Purchasing Managers' Index: The Fastest Read on Activity

A purchasing managers' index asks a standing set of firms one question: compared with the period before, is activity higher, the same or lower. The index reports the proportion answering higher, with the same counted half. Asking is faster than counting, so the reading arrives first. The count measures breadth rather than size, so a reader who treats it as a growth rate has read a count as a quantity.

Two ideas already settled do the work below. One of them is that any indicator is a thing somebody built, so four questions decide what it is worth: what gets counted, whose answers get counted, how those answers are weighted, and how quickly the result appears. A purchasing managers' index gives an unusual set of answers to those four, and every difficulty below comes out of one of them.

The other is a volume indexA measure built by counting quantities that were actually produced and weighting each of them by how much of the total it accounts for. Nobody is asked anything; the quantities are collected., built by counting quantities rather than by asking anybody anything. A number that was asked for and a number that was counted answer two different questions. The volume index stands on the other side of every comparison below.

Everything new here fits into a single line, and that line then does the lifting for everything that follows. A purchasing managers' index is a count of firms, and a count of firms carries no information about size at all.

What does a purchasing managers' index actually ask a firm?

Picture the form. Copies go to a panelThe set of firms a survey puts its questions to, chosen once and then asked the same thing period after period, so that the answers can be lined up against each other rather than compared across a changing group. of firms, and inside each firm the form reaches one named person who does the buying: the person who knows, without looking anything up, whether the place is busier than it was. On new orders, on production, on employment, on the prices being paid to suppliers, the form asks the same shape of question every time.

The shape of that question carries the whole guide, and it repays slow reading. Compared with the period before, is this higher, the same, or lower. Three answers exist, and the respondent picks one.

Notice what is missing. There is no box for how much. The respondentThe person at a firm who actually completes a survey form. Usually one individual, answering on behalf of the whole firm, and identified once so the same desk answers each period. is never asked to say that production rose 2.00 per cent, or fell 3.00 per cent, or moved by any amount whatever. A firm that doubled its output ticks the same box as a firm that scraped past last period by a hair, and once both ticks are in the pile there is nothing left to tell them apart.

No firm is asked by how much, so the index cannot contain that information however it is later processed. The point is worth sitting with, and it is not a limitation of any particular survey or any particular country. The limit is a fact about the data that goes in. Averaging, seasonally adjusting, smoothing, weighting, combining several questions into one headline: no operation performed on a pile of ticks can recover a quantity that was never written down.

The everyday version runs like this. A walk down a lane of ten shops, putting each shopkeeper a single question, is this month better than last month, returns ten answers, and those ten answers say something real. Nobody was ever asked for an amount, so the ten answers do not say whether the lane took more money. The shop with the largest turnoverThe total value of sales passing through a business over a period, counted before any cost is taken off it. A large turnover and a good month are different things. answered with exactly one word, the same as the smallest.

What is a diffusion index, and where does 50.0 come from?

A diffusion index is the arithmetic that turns a pile of ticks into one number, and it is simpler than its name. Count the firms answering higher. Count the firms answering the same and take half of that count. Add the two, divide by the number of firms who answered at all, and multiply by a hundred.

Worked on a panel of a hundred firms in the Republic of Sankhya, an invented economy carrying invented figures throughout: sixty firms answer higher, forty answer lower, none answers the same. Sixty plus half of nothing is sixty, over a hundred firms, times a hundred, and the reading is 60.0. Shifting the same panel: fifty-five answer higher, ten answer the same, thirty-five answer lower. Fifty-five plus five is sixty again, and the reading is 60.0 once more, from a different set of answers.

The second line shows why the half is there. A firm reporting no change is pulling in neither direction, so it is counted as standing exactly on the fence, and the effect is that a panel where nobody moves at all lands on 50.0.

Fifty is the boundary between more firms improving and more firms worsening, and that is the entire meaning of the number. Above 50.0, the higher answers outnumber the lower ones. Below 50.0, the lower answers outnumber the higher ones. At 50.0, the two counts balance.

Now the two things 50.0 is not. Between them they account for most of the mistakes made with this figure.

Fifty is not zero growth. Zero growth is a statement about a quantity, and no quantity was collected, so the reading cannot make that statement even in principle. A panel can sit exactly on 50.0 while output rises, and it can sit exactly on 50.0 while output falls, and both cases are worked further below.

Fifty is also not an average. Nothing was averaged: the reading is a headcount expressed out of a hundred. The distance from 50.0 is a distance in index pointsOne unit on the scale an index is expressed in. A point is not a per cent, and there is no conversion between the two: they are different kinds of quantity wearing similar clothes. and not in per cent of anything. A count and a quantity are not the same sort of thing, so reading the distance above 50.0 as a growth rate is an error of kind rather than of degree, and it is the commonest error made with this figure.

Why is an asked number ready before a counted one?

Because a question can be answered before a quantity can be counted, and the gap between those two things is measured in weeks of work rather than in minutes of effort.

Follow the short route first. A form goes out to a panel that already exists and already knows the questions. The person at each firm ticks one box for each item, from what they already know, without opening a ledger. The answers come back. Somebody counts the ticks. The counting is a headcount, so there is nothing to check, nothing to value, nothing to weight and nothing to reconcile against anything else. The reading exists.

Now the long route. Quantities have to be collected from establishments, and a quantity has to be defined before it can be reported, checked after it is reported, converted into a common unit, weighted by how much of the total each item accounts for, and aggregated. Every one of those steps is a place where a return arrives late or arrives wrong and has to be chased.

Speed is bought with precision, and the purchase is made at the moment the form asks for a direction instead of a number. The survey reading is available early precisely because it refused to collect the quantity that takes time to collect. None of that is a criticism. The refusal is the design, working.

What does a reading of 60.0 tell the analyst, and what does it not?

The reading states one thing precisely. Sixty per cent of the firms that answered reported improvement, once the fence-sitters are counted half. Breadth of that kind is a real, checkable, useful fact, and no other release delivers it as quickly.

The list of things the reading does not state is longer, and it matters more.

A reading of 60.0 does not mean output rose 60.00 per cent. The reading does not mean output rose 10.00 per cent. The more sophisticated version of the same error treats the ten points above 50.0 as if points converted into per cent. Nothing on the form asked about a per cent, so the reading does not mean output rose by any per cent at all.

The reading also says nothing about the size of the improvement at any single firm. Sixty firms reported higher. One of them may have added a shift; another may have sold three more units than last period and ticked the same box. The reading cannot separate those two firms and was never built to.

A reading of 60.0 is a statement about how many, not about how much, and the two are different questions with different answers. With that line held, everything that follows is arithmetic. Let it slip and the next section looks like a paradox instead.

Why can the reading rise while output falls?

Go back to the lane of ten shops, because the whole difficulty fits inside it and needs no economics at all.

Six of the ten shopkeepers report that this month was better. Four report that it was worse. Six out of ten is a reading of 60.0, comfortably above the boundary, and stopping there would leave the impression that the lane had a good month.

Now ask the question the form never asks. The six shops that improved are small: between them they turn over Rs 6,00,000/- a month. The four that worsened include the wholesaler at the corner, and between them those four turn over Rs 14,00,000/-. The lane turns over Rs 20,00,000/- in total, so the improving shops account for 30.00 per cent of it and the worsening shops for 70.00 per cent.

The six improving shops each did 2.00 per cent better, and on Rs 6,00,000/- that is Rs 12,000/- more. The four worsening shops each did 3.00 per cent worse, and on Rs 14,00,000/- that is Rs 42,000/- less. Take one from the other and the lane took Rs 30,000/- less than last month. On turnover of Rs 20,00,000/- that is a fall of 1.50 per cent.

Six of ten shopkeepers said better. The lane took less money. Both statements are true, neither is a mistake, and they disagree because one of them counted shopkeepers while the other weighed rupees.

Now the same shape at panel scale, on the hundred firms of Sankhya. Sixty firms report improvement, giving a reading of 60.0 against a boundary of 50.0. The sixty firms reporting improvement hold 30.00 per cent of the panel's output, and their output rose 2.00 per cent. The forty firms reporting worsening hold 70.00 per cent, and their output fell 3.00 per cent.

