Welcome to the long anticipated end of 2020, or at least as close to it as we're willing to get this year! This is the seventh annual edition of our year-ending tradition of celebrating the biggest stories in math from the twelve preceding months, at the end of which, we'll identify the biggest math story of the year.

The criteria we use in selecting the stories that make our year-end list is that the maths they involve must either resolve long-standing questions, have real practical applications, or otherwise have real world impact. If you want more, deeper information about the topics covered in our summary of math stories for 2020, be sure to follow the links to additional background material.

We've found three main themes around which to organize this year's edition. Let's get straight to it!

Cracking Old Problems

2020 saw a lot of progress toward solving problems that have been challenging mathematicians for 50, 90, 100, and 270 years. The youngest problem in this category was the deciphering of the "340 Cipher", which California's Zodiac Killer taunted police with a half century ago.

The cipher was finally cracked in 2020 by a team of amateur codebreakers, David Oranchak, Sam Blake, and Jarl Van Eycke, who combined their skills in encryption, applied maths, and computer programming along with some basic intuitions to break the killer's code. The featured video in this section is the fifth installment in their series describing how they tested over 650,000 variations of the cipher to work out how to successfully read it.

The 90-year old problem that was finally solved in 2020 dealt with Keller's Conjecture, which predicts that if you cover a space with identical tiles, at least two of the tiles would have to share an edge. That proposition seems straightforward, but Keller really took it to the next level, and then some, by conjecturing that it would also apply in higher dimensions. Previous generations of mathematicians proved Keller's conjecture would work up through at least six dimensions and also proved it wouldn't hold in eight-or-higher dimensional spaces, leaving an open question of whether it would or would not hold in seven dimensions.

In 2020, professional mathematicians Joshua Brakensiek, Marijn Heule, John Mackey, and David Narváez used a cluster of 40 computers to finally prove, once and for all, that the Keller Conjecture is true in seven dimensions. The practical accomplishment here was the application of discrete graph theory to search for nonlinear codes called "cliques", which in addition to being useful for determining whether the Keller Conjecture might hold for a given dimensional space, can also be applied to speed data transmission.

The 100 year old problem that was solved during 2020 relates to how fluids diffuse within a closed space, which has been an highly relevant issue during 2020 given the airborne transmission of the SARS-CoV-2 coronavirus. Previously, solving problems involving diffusion processes could only be done approximately, requiring extensive computing resources. Mathematician Luca Giuggioli worked out how to more easily frame these kinds of problems for direct solution, which offers great promise for solving problems across a wide number of practical applications much more efficiently. In an ordinary year, this story would be a leading contender for the biggest math story of the year, but this is 2020.

At 270 years, the oldest problem is also a geometry problem, but involves a hungry goat, which makes it perhaps the most fun math story of the year. Quanta Magazine describes the scenario:

Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to exactly half an acre?

Believe it or not, it wasn't until Ingo Ullisch applied techiques from the mathematical field of complex analysis that a mathematical formula was developed to precisely determine the length of the goat's rope to solve the problem!

Finding the Limits

2020 was a year in which more mathematicians gained direct experience in confronting Gödel's incompleteness theorems, which sets limits on what problems can be solved.

In 2020, some mathematical laws that have previously been advanced to describe real world observations have been found wanting. For example, Zipf's Law, a relatively simple relationship that has long been used to model population growth in cities, has turned out to not be complex enough to capture dynamic changes in populations over time.

Meanwhile, Benford's Law, which describes how often the digits 1 through 9 appear as the first digit of values within a dataset that has been successfully used to detect accounting fraud, turned out to be the wrong tool to use to detect potential election fraud in the U.S.

Those previous examples represent the narrowing of the boundaries where the mathematical principles involved may be successfully used. But 2020 also saw a major expansion of the boundaries of problems that can be solved with the introduction of a new proof that establishes that quantum computers may be used to solve problems conventional computers cannot. Quanta Magazine explains how the proof developed by Henry Yuen, Zhengfeng Ji, Anand Natarajan, Thomas Vidick, and John Wright expands the boundaries for what problems can be solved with the new computational technology:

The new proof establishes that quantum computers that calculate with entangled quantum bits or qubits, rather than classical 1s and 0s, can theoretically be used to verify answers to an incredibly vast set of problems. The correspondence between entanglement and computing came as a jolt to many researchers.

“It was a complete surprise,” said Miguel Navascués, who studies quantum physics at the Institute for Quantum Optics and Quantum Information in Vienna.

The proof’s co-authors set out to determine the limits of an approach to verifying answers to computational problems. That approach involves entanglement. By finding that limit the researchers ended up settling two other questions almost as a byproduct: Tsirelson’s problem in physics, about how to mathematically model entanglement, and a related problem in pure mathematics called the Connes embedding conjecture.

