polls is 1.48% towards Synema. The corrected correction suggests she is about 2.1% ahead not 1.6% ahead. This is enough to have a fairly impressive effect on the calculated probabilities eyeballing a cumulative normal distribution, I think they would give Synema about a 2/3 chance instead of 60.3% if they used my adjusted adjustment.

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Opinions on Text of the 14th Amendment Differ. One side has a point.

Ian Millhouser correctly denounces not only Trump’s assault on the 14th amendment but also reporters who print absolutely false assertions.

The issue is Trump’s clearly false claim that he can eliminate birthright citizenship by executive order.

In fact “All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States … ” – US Constitution Amendment 14.

Millhouser’s post is too good to summarize, click the link.

Importantly he nails The New York Times tweeting the absolutely 100% false assertion that ” It is unclear whether he can do so unilaterally”.

He also catches CNN falsely saying it is “unclear” and NPR falsely claiming it”isn’t settled”.

The FBI has found no clear evidence that they are deliberately undermining the US Constitution and the very idea of Constitutions. In fact (as in the case of the dread New York Times headline) disgracefully printed 2 years + 1 day ago) they consider it safe to assert a negative. The principle that one can’t prove a negative is turned on its head. They assume it is safe to write and say “unclear” and to say “isn’t”.

I absouutely reject the claims that it is unclear whether the reporters who did this shouldn’t be roasted over a slow fire and that it isn’t settled whether the editors who allowed them too shouldn’t be skinned alive.

I just want to add a few comments.

First Millhouser doesn’t waste space noting that Donald Trump has no legislative authority whatsoever. He claims to be able to rewrite the Constitution by executive order. He can’t even rwrite the law. An executive order must be instructions as to how to faithfully execute the law written by Congress.

I think conservatives (if any read angrybearblog) may suspect me of hypocrisy since I never denounced Obama’s executive orders. They would be wrong. Obama (and his hardworking staff) always explained the basis in law and precedent for his orders. Even DAPA and DACA which seemed extreme even to sympathetic observers, were clearly authorized by the Immigrationa and Naturalization Act which grants the executive vast discretion and legally the same as an uncontroversial executive order signed by George H W Bush (not to mention that DACA was uncontroversial when issued). DAPA was blocked by an extremist judge not on the grounds that it went beyond the INA but on the grounds that it wasn’t preceded by a period of public comment as required by some other law (I think it’s called the administrative procedures act).

In contrast Bush’s absurd claim that he could create military commissions by executive order was rejected by a Conservative Supreme Court.

Another minor point — the “subject to the jurisdiction of ” phrase clearly was intended to say that Native Americans who live in territory not claimed by any great power or by the US Government are not US citizens. This is clear from the relevant context in the main body of the Constitution “excluding Indians not taxed” (search for the dread words “three fifths” and scroll left past a comma). The borders of the USA were not clearly defined when the 14th amendment was drafted. There were treaties with Mexico, Russia, and the British Empire which roughly defined approximately the current borders (except for Hawaii, Guam, Puerto Rico, the US Virgin Islands, American Samoa and what’s left of the Norther Marianas Islands after typhoon Yutu). There were also treaties with native American tribes which hadn’t yet been broken which defined a smaller but aggresively expanding country. The 14th amendment said that, for example, people born in Oklahoma are not necessarily US citizens (don’t worry doesn’t apply to the native born president eligible Senator Professor Elisabeth Warren because that treaty was broken sooner than she was born).

By the way, Don Jr, Erik, Ivanka and Barron don’t have to worry that their dad will deprive them of US citizenship. He is, to our everlasting shame, a US citizen who lived in the USA at least 6 years after turning 14, so they are native born US citizens just like Rafael “Ted” Cruz and just as Barack Obama would be even if he had been born in Mombassa.

Finally Millhouser undestated his case again when he wrote

the Fourteenth Amendment’s words are clear, and the Supreme Court settled any lingering doubts over their meaning in its 1898 opinion in Wong Kim Ark.

In fairness, Wong Kim Ark was not a unanimous opinion — it was a 6-2 decision handed down over a dissent from Chief Justice Melville Fuller. In his dissent, Fuller argued that the Fourteenth Amendment secretly contains a missing word. “Born in the United States, and subject to the jurisdiction thereof,” he claimed, means that a person was “born or naturalized under such circumstances as to be completely subject to that jurisdiction, that is, as completely as citizens of the United States” (emphasis added). Thus, the child of non-citizens may not be “completely” subject to American jurisdiction because they also may also be “subject” to a “foreign power” — their parents country of origin.

The implications of this dissent are simply breathtaking. Had it become the law — and just in case this point is unclear, a dissenting opinion is, by definition, not the law — Fuller’s dissent would establish that any child of non-citizens, even the child of two lawful permanent residents, would not be a citizen.

In fact, the dissent would imply that Don Jr, Erik, Ivanka, Barron and my daughters are not US citizens because their mothers weren’t at the times of their birth. If any taint of foreigness were poison, than one foreign citizen parent would be enough for exclusion.

But, fortunately, Fuller completely invalid assertion of “completely” was absurd and outvoted 6 to 2.

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Does fivethirtyeight process the numbers too much ?

Or not enough. Nate Silver has long performed fairly complicated calculations with (lots of) raw data. Even back when he was Poblano at DailyKos this was highly controversial. Now that he leads a huge team at, it is almost necessary just to decide whether to trust them, because it is very time consuming to read their explanations of their algorithms.

In particular, obsessive poll watchers such as your humble correspondent, have noted that Senate ratings by and don’t always move together. Very often the difference between the complicated calculations at and the simple averages at is greater than the change of either from week to week.

One very important (and controversial) aspect of the approach is correcting raw polls

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