Weigh each group by the share of output it holds. The improving firms contribute 30.00 per cent of the total multiplied by their 2.00 per cent gain, giving plus 0.60 per cent. The worsening firms contribute 70.00 per cent multiplied by their 3.00 per cent fall, giving minus 2.10 per cent. Add the two and output changed by minus 1.50 per cent. Start the panel at 100.00 units of output and it finishes the period at 98.50.

More firms improved and output still fell, and neither figure is wrong: the diffusion reading counted firms while the weighted change weighed quantities. There is no reconciliation to perform. There is no contradiction to reconcile. Two measures asked two questions and each answered its own correctly.

Can the same panel produce the opposite disagreement?

The same panel can, and a reader who has only ever seen the case above will draw the wrong lesson from it. The wrong lesson is that a diffusion reading overstates. A diffusion reading does not overstate. The reading measures something else, and something else can land on either side.

Take the same lane and swap which shops had the good month. Now the four large shops, the ones turning over Rs 14,00,000/- between them, each do 2.00 per cent better, and that is Rs 28,000/- more. The six small shops, turning over Rs 6,00,000/- between them, each do 3.00 per cent worse, and that is Rs 18,000/- less. Four of ten saying better is a reading of 40.0, below the boundary. And the lane took Rs 10,000/- more, on turnover of Rs 20,00,000/-, a rise of 0.50 per cent.

At panel scale the arithmetic is the same. Forty firms report improvement, giving a reading of 40.0. The forty improving firms hold 70.00 per cent of output and gain 2.00 per cent, contributing plus 1.40 per cent. The sixty reporting worsening hold 30.00 per cent and fall 3.00 per cent, contributing minus 0.90 per cent. Output changed by plus 0.50 per cent, from 100.00 units to 100.50.

A reading below the boundary sat beside output rising, and that proves the reading is not a biased estimate of growth but a measurement of something different. The direction of the disagreement is set by which firms are the large ones. Size never entered the form, so no reading contains that information.

What does a diffusion reading leave out?

Three things, and they are worth naming separately because a reader who can name them can use the reading properly.

The reading leaves out size, the whole of the section above. Every firm in the panel counts once, whether it employs eight people or eight thousand, so the reading is a democracy of firms sitting on top of an economy that is nothing of the sort.

The reading leaves out everything happening to firms that are not in the panel. A panel is chosen and then kept, and keeping it is exactly what makes the answers comparable from period to period. The price is that a firm outside the panel can double or close and the reading will not notice.

The reading leaves out the difference between a small improvement and a large one, at the level of the single firm. The distinction was discarded at the moment the form offered three boxes, and once discarded it is not recoverable.

Discarding size is not a defect sitting alongside the speed; it is the same design decision that buys the speed. A firm asked for a direction answers today, from a person who did not have to look anything up. The same firm asked for a quantity has begun a process of collection and checking that the whole point of the survey was to skip. Removing the discard removes the speed with it. The limitation and the advantage cannot be traded off against each other: there is only one decision there, and both properties are on the same side of it.

How does an analyst actually use a count of directions?

As a count of directions, and never as anything else. An analyst covering a set of manufacturers has one question in front of them each period: is the change under way narrow or broad. A move confined to a handful of large plants and a move visible at most firms in the sector call for different follow-up work, and a diffusion reading answers that question earlier than anything else available.

The analyst never puts the reading into a sentence about magnitude. The reading goes into a note as breadth, and beside it goes a counted quantity, and only the pair together supports a sentence about how much moved. When the two point the same way, the note says the change is both broad and visible in quantities. When they point opposite ways, that disagreement is itself the finding. The movement is concentrated in firms of one size, and the analyst now knows which end of the size distribution to look at.

A lender looking at a manufacturing borrower reads it the same way, one step further out. Breadth tells the lender whether a borrower's difficulty is a firm-level problem or a sector-wide one, and that is a different question from how large the difficulty is. The professional use of a diffusion reading is as an early answer to a narrow question, held apart from the quantity question rather than substituted for it.

And the discipline that makes all of it work is the one this guide began with: ask what the reading counts. If it is a count of firms, it cannot answer a question about quantities, however early it arrives and however precise the decimal looks.

The Republic of Sankhya, its panel of a hundred firms and the ten shops in one lane are invented.
Educational material. Not advice on any investment, tax, budget or market position.