Common mistake 1 with Rebased to 100

Choosing a base year that flatters the argument. This is the most common abuse of the chart, and it is invisible to the reader unless the base is stated.

Common mistake 2 with Rebased to 100

Reading the gap between two indexed lines as a quantity. It is a ratio of ratios and has no units.

Common mistake 3 with Rebased to 100

Indexing a series that already is a rate. Inflation is already a normalised quantity; indexing it produces a number nobody can interpret.

Common mistake 4 with Rebased to 100

Changing the base to make a series look better and not saying so. Every rebasing is defensible and the choice is an argument, so it belongs in the caption.

EconStatsCraft › Rebased to 100

Rebased to 100

Sets every series to 100 in its first period, so a series in rupees and one in tonnes become directly comparable and the question becomes "which grew faster". The chart economists reach for most often and the one most often missing from software.

What it needs

Time or period
Series to compare - Two or more, in any units.

The intuition

Two series in different units cannot be compared on one axis - a price index near 200 and an exchange rate near 90 tell you nothing side by side. Rebasing divides every series by its own value at a chosen date and multiplies by 100, so all of them start together and the chart shows relative growth from that point. It is the right chart for "which grew faster" and the wrong one for almost everything else.

When to use it

Whenever the question is "which grew faster" rather than "which is bigger". Also whenever two series would otherwise need two axes: a dual axis invites the reader to compare two arbitrary scalings, and an index removes the arbitrariness.

Where the estimator comes from

For a series x_t and base period b, the rebased series is I_t=100\times\frac{x_t}{x_b}. Growth from the base reads directly off the index: I_t-100 is the percentage change since b. But growth BETWEEN two later dates does not, because \frac{I_t}{I_s}=\frac{x_t}{x_s} regardless of the base - the ratio is base-invariant while the DIFFERENCE I_t-I_s is not. That is the whole arithmetic behind the chart's usefulness and its principal trap: differences in index points are not comparable across series that have drifted apart.

The model

I_t=100\times\frac{y_t}{y_{0}}

What it assumes

The base period is comparable across series. Every series is rebased to ITS OWN first observation, so if one starts in a recession and another in a boom, the index exaggerates the first one's growth. Restrict the sample to a common, unremarkable base period before reading too much into it.
The first value is not zero or missing. The app skips a series whose base is zero rather than dividing by it.
The series are positive throughout. An index built on something that crosses zero is meaningless - a growth rate, for instance, should be plotted in levels, not indexed.
The base period is representative rather than convenient. Basing on an unusual year makes every later reading a comparison with an anomaly.
The series are comparable at the base. Rebasing forces every series through 100 at one date, which manufactures agreement there and says nothing about whether the levels were ever comparable.

Statistical properties

The base period is a choice that changes the picture entirely. Basing at a date when one series happened to be at a trough makes it look like the strongest performer for the rest of the chart.
Index points are not percentages after the base period. A series moving from 150 to 165 has grown 10%, not 15 points-worth of anything comparable to a series moving from 100 to 115.
Ratios are base-invariant, differences are not. Any statement of the form "A grew faster than B between 2015 and 2020" should be computed from the ratio, and is then independent of where the base was set.
A series that crosses zero or is negative cannot be rebased. The denominator vanishes or the sign flips, and the resulting chart is meaningless rather than merely odd.
Rebasing destroys the level. A chart of rebased GDP tells you nothing about which economy is larger, which is often the more important fact.
For a series that is already an index or a percentage on a common scale - yields, inflation rates - rebasing is actively harmful: it converts comparable units into incomparable ones.

How to read the output

Only ratios are meaningful. A series at 180 has grown 80% since the base; a series at 180 against another at 120 has grown 50% MORE, not 60 points more.
The base year is a choice and it changes the picture. Say which year it is, and check whether the ranking survives moving it.
On a log scale an index becomes a straight line under constant growth, which makes a change in the growth RATE visible as a change in slope. That is usually what the question is really about.
The index is a ratio to the base, so differences between two indexed series are differences in growth from the base date - not differences in level, which the rebasing has deliberately erased.
A gap that opens early persists in the picture for the rest of the chart even if both series grow identically afterwards.

A worked reading

A CPI series of 183.31, 190.0, 205.5, 241.2. Based at the first observation it reads 100, 103.65, 112.105, 131.58 - so prices are 31.6% above the start. Base it at the third observation instead and the same data reads 89.202, 92.457, 100, 117.372. Neither is wrong and they tell different stories, one of steady growth from a floor and one of a mid-sample turning point. What survives both is the ratio: 241.2/205.5 = 1.174 either way, which is why any comparative claim should be built from ratios rather than from the position of the lines.

Symptom → diagnosis → what to do

If you see this	It means	Do this
One series looking dominant	Check where the base sits for it	Move the base and see whether the story survives
A rebased series going negative	The original crossed zero	Rebasing is not defined. Plot levels or differences
Rebasing a set of yields	They were already comparable	Plot them directly
Reading index-point differences as percentages	Only true at the base	Use ratios
Base period at an outlier	The whole chart inherits that anomaly	Base on an average of several periods
Needing to compare levels	Rebasing has removed them	Show levels on a log scale instead

Common mistakes

Choosing a base year that flatters the argument. This is the most common abuse of the chart, and it is invisible to the reader unless the base is stated.
Reading the gap between two indexed lines as a quantity. It is a ratio of ratios and has no units.
Indexing a series that already is a rate. Inflation is already a normalised quantity; indexing it produces a number nobody can interpret.
Changing the base to make a series look better and not saying so. Every rebasing is defensible and the choice is an argument, so it belongs in the caption.

Where to read this properly

ILO et al., Consumer Price Index Manual: Concepts and Methods (2020), ch. 1 and 15.
Diewert (1976), "Exact and Superlative Index Numbers", Journal of Econometrics 4(2).
Hyndman and Athanasopoulos, Forecasting: Principles and Practice (2021), ch. 2, on transformations for comparison.

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Rebased to 100

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

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