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Movements that are not trends

Covers AS91226

Why a published series can move when the economy has not

A trend is a sustained change in the thing being measured — prices actually rising faster, firms actually hiring more.
Some movements in a published series are produced by how the number is built, not by anything happening in the economy.
Extrapolating one of those movements produces a confident forecast of something that was never happening. So a movement has to be tested before it is treated as a trend.
Four things make a series move without the economy changing: a base effect, a seasonal pattern, a denominator change and a composition change. A fifth — a definitional break — makes a series jump for purely administrative reasons.

Base effects — the annual rate moves because of what happened a year ago

An annual percentage change compares the latest period with the same period a year earlier:

$\text{annual \% change} = \frac{\text{value now} - \text{value 12 months ago}}{\text{value 12 months ago}} \times 100$

So it moves for two reasons, not one:
- the latest figure changed, or
- the figure it is being compared against dropped out of the comparison.
A base effect is the second one. When an unusually large rise from a year ago leaves the twelve-month window, the annual rate falls — even if prices are rising at exactly the same pace this quarter as last quarter.

Why it matters most for inflation

Annual CPI inflation falling from 6% to 3% can mean prices are rising half as fast, or it can mean a single large shock a year ago has washed out of the comparison while current price rises continue unchanged.
The two look identical on a graph of the annual rate, and completely different on a graph of the quarterly rate.
The check is always the same: put the quarterly change beside the annual change. If the quarterly change is steady while the annual rate falls, the fall is a base effect.

Seasonal movements — the same change happens every year

Many New Zealand series have a strong, entirely predictable seasonal pattern: unemployment falls every summer with the horticultural harvest and peak tourism; merchandise exports peak with the dairy and kiwifruit seasons.
A quarter-on-quarter change in an unadjusted series confuses the season with the trend.
Two ways to deal with it:
- use the seasonally adjusted series, which has the recurring pattern removed, or
- compare with the same quarter a year earlier, which compares like with like — but this reintroduces the base-effect problem above.
Say which you have used. They answer different questions and can point in different directions in the same quarter.

Denominator changes — a rate moves because of what it is divided by

Every rate is a fraction, so it moves when the bottom changes, not only the top.
The unemployment rate is the unemployed divided by the labour force. Discouraged workers leave both, so their departure lowers the rate without anyone finding a job.
Real GDP per capita is real GDP divided by population. It can fall while real GDP rises, if population rises faster.
The check: whenever a rate moves, ask what happened to the number underneath it. For unemployment that number is total employment; for per-capita GDP it is real GDP itself.

Composition changes — the average moves although no individual did

An average moves when the mix of things being averaged changes, even if every individual value stays the same.
The average wage rises if low-paid jobs disappear and high-paid jobs remain, even though no worker received a pay rise. The average of the survivors is higher because the bottom of the distribution was removed.
The same happens to average export prices when a low-value product stops being exported, and to average house prices when sales shift toward a more expensive suburb.
The check: use the median as well as the mean, or break the series down by type — product, region, industry — and see whether each part moved or only the mix.

Definitional breaks, rebasing and revisions

A definitional change is not an economic event. If the CPI basket is re-weighted, the HLFS definition is amended or an index is rebased to a new year, the series can jump for administrative reasons alone.
Revisions. GDP and trade figures are published as provisional estimates and revised as more complete returns arrive. A trend built on the first estimate of the most recent quarter can reverse when that quarter is revised.
What to do about both:
- state where the break falls, and never calculate a percentage change across it
- say when a figure is provisional, and give the most weight to periods that have been revised

The five checks before calling a movement a trend

The comparison period — is the annual rate moving because of the latest figure, or because of the one a year ago? Put the quarterly change beside it.
The season — is the series seasonally adjusted, and does the comparison compare like with like?
The denominator — for any rate, what happened to the number underneath?
The composition — for any average, did the values move or did the mix?
The break — has the definition, the weighting or the base year changed, and is the latest figure provisional?

Tips and Tricks

Falling annual inflation does not mean prices are falling. It means prices are rising more slowly than they were a year ago. Prices are falling only when the index itself goes down, which is deflation and is rare. Writing "prices fell" when the annual rate fell from 6% to 3% is the most common wording error in this topic.

Never extrapolate an annual rate without looking at the quarterly one first. If the fall in the annual rate is a base effect, the annual rate will stop falling the moment the large figures have finished washing out — so a forecast that projects the fall onward will be badly wrong within two quarters.

A rate and a number can move in opposite directions, and both be correct. The unemployment rate can fall while the number of people employed also falls. Quote both, and say which one answers the question you asked.

Label a definitional break on the figure itself. A vertical line and a note is enough. A percentage change calculated across a break is not a result, and a reader cannot tell that you knew unless you say so.

Worked ExampleIs the fall in inflation real?

