Political Calculations
Unexpectedly Intriguing!
July 22, 2016
Solenoid Perfectoid Space - Source: MSRI - https://www.msri.org/system/cms/files/83/files/original/141109_Emissary-Fall-2014-Web.pdf

There are some really exciting developments starting to bubble up like perfectoid spaces in mathematics.

Talk about a sentence that we never thought we'd ever write, because:

  1. The concept of perfectoid spaces has only been around since 2010, having been introduced in a remarkable paper by then-grad student Peter Scholze.
  2. They've gone from newly introduced exotic concept to powerful tool in an amazingly short period of time.

It's that second thing that's motivated us to write on the topic today.

Here's the best, simplest description we could find of what they are (we've added the links to good starting point references for the different mathematical fields mentioned):

Scholze’s key innovation — a class of fractal structures he calls perfectoid spaces — is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together.

By far reaching ramifications, they're referring to the use of the new tool to greatly simplify mathematical proofs, such as Scholze did in rewriting a proof of the Local Langlands Correspondence, which had originally required 288 pages, in just 37 pages.

That's possible because of what perfectoid spaces can do in being able to transform very difficult math into much easier math to do, which was Scholze's breakthrough in the field (we've added some of the links in the following passage again for reference purposes).

He eventually realized that it’s possible to construct perfectoid spaces for a wide variety of mathematical structures. These perfectoid spaces, he showed, make it possible to slide questions about polynomials from the p-adic world into a different mathematical universe in which arithmetic is much simpler (for instance, you don’t have to carry when performing addition). “The weirdest property about perfectoid spaces is that they can magically move between the two number systems,” Weinstein said.

This insight allowed Scholze to prove part of a complicated statement about the p-adic solutions to polynomials, called the weight-monodromy conjecture, which became his 2012 doctoral thesis. The thesis “had such far-reaching implications that it was the topic of study groups all over the world,” Weinstein said.

When we discuss math, we like to focus on the practical applications to which it can be put. In this case, mathematician Bhargav Bhatt, who has collaborated with Scholze on several papers, gets to the bottom line for why perfectoid spaces will matter for solving real world problems (reference links added by us again).

Namely, as perfectoid spaces live in the world of analytic geometry, they actually help study classical rigid analytic spaces, not merely algebraic varieties (as in the previous two examples). In his “p-adic Hodge theory for rigid-analytic varieties” paper, Scholze pursues this idea to extend the foundational results in p-adic Hodge theory, such as Faltings’s work mentioned above, to the setting of rigid analytic spaces over Qp; such an extension was conjectured many decades ago by Tate in his epochmaking paper “p-divisible groups.” The essential ingredient of Scholze’s approach is the remarkable observation that every classical rigid-analytic space over Qp is locally perfectoid, in a suitable sense.

Which is to say that a whole lot of problems that have proven to either be very difficult to solve or have evaded solution by other methods might yield easily to solution by the newly developed mathematical theory of perfectoid spaces. For a field like mathematics, that's a huge deal!

We'll close with Peter Scholze speaking on perfectoid spaces in 2014.


July 21, 2016

We have a new example of junk science today, which might perhaps be better described as bad analysis that checks off one of the more significant boxes in our junk science checklist. Specifically, today's example trips over the checklist category for Inconsistencies, which is where we are most likely to find the effects of deceptive maths and abusive statistics.

How to Distinguish "Good" Science from "Junk" or "Pseudo" Science
Aspect Science Pseudoscience Comments
Inconsistencies Observations or data that are not consistent with current scientific understanding generate intense interest for additional study among scientists. Original observations and data are made accessible to all interested parties to support this effort. Observations of data that are not consistent with established beliefs tend to be ignored or actively suppressed. Original observations and data are often difficult to obtain from pseudoscience practitioners, and is often just anecdotal. Providing access to all available data allows others to independently reproduce and confirm findings. Failing to make all collected data and analysis available for independent review undermines the validity of any claimed finding. Here's a recent example of the misuse of statistics where contradictory data that would have avoided a pseudoscientific conclusion was improperly screened out, which was found after all the data was made available for independent review.

The following analysis shows the importance of the work that is often done in near-anonymity to replicate and validate the results of analysis where unique findings are made, which is only possible when the data behind the analysis is available. Unfortunately, today's example of junk science won't be the last time we'll be discussing an example in this category, thanks to the special efforts of a repeat offender.

