For ease of comparison, BEA publishes percent changes in most quarterly estimates at annual rates. If GDP increases 3.0 percent from year 1 to year 2 and increases at an annual rate of 3.6 percent in the first quarter of year 3, it is easy to see that the first-quarter growth rate is larger than the growth for year 2. If the growth rate in the first quarter of year 3 was presented at the quarterly rate of 1.0 percent, comparing it to the year 2 growth rate is more difficult. A quarterly percent change at an annual rate shows what the percent change would be if the quarterly rate continued for four quarters. It is computed by compounding the quarterly rate for four quarters.

• A simple formula for computing the percent change from quarter 1 to quarter 2 at a quarterly rate is:

((level of quarter 2/level of quarter 1)-1)*100

Here is an example of this equation in action. If real GDP is \$10,597.1 billion (annual rate) in the fourth quarter of 2003 and \$10,493.1.billion in the third quarter, the steps of calculating the quarter-to-quarter percent change are as follows:

First, we divide \$10,597.1 billion by \$10,493.1 billion, which equals
1.009911

Second, we take 1.009911 and subtract 1.0, which equals 0.009911

Third, we take 0.009911 and multiply by 100, which equals 0.9911

When we round this number to the nearest tenth of a percent, we get 1.0.
Thus, we see that real GDP increased from the third quarter of 2003 to the
fourth quarter of 2003 by 1.0 percent at a quarterly rate.

• A simple formula for computing the percent change from quarter 1 to quarter 2 at an annual rate is:

(((level of quarter 2/level of quarter 1)^4)-1)*100

Using the same third and fourth quarter estimates of real GDP, here are the steps for computing the percent change at an annual rate:

First, we divide \$10,597.1 billion by \$10,493.1 billion, which equals
1.009911

Second, we raise this to the fourth power, which equals 1.040237

Third, we take 1.040234 and subtract 1.0, which equals 0.040237

Fourth, we take 0.040237 and multiply by 100, which equals 4.0237

When we round this number to the nearest tenth of a percent, we get 4.0.
Thus, we see that real GDP increased from the third quarter of 2003 to the
fourth quarter of 2003 by 4.0 percent at an annual rate.

For some volatile quarterly series, such as corporate profits, BEA publishes percent changes at quarterly rates rather than at annual rates, because the comparability issue mentioned above is less important and because annual rates of change may be misleading.

BEA publishes percent changes for monthly series, such as personal income and outlays, at monthly rates, because producing them at annual rates excessively exaggerates the month-to-month changes, which outweighs the comparability advantage.

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