A price index is published quarterly. ⚠️ Invented data, for method only.

Quarter	Price index
Q1	100.0
Q2	103.0
Q3	104.0
Q4	104.5
Q5	105.0
Q6	105.5
Q7	106.0
Q8	106.5

A student reports that annual inflation has fallen sharply and forecasts that it will keep falling.

(a) Calculate the annual inflation rate at Q5, Q6, Q7 and Q8. (b) Calculate the quarterly inflation rate over the same quarters. (c) Say what is actually happening, and what is wrong with the forecast.

Step 1 — (a) Annual inflation: compare each quarter with the same quarter a year earlier

Four quarters back, so Q5 is compared with Q1, Q6 with Q2, and so on.

$\text{Q5}: \frac{105.0 - 100.0}{100.0} \times 100 = 5.00\%$

$\text{Q6}: \frac{105.5 - 103.0}{103.0} \times 100 = 2.43\%$

$\text{Q7}: \frac{106.0 - 104.0}{104.0} \times 100 = 1.92\%$

$\text{Q8}: \frac{106.5 - 104.5}{104.5} \times 100 = 1.91\%$

The annual rate has fallen from 5.00% to 1.91% in three quarters. On its own this looks like a dramatic slowdown.

Step 2 — (b) Quarterly inflation: compare each quarter with the one before it

$\text{Q5} \rightarrow \text{Q6}: \frac{105.5 - 105.0}{105.0} \times 100 = 0.476\%$

$\text{Q6} \rightarrow \text{Q7}: \frac{106.0 - 105.5}{105.5} \times 100 = 0.474\%$

$\text{Q7} \rightarrow \text{Q8}: \frac{106.5 - 106.0}{106.0} \times 100 = 0.472\%$

Prices are rising at almost exactly the same pace every quarter — about 0.47%. Nothing has slowed down at all.

Step 3 — (c) Find where the annual fall came from

Look at what left the comparison, not at what entered it.

The index rose 3.0 points between Q1 and Q2 — by far the largest single-quarter rise in the series. While that jump sat inside the twelve-month window it made the annual rate large. As soon as the comparison moved from Q5 against Q1 to Q6 against Q2, that jump dropped out, and the annual rate collapsed.

This is a base effect. The fall was caused by what happened a year ago, not by anything happening now.

Step 4 — Check the two figures are consistent

A steady 0.472% a quarter compounds over four quarters to:

$1.00472^4 = 1.0190 \Rightarrow 1.90\%$

Which matches the 1.91% annual rate at Q8. So the annual and quarterly figures are describing the same economy — the annual one just took a year to catch up with it.

Step 5 — What is wrong with the forecast

The student projected the annual rate onward, expecting it to keep falling toward zero.

But the annual rate fell because the large Q2 rise washed out, and it has now finished washing out. From Q8 onward the annual rate is simply four quarters of 0.47% added together, so it will flatten out at about 1.9%, not continue to zero.

The forecast extrapolated a movement that had already stopped happening.

Step 6 — What the student should report instead

$\text{annual rate} \downarrow \text{ with quarterly rate steady} \Rightarrow \text{base effect, not disinflation}$

Movements that are not trends

Covers AS91226

Why a published series can move when the economy has not

A trend is a sustained change in the thing being measured — prices actually rising faster, firms actually hiring more.
Some movements in a published series are produced by how the number is built, not by anything happening in the economy.
Extrapolating one of those movements produces a confident forecast of something that was never happening. So a movement has to be tested before it is treated as a trend.
Four things make a series move without the economy changing: a base effect, a seasonal pattern, a denominator change and a composition change. A fifth — a definitional break — makes a series jump for purely administrative reasons.

Base effects — the annual rate moves because of what happened a year ago

An annual percentage change compares the latest period with the same period a year earlier:

$\text{annual \% change} = \frac{\text{value now} - \text{value 12 months ago}}{\text{value 12 months ago}} \times 100$

So it moves for two reasons, not one:
- the latest figure changed, or
- the figure it is being compared against dropped out of the comparison.
A base effect is the second one. When an unusually large rise from a year ago leaves the twelve-month window, the annual rate falls — even if prices are rising at exactly the same pace this quarter as last quarter.

Why it matters most for inflation

Annual CPI inflation falling from 6% to 3% can mean prices are rising half as fast, or it can mean a single large shock a year ago has washed out of the comparison while current price rises continue unchanged.
The two look identical on a graph of the annual rate, and completely different on a graph of the quarterly rate.
The check is always the same: put the quarterly change beside the annual change. If the quarterly change is steady while the annual rate falls, the fall is a base effect.