This accomplishment is a very big deal, which will drive a lot of development for quantum computing technology. Again, in an ordinary year, this story would be a leading contender for the title of the biggest math story of the year, but it came in 2020.

A Year Defined by Mistakes

The featured video in this section is about the world's first documented math mistake, which dates back several thousand years to the days of ancient Sumeria. The video is relevant because two significant math mistakes that took place in 2020 have affected the lives of billions of people, which makes 2020's math mistakes the biggest math story of the year.

Both mistakes, perhaps unsurprisingly at this point of the year, are related to the coronavirus pandemic. Both mistakes came early in the pandemic and drove public policy responses to the spread of SARS-CoV-2 coronavirus infections, and in turn, are directly responsible for the year's economic recessions in many regions of the world.

The first math mistake that helped define 2020 came from an epidemiological model developed by Neil Ferguson at Imperial College London (ICL). In March 2020, Ferguson and public health officials heavily promoted the projected outcome of the ICL model's "do nothing" scenario, which projected 2.2 million deaths in just the U.S. and another 500,000 deaths in the U.K. to justify the early policy response of imposing lockdowns, the government mandated closure of businesses and orders for residents to stay at home.

But the assumptions encoded within the ICL model were providing results that proved to be off by several orders of magnitude from reality. Worse, the mistakes evaded detection by the ICL model's promoters because the code itself was virtually impenetrable, filled with excessively complex patches, kludges and other band-aid type programming and no connection to "ground truth" data for its 450 parameters. These issues did not become known until Ferguson finally made the code available for public review, with the outcome that trillions of dollars of economic losses around the world occurred because of the unstable projections that emerged from the ICL model's "black box".

Ultimately, not even Neil Ferguson believed his model's results. After it was discovered he had repeatedly violated the stay-at-home orders he promoted, he was forced to resign in disgrace from his role as a government adviser in the U.K.

The second math mistake that helped define 2020 appears to have resulted from the misplacement of a decimal point by the U.S. National Institutes of Health.

The error was such that it amplified the NIH's estimates of projected deaths from novel coronavirus infections in a way that seemed to provide confirmation of the ICL model's flawed projections. A post-mortem of the math error describes its impact:

Sampling bias in coronavirus mortality calculations led to a 10-fold increased mortality overestimation in March 11, 2020, US Congressional testimony. This bias most likely followed from information bias due to misclassifying a seasonal influenza IFR as a CFR, evident in a NEJM.org editorial. Evidence from the WHO confirmed that the approximate CFR of the coronavirus is generally no higher than that of seasonal influenza. By early May 2020, mortality levels from COVID-19 were considerably below predicted overestimations, a result that the public attributed to successful mitigating measures to contain the spread of the novel coronavirus.

Because of these mistakes, 2020 was all too often defined by the wrong policies being put into place at great harm and cost to society in fear of a projected massive death toll from the coronavirus. No wonder then that one of the more important math-related headlines for the year was "Modeling COVID-19 data must be done with extreme care, scientists say".

To be fair, maths done properly have greatly aided the development of vaccines and more appropriate public policy responses to the coronavirus pandemic. Never-the-less, these two mistakes together represent the biggest math story of 2020, helping to make the year what it was: a truly "Kushim"-ed up affair (watch the video to catch the reference!)

Update 29 December 2020: Just published peer-reviewed research highlights the ICL model's deficiencies. For a nontechnical summary of findings, see the press release via MedicalXpress: Model used to evaluate lockdowns was flawed.

Previously on Political Calculations

The Biggest Math Story of the Year is how we've traditionally marked the end of our posting year since 2014. Here are links to our previous editions, along with our coverage of other math stories during 2020:

• The Biggest Math Story of the Year (2014)
• The Biggest Math Story of 2015
• The Biggest Math Story of 2016
• The Biggest Math Story of 2017
• The Biggest Math Story of 2018
• The Biggest Math Story of 2019
• The Biggest Math Story of 2020
• The Survival Function of Roman Emperors
• The Math Helping AI See the World Better
• A Proof for Batchelor's Law
• How Fast Could China's Coronavirus Spread?
• Maths on the Back of an Envelope
• Estimating Economic Impacts from a Disaster Shock
• A Pie Chart for Pi Day
• Simulating an Epidemic
• What Is m?
• How Do False Test Outcomes Affect Estimates of the True Incidence of COVID-19
• Why the Media Can't Do Math
• Very Similar, But Different, Triangles
• Governor Cuomo and the Coronavirus Models
• John Conway's Game of Life
• The Hand That Draws The Circles That Draw The Hand
• Slicing Up Conway's Knot and Learning To Think Four Dimensionally
• Diffusion and Random Walks
• The Mathematical Packing Efficiency of Penguins
• 602,214,076,000,000,000,000,000
• Benford's Law and the Trustworthiness of COVID-19 Case Counts
• Of Storks, Statistics, and Cigarettes
• How Pooling COVID-19 Test Samples Is Super Beneficial
• The Limits of Microsoft Excel
• Three and a Half Thousand Year Old Fractions
• Four Minutes of Infinite Patterns
• When Benford's Law Breaks Down
• Replacing Zipf's Law in Modeling Growth of Cities