Let's get to it then, shall we?

Everyone knows about lies, damned lies, and statistics. The quote has been attached to Mark Twain who apparently attributed it to British Prime Minister Benjamin Disraeli. It remains among popular clichés because there is universal truth to it, a sort of caveat emptor lying in the background whenever one consumes an argument. Nowhere is that more the truth than economics and finance, disciplines almost (nowadays) entirely populated with statistics and very little else.

Given the rather extreme nature of the times, extreme statistics are more prevalent perhaps than at any other point. They run the spectrum, as do human intentions, from the purely mistake to the malicious. The better stats, as the best lies, are often difficult to discern because they contain a great deal of truth; requiring a great deal of further analysis and scrutiny to unpack the error or mistake. Sometimes, however, it takes very little effort (reflecting both on the numbers and the person wielding them).

Prominently displayed on the front page of Yahoo! Finance recently was an article whose purpose was just so barely disguised. You can and should read the whole piece, but the gist is essentially that we shouldn't worry about very high valuations to the current stock market because valuations aren't so simple. The expert quoted in the article declares that PE's at this point, well above 20x, "do not contradict the bullish case for stocks." The reason is low inflation and related low interest rates; an argument proposed and reiterated many, many times before.

There are statistics for this view, including a neat chart showing the relationship between PE's for the S&P 500 and their coincident inflationary circumstances (represented by the 1-year change in the CPI).

Inflation vs. S&P 500 P/E Ratio (Jan. 1965 through Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Yahoo.jpg

Using Robert Shiller's data for the historical S&P 500, inflation, and earnings, I recreated the same chart with very nearly the same results.

PE vs. Inflation (Jun. 1965 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Yahoo-65-16.jpg

Running a simple, exponential regression (a polynomial regression finds a better fit, but raises the objection of being fitted), you do find a relationship that argues in favor of the proposition; inflation and PE's are to some degree negatively correlated.

PE vs Inflation with Regression (Jun. 1965 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Regress-65-16.jpg

Because I found the same as projected in the article, I can confidently declare it nonsense. I did not test for statistical significance in the regression because it simply wasn't necessary; this argument falls apart long before the math.

This is simply a case of, at best, circular logic or, at worst, intentional obfuscation. The first clue is the time frame itself, starting right on the cusp of the Great Inflation. Given the much further history of Shiller's data, we need not be so discerning. Going back further to the 1870’s provides a much different result.

PE vs Inflation (Jan. 1872 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Full.jpg

The regression using this full dataset is far, far less compelling. You don’t even need the regression to see the distribution – the densest area of the scatterplot above is between 0% and 5% inflation and 10 and 20 times earnings.

PE vs Inflation with Regression (Jan. 1872 to Jun. 2016) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Full.jpg

There is still, however, some mathematical relationship even though the R-squared is especially low. If we perform our own transformations in framing the time period, this apparently inverse correlation is revealed more clearly. If we instead end with only through the last part of the Great Inflation, to December 1979, we actually find very little to support the hypothesis.

PE vs Inflation (Jan. 1872 to Dec. 1979) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-1872-1979.jpg

There is actually very little reasonable correlation between inflation and PE's to this point in history; a slightly detectible hint but without a whole lot of variation. Notably absent are those more extreme, higher valuations that perform the upward transformation in the original regression. Moving forward in time to December 1994, we find some indication of a greater cluster starting to move up the axis (the Great "Moderation"), but still nothing like the original premise.

PE vs Inflation (Jan. 1872 to Dec. 1994) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-1872-1994.jpg

It isn’t until we add the latter half of the 1990’s and the dot-com bubble that these “positive” valuation outliers suddenly appear (the rest of them don’t show up until, ironically, the Great Recession when earnings fell very far in coincidence to disinflation and even negative inflation). This is, of course, wholly unsurprising.

PE vs Inflation (Jan. 1872 to Dec. 2000) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-1872-2000.jpg

But there is more to the deception, which is why the Great Inflation period was included. If we isolate just age of asset bubbles, the relationship once more disappears almost entirely.

