3.2.1.3 - Index numbers and price indices

Base years and relative change

An index number expresses a variable relative to a chosen reference period, making its proportional change easier to see.

The base year normally has an index of 100. For a simple index:

In an illustrative economy, output rises from £400 billion in Year 1 to £460 billion in Year 2. With Year 1 = 100, the Year 2 index is $460/400\times100=115$. Output is 15% above the base-year value. An index of 115 does not mean output is £115 billion, and the index has no currency unit.

Indices also describe employment, wages, productivity and quantities of output. Specify which variable is indexed: an index of money GDP can rise because prices rise, whereas a real-output index removes price changes. Two countries both having index 120 only tells us that each is 20% above its own base-year value; their output levels can differ enormously.

The denominator for a percentage change is the starting index, not automatically 100. If an output index rises from 120 to 126, it increases by 6 index points but by $(126-120)/120\times100=5\%$. The two answers coincide numerically only when the starting index is 100.

Rebasing an index

Rebasing changes the reference period without changing the underlying economic observations or their proportional changes.

To make a different year equal to 100, divide every old index by that year's old index and multiply by 100:

Consider this illustrative output series. To change the base from Year 1 to Year 2, divide by 120, not by the new base value of 100.

The Year 2–3 increase remains 5%: $(126-120)/120\times100$ equals $(105-100)/100\times100$. The index-point increase changes from 6 to 5 because the scale has changed. Rebasing cannot create growth, alter purchasing power or remove inflation from money values. Keep extra precision in intermediate calculations and round only the final result.

When combining two published series, first check their definitions and reference years. Re-expressing both on the same base helps compare growth paths; it does not make different populations, output definitions or price-adjustment methods identical.

Building a weighted price index

A price index combines price changes across a basket of goods and services, giving greater importance to items on which more money is spent.

Suppose this illustrative basket has base-period expenditure weights. The item indices compare like-for-like prices with the same base period.

The basket's price level is 18% above its base-period level. Equivalently, weights written as shares give $0.30(120)+0.20(150)+0.50(104)=118$. If weights sum to 1, do not divide by 100 again. An unweighted mean, $(120+150+104)/3=124.67$, would incorrectly give energy as much importance as all the other goods and services together.

For a fixed basket, weights reflect base-period spending, which depends on both quantities and prices. They are not simply the number of products in each category. A household devoting 40% of its budget to energy would experience a different combined price change from this basket, even if it faced the same individual price rises. Index weights therefore determine which price changes matter most to the overall result.

Price levels and inflation rates

The price index measures a price level relative to a reference period; inflation measures the percentage change in that level over a specified interval.

Annual inflation compares an index with its value a year earlier. Monthly inflation instead uses the previous month; these measures answer different questions. For successive years: