Mega Millions Frenzy

Mega Millions Frenzy

It’s difficult to make economic forecasts in uncharted territory but lottery officials have set a new standard for missing the mark.  Everyone realized that the Mega Millions jackpot would set a new record and that lottery sales would surge, but no one knew by how much.  Lottery officials consistently underestimated sales over the past few days.  The first announced Mega Millions jackpot was $460 million but reached $640 million by the end of the week.  Higher jackpots result from higher ticket sales, but more than two-thirds of new sales revenue goes to the states and consolation prizes.  This means that Mega Millions sales over the past three days were almost three times higher than suggested by the original advertised jackpot. 

Lottery officials seem to have badly underestimated Mega Millions frenzy.  Are lottery officials really that bad at forecasting sales?  Lottery officials are almost certainly required to make cautious forecasts so that the advertised jackpot rarely overstates the actual jackpot.  Do regulations requiring lottery officials to systematically underestimate jackpots depress sales?

Perhaps not, because conservative forecasts may promote sales as gradual increases in advertised jackpots are reported by the news media.  An unbiased forecast would be revised down as often as it is revised up, but a decrease in the advertised jackpot could provide negative publicity.  Would we have seen the same Mega Millions frenzy if the advertised jackpot had been revised down during the past few days?

The nature of Mega Millions arithmetic means that if a jackpot has accumulated over time, as we observed from January 24 until this week, increases in the size of the advertised jackpot during the week is bad news for the customer.  This is because rising sales during the week increase the jackpot by far less than they increase the chance of a winning ticket sharing the jackpot.

If the actual jackpot had been $460 million as originally “forecast” by officials, the winning ticket would have been expected to generate a payout about 20% more than Friday’s winning tickets from a much larger jackpot.  With fewer sales during the week the most likely outcomes are that a winning ticket shares the jackpot with one other contestant or receives the prize alone.  As sales grew during the past few days it became much more likely that the jackpot would be split three ways, which is what happened last night.

Unless lottery officials change the Mega Millions rules we won’t see a jackpot this large for at least five years.  The accumulated jackpot grew to record levels because over 800 million tickets didn’t match the winning numbers over 18 previous drawings.  The odds of this happening are less than one in one hundred.  Over the past four years the typical jackpot was awarded after accumulating over 8 weeks, and Friday’s jackpot was just the third that had accumulated for more than 15 drawings.

When the next record jackpot occurs players should be skeptical of the initial jackpot announcements and expect the advertised amounts to increase as the next Mega Millions frenzy appears to gain momentum.  When this happens players should also remember that jackpot increases during a week of record Mega Millions sales actually decrease the expected payout from a winning ticket.

Why a Mega Millions Ticket is a Good Bet, But… (Revised 03.30.2012)

The Mega Millions multi-state lottery is now advertising a jackpot of $640 million for tonight’s drawing. The cash value of the jackpot is $460 million, a more accurate estimate of the present value of the prize. The jackpot has accumulated because there has been no winner for 18 consecutive drawings – since January 24th. This means that those of us who buy Mega Millions tickets for the first time this week have been subsidized by the millions of players who contributed to the jackpot over the past two months.

The probability of correctly selecting all six numbers for Friday’s drawing is one in 175 million. It is likely that there will be multiple jackpot winners. Even after taking this into account, the expected value of a one dollar Mega Millions ticket is about 90 cents.

About 18 cents of every dollar collected from Mega Millions sales are used to pay consolation prizes. Another 32 cents of each dollar goes into the cash jackpot. The cash value of Friday’s drawing is estimated to be about $200 million higher than in Tuesday’s drawing. In other words lottery officials expect about 625 million lottery tickets to be sold between now and Friday.

If lottery officials are correct there is a 96% chance that someone will pick the winning numbers on Friday, and the expected number of winners, conditional on the jackpot being awarded, is about 3. This means that even after splitting the jackpot, the expected value of a Mega Millions ticket is about 90 cents (including 18 cents in expected consolation prizes).

In general state sponsored lottery games have low expected values for players, relative to other forms of gaming. Lotteries pay out about half of their proceeds in prizes, on average. The rollover nature of the jackpot in state lotteries means that a lottery ticket will have a high expected value on occasion. Until the recent surge in sales, this week would have been the highest expected value for a Mega Millions ticket in the history of the game.

Finally, because the jackpot will be taxed at a fairly high rate a Mega Millions ticket is not a good investment, as Ben Casselman of the Wall Street Journal has noted. After taxes the expected value of a Mega Millions ticket is now much less than $1, unless the top marginal tax rate falls substantially over the next twenty years, which is doubtful. However most gambles with long odds, such as a super trifecta bet at the racetrack, have a pre-tax expected value that is lower than the cost of the wager. So the Mega Millions is an unusually good bet for people who enjoy gambling small amounts at long odds, but it would be a bad investment.

Social Insecurity

Jared Bernstein’s blog post last week on “Retirement Insecurity” was an excellent example of misguided economic analysis and commentary.  Although he correctly noted that many middle-income workers have small amounts of assets in private savings and pension plans, his policy proposals for encouraging middle class saving were alarming.  Tax reform is the most sensible way to encourage saving.  All returns on savings could be tax deferred with no penalty for early withdrawals.  This would encourage middle class saving not just for retirement, but also for a child’s education, a possible spell of unemployment, and emergencies or other unexpected events.

Bernstein believes that “the way things are currently set up, the marketplace just isn’t providing future retirees with affordable options” because “there’s a real market failure here.”  He also argues that Social Security “addresses that market failure” but doesn’t go far enough and advocates further government intrusion through a system “where state or federal governments would set up public pension plans that guaranteed a modest return.”  According to Bernstein “a bit of a consensus is forming” for government intervention to form large pools of workers because “as with health care reform, pooling risk is the best way to dilute it.”  

The double taxation of saved income is the reason why retirement savings and pension plans are tied to one’s employer.  If all savings accounts received the same tax treatment as pension plans or 401k plans there would be no reason for workers to save for their retirement through their employer.  If the marketplace isn’t providing future retirees with affordable savings options (something I doubt) it’s probably because of our tax code not a “market failure.”  It is irresponsible for Bernstein to allege “market failure” when the low savings rates he describes are the result of government tax policies.

The viewpoints of Bernstein, former Chief economist for Vice President Joe Biden and Executive Director of the White House Middle Class Working Families Task Force, are disturbing because he proposes government solutions for nonexistent problems.  Although it is true that pooling risk is the best way to diversify risk one can simply achieve this goal by investing in a variety of stocks and bonds through mutual funds.  There is absolutely no reason for either state governments or the federal government to form investment pools for workers.  The mutual fund industry is thriving and liquid without this type of government intervention.  Middle class workers can easily invest in these funds and would save more if we eliminated the double taxation of saved income.

Bernstein views the Social Security system as a solution to his imagined market failure.  Most young people would disagree.  They are skeptical that they will receive the present value of the dollars they contribute to Social Security and half don’t believe the system will exist by the time they retire.  The Social Security system does not allow children (unless they are disabled) to collect survivor benefits after they reach the age of 18.  This means that the adult child of a middle class worker will receive zero if the parent died at age 72 (the average life expectancy of an African American male).  At age 72 a middle class worker will have paid over $200,000 into the system over 40 years and collected a small fraction of that in benefits.  If left-leaning economists like Bernstein are concerned about low savings rates and the lack of income and wealth mobility for working class families in the U.S., they should favor private retirement accounts as an alternative to Social Security.

Low savings rates and an unequal distribution of financial wealth are causes for concern.  Bernstein’s suggestions for more government intervention are misguided.  We can encourage middle class families to save more through tax and Social Security reform.  This will also reduce inequality in the distribution of financial wealth and make it easier for working class families to transfer wealth from one generation to the next.


Upsets and March Madness

The last decade of men’s college basketball has seen increased parity between the power conferences and mid-major conferences.  Friday’s NCAA Tournament results epitomize this shift.  Prior to Friday number 2 seeds won 96.4% of their games against number 15 seeds over the past 27 years.  Both number 15 seeds defeated their second seeded opponents when Lehigh upset Duke and Norfolk State upset Missouri on Friday.  These upsets would have been even more surprising had they occurred in the 1980’s and 1990’s when the gap between college basketballs’ haves and have-nots was much wider.  In the past decade the NCAA’s pod system has given more favorable site assignments to highly seeded teams and limited the number of upsets mitigating the impact of increased parity.

