There is a remarkably linear relationship between median and average new home sales prices in the United States. The following chart reveals that pattern for annual data reported by the U.S. Census Bureau for new home sales from 1963 through 2017 on a logarithmic scale.

The amazing thing about this relationship is that it has held very consistently even as home prices in the U.S. have experienced both rising and falling trends through these years, where median and average home sale prices have generally increased and decreased in sync with each other. So much so that if we only had the median sale price data for a given period, we could reasonably estimate the average sale price for the same period within 2.7 percent of its recorded value about 68 percent of the time, and within 8.2 percent of its recorded value about 99% of the time.

While the relationship behind this math was developed using new home sales price data, it appears to also hold for existing home sales data with a similar margin of error.

Try it for yourself! Just enter the median new home sales prices for your period of interest in the following tool, and we'll take care of the rest! [If you're reading this article on a site that republishes our RSS news feed, please click here to access a working version of the tool on our site.]

For the default data, for a median home sale price of $220,000, we would expect the average home sale price in the U.S. in the same period of time to fall within several percent of $267,100, the value our tool finds after rounding to the nearest $100 increment.

Altogether, the relationship we've now established between median and average home sale prices in the United States enables a particular line of analysis that we've been seeking to do for some time, which hasn't been possible because the relative lack of availability of data for average home sale prices. Which is a strange thing to say because usually when we're looking for data that many reporting agencies don't realize may involve lognormal distributions, it's a lot easier to find averages than it is to get medians. It's a real credit to the outfits that do recognize this pattern in real estate prices that they properly report median sale price data as being representative of the prices that most home buyers are paying, where we hope they come to recognize that mean sale prices provide additional valuable information about these markets that should also be tracked and reported.

References

U.S. Census Bureau. Median and Average Sales Prices of New Homes Sold in United States. [PDF Document]. 23 April 2018. Accessed 12 January 2019.

John Bogle, the man who made passive, low-cost index investing a real world thing and who, as a result, built Vanguard into one of the world's largest investment management firms, passed away on 16 January 2019 at Age 89.

The idea of index investing that Jack Bogle championed proved to be very a big deal, which is why the index fund made Tim Harford's list of 50 Inventions That Made the Modern Economy (the UK edition is 50 Things That Made the Modern Economy), where we can strongly recommend the 10-minute podcast episode of the related BBC radio series if you want to learn more about its history.

If your available time is shorter than that, Jack Bogle once claimed that he could teach the essentials about investings in just a few minutes. In 2010, the Bogleheads' Ricardo Guerra put him to the challenge, where he distilled a lifetime of learning about successful investing into 3 minutes and 42 seconds....

Back in October 2006, we participated in a chapter-by-chapter review of the original edition of The Bogleheads' Guide to Investing (now in its second edition), where we had the honor of reviewing the final chapter of a book that sought to capture Jack Bogle's wisdom....

That was a lucky break for us, because the final chapter summarized all the lessons presented throughout the book, which gave us the opportunity to further condense Jack Bogle's thoughts on investing into just six lines, although with quite a few links to follow for deeper insights gleaned by the other participants in the project:

• Choose and live a sound financial lifestyle.
• Start to save early, invest regularly and diversify your investments!
• Don't invest in things you don't understand.
• Pay attention to investing costs and especially taxes!
• Plan! Plan! Plan! Plan! Plan! Plan! Plan!
• Avoid fads and master your emotions.

Today, millions of people are considerably richer than they might otherwise have been because of what Jack Bogle wrought. That's one hell of a legacy in the financial world!

Back in 2009, we wrote about Hauser's Law, which at the time, we described as "one of the stranger phenomenons in economic data". The law itself was proposed by W. Kurt Hauser in 1993, who observed:

No matter what the tax rates have been, in postwar America tax revenues have remained at about 19.5% of GDP.