PE vs Inflation (PE Bubble) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Bubble-1.jpg

PE vs Inflation (PE Bubble with Regression ) - Source: http://www.alhambrapartners.com/wp-content/uploads/2016/07/ABOOK-July-2016-PE-Bubble-Regression.jpg

A regression function that plots almost vertically means that PE valuations have moved around almost totally independent of the CPI. In other words, without including the Great Inflation period and its immediate aftermath to fill in the bottom right there is again no mathematical significance between inflation and PE's. In isolation, the market valuation since 1995 just doesn't bear any resemblance to inflation, leaving it as a function of some other independent condition (such as monetary agency). It is only by included the “other” extreme of low valuations and high inflation of the 1960’s and 1970’s that gives this assertion of causation the thin veneer of validity.

But that is hardly the same scheme as what was proposed. What these figures show is really much different; from 1965 forward, the most that can be said is that there were generally lower valuations as high consumer inflation raged before the 1980’s. After 1995, there was generally much higher valuations and lower inflation. It does not follow, then, that valuations are determined by inflation – at all. Causation would appear to be among the “error” terms or more likely independent variables left out entirely, which is what the full data set suggests. There is no data suggesting what valuations would do with very high inflation (recorded in the CPI) after 1995 because it hasn't happened; likewise with low inflation during especially the 1970’s.

These are cases, then, that must be taken in isolation, not as a universally-applied “rule” or even suggestion. To add one is a blatant misuse of correlation, again an indictment first suggested by starting with and only including the period after January 1965. Including the Great Inflation and its opposite extreme muddies the interpretation because you can't immediately discern the separate circumstances as separate. To claim that low inflation after 1995 supports high valuations is tantamount to wholly biased selectivity; there is no evidence to prove (or disprove) the assertion, an invalidation in statistics as well as basic logic. All the math shows is that there was low inflation.

That is really what the full data tells us, with one very important contextual addition. Comparing the years without the dot-com bubble and finding very little relationship means that it is only through the high valuations of the dot-com era (and to a lesser extent more recently) that gives this idea its apparent (and still wrong) relevance. That would mean the original premise contained in the article is using the incident high valuations of the dot-com bubble because they occurred during a period of low CPI inflation to propose that high valuations today aren't threatening because we still find low CPI inflation. It essentially advises that the last big stock bubble justifies why we shouldn't be worried about another one.

That was Twain's, as Disraeli's, point all along. If you have a strong argument you don't need to resort to bad math to make it; bad math is instead used, often intentionally, to obscure the weakness.


Snider, Jeffrey P. Valuation Fallacies. Alhambra Investment Partners. [Online Article]. 18 July 2016. Republished with permission.

Shiller, Robert. U.S. Stock Markets 1871-Present and CAPE Ratio. [Excel Spreadsheet]. Accessed 18 July 2016.

Political Calculations. How To Detect Junk Science. [Online Article]. 19 August 2009.


July 20, 2016

Nearly a month ago, we presented our "most likely" prediction for how the U.S. Bureau of Economic Analysis will revise the U.S.' Real Gross Domestic Product on Friday, 29 July 2016.

Let's recap what we forecast, picking things up from after we described how we went from estimating the "maximum potential" size of the revision to the "maximum likely" size of it, before we drilled down to what we think will be the "most likely" amount by which real GDP will be revised through the fourth quarter of 2015:

Previously Reported and Revised Real GDP, 2005-Q1 Through 2015-Q4, per BEA Regional Data released on 2016-06-14, Revised to Account for 'Overseas' GDP, with Date Correction - was 14 June 2015, now corrected to 14 June 2016 - previous chart here: https://2.bp.blogspot.com/-EzKqOVcLGC4/V2XJce71MhI/AAAAAAAANkk/uxCWYmwSK98c6baRUFRi1-NmNArdwz1qgCLcB/s1600/Political-Calculations-2016-GDP-Revision-Projection-spanning-2005Q1-to-2015Q4.png

But the "maximum likely" revision of -1.4% of previously reported GDP through 2015-Q4 is not the "most likely" size of the upcoming revision to the nation's GDP will be, because the BEA's plans for the revision of the national level GDP data will only cover the period from 2013-Q1 through 2016-Q1.