 Today the best players often stay for a single year of college basketball before turning pro.  Consequently the top seeds are usually less experienced and start more freshman than many of the lower seeded teams.  This was not true in the early years of the 64 team format, when teams from traditional powers such as Kansas, Kentucky, North Carolina, and Duke had more talented players and more experienced teams.

March Madness upsets are now more likely to occur because the gap between top and lower seeded teams is the smallest since the 64 team format was introduced in 1985.  One way to measure the gap between stronger and weaker teams is through the Ratings Percentage Index, or RPI.  Teams with a higher RPI have defeated better teams that played stronger schedules during the regular season. 

The RPI methodology has changed over the years, so I compare relative RPI differentials in first round tournament games.  The smallest RPI differentials are in games between teams seeded 8 and 9, and the next smallest differentials are in games between teams seeded 7 and 10.  I normalize the double difference in RPI in opening games involving 7-10 and 8-9 seeds as a baseline for measuring other RPI differentials.

During the 1980s and 1990s the relative RPI differential for the average number 5 seed was 6.6 times the baseline RPI differential.  Over the past 6 tournaments the average number 5seed faced a relative RPI differential that was only 1.5 times the baseline differential.  The same is true for other highly seeded teams.  During the 1980s and 1990s the RPI differential for the average 2seed was 24.4 times the baseline RPI differential, and has dropped to only 8.3 times the baseline differential in the past 6 tournaments.

This means that today’s number 12 seeds are similar in strength to number 10 seeds in the 1980s and 1990s, and number 15 seeds are similar to previous number 12 seeds.  As I mentioned in an earlier post, my research with Todd McFall indicates that the NCAA’s pod system has mitigated the effects of increased parity by giving more favorable site assignments to the top four seeds in each region.  Despite what we observed Friday night, more favorable site assignments for the top 4 seeds in each region has reduced the number of upsets during the first weekend of March Madness.

In March Madness There’s No Place Like Home

The NCAA Men’s Basketball Tournament is reality entertainment at its best.  The NCAA Selection Committee seeds the tournament to increase the chance that stronger teams advance further.  A tournament structure that increases the likelihood that the best teams play in the Final Four increases television ratings and causes networks to bid more for the rights to March Madness.

The NCAA began using the pod system in 2002 to assign teams to first round sites.  The pod system means that teams from different regions can play early round games in the same city in order to reduce travel distances and costs.  In a study with Todd McFall, of Wake Forest University, we found that the pod system favors the top 16 teams in the country.  The new rules have reduced travel distances for teams seeded two through four in each region.  Top seeded teams had shorter travel distances to first round sites even before the pod system and teams seeded five through sixteen have not seen a decline in travel distances since 2002.

A good example of the impact of the pod system is Duke’s game tonight against Lehigh.  Both North Carolina, the number one seed in the Midwest, and Duke, the number two seed in the South, will play tonight in Greensboro.  Before the pod system, Duke would have likely travelled to either Nashville or Louisville to play South regional games.  Greensboro is just 54 miles from Durham, giving the Blue Devils a clear advantage over a team from Bethlehem, Pennsylvania.

Playing games closer to campus improves a team’s performance.  Our study of over 1700 tournament games found that playing in a team’s home state was worth 1.3 points, and each 100 miles further one’s opponent must travel is worth and additional .14 points.  Combining these two effects, we expect Duke’s margin of victory over Lehigh to be 1.92 points more than if they played at a truly neutral site.  This advantage is comparable to the difference between receiving a two-seed rather than a three-seed in the tournament.

The NCAA gives more favorable seeds to basketball teams with better strength of schedules and higher RPIs.  The NCAA has extended this to giving more favorable first round site assignments to the top 16 teams in the country.  All else equal, this means we are more likely to see fewer upsets of teams ranked in the top four in each region, early in the tournament.  Although this lowers the chance of Cinderella teams advancing to the Elite Eight and Final Four, it will probably produce more competitive games between higher ranked teams late in the tournament.