We've now officially reached the end of our year, since this is Political Calculations final post for 2020. Thank you for passing time with us this year and have a Merry Christmas and a wonderful holiday season. We'll see you again in the New Year, which we'll kick off with another annual tradition by presenting a tool to help you find out what your paycheck will look like in 2020 after the U.S. government takes its cut from it....

But before we go, we have one last video, from the invaluable Quanta Magazine, featuring their take on the biggest breakthroughs in math and computer science in 2020:

See you in the new year!

Once again, for the second year in a row, Mariah Carey's All I Want For Christmas Is You is the top song on the charts this week in the U.S. And just so we're clear, that's Mariah Carey's version of All I Want For Christmas Is You that was originally released in 1994.

We're not quite as tired of it as we are of the dreaded 12 Days of Christmas song, but we're getting there given how overplayed it becomes this time of year. Overplayed enough where we are finding a mashup of it with Radiohead's Creep to be more worthy of a listen, though it takes a while for the lyrics to break through the uptempo introduction.

All in all, it is surprising how well the Radiohead-Mariah Carey mashup works. Now, if someone could deal with the standalone dread that is The Little Drummer Boy, which not even the talents of Bing Crosby and David Bowie or Pentatonix could rescue, we would declare a Christmas miracle!

Friday, 18 December 2020 was a quadruple witching day on Wall Street, as stock index futures, stock index options, stock options, and single stock futures for 2020-Q4 all expired simultaneously. It may not feel like it quite yet, but for all practical purposes, where the markets are concerned, we are now in the first quarter of 2021!

That change of financial calendar also applies for dividend futures, which saw quite a lot of noisy activity before the quad witching day's trading ended. We've learned from experience that it takes several days for the end-of-quarter noise to subside and a clear signal for the future of dividends to emerge, which is where we're at today. That signal however won't have emerged before we sign off for 2020 ourselves and go on holiday, as our annual tradition of celebrating the biggest math story of 2020 will go live sometime late on Wednesday, 23 December 2020.

Until we return in 2021, we can confirm that investors have remained focused on the future quarter of 2021-Q2 during December 2020's week of four witches, following their having shifted their forward-looking focus to that distant future quarter on 11 December 2020. The latest update for the alternative futures chart for 2020-Q4 shows the dividend futures-based model's projections for the S&P 500 (Index: SPX) through the rest of the 2020 calendar year.

The market-moving news headlines we've pulled from the newsflow of the week that was is deceptively light, where perhaps the biggest news of the week was the announcement of the Fed's plans to provide quantitative easing-like monetary support for the indefinite future. Meanwhile, the Fed's minions appear to be working hard to convince the markets that the Fed won't be doing much more to boost the economy anytime soon.

Monday, 14 December 2020

• Signs and portents for the U.S. economy:
• Oil prices steady after 6 weeks of gains, pressured by glut
• U.S. lawmakers plan to split $908 billion COVID-19 plan into two parts: source
• ECB minion hits rewind button, reiterates last week's news:
• With eye on exchange rate, Panetta says ECB ready to do more
• S&P 500 ends down after vaccine roll-out, mega-M&A

Tuesday, 15 December 2020

• Signs and portents for the U.S. economy:
• Oil rises, as investors focus on vaccine rollout, brush off recovery concerns
• Facing year-end cut off, U.S. banks scramble to extend COVID accounting relief
• U.S. manufacturing production solid; imported inflation muted
• Fed minions poised to consider actions sometime next year!
• Fed will be tested in 2021 as vaccines boost U.S. economic outlook
• China sees post-pandemic growth, sees cash as tool to minimize inequality:
• China's factory recovery steps up as export, consumer demand grows
• China central bank urges wider acceptance of cash as payments go digital
• ECB minions looking to boost investor interest in banks:
• ECB eases COVID-19 crisis ban on dividends as outlook improves
• Wall Street ends higher on stimulus optimism, Apple boost