Seasonal movements — the same change happens every year

Many New Zealand series have a strong, entirely predictable seasonal pattern: unemployment falls every summer with the horticultural harvest and peak tourism; merchandise exports peak with the dairy and kiwifruit seasons.
A quarter-on-quarter change in an unadjusted series confuses the season with the trend.
Two ways to deal with it:
- use the seasonally adjusted series, which has the recurring pattern removed, or
- compare with the same quarter a year earlier, which compares like with like — but this reintroduces the base-effect problem above.
Say which you have used. They answer different questions and can point in different directions in the same quarter.

Denominator changes — a rate moves because of what it is divided by

Every rate is a fraction, so it moves when the bottom changes, not only the top.
The unemployment rate is the unemployed divided by the labour force. Discouraged workers leave both, so their departure lowers the rate without anyone finding a job.
Real GDP per capita is real GDP divided by population. It can fall while real GDP rises, if population rises faster.
The check: whenever a rate moves, ask what happened to the number underneath it. For unemployment that number is total employment; for per-capita GDP it is real GDP itself.

Composition changes — the average moves although no individual did

An average moves when the mix of things being averaged changes, even if every individual value stays the same.
The average wage rises if low-paid jobs disappear and high-paid jobs remain, even though no worker received a pay rise. The average of the survivors is higher because the bottom of the distribution was removed.
The same happens to average export prices when a low-value product stops being exported, and to average house prices when sales shift toward a more expensive suburb.
The check: use the median as well as the mean, or break the series down by type — product, region, industry — and see whether each part moved or only the mix.

Definitional breaks, rebasing and revisions

A definitional change is not an economic event. If the CPI basket is re-weighted, the HLFS definition is amended or an index is rebased to a new year, the series can jump for administrative reasons alone.
Revisions. GDP and trade figures are published as provisional estimates and revised as more complete returns arrive. A trend built on the first estimate of the most recent quarter can reverse when that quarter is revised.
What to do about both:
- state where the break falls, and never calculate a percentage change across it
- say when a figure is provisional, and give the most weight to periods that have been revised

The five checks before calling a movement a trend

The comparison period — is the annual rate moving because of the latest figure, or because of the one a year ago? Put the quarterly change beside it.
The season — is the series seasonally adjusted, and does the comparison compare like with like?
The denominator — for any rate, what happened to the number underneath?
The composition — for any average, did the values move or did the mix?
The break — has the definition, the weighting or the base year changed, and is the latest figure provisional?

Tips and Tricks

Worked ExampleIs the fall in inflation real?

A price index is published quarterly. ⚠️ Invented data, for method only.

Quarter	Price index
Q1	100.0
Q2	103.0
Q3	104.0
Q4	104.5
Q5	105.0
Q6	105.5
Q7	106.0
Q8	106.5

A student reports that annual inflation has fallen sharply and forecasts that it will keep falling.

Step 1 — (a) Annual inflation: compare each quarter with the same quarter a year earlier

Four quarters back, so Q5 is compared with Q1, Q6 with Q2, and so on.

$\text{Q5}: \frac{105.0 - 100.0}{100.0} \times 100 = 5.00\%$

$\text{Q6}: \frac{105.5 - 103.0}{103.0} \times 100 = 2.43\%$

$\text{Q7}: \frac{106.0 - 104.0}{104.0} \times 100 = 1.92\%$

$\text{Q8}: \frac{106.5 - 104.5}{104.5} \times 100 = 1.91\%$

The annual rate has fallen from 5.00% to 1.91% in three quarters. On its own this looks like a dramatic slowdown.

Step 2 — (b) Quarterly inflation: compare each quarter with the one before it

$\text{Q5} \rightarrow \text{Q6}: \frac{105.5 - 105.0}{105.0} \times 100 = 0.476\%$

$\text{Q6} \rightarrow \text{Q7}: \frac{106.0 - 105.5}{105.5} \times 100 = 0.474\%$

$\text{Q7} \rightarrow \text{Q8}: \frac{106.5 - 106.0}{106.0} \times 100 = 0.472\%$

Prices are rising at almost exactly the same pace every quarter — about 0.47%. Nothing has slowed down at all.

Step 3 — (c) Find where the annual fall came from

Look at what left the comparison, not at what entered it.

This is a base effect. The fall was caused by what happened a year ago, not by anything happening now.

Step 4 — Check the two figures are consistent

A steady 0.472% a quarter compounds over four quarters to:

$1.00472^4 = 1.0190 \Rightarrow 1.90\%$

Which matches the 1.91% annual rate at Q8. So the annual and quarterly figures are describing the same economy — the annual one just took a year to catch up with it.

Step 5 — What is wrong with the forecast

The student projected the annual rate onward, expecting it to keep falling toward zero.

The forecast extrapolated a movement that had already stopped happening.

Step 6 — What the student should report instead

$\text{annual rate} \downarrow \text{ with quarterly rate steady} \Rightarrow \text{base effect, not disinflation}$