In 2009, we found total tax collections the U.S. government averaged 17.8% of GDP in the years from 1946 through 2008, with a standard deviation of 1.2% of GDP. Hauser's Law had held up to scrutiny in principal, although the average was less than what Hauser originally documented in 1993 due to the nation's historic GDP having been revised higher during the intervening years.

We're revisiting the question now because some members of the new Democrat party-led majority in the House of Representatives has proposed increasing the nation's top marginal income tax rate up to 70%, nearly doubling today's 37% top federal income tax rate levied upon individuals. Since their stated purpose of increasing income tax rates to higher levels is to provide additional revenue to the U.S. Treasury to fund their "Green New Deal", if Hauser's Law continues to hold, they can expect to have their dreams of dramatically higher tax revenues to fund their political initiatives crushed on the rocks of reality.

Meanwhile, the U.S. Bureau of Economic Analysis completed a comprehensive revision to historic GDP figures in 2013, which significantly altered (increased) past estimates of the size of the nation's Gross Domestic Product.

The following chart shows what we found when we updated our analysis of Hauser's Law in action for the years from 1946 through 2018, where we're using preliminary estimates for the just-completed year's tax collections and GDP to make it as current as possible.

From 1946 through 2018, the top marginal income tax rate has ranged from a high of 92% (1952-1953) to a low of 28% (1988-1990), where in 2018, it has recently decreased from 39.6% to 37% because of the passage of the Tax Cuts and Jobs Act of 2017.

Despite all those changes, we find that the U.S. government's total tax collections have averaged 16.8% of GDP, with a standard deviation of 1.2% of GDP. Applying long-established techniques from the field of statistical process control, that gives us an expected range of 13.2% to 20.5% of GDP for where we should expect to see 99.7% of all the observations for tax collections as a percent share of GDP.

And that's exactly what we do see. The next chart zooms in on the total tax collections as a percent share of GDP data from the first chart, and adds the data for individual income tax collections as a percent share of GDP below it.

What we find is that the federal government's tax collections from both personal income taxes and all sources of tax revenue are remarkably stable over time as a percentage share of annual GDP, regardless of the level to which marginal personal income tax rates have been set. The biggest deviations we see from the mean trend to be associated with severe recessions, when tax collections have tended to decline somewhat more than the nation's GDP during periods of economic distress.

We also confirm that the variation in total and personal income tax receipts over time is well described by a normal distribution. We calculate that personal income tax collections as a percentage share of GDP from 1946 through 2018 has a mean of 7.6%, with a standard deviation of 0.8%.

For both levels of tax collections, if Hauser's Law holds, we would then expect any given year's tax collections as a percent of GDP to fall within one standard deviation of the mean 68% of the time, within two standard deviations 95% of the time, and within three standard deviations 99.7% of the time. And that is what we observe with the reported data from 1946 through 2018.

As for high tax revenue aspirations, we can find only three periods where tax collections rose more than one standard deviation above the mean level.

1. In 1968, the Democratic U.S. Congress and President Lyndon Johnson passed a 10% income surtax that took effect in mid-year, which suddenly raised the top tax rate from 70% to 77% (which increased the amount collected from top income tax earners by 10%.) Coupled with a spike in inflation, for which personal income taxes were not adjusted to compensate, this tax hike led to outsize income tax collections in that year.
2. The sustained high inflation of 1978 (7.62%), 1979 (11.22%), 1980 (13.58%) and 1981 (10.35%) led to higher tax collections through bracket creep, as income tax brackets in the U.S. were not adjusted for inflation until 1985 as part of President Ronald Reagan's first term Economic Recovery Tax Act.
3. Beginning in April 1997, the Dot Com Stock Market Bubble minted a large number of new millionaires as investors swarmed to participate in Internet and "tech" company initial public offerings or private capital ventures, which in turn, inflated personal income tax collections. Unfortunately, like the vaporware produced by many of the companies that sprang up to exploit the investor buying frenzy, the illusion of prosperity could not be sustained and tax collections crashed with the incomes of the Internet titans in the bursting of the bubble, leading to the recession that followed.

