PMI vs IIP: Why Breadth and Volume Can Disagree

One of the two asks a set of firms whether conditions improved and counts the answers. The other counts what those firms actually produced and weights each by size. So one reads breadth and the other reads volume. When the firms improving are not the firms producing most, the two point opposite ways, and both readings are correct.

The difference between the two is not a difference in quality. The difference is in the weight each record hands a firm. A survey record gives every firm the same weight, whichever firm it happens to be. A volume record gives every firm the weight of what it actually made. Change nothing else at all, and those two rules can read the same period in opposite directions.

Every figure in this guide belongs to the Republic of Sankhya, an invented economy used here so that the arithmetic can be shown twice and checked by hand. Each figure carries the vintageThe version of a published figure at a particular moment. A release can be corrected later, and the earlier version stays on the record as what was known at the time. it was written at.

What does the Purchasing Managers' Index count?

Start with what the form asks. A purchasing managers' survey goes out to the same set of firms each period and asks each one a short list of questions with three boxes against every question: better than last period, about the same, or worse than last period. The form is filled in by a respondentThe person at a surveyed firm who actually fills in the form, usually someone who handles purchase orders and therefore sees a change in demand before the accounts do. who sits close to the ordering desk. Sitting that close to the orders is why the answers arrive early. The survey panelThe fixed set of firms a survey returns to every period, so that answers can be compared against the same firms rather than against a fresh crowd each time. stays the same from one period to the next, so the answers are comparable.

Then look at what is done with those answers. The answers are counted. The share of firms answering better, plus half the share answering no change, becomes a single number expressed per 100 firms, and 50.0 is the line at which the firms reporting better exactly balance the firms reporting worse. Above 50.0, more firms improved than worsened. Below 50.0, more worsened than improved. One number is the entire output of the exercise, and it stands for a count of answers.

Notice the question the form never asks: how much. A firm that produced one extra crate and a firm that produced ten thousand extra crates tick the same box. The quantity was never collected in the first place, so nothing downstream can tell them apart. The missing quantity is not a gap somebody forgot to close. Leaving quantity out is the construction, and it is why the survey is quick: a direction takes a second to report and a quantity takes a month to compile.

What does the Index of Industrial Production weigh?

Now the other record, built the opposite way round. An industrial volume index collects quantities. For each item on its list it takes what was produced this period, compares that with what was produced in an earlier base periodThe earlier period a figure is measured against. Its own size decides how large the per cent change looks, which is why two identical quantities can produce very different growth numbers., and then combines the items using a weight for each one, where the weight reflects how much of industrial output that item accounted for when the weights were set. The combination produces an index levelA number that means nothing on its own and only reads against its own earlier values, because it was set to a round figure in a chosen starting period., and the change in that level is a per cent change in volume.

Magnitude is what this record carries, and magnitude is the whole point of counting quantities. Because the quantities underneath were counted in units rather than described in words, the index can say that output rose 1.50 per cent, or fell 1.50 per cent, and mean it arithmetically. A large factory moves the index a great deal and a tiny one barely moves it, exactly in proportion to what each one made.

The volume index gives up reach in exchange for that magnitude. Industry is 22.00 per cent of output in the Sankhya figures used here, leaving 78.00 per cent of that invented economy outside the index altogether. Services, farms and everything else are simply not in it. A limit of scope is not a failing, in the same way a bathroom scale is not defective for declining to measure height. Quoting an industrial volume number as though it described activity in general overstates what was measured.

The everyday version of the pair is one street. Asking a hundred households whether their electricity bill went up and counting the hands establishes how widespread the increase was, and nothing about its size. Adding up the units on every bill instead, weighting each household by how much it draws, establishes how much total consumption moved, and nothing about how many households were affected. Same street, same month, two different questions.

What is the difference between counting firms and weighing output?

Here is the whole difference, and everything else follows from it. The survey gives every firm one vote. The volume index gives every firm a vote in proportion to what that firm makes.

A small firm and a large firm count equally in the count of answers, and nowhere near equally in the weighted volume. Take a hundred firms in which six of them make most of the output. The survey hears six voices out of a hundred from those six firms, no more. The volume index hears very little other than those six. Both records are looking at the same hundred firms over the same period, using the same underlying reality. The two records are running different ballots on it.

Once that is clear, a disagreement between the two stops being strange and starts being predictable. A disagreement needs exactly one condition to be true: the firms which moved are not the firms which produce. Nothing has to go wrong for it to happen. Nobody has to make an arithmetic error, no returns have to arrive late, and no seasonal adjustment has to misfire. Two ballots with different weights were never obliged to agree, and the surprise would be if they always did.

The everyday version is a housing society with a hundred flats voting on repainting the building. One vote per flat gives one result. One vote per square foot of flat gives another. Neither ballot is rigged, and neither is counted wrongly. If the small flats want paint and the large ones do not, the two results point opposite ways, and the pair of results shows something a single result never could: that the wish for paint is widespread and concentrated in the small flats.

Why can the two point opposite ways at the same time?

Worked through in numbers, twice, the mystery disappears. Every input below is published so that both readings can be recomputed by hand. One thing holds in particular in the second case: the two moves stay exactly where they were, at a gain of 2.00 per cent and a loss of 3.00 per cent, and the only quantities that swap are the output shares. The shares are therefore the single thing that could have flipped the sign.