Where The Jobs Are

Job growth has been concentrated in three sectors: health care and education, professional and business services, and leisure and hospitality sectors.  In the past two years employment in these sectors have grown more than twice as fast as the rest of the economy and accounted for more than 3/4 of job growth.

Employment in the past two years increased by 3.4 million overall, and by:

  • 1.18 million jobs in Professional and Business Services
    • Over 500,000 of these jobs have been in Temporary Help Agencies.
  • 595,000 jobs in Leisure and Hospitality
    • Over 420,000 of these jobs were in Restaurants
  • 806,000 jobs in Health Care and Education
    • Home Health Care Services and Outpatient Care Centers are growing three times faster than the rest of the sector

There is no indication that these trends are about to change.  Over the past three months employment in these sectors accounted for 2/3 of the net new jobs created.  In addition, these sectors account for three out of five private sector job openings.  Job openings in leisure and hospitality have seen the largest increase – up 53% from one year ago.

Traditionally, employment in construction and durable goods manufacturing rebounds the most during economic recoveries.  During this recovery, however, construction employment has not increased in two years.  Moreover, employment in restaurants has increased more in the past two years than employment in all durable goods industries combined.

Real Estate and Small Business

Start-ups and new businesses are extremely important for job creation and employment growth.  The strength of the economic recovery depends on the rate of new business formation and the employment gains from these start-ups.   Real estate is the primary asset for many small businesses and the collapse of residential and commercial property values devastated their balance sheets.  Declining real estate values have also reduced the net worth of entrepreneurs and likely slowed the rate of small business creation.

The latest Federal Reserve’s Flow of Funds Report, which was released last week, indicates that real estate is a substantial component of the assets of non-corporate non-financial businesses.  In 2007, prior to the collapse of real estate property values, the market value of real estate accounted for

  • 69% of the assets of non-corporate businesses
  • 33% of the assets of corporate businesses

Moreover, residential real estate accounted for the majority of the real estate holdings by non-corporate businesses and 41% of all assets of these businesses.

The sharp decline in residential and commercial real estate values during the Great Recession had an enormous impact on the balance sheets of non-corporate businesses.  The plunge in real estate prices accounted for 99.9% of the decline in the value of their assets between 2007 and 2009.  The value of real estate owned by non-corporate businesses has increased since 2009, but for each $8 decline in property values there has been only $3 in gains between 2009 and the end of 2011.  The recession has taken its toll on small businesses; the asset value of all non-corporate businesses is 10% below the pre-recession level, while corporate businesses are worth more than in 2007.

The decline in real estate property values devastated the balance sheets of small businesses and probably reduced the rate of new business formation and job creation.  The latest Federal Reserve data indicates that corporate businesses are worth more than they were prior to the downturn, while non-corporate businesses have declined in value.  Real estate is the primary asset for most small and new businesses, which account for much of new job creation.  Depressed real estate values remain a drag on small businesses.  Small and new businesses will not be an engine of growth until residential and commercial real estate values recover.

Higher Education and the Labor Market Recovery

The February jobs report generated a lot of buzz: employment increased by almost 2.6 million in the past twelve months according to the household survey.  Unfortunately a more careful examination of the data indicates that there has been no recovery for workers with a high school diploma or GED, or for high-school dropouts.  The jobs gap for less educated workers is a structural, not cyclical, labor market problem.  Moreover, the fastest grow segment of the labor market is part-time employment for adults age 20-24, most of whom are enrolled in a two-year or four-year college.  One out of five jobs added in the past year were part-time jobs for college-age young adults. 

There are three groups of workers that account for all of the employment gains in the past twelve months: adults with a college degree, adults with some college education, and part-time workers between the age of 20 and 24. 

Here is how employment has increased in the past twelve months:

  • An increase of 3.0% (1.31 million) for college graduates age 25 and above.
  • An increase 2.2% (753,000) for adults age 25 and above with some college education.
  • An increase of 10.7% (527,000) in part-time employment of adults age 20-24.
  • No change in employment for the rest of the labor force.