Now, what about those other taxes? Zubin Jelveh looked at the data back in 2008 and found that as corporate income taxes have declined over time, social insurance taxes (the payroll taxes collected to support Social Security and Medicare) have increased to sustain the margin between personal income tax receipts and total tax receipts. This makes sense given the matching taxes paid by employers to these programs, as these taxes have largely offset a good portion of corporate income taxes as a source of tax revenue from U.S. businesses. We also note that federal excise taxes have risen from 1946 through the present, which also has contributed to filling the gap and keeping the overall level of tax receipts as a percentage share of GDP stable over time.

Looking at the preliminary data for 2018, which saw both personal and corporate income tax rates decline with the passage of the Tax Cuts and Jobs Act of 2017, we see that total tax receipts as a percent of GDP dipped below the mean, but still falls within one standard deviation of it, just as in over two-thirds of previous years. Tax receipts from individual income taxes however rose slightly, despite the income tax cuts that took effect in 2018, staying above the mean but still falling within one standard deviation of it.

Hauser's Law appears to have held up surprisingly well over time.

References

Bradford Tax Institute. History of Federal Income Tax Rates: 1913-2019. [Online Text]. Accessed 13 January 2019.

Tax Foundation. Federal Individual Income Tax Rates History. [PDF Document]. 17 October 2013.

U.S. Department of the Treasury. September 2018 Monthly Treasury Statement. [PDF Document]. 17 October 2018.

U.S. Bureau of Economic Analysis. National income and Product Accounts Tables. Table 1.1.5. Gross Domestic Product. [Online Database]. Last Revised: 21 December 2018. Accessed: 14 January 2019.

U.S. White House Office of Management and Budget. Budget of the United States Government. Historical Tables. Table 1.1. Summary of Receipts, Outlays, and Surpluses or Deficits (-): 1789-2023. Table 2.1. Receipts by Source: 1934-2023. [PDF Document]. 12 February 2018.

One of the most important and perhaps least well known metrics for the U.S. stock market is the growth rate of dividends for the S&P 500, which is why we started a new series to feature it last year.

The following chart visualizes the year over year growth rate of the S&P 500's trailing year dividends per share for each month of the 21st Century, starting from the beginning of the last year of the 20th Century and continuing through December 2018, with a bonus projection of the currently expected future for S&P 500 dividend growth through March 2020.

We've also indicated the National Bureau of Economic Research's official periods of recession in the 21st Century (so far!) on the chart.

As for how to best use this data, you really want to pay close attention to how fast the growth rate of dividends per share is changing, where negative accelerations for dividends generally coincide with falling stock prices, and positive accelerations tend to coincide with rising stock prices. Also, if you compare the projected future for 2018 with what actually happened for the S&P 500's dividend growth rate, 2018 was a year that mostly lived up to early expectations.

That's not always the case, where we've seen dramatic changes in those expectations in this century, particularly when the U.S. economy fell into recession. If there's one observation that you want to take away from the chart however, it is perhaps Tadas Viskanta's observation that "recessions are a dividend killer"!

Previously on Political Calculations

• The Growth Rate of S&P 500 Dividends in the 21st Century (2018)
• The Growth Rate of S&P 500 Dividends in the 21st Century (2019)

2019 is off to a rollicking start for the S&P 500 (Index: SPX), which appears to have launched into its first Lévy flight event in 2019.

If that's not a term you're readily familiar with, here's what that means. A Lévy flight is similar to a random walk for stock prices, but instead of the relatively small changes in stock prices that characterize a true random walk, it is characterized by the sudden emergence of comparatively large changes - more so than would be predicted by a normal distribution.