Wednesday, 16 December 2020

• Signs and portents for the U.S. economy:
• Oil prices rise on vaccine optimism and weaker dollar
• U.S. retail sales decline further as COVID-19, lack of additional fiscal stimulus weigh
• U.S. Congress 'closing in' on $900 billion COVID-19 aid bill
• U.S. business inventories increase solidly in October
• Busiest U.S. seaport, buried in imports, plucks out toys to load Santa's sleigh
• Fed minions meet, commit to keep QE alive:
• As Fed meeting looms, investors brace for higher Treasury yields in 2021
• Fed vows to buy bonds until it sees 'substantial progress' in economic recovery
• Instant View: FOMC - Rates unchanged, cash to keep coming
• Fed extends pandemic-related dollar 'swap' lines for 9 other central banks
• Bigger trouble all over, as suggested by imports:
• Euro zone trade surplus swells as exports recover more than imports
• Japan posts record run of export declines on soft U.S., China demand
• Bigger bailout coming to Eurozone borrowers:
• EU to help banks to jettison loans soured by COVID
• Nasdaq ends at record high as investors await stimulus

Thursday, 17 December 2020

• Signs and portents for the U.S. economy:
• Oil prices rise, touch 9-month high on U.S. stimulus progress
• COVID-19 restrictions push U.S. weekly jobless claims to three-month high
• As coronavirus aid talks drag on, U.S. Congress prepares stopgap vote to avoid shutdown
• U.S. housing starts, building permits power ahead in November
• Bigger trouble in Eurozone as deflation continues, Russia sees falling incomes:
• Euro zone inflation confirmed as negative in Nov for fourth month
• Russia's Putin says real incomes to fall around 3% in 2020
• S&P 500, Nasdaq hit record as investors eye fiscal stimulus

Friday, 18 December 2020

• Daily signs and portents for the U.S. economy:
• Oil settles up, marking seventh straight weekly gain
• Trump signs into law stopgap funding bill to avoid government shutdown
• Fed minions lay out case for no changes in monetary policy, want to get involved in other things:
• Fed's Clarida says current policy 'exactly where we want it'
• Fed’s Kaplan says will be time to pull back on bond buying when economic recovery is clear: WSJ
• Fed sees 'strong capital levels' at banks after stress tests, greenlights share buybacks
• Fed keeps countercyclical capital buffer at zero
• Fed's Brainard lays out case for Fed's climate change focus
• Bigger stimulus to continue in China:
• China says will keep policy support for economic recovery, no abrupt shift
• Wall Street closes lower as stimulus rally cools, Tesla volume jumps
• Tesla shares jump to record high ahead of S&P 500 debut

If you're looking for a bigger picture of the news of the week, Barry Ritholtz has you covered with his weekly review of the positives and negatives he found in the week's economics and markets news over at The Big Picture.

The week ahead should see a fiscal spending deal come out of the U.S. Congress, which we don't think will do much to reset the forward time horizon of investors.

The next edition of our S&P 500 chaos series will arrive early on Monday, 4 January 2020, when we'll also recap the more significant news headlines from the two previous, holiday-shortened trading weeks. Thank you for joining us for our analysis in 2020, we look forward to continuing to project the future for the S&P 500 in 2021.

We got up early this morning to wrap up our Christmas shopping for 2020. We weren't very imaginative this year, in that we decided to go out and get as many things as we could from the dreaded "12 Days of Christmas" song from a local PNC branch, the only place we know that carries all the items listed in the carol.

Or would, if it weren't for the coronavirus pandemic. Some things on the list just aren't available this year, so our gift recipient will get no dancing ladies, no lords-a-leaping, no pipers piping, and no drummers drumming.

Here's the receipt for all the rest....

The good news is that at $16,163.14 before sales tax, the bill this year for the available line items is $22,825.45 cheaper than in 2019. With the state government's lockdown orders, all the ladies, lords, pipers, and drummers are subject to a stay-at-home order and are thus not available in 2020.

Of course, we're really taking the cheap route in only getting one set of each of the items listed in the "12 Days of Christmas" song. If we were to take the cumulative math resulting from all the repetition in the song seriously, the pre-tax bill for 2020 for the items we can buy would be $105,561.80.

The median sale prices of new homes sold in the U.S. has begun rising slightly faster than median household income in the last several months, indicating that new homes have become slightly less affordable than they were earlier this year.

Measured as the ratio of the trailing twelve month averages of monthly median new home sale prices and median household income, the median sale price of new homes sold in the U.S. has slowly risen from a low of 4.88 times median household income in April and May 2020 to a high of 4.95 times median household income in September and October 2020. The following chart shows the developing rising trend in the context of the available historical data for both data series since 1968. (Please click here to see a full-size version of the chart).