Almost all of the employment gains in the recovery have accrued to college graduates, part-time workers who are college students, or adults who previously attended college.  About 51% of job gains in the past year were achieved by college graduates, 29% by adults who attended college but did not receive a bachelor’s degree, and the remaining 20% by part-time jobs for adults in their early 20s, the majority of whom are college or community college students.  The remaining 40% of the workforce have seen no net new jobs in the past year.

It is quite remarkable that college-age workers in part-time jobs are responsible for 20% of employment growth in the past year even though they are less than 4% of the workforce.  Many students have delayed college completion and took a part-time job, because of the weak labor market.  These students want full-time employment that will allow them to utilize their education and training, move out of their parents’ homes, and repay their student loan debt.  The growth in part-time employment of college students is an indication of the labor market’s underlying weakness.

Comparing Half-time in America to Morning in America

The Bureau of Labor Statistics just released another solid jobs report, for February.  The labor market is recovering from the recession, but payroll employment is growing much more slowly than it was in early 1984.  Moreover, the unemployment rate remains stubbornly high relative to 1984 and previous recoveries.

Payroll employment grew by:

  • 926,000 jobs in the first two months of 1984 or about 1.0 percent
  • 511,000 jobs in the first two months of 2012 or about 0.4 percent

Employment grew 2.5 times faster in early 1984 than in early 2011.  Payroll employment needed to increase by 1.33 million jobs rather than 511,000 jobs in the first two months of 2012 to be comparable to 1984.

The current unemployment rate of 8.3% is slightly higher than the unemployment rate of 7.8% in February, 1984.  The natural unemployment rate in 1984 was higher because the workforce was less mature.  Younger and less experienced workers tend to have higher unemployment rates because they are often switching jobs.  It is therefore more accurate to compare unemployment rates by age group.

The table below shows that, age-group by age-group, the unemployment rate in 2012 is 0.7% to 4.4% higher than in 1984.

Age Group

Unemployment Rate February 2012

Unemployment Rate February 1984






























*Not Seasonally Adjusted for these Age Groups

 The unemployment rates of young workers and seniors are much higher today than in 1984.  The unemployment rate of prime working age adults, age 35-54, is about 1.5% higher than in 1984.

Despite a few solid jobs reports, the labor market recovery remains weak by historical standards.  Employment growth is not as robust, unemployment rates are higher, and a higher fraction of the unemployed have been out of work for at least six months compared to earlier recoveries

Billionaires and the Top .0001%

Forbes magazine just released its list of the world’s 1,226 billionaires ranked by their net worth.  There are several interesting observations about the list.  First, there is considerable inequality in wealth among billionaires.

  • The top 5% of billionaires account for more than 28% of all billionaire wealth.
  • The average billionaire in the top 10% is worth almost 15 times more than the average billionaire in the bottom 10%.
  • The Gini coefficient for the billionaire wealth distribution is about 0.50

The distribution of wealth among billionaires is more unequal than incomes in the U.S. but more equal than the overall distribution of financial wealth in the U.S.

The U.S. is one of ten countries with more than one billionaire per million residents (and a population of at least one million).  The table below lists these countries and indicates that Hong Kong has many more billionaires per capita, and their wealth is a higher fraction of GDP[1] than in the other nine countries.  Another notable fact is that the U.S. and Sweden look fairly similar.  This is surprising because most studies indicate that income inequality is substantially lower in Sweden than in the U.S.


Billionaires per Million Residents

Billionaire Wealth as % of GDP

Hong Kong












United States


















Comparisons of wealth among the very rich, or between the very wealthy and the population as a whole are interesting, but should probably not drive policy debates (despite the so-called Buffet Rule).  First, wealth creation is not a zero sum game, so fewer billionaires per capita would not be a desirable policy goal.  Second, the tax and social welfare policies of Sweden and the United States are quite different, yet the two countries have similar numbers of billionaires per capita and Sweden’s billionaires own a larger share of the country’s wealth.

[1] GDP is, of course, a measure of a country’s income/production not wealth, but it is probably measured more reliably than wealth and is correlated with a country’s aggregate wealth.

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