From our perspective, Lévy flight events can occur whenever investors shift how far forward in time they are looking into the future as they go about setting current day stock prices, where the differences in expectatations for the sustainable portion of future earnings associated with these different points of time drive these outsized changes in stock prices. For the first Lévy flight event of 2019, that shift appears to be from the distant future quarter of 2019-Q4 back to the current quarter of 2019-Q1.

It was even sort of predictable, where we described what would happen if investors acted to shift their forward-looking attention just as they appear to have, well before the market even opened last week.

• If investors remain focused on the distant future quarters of 2019-Q3/2019-Q4, the S&P 500 can be expected to generally follow a downward trajectory throughout 2019-Q1, falling into a true bear market for the index.
• If investors shift their attention toward 2019-Q1, the effect would be to boost stock prices higher, where they would largely move sideways during the quarter with respect to their current level.
• Should investors shift their forward-looking focus to 2019-Q2, the market would see a significant rally above its current level.

Investors chose Door #2 in this real-life Monty Hall problem!

Meanwhile, because we've now entered the period of time where it will be relevant, we've redrawn our redzone forecast to correspond with this selection, anchoring its starting point with where the S&P 500 closed on Friday, 11 January 2019. If you want to know more about our assumptions in generating the forecast, we've incorporated them in the annotations on the chart.

With the Fed's future actions now fading into the background noise after dominating much of the market-related news headlines last week, we can perhaps look forward to investors sustaining their focus on 2019-Q1 as earnings season gets under way in the week ahead. That should mean the end of the first Lévy flight event of 2019, with smaller stock price movements from day to day, but this is also when a number of companies will change investor expectations for the future, which can change stock prices as investors rapidly absorb all new information.

Speaking of new information, here are the major market-moving headlines from the past week....

Monday, 7 January 2019

• Oil rises; lifted by OPEC cuts, steadying stock market
• Fed's Bostic sees one U.S. interest rate hike this year
• U.S., China can reach trade deal 'we can live with': U.S. Commerce secretary
• Amazon and Netflix push Wall Street higher

Tuesday, 8 January 2019

• Oil prices rise over 2 percent on trade talk optimism
• Apple, Facebook propel Wall Street to three-week peak

Wednesday, 9 January 2019

• Oil up more than 4 percent on U.S.-China trade talk hopes, OPEC cuts
• Bigger trouble developing in China: China to further cut taxes for smaller firms: state TV
• China pledges to buy 'substantial amount' of U.S. goods: USTR
• Many Fed policymakers urged patience on future rate hikes: minutes
• Fed policymakers say U.S. rate hikes can wait, for now
• U.S. Fed may be open to changes to balance sheet plan, minutes show
• Not getting the message yet: Fed may still need to hike rates twice this year: Rosengren
• Wall Street extends rally as chipmakers rebound

Thursday, 10 January 2019

• Oil rises again but global economic concerns cap gains
• U.S. oil export boom sparks a battle to build Texas ports
• Fed hawk capitulation: Fed's Powell again stresses patience as U.S. economy's 'narrative' unfolds
• Fed's No. 2 says U.S. policy would react if 'crosswinds' persist
• Fed wouldn't wait too long responding to overseas slowdown: Clarida
• Fed at 'end of road' on rate hikes, Bullard says
• Fed's Evans repeats view that Fed can wait on rate hikes
• Stocks rise for fifth straight day as the Fed supports

Friday, 11 January 2019

• Oil falls nearly 2 percent amid global economy concerns but ends week higher
• Bigger trouble developing in China:
  • China to cut company tax and fees further to spur growth: minister
  • Exclusive: China to set lower GDP growth target of 6-6.5 percent in 2019 - sources
  • China banks' bad loan ratio climbs to 10-year high at end-2018
• Wall Street's five-day rally flickers out as earnings near

Barry Ritholtz listed the week's positives and negatives in his weekly succinct summary of the major economics and market-related news, and deployed the word "stalement"! What does that mean? It's defined in the Urban Dictionary!...