Our latest analysis of the trend for median household income, the denominator of the relative affordability ratio for new homes, is available here. Meanwhile, a up-to-date chart featuring the median and average sale prices of new homes sold in the U.S. from January 2000 through October 2020 confirms a rising trend for new homes following their rapid bottoming early in the period of the coronavirus recession.

The references section below provides access to our sources for the raw data presented in the charts above.

References

U.S. Census Bureau. Median and Average Sales Prices of New Homes Sold in the United States. [Excel Spreadsheet]. Accessed 25 November 2020.

U.S. Census Bureau. Income, Poverty, and Health Insurance in the United States: 2018. Current Population Survey. Annual Social and Economic Supplement (ASEC). Table H-5. Race and Hispanic Origin of Householder -- Households by Median and Mean Income. [Excel Spreadsheet]. 10 September 2019.

U.S. Bureau of Economic Analysis. Table 2.6. Personal Income and Its Disposition, Monthly, Personal Income and Outlays, Not Seasonally Adjusted, Monthly, Middle of Month. Population. [Online Database (via Federal Reserve Economic Data)]. Last Updated: 25 November 2020. Accessed: 25 November 2020.

U.S. Bureau of Economic Analysis. Table 2.6. Personal Income and Its Disposition, Monthly, Personal Income and Outlays, Not Seasonally Adjusted, Monthly, Middle of Month. Compensation of Employees, Received: Wage and Salary Disbursements. [Online Database (via Federal Reserve Economic Data)]. Last Updated: 25 November 2020. Accessed: 25 November 2020.

Sentier Research. Household Income Trends: January 2000 through December 2019. [Excel Spreadsheet with Nominal Median Household Incomes for January 2000 through January 2013 courtesy of Doug Short]. [PDF Document]. Accessed 6 February 2020. [Note: We've converted all data to be in terms of current (nominal) U.S. dollars.]

Political Calculations. Alternate Median Household Income Estimates, January 2020, February 2020, March 2020, April 2020, May 2020, June 2020, July 2020, August 2020, September 2020, October 2020.

This is the last time we're going to look at Arizona's experience with COVID-19 in 2020, so we thought it was a good time to answer some questions that have been hanging out for a while. Let's get right to it!

What effect did the Thanksgiving holiday have on Arizona's COVID trends?

This is a question we've been waiting for the data to fill in for a couple of weeks, where it is now complete enough to tell the answer is: None.

If the high volume of social mixing anticipated during the Thanksgiving holiday was going to change the trajectory of COVID-19 cases, hospitalizations, and deaths for the worse, as was feared, we would see an upward shift in the trends for these statistics starting as early as 10 days after the event.

Instead, we see the Thanksgiving holiday affected when people were tested for COVID-19 infections, which creates some noise in Arizona's data for confirmed cases. But aside from that holiday-related anomaly, we've seen no meaningful change in the trend that began with the political campaign events taking place in the state during the period of 23-25 October 2020.

But don't take our word for it. We have four charts to back that assessment up (newly confirmed cases, new hospital admissions, ICU bed usage, and deaths), where only the chart for Arizona's COVID-19 deaths does not yet confirm that observation. And that's only because it takes so much longer for the coronavirus-related deaths associated with a given event to take place and be reported.

Has mask wearing made a difference?

The short answer is: Apparently yes. We have two periods where we can compare a non-mask-wearing period with a mask-wearing period. The non-mask-wearing ran from 25 May 2020 through 2 July 2020, which covers the period of time from 10 days after Arizona lifted its stay-at-home order on residents and allowed most businesses to reopen following its initial lockdown order until 13 days after when Governor Doug Ducey issued an executive order allowing counties and local governments to require masks and set other operating restrictions on businesses. During this period, the number of new COVID-19 infections in Arizona was rising by an average of 62 cases per day. Here's the chart for cases again.

The second period ran from 3 October 2020 through 1 November 2020, which corresponds to the period 10 days after when most of the operating restrictions Governor Ducey had imposed on high-exposure risk businesses at the end of June 2020 were lifted in most counties in the state to 10 days after the October 2020's political events that increased the rate of incidence of new infections in Arizona.

During this second period, Governor Ducey's executive order allowing counties and local jurisdictions to require mask wearing and to set other operating restrictions on businesses has remained in effect. Consequently, in places where 94% of Arizonans live, the rate of mask-wearing compliance has remained high, but with businesses operating at levels similar to what they did following the state's initial lockdown period. During this period, the rate the number of new COVID-19 infections in Arizona was rising by an average of 31 cases per day, half that of the period prior to counties and local governments being able to require masks be worn (this is shown as the "Post-Event H Trendline" on each chart).

