This is the first of a new math/stats newsletter that Bill Briggs and I will send on occasion. It is designed primarily for users of our textbooks (Using and Understanding Mathematics; Statistical Reasoning for Everyday Life), but may also be of general interest to others. It will include brief items of current news, along with suggested problems and discussion questions that you may use in class.
Now, for our first update, with three items: two on big numbers in the news, and one on a major statistical study that has affected the life of millions of people.
1. That’s a LOT of money! Last year, Congress passed a new prescription drug benefit for Medicare that was supposed to cost $400 billion over the next 10 years. This year, the cost estimate has been raised to $530 billion. The rapid change in the estimate has upset a lot of people, and some are questioning whether the more recent figure was deliberately hidden at the time Congress was voting. It will be interesting to follow the controversy… but monetarily it is the tip of the iceberg. Hidden deeper in the news, you’ll find new estimates about the long-term shortfalls in both Medicare and Social Security, and it’s not pretty. For example, a 2002 study by the Treasury Department estimated that the shortfall in Medicare and Social Security would be $44 trillion over the next 75 years. In other words, the projected amount that will be owed in benefits for these programs over the next 75 years is $44 trillion greater than the taxes that will be collected for them. And this study was done before the new prescription drug benefit was passed.
Here are some suggested exercises and discussion questions for class:
- Suppose Congress decided to address the projected shortfall by increasing Social Security and Medicare taxes. If the $44 trillion were to be collected in taxes evenly over the 75 years, how much would need to be collected each year? Compare this amount to current government tax revenues, which are a little less than $2 trillion per year. (Answer: $44 trillion/75 years = about $600 billion per year. This is about 30% of current total tax revenue. In other words, we’d need to increase overall taxation by about 30% in order to make up for the projected shortfall.)
- Social Security and Medicare are currently paid for by "FICA" taxes, not by general income taxes. Of the government’s roughly $2 trillion in current annual tax revenue, FICA taxes contribute about 35%, or $700 billion. Suppose the tax increase in the prior question is an increase only in FICA taxes. How would it change the FICA tax rate? Note that FICA taxes are currently set at 15.3% of wages, with half paid by the employer and half paid by the employee (self-employed people pay the full 15.3% themselves). [Answer: Above, we found that taxes would need to be increased by $600 billion per year; if this is all FICA, then it means FICA taxes would nearly double (rise by 86%). So the new FICA rate would be around 30%.]
- Is it politically realistic to imagine raising the FICA rate as much as you found above? Can you think of any other alternative ways to address the projected shortfall? (Discussion points: most will say it’s not very politically realistic, but the only real alternatives are to raise other types of taxes or cut future benefits or have the government debt skyrocket.)
- All of this is based on projections for the next 75 years. Historically, budgetary projections even for one or a few years have proven to be notoriously inaccurate. Should we worry about a shortfall from a 75-year projection? Why or why not? (Discussion points: This is highly debatable, since a small change in the projected economic growth rate could lead to large swings in the shortfall projections. Nevertheless, the current projection tells us that something significant will have to happen to avoid the "fiscal train wreck" that many economists fear.)
- A note on references: In Using and Understanding Mathematics, Third edition, Unit 4D has a discussion of FICA taxes and Unit 4E has a general discussion of the federal budget including Social Security. You can also use the Addison Wesley Research Navigator (http://www.researchnavigator.com) to search for recent articles about these budgetary issues in the New York Times and other news sources.
2. Microsoft Penalty. The European Union has issued a ruling finding that Microsoft abused its monopoly position, and has fined the company $630 million. Microsoft is appealing the ruling and the fine.
Questions for class:
- Suppose the $630 million fine holds. Microsoft’s current share price gives the company a total market value of about $270 billion. The company also has about $50 billion in available cash (liquidity). Use these facts to put Microsoft’s fine in perspective by imagining that YOU were fined an amount that is equivalent as a percentage of your net worth or your available cash (e.g., bank account balance). About how much would your fine be? How would it compare to, say, the fine you pay for a speeding ticket? (Answers will vary depending on a student’s personal circumstances, but the relevant facts are: the Microsoft fine as a percentage of the company’s market value is about 0.2%; the fine as a percentage of its available cash is about 1.3%. So, e.g., if a student has available cash of $5,000, the equivalent percentage fine would be $65 — similar to a typical speeding ticket.)
- If you are an investor, should the amount of the fine be a major concern for the future of Microsoft? (Answer: clearly not.)
- Are there other reasons why investors should be concerned about the EU ruling? (Discussion points: given the small impact of the fine itself, the greater issues are those that would affect how Microsoft can develop and market products in the future. You can use the Research Navigator (http://www.researchnavigator.com) to find articles about the ruling, and discuss what YOU might do if you owned Microsoft shares — or whether it’s a good time to buy them…)
3. Vaccinations and autism: In 1998, a British medical journal published a statistical study linking childhood vaccinations to autism. This study led millions of people (especially in Great Britain, but also in the U.S. and elsewhere), to forego vaccinations for their children. Just a few weeks ago, 10 of the original 13 authors of the study published a retraction, saying they erred in their conclusions. Thus, according to these authors of the paper, there is no current evidence to support the idea that there is any link between vaccinations and autism.
Questions for class:
- Let’s assume that the 10 authors who signed the retraction are correct — the original paper was wrong, and there is no evidence for a link between vaccinations and autism. Do you think people who have foregone vaccinations in the past few years would have behaved differently if the original study had never been published? Why or why not? (Answer: clearly yes. Vaccinations prevent diseases that are sometimes deadly. Very few people would skip vaccinations if there were no side effects to worry about. The autism study suggested a serious side effect, and influenced the choice made by millions of people.)
- No one knows exactly how many people did not get vaccinations or how many children got sick as a result. But let’s make some simple estimates. Suppose that 10 million children were not vaccinated, and that 1 in 10,000 became seriously ill or died as result. How many children were affected? (Answer: this is a simple numerical problem. Answer is 1,000 children.)
- The original study was based on just 12 children with autism, and took place 8 years after they were vaccinated. The original conclusions were largely based on parent memories of when autism symptoms started, and their claims that the timing was closely linked to the time of the vaccinations. Should the conclusions have been considered strong in the first place? (Answer: clearly not. Even without a retraction, the original statistical evidence was very weak. Reference: have students study our guidelines for evaluating statistical claims, which you can find in Unit 5B of Using and Understanding Mathematics or Chapter 1 of Statistical Reasoning in Everyday Life.)
- It’s quite likely that most of the millions of people who did not get vaccinations because of this study have not heard of the retraction. Thus, their children will remain unvaccinated. Suppose you were a national health official, how would you seek to get the word out to these many parents? Do you think they will believe the retraction? How would you explain the change in scientific perspective on this question? (Discussion points: it might be particularly interesting to discuss the difficulty of retracting front page news of any type…)
- Overall, do you think it was a mistake for a medical journal to publish the original study? Would the journal have been criticized for NOT publishing it? How should journals decide when the evidence is strong enough to warrant publication? (Discussion points: This is highly debatable, since it goes to the question of who should decide whether the evidence is strong enough to warrant publication. Could lead to an interesting discussion of the peer review process along with its benefits and potential pitfalls.)
Hope you find these updates useful. Again, please feel free to reply, or to send your own suggestions for math or statistics updates based on current news.