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Annualizing Data
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How to annualize percent
changes in quarterly and monthly data |
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The Economic Problem
Annualizing Data Facilitates Comparison
of Growth Rates of Various Time Periods
Suppose Texas employment grew 0.92
percent in the first five months of a particular year. Then
in June and July, employment advanced 0.15 percent and 0.22
percent, respectively. Would employment growth in June and
July be above or below the pace set in the first five months
of the year?
While this simple problem could probably
be tackled in a few different ways, the most common one is
a process called data annualization. In this method, growth
rates are adjusted to reflect the amount a variable would
have changed over a year’s time, had it continued to grow
at the given rate. The result is a percent change that is
easily comparable to other annualized data.
In this case, the 0.92 percent translates
into an annualized 2.22 percent. The 0.15 becomes 1.81 percent
(annualized), and the 0.22 figure becomes 2.67 percent (annualized).
Thus, employment growth in June was below the rate established
in the first five months, while the July figure was above
it, in annualized terms. This kind of data adjustment is very
common in economic analysis. It allows for quick comparison
of percent changes, no matter the time period.
Technical Solution
The formula for annualizing monthly
data is straightforward:
| Equation 1 |
 |
| NOTE: For quarterly data, use 4 instead
of 12. |
where 
and
– 1 are the values of the economic variable in months
m and m –1, respectively (for example,
m = February, then m – 1 = January),
and 
is the annualized percent change.
For year-to-date calculations on monthly
data, the formula is:
| Equation 2 |
 |
| NOTE: For quarterly data, use the
fourth quarter instead of December, and q = 1, 2, 3, 4
instead of m = 1, 2, 3…12. |
where 
is the value of the economic variable in the December of a
given year, m is the number of the month in question,
is the value of the economic variable in the mth
month of the given year, and 
is the annualized year-to-m percent change.
Real-World Example
Table 1 uses these two formulas to calculate
the values cited in the Economic Problem section above.
| Table 1 |
| Month |
Employment
(thousands) |
Monthly
Percent Change (not annualized) |
Monthly
Percent Change (annualized) |
| December |
9,452.5 |
n/a |
n/a |
| January |
9,465.2 |
.13 |
1.62 |
| February |
9,472.9 |
.08 |
.98 |
|
March |
9,498.3 |
.27 |
3.27 |
|
April |
9,516.3 |
.19 |
2.30 |
|
May |
9,539.5 |
.24 |
2.96 |
|
June |
9,553.8 |
.15 |
1.81 |
|
July |
9,574.8 |
.22 |
2.67 |
|
|
|
|
| May/Dec |
n/a |
.92 |
2.22 |
|
On the July row, 0.22 is found by calculating
the percent change between 9,553,800 (June) and 9,574,800
(July). The annualized figure of 2.67 is found by applying
Equation 1: Divide 9,574,800 by 9,553,800, raise this quotient
by 12, subtract 1, and multiply the whole thing by 100 (Calculation
1). This rate represents the amount employment would
have increased for the year had it expanded at that monthly
rate all 12 months. The calculation for the other months is
the same.
| Calculation 1 |
 |
In the last row, the 0.92 figure is
found by calculating the simple percent change between 9,452,500
(December) and 9,539,500 (May). The annualized figure of 2.22
percent is found by applying Equation 2: Divide 9,539,500
by 9,452,500, raise this quotient by 2.4 (12/5), subtract
1, and multiply the whole thing by 100 (Calculation 2).
This rate represents the amount employment would have increased
for the year had it continued to expand at the pace set between
January and May.
| Calculation 2 |
 |
| Glossary
at a Glance
Annualize: Adjusting
a growth rate to reflect the amount a variable
would have changed over a year's time had it continued
to grow at the given rate. |
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