The reason the answer to this question is not simply "Yes" is because mask wearing is not the only restriction that local governments implemented. They've also set capacity limits, required protective shields to protect business employees from potentially infected customers, and have mandated other measures that also would have an impact in addition to requiring the public wear masks while at businesses. All of which muddies the water for clearly determining if mask wearing is the primary influence in reducing the rate of new infections.

The most honest answer we can give with the available data is that mask wearing along with these other restrictions do make a difference.

What caused Arizona's uncontrolled surges in coronavirus cases?

The simplest answer is: Political activism. We've previously covered the deadly impact of Arizona's anti-police protests, but the impact of political campaign events in the state before the 3 November 2020 elections cannot be understated since larger numbers of people were involved, which you can see in the charts as the difference between the trajectory of COVID-19 cases, hospital admissions, ICU bed usage, and deaths and the "Post-Event H Trendline" shown on each. This assessment applies across Arizona and across political parties, where counties that went for Biden have been hit hard with surging coronavirus infections, just as other counties have that went for Trump or that were split between both presidential candidates.

The data suggests the best advice we can give to anyone seeking to avoid becoming infected with the SARS-CoV-2 coronavirus is to avoid any personal contact with political activists.

Previously on Political Calculations

We've been covering Arizona's experience with the coronavirus pandemic since the state first became a national hotspot early in the summer of 2020. Here's our previous Arizona coronavirus coverage presented in reverse chronological order, with a sampling of some of our other COVID analysis!

• The Deadly Intersection of Anti-Police Protests and COVID-19
• 2020 Campaign Events Drive Surge in Arizona COVID Cases
• Arizona Arrives at Critical Junction for Coronavirus Cases
• Arizona To Soon Reach A Critical Junction For COVID-19
• Getting More Than Care from Arizona's COVID ICU Beds
• Arizona's Decentralized Approach to Beating COVID
• Going Back to School with COVID-19
• Arizona Turns Second Corner Toward Crushing Coronavirus
• Arizona's Coronavirus Crest in Rear View Mirror
• The Coronavirus Turns a Corner in Arizona
• A Delayed First Wave Crests in the U.S. and a Second COVID-19 Wave Arrives
• The Coronavirus in Arizona
• A Closer Look at COVID-19 Deaths in Arizona
• The New Epicenter of COVID-19 in the U.S.
• How Long Does a Serious COVID Infection Typically Last?
• How Deadly is the COVID-19 Coronavirus?
• Governor Cuomo and the Coronavirus Models
• How Do False Test Outcomes Affect Estimates of the True Incidence of Coronavirus Infections?
• How Fast Could China's Coronavirus Spread?

References

We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard. [Online Application/Database].

Maricopa County Coronavirus Disease (COVID-19). COVID-19 Data Archive. Maricopa County Daily Data Reports. [PDF Document Directory, Daily Dashboard].

Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Andrew S. Azman, Nicholas G. Reich, Justin Lessler. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Annals of Internal Medicine, 5 May 2020. https://doi.org/10.7326/M20-0504.

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. Updated 10 September 2020.

COVID Tracking Project. Most Recent Data. [Online Database]. Accessed 15 December 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

How much, and on what, was the average American household spending in a year before the coronavirus pandemic?

The Consumer Expenditure Survey (CEX) for 2019 provides the most definitive answer to that question, which we can compare with the previous 35 years worth of annual data to see how consumer spending has changed over time. Produced as a joint product of the U.S. Bureau of Labor Statistics and the U.S. Census Bureau, the CEX compiles the information collected through tens of thousands of surveys, diaries and interviews submitted by U.S. households, or "consumer units" as the BLS' data jocks affectionately call them, which provides a tremendous amount of insight into how Americans allocate their limited resources.

In 2019, the average amount spent per American 'consumer unit' household was $63,036, which was up 3% (or $1,812) from 2018's level.

We've broken down that spending by major category and visualized the data from 1984 through 2019.

Illustrating the same major expenditure categories as a percent of the average annual expenditures of a U.S. household/consumer unit makes it easy to see the trends for each of the major categories.

We have one last chart to show how consumer spending has evolved over the 36 years from 1984 through 2019. The expenditures shown on the bottom of the chart, in shades of purple, show those expenditures whose share among the total has increased over time, while the expenditures shown toward the top of the chart, in shades of green, show the household expenses whose share of total spending has fallen.

Here's the list of major categories of consumer expenditures whose share has risen from 1984 through 2019:

• Housing
• Financial Products (Life Insurance, Pension Savings & Social Security)
• Health Care (Health Insurance and Medical Expenses)
• Charitable Contributions
• Education

And here's the list of major categories of consumer expenditures whose share has declined over the 36 years for which the data is available:

• Apparel and Other Products
• Food and Alcoholic Beverages
• Transportation
• Entertainment

Next year's data will be fascinating since almost all of 2020's data will have been affected by the impact of the coronavirus pandemic. We'll have to wait until sometime in September 2021 to get complete data for 2020, but we may get a preliminary glimpse from interim Consumer Expenditure Survey results earlier in 2021.

