This article appeared in the business section of my local paper last Sunday and it really caught my attention. Seems like really basic stuff now, but after reading it, I realized I haven't always viewed percentages the way I should be. Depending how you view a percentage increase or decrease, a completely different picture can be painted.
Brush up on math to grasp economy
By Edward Lotterman
Article Last Updated: 06/21/2008 03:13:59 AM CDT
Everybody is familiar with percentages but their details still trip people up, particularly when communicating economic news. Here are a few pitfalls to avoid.
There is an important distinction between an 'increase of X percent' and an 'X percentage point increase.' For example, Argentina taxes many farm exports stiffly. In March, it increased the export tax on soybeans from 35 percent of the export value to 44 percent.
A recent wire service story describing the resulting protests said farmers had blocked roads "in response to a nearly 10 percent increase in export taxes." Yes, the taxes did increase by 9 percent of the value of shipments. But moving from 35 percent to 44 percent has increased the tax rate by more than one-fourth.
If export levels stayed the same, tax revenues would increase by 25.7 percent. Stating it that way gives a different impression than to say "a 10 percent increase in export taxes."
A similar distinction trips up many of my students. In an assignment for introductory macroeconomics, I pose the following problem: "The unemployment rate increases from 4 percent of the labor force to 5 percent. What is the percentage increase in the number of unemployed people?"
At least half the students will answer "1 percent," the number of points by which the unemployment rate changed. But a one-point increase in the rate from 4 percent to 5 percent is a 25 percent increase in the number of unemployed people.
The difference between 1 percent
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and 25 percent has enormous implications for anyone running a state employment agency or the number of people applying for food stamps or seeking groceries at food shelves. A 1 percentage point increase in the unemployment rate causes a much larger increase in people seeking help.
Some people also are confused when month-to-month changes are presented at an annualized rate.
For example, the Consumer Price Index for February 2008 was 0.29 percent (29 hundredths of 1 percent) higher than it had been in January. If it kept increasing at the same rate, over one year the increase would be 3.6 percent. Headlines present it as "Consumer prices up 3.6 percent in February." Most people understand that as an annualized rate, but some think prices actually went up that much in one month.
Year-over-year increases also can confuse. A few months ago, a headline read "Foreclosures up 60 percent in February." The article explained that the number of foreclosure filings in February 2008 were 60 percent higher than in February 2007.
This particular article carefully explained it as a year-to-year change and noted that the number of new foreclosure filings actually had dropped 4 percent from January to February 2008.
Looking at the data over a longer time span showed that foreclosure filings were pretty level from August 2007 through February 2008. Most of the jump was from February to August of last year. But the headline gave the impression of rapid acceleration in February.
St. Paul economist and writer Edward Lotterman can be reached at elotterman@pioneerpress.com.