That means that it will miss the discrepancy that opens up in 2012-Q3 and 2012-Q4 between the just-revised state level GDP and previously indicated overseas federal GDP and its previously recorded national level GDP. That discrepancy is just over $55.1 billion in terms of constant 2009 U.S. dollars in 2012-Q4, which itself is over 24% of the full $225.7 billion discrepancy that our previous calculations indicates between the pre-revised national level real GDP and the post-revised state level GDP data through 2015-Q3.

Because the BEA won't be including that $55.1 billion portion of the discrepancy from 2012, the "most likely" size of the revision that it will report at the end of July 2016 is therefore -1.1%, which is 24% less than the "maximum likely" revision of -1.4% we previously calculated.

After the BEA's annual revision of GDP for the 50 states and the District of Columbia on 14 June 2016, there is only one factor left that can affect the amount by which the BEA will actually revise the nation's total real GDP next week - the contribution of overseas federal military and civilian government activities, or as we've described it, the "hidden GDP of war".

There are three scenarios in how that one factor can play out:

  1. If that contribution is greater than what the BEA has previously indicated, the amount by which real GDP through 2015-Q4 will be adjusted will be smaller. So instead of being reduced by 1.1% as we've projected to be "most likely", it would instead be reduced by a smaller percentage, or in the very unlikely case that contribution is much, much greater, real GDP through 2015-Q4 could be adjusted upward. For this scenario to occur, it would mean that the U.S. government was much more engaged in fighting wars overseas in a way that adds to the nation's GDP than it has previously indicated. This is the "under" scenario.
  2. If that contribution is less than that the BEA has previously indicated, the amount by which real GDP through 2015-Q4 will be adjusted downward will be larger, going in the direction of what we calculated would be the maximum likely revision. For this scenario to occur, it would mean that the U.S. government was engaged in less "productive" military and civilian government activities overseas than it has previously indicated. This is the "over" scenario.
  3. If the contribution is the same as what the BEA has previously indicated, then we'll see the "most likely" scenario we calculated be the actual result. Real GDP through 2015-Q4 would be decreased by about 1.1% from the level that was recorded earlier this year on 29 March 2016. This might be considered the "null" scenario.

To make that question more interesting, we asked our most dedicated readers [1] to click through and answer a SurveyMonkey poll, which we've now closed. The results of that poll are presented in the following chart.

SurveyMonkey Poll Results

As you can see, our poll produced a 40-40-20 split. 40% of the poll participants indicated they thought Scenario #1 was more likely, 40% predicted Scenario #2 would be a reality, and 20% believed in the Scenario #3 "no change from our forecast outcome" outcome.

While those results seem nearly split down the middle, what they really indicate is that the majority of the poll participants believe that the actual adjustment to real GDP through 2015-Q4 will be different from our "most likely" forecast for the size of the July 2016 national revision. What is equally split down the middle is the direction in which it will be adjusted, with no clear collective prediction emerging from our poll.

Where is Philip Tetlock when you need him?


[1] We had problems with generating working code to embed the survey directly in our post, so we were stuck with providing a link for readers to click through to participate in the survey. That's the sort of hassle that only the most dedicated readers would endure, so we greatly appreciate the extra effort on the part of all the participants who registered their own prediction for how this one aspect that will affect the actual size of the upcoming GDP revision. Thank you!


July 19, 2016

Last week, while visiting Bozeman, Montana, Matt Kahn looked out over all he surveyed and said:

I'm in Bozeman, Montana. While there are 40,000 people in this city. I see a lot of open space. Google taught me that Montana has 380,000 square kilometers of land. Suppose that 50% of that can be built upon. Suppose we built up at Hong Kong's density of 7000 people per square mile. So, we would re-create dense cities at a higher latitude. Let's do some math. 190,000*7000 = 1.33 billion people could live in Montana. This migration and real estate construction would create great wealth. Now, given that the U.S population has only 340 million people --- we could open up migration for those who could jump over Don Trump's wall and house them. This example is meant to show folks how urbanization facilitates adaptation. We need to use our resources more efficiently.

Why do I focus on Montana? It is towards the North and it is off the coast and there is plenty of land here. Yes, this land has some economic activity taking place on it right now but urban use would be more valuable. I am now working on a natural disaster project with Leah Boustan and Paul Rhode and once I can access our disaster data, I will update this post to see whether Montana is exposed to more disasters than would be predicted given its size.

