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# The Economist's Toolbox

## Watch Out!

When you are considering economic data and other numbers, for example financial data, watch out for the following ways of misinterpreting information.

### Correlation Is Not Causality

Just because two variables seem related, one is not necessarily causing the other to occur. For example, suppose in our earlier example of the average U.S. temperature and growth in GDP, we found that the higher the average temperature, the higher the growth rate in GDP.

##### EconoTip

An old joke may help you remember that correlation is not causality. Jimmy keeps whistling all the time. Jane asks him why. He says, “It keeps the elephants away.” Jane says, “But there are no elephants around here.” Jimmy says, “See? It's working.”

It would be premature to assume that the higher average temperatures were causing the higher growth, simply because high temperature and high growth were correlated. (Correlated is a mathematical term meaning that two variables move together, in an inverse or positive relationship, in a consistent manner.)

A causal relationship between high temperature and high nationwide economic growth could conceivably exist. However you would need to do further analysis—of variables such as farm production, travel expenditures, and so on—to determine that.

### Don't Play with Percentages

Growth rates and values expressed as percentages should be handled, and listened to, carefully.

First, when you or anyone else expresses a value—such as the dollar amount of the federal budget deficit for this year—as a percentage of another value, such as GDP, be sure that 1. it is clear what that other value is and 2. there is a logical relationship between the two values. For instance, if the budget deficit is expressed as a percentage of GDP, what year GDP are we talking about? Last year's? This year's forecasted GDP? Or what? (For that matter, which year's budget deficit are we talking about?)

And if the budget deficit is being expressed as a percentage of GDP, is that a valid way of expressing it? It may be and, indeed, it sometimes is expressed that way. Yet, the usual intention in expressing the budget deficit as a percentage of GDP—or for that matter in expressing anything as a percentage of GDP—is to make it appear small. After all, nothing is larger than GDP.

Second, be careful of growth rates. For example, suppose someone says, “Incomes in the highest (or lowest) one-fifth of the population have grown 5 percent.”

##### EconoTalk

Growth rates for part of the year are usually annualized. A newsperson might say, “The economy grew at an annual rate of 4 percent during the first quarter of this year.” That means that if the economy kept growing at the rate that it grew in the first quarter, it will be 4 percent larger than the economy (meaning real GDP) of the previous year.

The first issue is, of course, are we talking about nominal or real income? If it's nominal, it might not be really real.

The second issue is the period being considered. Are we talking about the rate of income growth in the first quarter of this year compared with that of the first quarter of last year? Or are we comparing that of the most recent full year with the year before that? Or are we comparing the rate of income growth in the first quarter of this year with the rate for all of last year?

If that last situation is the case, then be sure that the first quarter growth rate has been annualized, meaning multiplied by four (because there are four quarters in the year). To annualize a rate of growth, you simply multiply the actual, numerical rate of growth by the appropriate number—twelve for a monthly rate, four for quarterly rate, and two for a six-month rate.

Also be careful when dealing with the growth rate of any value that is expressed as a percentage. Potential confusion surrounds a statement like, “Unemployment increased by 2 percent last year.” If the unemployment rate rose from 4 percent to 6 percent, then the correct way to say that is, “The unemployment rate increased by 2 percentage points.” That way you are clearly saying that unemployment rose from .04 (four one-hundredths, or 4 percent) of the workforce to .06 (six one-hundredths, or 6 percent) of the workforce.

### A Few Final Points

Finally, think critically when you hear the following statements:

The rate of growth is falling.”

This means that growth is still positive, not negative. Politicians of both parties are fond of pointing out that they are cutting the rate of growth in spending in Washing-ton. Yet government spending keeps growing. Clearly, a lower rate of growth still generates growth. Only an actual reduction in the level of spending will reduce spending.

Average (income, spending, production, etc.) is (higher, lower, etc.) than last year's.”

In most situations, economists use the median rather than the average to summarize a set of values. That's because the average—also known as the mean—is more subject to being raised or lowered by extremely high or low values among the data.

Let's define our terms. The mean is calculated by adding up each value in a set of data and dividing the total by the number of values. Suppose we have the following figures for household income for seven households:

Household Income (\$)
A 94,000
B 41,000
C 40,000
D 39,000
E 38,000
F 37,000
G 37,000

The average household income is about \$46,600 (which equals the total of the seven incomes, \$326,000, divided by 7). The mean is not representative of the level of income among these seven households. It is well above six of the seven incomes. That, of course, is because the mean is being pulled up by the income of \$94,000.

The median is the central value—the value in the center when all of the values are arrayed from highest to lowest or lowest to highest. In our example here, the median value of \$39,000 is far more representative of the level of income of most of the households in the group.

Although I have obviously constructed this sample to make the point about the median being preferable to the mean, the fact is that, in economics, income figures (among many others) usually are reported, presented, and analyzed as median values rather than averages. Beware of averages when you hear them quoted, and use them carefully when you do use them.

Holding everything else constant.”

Actually there is nothing wrong with using this phrase, which is used often by economists. It indicates that you are going to be isolating the effect of a change in one variable, such as interest rates, on another variable, such as borrowing. The phrase—which is often rendered in the Latin, ceteris paribus and which also can be translated as “holding all else equal”—means that the analysis assumes that nothing changes except the variable being analyzed.

Economists know that this is not the way things work in the real world, and you should, too. But for the purposes of understanding a single variable, it is a useful and widely used convention.

Excerpted from The Complete Idiot's Guide to Economics © 2003 by Tom Gorman. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.

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