References

U.S. Bureau of Labor Statistics. Consumer Expenditure Survey. Multiyear Tables. [PDF Documents: 1984-1991, 1992-1999, 2000-2005, 2006-2012, 2013-2019]. Reference URL: http://www.bls.gov/cex/csxmulti.htm. 9 September 2020. 

Keeping with 2020's theme of stock price volatility, investors appear to have shifted their forward-looking focus once again in a new Lévy flight event.

The latest Lévy flight was much less dramatic than the previous one that took place in the second week of November 2020, when investors shifted their forward time horizon outward from 2020-Q4 to 2021-Q3. That event was prompted by the news of Pfizer's successful COVID-19 vaccine development, which was quickly reinforced by Moderna's and AstraZeneca's COVID successful vaccine development announcements.

The latest shift in the forward-looking focus of investors came as the Trump administration successfully pushed the U.S. Food and Drug Administration to approve Pfizer's vaccine for emergency use, which came faster than had previously been expected.

The FDA's approval accelerated the timetable for the deployment of an effective vaccine in the United States, which coincides with the new Lévy flight event as the latest update of the alternative futures chart indicates investors shifted their focus from 2021-Q3 inward toward 2021-Q2.

This change pulled stock prices downward, as the expectations for the change in the year-over-year growth rate of the S&P 500's dividends in 2021-Q2 are less positive than they are for 2021-Q3. We characterize this change as "less dramatic" than the previous Lévy flight event because the difference between 2021-Q2 and 2021-Q3 is smaller than the difference between 2020-Q4 and 2021-Q3.

While the FDA's COVID-19 vaccine approval was the biggest news story of the week, other stuff happened to influence investor expectations, where we've captured the main market moving headlines of the week in the list below.

Monday, 7 December 2020

• Signs and portents for the U.S. economy:
• Pandemic's uneven march across U.S. paved way for wider outbreak
• U.S. Congress to vote on stopgap bill as COVID-19 aid talks continue
• Oil falls amid surging virus cases and U.S.-China tensions
• Bigger trouble as COVID looms, other factories slow:
• China's exports surge on hot demand for PPE, remote working tech
• German factories gloomier about production in coming months: Ifo
• Brazil auto recovery stalls as parts shortages loom
• Germany, U.K. economies see positive signs:
• German industrial output surges on booming car sales
• England's malls attract Christmas shoppers after lockdown ends
• ECB minions being pressured to act:
• Enough talk, time for action: Five questions for the ECB
• Nasdaq closes at record high as growth names get a lift

Tuesday, 8 December 2020

• Signs and portents for the U.S. economy:
• Oil steady as COVID-19 cases, lockdowns dampen vaccination news
• China's Wang vows to uphold trade deal during Biden administration: U.S. business group
• U.S. Senate's McConnell urges dropping liability, state aid in next coronavirus package
• Bigger stimulus developing in Japan:
• Japan unveils $708 billion in fresh stimulus with eye on post-COVID growth
• Japan stimulus package will likely boost GDP by around 3.6%, Suga says
• Wall Street closes higher on vaccine lift; S&P 500, Nasdaq at records

Wednesday, 9 December 2020

• Signs and portents for the U.S. economy:
• Oil steadies, shrugging off unexpected massive U.S. crude stock build
• McConnell says Congress still needs path forward on COVID-19 aid
• U.S. job openings rise, but labor market slowing
• Wall Street ends lower on stimulus uncertainty, Facebook weighs
• Facebook faces U.S. lawsuits that could force sale of Instagram, WhatsApp

Thursday, 10 December 2020

• Signs and portents for the U.S. economy:
• Brent rises above $50/bbl for first time since March on vaccine optimism (reuters.com)
• Spiraling COVID-19 cases driving up U.S. layoffs; inflation still benign
• U.S. Senate vote on spending could slip to Friday, Pelosi suggests longer COVID-19 timeline
• Bigger stimulus finally rolling out in Eurozone:
• EU leaders unblock 1.8 trillion euro budget, recovery fund, eye climate goals
• ECB minions roll out more stimulus too, but worries about Euro becoming too strong:
• ECB gives euro zone new shot in arm to fight pandemic
• ECB to monitor euro appreciation 'very carefully': Lagarde
• Euro jumps as ECB goes easy, stocks little changed
• Wall Street shakes off labor market data with stimulus in focus