We love this kind of blogging from econ professors because it makes for a quick and dirty tool development project! We've taken Kahn's algebra and built a tool to do it, where anyone can substitute the default data for Montana and Hong Kong (Hong Kong's population density is nearly 7,000 people per square kilometer) with the region or population density of their choice. Including you, where if you're accessing this post on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool so you can!

Area and Population Density Data
Input Data Values
Total Geographic Area [square kilometers]
Percentage of Land That Can Be Built Upon [%]
Target Population Density for Area to Be Built Upon [people/square kilometer]

Potential Population for Area
Calculated Results Values
Supportable Population

Since the topic of disasters came up, the biggest lurking natural disaster that has been proposed for Montana would be an eruption of the Yellowstone supervolcano, which in terms of potential scale, would make the plot of a big budget Hollywood disaster movie look like a straight to video animated sequel to a less-than-popular children's movie.

The timebomb under Yellowstone: Experts warn of 90,000 immediate deaths and a 'nuclear winter' across the US if supervolcano erupts

  • It could release 1 ft layer of molten ash 1,000 miles from the National Park
  • It would be 1,000 times as powerful as the 1980 Mount St Helens eruption
  • A haze would drap over the United States, causing temperatures to drop
  • Experts say there is a 1 in 700,000 annual chance of a eruption at the site.

The odds of such an event are everything in determining whether we should build out Montana to be the home of 1.33 billion people.

BozeMan Life - Source: http://prevention.mt.gov/VISTA/About-Montana#

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July 18, 2016

The second week of July 2016 was one of those rare weeks when our futures-based model for projecting the future closing value of the S&P 500 was very nearly dead on target for every day of the week, as long as you recognize that target was fixed by investors focusing on the second quarter of 2017 (2017-Q2) in making their current day investment decisions.

You don't have to take our word for it. We animated what our model forecast and how the S&P 500 actually performed for your entertainment, provided of course that you're entertained by watching the projected trajectories that our futures-based model generates flop about like a fish while, at the same time, the actual trajectory that the S&P 500 takes is overlaid on top of those projections. If you're viewing this post on a site that republishes our RSS news feed and the animation doesn't play, we've posted a YouTube video version of the animation as well.

Alternative Futures - S&P 500 - 2016Q3 - Standard Model - Animation: 21 June 2016 through 15 July 2016

In putting the animation together, we're taking advantage of a unique opportunity to show the formation of an echo on our model's projections of the future, which developed as a direct response to the market's reaction to the Brexit vote outcome on 24 June 2016 through 25 June 2016.

Starting on 21 June 2016, the animation shows first what the future looked like going into the Brexit vote, then how our model's projections of the future changed in response to the aftermath of the Brexit vote. That outcome shows up as an echo in our model's projections, which appears one month after the actual event occurred. The echo is the result of our model's use of historic stock prices as the base reference points from which we project the future for stock prices.

Beginning on 27 June 2016, the animation then shows the trajectory of the S&P 500's closing daily value on each trading day, which reveals how stock prices reacted as investors shifted their forwarding looking focus from one point of time in the future to another.

The first takes place as a Lévy flight from 27 June 2016 to 30 June 2016, when investors shifted their attention from the expectations associated with 2016-Q3 in the immediate aftermath of the Brexit vote to the more distant future of 2017-Q1.

The stock market's focus then held on 2017-Q1 from 30 June 2016 through 7 July 2016. On 8 July 2016, the collective focus of investors shifted in a second Lévy flight, from 2017-Q1 to the even more distant future of 2017-Q2, where it held through the rest of the week, very closely matching the exact trajectory our futures-based model forecast associated with investors being very closely focused on that future quarter.

From the perspective that investors simply appear to have maintained their focus on 2017-Q2 through the entire week, it was a pretty boring week overall, even if some market observers were perplexed as to why stock prices behaved as they did in the face of a week of turmoil in many areas of the world.

But for the U.S. stock market, here is the news that we flagged as being the significant for the S&P 500 in Week 2 of July 2016.

Monday, 11 July 2016
Tuesday, 12 July 2016
Wednesday, 13 July 2016
Thursday, 14 July 2016
Friday, 15 July 2016

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