Has Declining Mathematical Literacy in the U.S. Contributed to the Economic Crisis?

The idea that students in the U.S. are behind other major nations in math and science has been discussed widely, and it’s backed up with hard data. For example, a study by the Program for International Student Assessment (PISA), administered by the Organization for Economic Cooperation and Development (OECD), found that 15-year-olds in the U.S. ranked 24th among other countries in math literacy and 26th in problem solving.

It’s telling that the math and science performance of students in the U.S. seems to decline as they progress through school and as the expected skill-set advances with age group. Elementary students test about on par with international peers, but in middle school they fall behind, culminating in the troubling results for the 15-year-olds in the PISA study.

Talk of problems with math and science education in the U.S. is nothing new, having emerged as a topic of attention in the media at least as far back as the 1970s. As a long-term issue, it raises the question of what has happened as students with inadequate mathematical literacy and problem solving skills have advanced into college and on to professional life.

I don’t currently have data to back this up, but it would seem that the students who do come out of high school with a strong grounding in math would gravitate toward the more math-intensive subjects like science, engineering, and biomedicine. For the rest, that leaves the less mathematically rigorous majors like business and liberal arts, in which students can struggle through the most basic required college math courses and then move on to advanced coursework in their chosen majors.

By extension, this would mean that some graduates less skilled in mathematics may have moved on to careers in fields like financial services, which, in turn, is problematic when you consider the increasingly complex nature of the financial instruments that have emerged over the past 20-30 years.

One such instrument is the securitized pool of subprime mortgages, which, now infamously, investors were allowed to purchase at 30-to-1 leverage. What does this mean, mathematically, and what level of math does it take to understand it?

As one of my math professors was fond of saying, the best way to understand something is to take “the simplest example,” so that’s what we’ll do. Let’s say I have $10 to invest, and I am allowed to invest it at “30-to-1 leverage.” Leverage is really a euphemism for debt. If I can invest my $10 at 30-to-1 leverage, it means essentially that I can use my $10 as collateral to borrow $300.

So let’s say I do that, and I use the borrowed $300 to buy a security consisting of 300 $1 loans (as I said, this is a simple example). For each year it’s outstanding, simple interest of 5 percent is payable on each $1 loan. Thus, for the first year, I can expect a profit of $0.05 on each of the loans, or $15 -- a handsome return, made possible by 30-to-1 leverage, of 150 percent on the 10 dollars of my own cash that I put up as collateral. My budget for the year is based on that expected return, including payments on the $300 I borrowed to buy the security, along with any other expenses -- after which, hopefully, I will retain a decent profit margin.

However, let’s assume everything doesn’t go quite as planned. I receive my interest payments on 285 of those loans, for a return of $14.25. But 15 of the borrowers, or about 5 percent, default. Here are the consequences:

• I’ve incurred a shortfall of $0.75, or 5 percent, on my budgeted revenue for the year, from which my expenses and profit margin were to have been derived.
• I’m now on the hook for the $15.00 in bad debt. If I can’t collect, the first $14.25 of that loss eats up the interest revenue I received, and the other 75 cents adds to the loss on my original $10.00 cash -- now 7.5 percent -- and that’s before paying my expenses, including the payments on the $300 I borrowed to buy the security.
• I would now do my best to mitigate this devastating loss, laying off staff and cutting other expenses, and filing claims with any company that may have insured me against losses. And so the cycle of crisis begins, with losses passed through the system from one stakeholder to the next.

This is a very simple model of what happened in the subprime mortgage crisis, and it illustrates how leverage has as much power to magnify losses when things go wrong as it does to magnify profits when things go right.

For the current discussion, it’s noteworthy that the math I used here is very simple -- using ratios and percentages to calculate expected interest, returns, etc. No advanced math is required -- no algebra, certainly no calculus. It’s elementary-school or at most middle-school stuff. It’s the sort of math that the cohort of fifteen-year-olds in the PISA study should have mastered well.

So how could this crisis have been allowed to happen? Did too many people in the financial community -- not to mention the grass-roots consumers who were taking out mortgages, negotiating home prices, and investing in the stock of banks that were issuing risky mortgages -- lack the math skills to comprehend the possible consequences? Or were they blinded to the magnitude of danger by the lure of potential profit?

While only simple math is required to see the inherently questionable risk in such a highly leveraged investment, there are other factors to consider when evaluating an investment, such as:

• How accurate are the valuations of the assets underlying the security -- the accuracy and stability of home prices, in this case
• How accurate are the assessments of the ability of the borrowers to repay, and of their default probability

These two considerations require somewhat more complicated math. Analyzing valuation accuracy, risk of loss, and default probabilities enters the realm of actuarial science and is highly vulnerable to any flawed assumptions or inaccuracies in the input data (garbage in, garbage out). Among such data flaws could be widespread misrepresentation of borrowers about their incomes, or prices that have been distorted by a speculative bubble. The results of an actuarial analysis should price the level of risk into the cost of the security and measure the risk, in terms of factors like expected default rates, against the expected return. But any inaccuracies in the original data or assumptions can lead to a misinformed decision.

If we look in this context at how the subprime mortgage crisis could have been allowed to occur, we see only a couple of explanations: (1) not enough people understood the math well enough to see what could go wrong, and/or (2) those who saw the potential for disaster (and, yes--there were a few lonely, expert voices crying in the wilderness) didn’t speak up loudly enough or act decisively enough.

