Base Year vs Index Number
Base Year and Index Number are two Economic Indicators & Data concepts in AP Economics that students often mix up. Base years are the reference periods an index is set equal to 100, so every other reading in the series is a percentage of that period's level. Index numbers express a value as a percentage of its own level in a chosen base period, which is set equal to 100. Here is how they compare side by side.
An index number means nothing until you know which period was chosen as the base and assigned the value 100. Every other value is that period's level as a percentage of the base, so 112 sits 12 percent above the base and 94 sits 6 percent below it. The choice of base never changes a growth rate calculated between two periods, because the base cancels out of the ratio, but it does change every reported level, which is why comparing two index series with different bases is meaningless. Statistical agencies rebase periodically to keep the reference period recent and the weights relevant, and rebasing rewrites the entire history of levels while leaving percentage changes intact. For real GDP, the base year does double duty: it is also the year whose prices are used to value output.
An index converts a series into relative terms by dividing each period's value by the base period value and multiplying by 100. That makes series comparable which could not otherwise be added, which is why prices for thousands of goods, output across dozens of industries and share values across firms all get reported as indexes. The cost is that an index has no units: a consumer price index does not say what a basket costs in dollars, only how its cost compares with the base period. Two conventions cause most student errors, the difference between a change in index points and a percentage change, and the fact that a level is uninterpretable unless you know the base. A weighted index also depends on how its weights are chosen, which is how two indexes measuring the same thing can drift apart.
Base Year vs Index Number: The Anchor and the Reading
| Base Year | Index Number | |
|---|---|---|
| What the term names | The reference period an index is anchored to | The values that anchoring produces |
| What it fixes | The prices or quantities held constant for comparison | Nothing; it is the output of the calculation |
| How you get it | Chosen by the agency, ideally a normal period with good data | Current level divided by base level, times 100 |
| Effect of changing the base | Rescales the entire series | Every reading takes a new value while the trend is untouched |
| Units | A date, such as a year or an average of several years | Unitless, because the units cancel in the ratio |
| Common mistake | Assuming a real series is priced in the year being reported | Reading a rise of 10 points as a rise of 10 percent |
Changing the base year changes every number and no conclusion
Take illustrative data. A basket costs 200 in the first period, 250 three years later and 300 six years later. Anchor the index to the first period and the readings are 100, then 250 over 200 times 100, which is 125, then 300 over 200 times 100, which is 150. Anchor it to the middle period instead and the readings become 200 over 250 times 100, which is 80, then 100, then 300 over 250 times 100, which is 120. Every single number changed. Now check what did not. Between the second and third periods the first series rises from 125 to 150, a change of 25 on a base of 125, which is 20 percent. The second series rises from 100 to 120, a change of 20 on a base of 100, which is also 20 percent. That is the property making index numbers useful and the base year very nearly arbitrary. The base sets the scale, and the ratios carry all the information. The one rule is that any comparison must use a single base throughout, since mixing two bases in one calculation produces a number that means nothing. Percentage change from an index is worked at /calculate/inflation-rate.
Points are not percent, and the base year is where that habit forms
The most common error with index numbers is treating a change in points as a change in percent. If an index moves from 150 to 160 it rose 10 points, but the percentage change is 10 divided by 150, which is about 6.7 percent. Reported as ten percent, that overstates the move by half. The mistake hides because in the base period the index equals 100, so points and percent coincide there and the shortcut looks safe. The second error concerns the base year itself. A series stated in base year prices is not stated in the prices of the year being reported, and that is deliberate. Holding old prices fixed is precisely how the quantity change is isolated. Agencies rebase from time to time because a very old base drifts out of date as the goods in the basket and their relative prices change, and a rebasing does not mean the previous figures were wrong. It means the yardstick has been repainted. When you compare two published figures, check they share a base before doing anything else with them. What a base-year-priced figure represents is set out at /glossary/real-value.
Frequently asked questions
What is a base year?
A base year is the reference period an index is anchored to, with its value set equal to 100 so that every other reading expresses a level as a percentage of that period. Agencies pick a period with reliable data and no unusual disruption, and they change it periodically as the economy shifts.
What does an index number of 125 mean?
It means the quantity being tracked is 25 percent higher than it was in the base period, because the base is set to 100 and the index is a ratio to that base multiplied by 100. It does not tell you anything about the level in dollars or units unless you also know what the base period level was.
Does changing the base year change the inflation rate?
No. Rebasing rescales every reading in the series, but the percentage change between any two periods stays the same, because that change is a ratio and the common base cancels out. This is why two agencies using different base years can still agree exactly on the rate of inflation.
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