Friday, 11 December 2020

• Daily signs and portents for the U.S. economy:
• Oil pulls back amid New York coronavirus curbs, gains for a 6th week
• U.S. producer prices rise moderately; COVID-19 seen taming inflation
• Fed minions claim internal disagreements mean U.S. economy is healthy:
• For the Fed, new data charts show family feuds may be a sign of health
• Bigger trouble developing in the U.K.:
• UK PM Johnson says no-trade deal Brexit is "very, very likely"
• BoE's Bailey says 'extensive' work with banks underway on negative rates
• Bigger stimulus still to roll out in Japan:
• BOJ likely to extend corporate aid schemes next week: sources
• ECB minions divided, but will roll out more stimulus:
• ECB's Lagarde bags hard-won deal, but battle with hawks has only begun
• ECB's Villeroy says financing conditions focus of latest stimulus decision
• Stimulus uncertainty hems in Wall Street; Disney soars

The listing of notable headlines is shorter than previous weeks because we've omitted many items related to the impending Brexit event for the United Kingdom and the European Union, which contributed a lot of noise in the week's news stream.

But if you want more, Barry Ritholtz outlines the positives and negatives he found in the week's economics and markets news over at The Big Picture.

It's that time of year again, or would be in any other year, when you might have attending your child's school band concert on your social calendar. All those long hours of practice you've had to endure listening to since school started will soon culminate in an musical experience that, for all its charms, will soon be quickly, if not also blissfully, forgotten by all.

Truth be told, the same problem often plagues highly talented professional musicians. It is often not enough in today's world to stand out solely on the merits of a skilled performance. That's particularly true for those musicians whose instruments of choice are the same as those used in children's band concerts.

Musicians who want their performance to stand out have to find a way of turning the proverbial knob up to eleven, which is what inventor Pat Vidas set out to achieve for trumpet players everywhere in U.S. Patent 4,247,283, which describes a Musical Instrument Adapted to Emit a Controlled Flame for the purpose of "enhancing" their performance. Here's how Vidas describes the benefits of using fire to make a musical performance more memorable.

As can be ascertained, many performances by musicians or artists are accompanied by special effects in order to further enhance the quality of the presentation and to entertain the audience. There are many modern groups who employ substantial visual and sound effects in conjunction with their performances and have gained widespread popularity based on the utilization of such additional effects together with the musical format.

In view of such considerations, the applicant herein has conceived of a trumpet which will emit a flame out of the bell of the trumpet whereby the flame is safely controlled by the musician. The apparatus offers a novel and sensational visual effect to an audience when the instrument is being played by a skilled practitioner. In terms of appreciation and audience reaction, the instrument creates aunique visual effect. The nature of the instrument is such that the trumpet can be played at the same time the flame is being emitted. The length and duration of the flame are completely under control of the musician, who therefore based on the composition being played, can control the flame according to the music.

Vidas' invention has been around since 1979, and believe it or not, still commands attention at live performances, such as trumpeter Folkert-Hans Tolsma demonstrates in the following 37 second long video from 2014.

And that's how you elevate a live trumpeting performance to the memorability of street juggling.

Inventions in Everything: Some Musical Selections from the Archives

• The Music Playing Bag of Nacho Cheese Flavored Tortilla Chips
• Shoes for Defying the Laws of Physics
• The Singing Stones

The combined value of goods traded between the U.S. and China rocketed up during October 2020 to reach the fifth-highest total on record, well above coronavirus pandemic recession levels.

The following chart tracks the combined value of trade between the U.S. and China from January 2008 through October 2020.

With January 2020's 'Phase 1' trade deal, the volume of trade between the U.S. and China should have begun recovering in February. Instead, it plunged through March 2020 with the coronavirus pandemic starting in China before starting to recover. In October 2020, the volume of trade is $10.5 billion higher than October 2019, as China has significantly ramped up its imports of U.S.-produced agricultural goods, led by soybeans.

Meanwhile, a gap of $10.6 billion has opened between the trailing year average of trade between the two nations and a 'No Coronavirus Pandemic' counterfactual through October 2020. This is the value of the loss of trade that is attributable to the pandemic.

Looking forward, with a resurgence of COVID-19 infections in much of the U.S., we anticipate the recent upward momentum in the U.S.' imports of Chinese produced goods will fall in the months ahead. This change is a direct consequence of the new lockdown orders that several states and local jurisdictions within the U.S. are imposing on the operations of businesses, which also include the return of stay-at-home orders for residents in some.

References

Board of Governors of the Federal Reserve System. China / U.S. Foreign Exchange Rate. G.5 Foreign Exchange Rates. Accessed 4 December 2020.

U.S. Census Bureau. Trade in Goods with China. Accessed 4 December 2020.