Or, perhaps more plausibly, the explanation could lie in some combination of the two factors. If so, the level of math literacy throughout society is even more important. If enough everyday homeowners, mortgage underwriters, investment bankers, and others throughout the population of stakeholders understand the math, they are more likely to make better decisions that would counteract the impact of those who may be capable of understanding the danger but, out of whatever motivation, are at best in denial or at worst deliberately ignoring it.

This is why it’s good to see that math and science education are among the priorities of the Obama administration. Combined with the greater public attention the crisis is generating to finance and economics, an increased level of mathematical sophistication throughout the country could lead to a future of better financial decisions by all stakeholders, from the boardrooms of the financial sector to grass roots consumers on Main street. This would make future crises of this magnitude far less likely. Sphere: Related Content

Samuel Hutchison Beer, Harvard Political Science Scholar, Dies at 97

Samuel Hutchison Beer, a noted Harvard University political scientist, died at the age of 97 on April 7, 2009.

For years, Beer was the world's leading expert in British politics, but he also studied the American political system, and was active in American politics as a lifelong Democrat and chairman of Americans for Democratic Action from 1959 to 1962. He worked on the staff of the Democratic National Committee and as occasional speech-writer for President Franklin D. Roosevelt in 1935 and 1936. He was a reporter for the New York Post in 1936 and 1937 and a writer at Fortune magazine in 1937 and 1938.

After his wartime duty as captain in artillery, Beer served in the U. S. military government in Germany in 1945. While at Oxford he traveled to Germany and noticed the rising threat of Nazism; after the war he was able to pursue his interest in the question of how so civilized a country, governed as a democracy, could lose so much.

When he returned to Harvard to teach in 1946, he gave a course on that topic and became the leader of an approach to comparative government that made sense of facts through the ideas of political, social, and economic theory. He began a Harvard course, "Western Thought and Institutions," that was as much history as political science, and as much political theory as comparative government. He continued this famous course for over 30 years, to the benefit and admiration of thousands of Harvard students.

Beer's first book was The City of Reason (1949), a study in the tradition of Oxford idealism that sees the reason inherent in human things rather than hovering above and critical of irrationalities. Avoiding the vague complacency of such a view, he launched the thorough study of British politics that made him celebrated in Britain as the man who knew their politics better than they did. In 1965 he published the book that secured his reputation, British Politics in the Collectivist Age, combining an analysis of postwar British socialism with the hard facts of political parties and pressure groups.

His study of American politics was crowned by the publication of his major work To Make a Nation: The Rediscovery of American Federalism in 1993. In it he stressed the original national purpose behind the idea of states' rights, often abused to diminish the American nation.

Always a partisan outside but never inside the classroom, Beer took a leading role in opposing the student rebellion of the late sixties at Harvard, criticizing the politicization of universities. In 1998 he also criticized the politicization of impeachment, testifying to the House of Representatives in the case of President Bill Clinton. Sphere: Related Content

Can We Learn Something from the Aussies?

Early in 2008, I was chatting with a colleague from Australia on my way to a sales meeting in Asia. I don’t quite recall how the conversation got started, but apparently signs of trouble in the U.S. economy had already started to spread in the international news, and my colleague asked me about it. Somehow the subject of unemployment came up.

“You don’t have services in the States for people who are unemployed, do you?” she asked.

I was a bit surprised to hear that, and clarified that we do indeed have an unemployment compensation system to help people who have lost one job through no fault of their own get through until they find a new one.

“But it’s very limited, isn’t it?” she replied.

“Well, yes,” I said. “It’s normally around three months, but in a particularly bad economic situation it’s sometimes extended.”

“It’s indefinite in Australia,” she said. “Some people even live off the dole.”

The conversation then, understandably, switched around to taxes, and she said that their heavy tax rate was what they sacrificed in exchange for a measure of security in Australia. She said that she understood that we don’t pay very much in the way of taxes in the U.S., but I responded that, when you add up our sales taxes, income taxes, fuel taxes, property taxes, state and local taxes, etc., our tax burden ends up being pretty heavy. I told her about our “Tax Freedom Day” concept which, last I heard, held that we all have to work until sometime in May before we can finally call our income our own.

“My tax bracket last year was 47 percent, by the way,” she said, which does translate to somewhat more than 5/12 of the year … but not a lot more.

It makes you wonder. Australians pay somewhat more in taxes than we do, but perhaps not a whole lot more. But seemingly they provide a better safety net for those who are having trouble. Is it a good tradeoff? Conservatives in the U.S. would argue that a huge social welfare system in the U.S. would be devastating to the economy.

But if the compared GDP growth rates for the past five years in Australia vs. the U.S. (see chart, data source indexmundi) are any indication, maybe this isn’t the case. Although Australia recently declared that its economy, as a result of the global crisis, is projected to shrink this year, they are doing better than we are on the unemployment front, with a jobless rate of 7 percent. And for the last five years, they beat us by a small margin in average annual GDP growth – 3.24 percent for Australia as opposed to 3.18 percent for the U.S.

Maybe a “welfare state” isn’t such a bad thing economically as the conventional wisdom in the U.S. leads us to believe. Is it possible that a larger and more expensive social safety net amounts to a form of “permanent stimulus?” Here in the States many of us don’t like the idea of handouts, and that’s understandable. But perhaps giving the poor a consistent level of money to spend and a reasonable minimum standard of living can have a beneficial and stabilizing effect on the economy, and a moderating effect on fluctuations driven by the booms and busts of business cycles.

Sphere: Related Content