Case one. Of the 100 firms in the Sankhya survey, 60 report better and 40 report worse. No firm reports no change, so the count reads 60.0 per 100 firms, above the 50.0 line. Now bring in the shares. The 60 improving firms carry 30.00 per cent of Sankhya output between them, and each one gains 2.00 per cent. Multiply 0.30 by 2.00 and their whole contribution is 0.60 per cent. The 40 worsening firms carry the remaining 70.00 per cent, and each one loses 3.00 per cent. Multiply 0.70 by minus 3.00 and their contribution is minus 2.10 per cent. Set the two contributions against each other, 0.60 per cent against 2.10 per cent, and what is left is minus 1.50 per cent. More firms improved than worsened, and output still fell.

Case two. Swap the two output shares and leave everything else untouched. Of the same 100 firms, 40 now report better and 60 report worse, so the count reads 40.0 per 100 firms, below the line. But this time the 40 improving firms carry 70.00 per cent of Sankhya output between them, and each still gains 2.00 per cent, so multiplying 0.70 by 2.00 makes their contribution 1.40 per cent. The 60 worsening firms carry 30.00 per cent, and each still loses 3.00 per cent, so 0.30 times minus 3.00 makes their contribution minus 0.90 per cent. Set the two against each other and the change comes out at plus 0.50 per cent. Fewer firms improved than worsened, and output still rose.

Neither reading is wrong in either case. The count is a correct count of answers and the weighted change is a correct weighted change in quantities. Each is exactly right about the thing it measures, and each is silent about the other thing. Look at what the pair delivers that neither figure delivers alone. Every firm moved by the same amount in both cases, so nothing about the depth of the movement changed between them. The change between the two cases is where the output sat: wide improvement in firms that make little, then narrow improvement in firms that make most. Concentration is what that difference describes, and the description exists only because the two records are free to disagree.

Invented Sankhya figures, vintage as written here. Only two rows differ between the columns, and both are shares. Multiplying each share by its move and adding the two products recovers either total.

Which of the two should be used, and for what?

The choice between the two turns on the question being asked rather than on preference. To establish how widely something is happening across firms, the count of answers is the record built to say so. The weighted volume never records how many firms moved, so it cannot say at all. To establish how much of the thing there is, the weighted volume is the record built to say so. The count of answers never records size, so it cannot say either.

Asking either record the other one's question produces a confident wrong answer, and a confident wrong answer is worse than no answer at all. A wrong answer with a decimal point on it gets written into a note and quoted onward. Reading a count of 60.0 as evidence that a lot more was produced invents a magnitude that was never collected. Reading a weighted fall of 1.50 per cent as evidence that most firms are having a worse time invents a headcount that was never collected either.

The everyday version: a school reports that 60 of its 100 students improved their marks, and separately that the total marks scored by the school fell. How many pupils improved is answered by the first number. The second number answers what happened to the school total. Put the second question to the first number and it returns something that sounds like an answer and is not one.

How are the two read together?

Put the two side by side and there are four combinations, no more. The count sits above or below 50.0, and the weighted volume is up or down. Each combination has a plain reading, and the plain reading is a sentence about firms and output rather than a verdict about the economy.

When both point the same way, the pair adds very little to either figure alone: many firms improving and more produced, or many firms worsening and less produced. The distribution is unremarkable, in the sense that the firms moving are roughly the firms producing.

The two mixed combinations are the informative ones. Each of them describes the distribution of what is happening, and neither figure carries a distribution on its own. A count above 50.0 with volume down says improvement is wide and sits in firms that make little. A count below 50.0 with volume up says improvement is narrow and sits in firms that make a lot. Both sentences hold something no single reading can: a statement about which firms the movement is in.

Case one of the Sankhya figures lands in the third row, at 60.0 with a weighted change of minus 1.50 per cent. Case two lands in the fourth row, at 40.0 with a weighted change of plus 0.50 per cent.

What does neither of the two establish?

Both records describe a period that has already finished, and both stop at description. Neither says why anything moved. A count of answers records that 60 firms said better, and holds no reason; a weighted volume records that quantity fell 1.50 per cent, and holds no cause. The reason lives in orders, prices, weather, credit and a dozen other places, and finding it is a separate piece of work that starts after the reading arrives.

Neither says what happens next either. A reading is a measurement of the past, and treating it as a forecast is a step the number itself never authorises. A comparison against a consensusThe average of what forecasters expected before a release, used as the line a published figure gets compared against. It moves independently of the figure itself. or a later revisionA corrected version of a figure published after the first one, issued when late returns arrive. The first version stays on the record as what was known at the time. is a different exercise again, with its own traps.

And two readings on a fifth of the economy are still two readings on a fifth of the economy. In the Sankhya figures used here, industry is 22.00 per cent of output, and neither record reaches into the other 78.00 per cent with any depth. Services barely appear in an industrial volume index, and a purchasing managers' survey that covers them is a separate survey with its own set of firms. Neither record is an aggregateAn economy wide total built by adding up the smaller parts, such as the output of every sector rather than one of them. for the whole economy, and neither claims to be.

What does an analyst do with a disagreement between the two?

The habit worth taking is a small one, and it changes what a divergence is for. An analyst who sees the count above 50.0 while the weighted volume is down does not treat that as a contradiction needing to be settled. The analyst treats it as a statement about concentration, and then goes looking for the concentration.

A divergence says the firms which moved are not the firms which produce, and that is a finding rather than a problem. The next questions are practical ones. Which items or industries hold the large weights in the volume index? Did those specific items move in the same direction as the survey answers? If the wide improvement is real and sits in small firms, then a later period in which the large firms turn as well would show the volume figure catching up, and if the large firms never turn, the wide improvement stays invisible in output for as long as that lasts.

A lender reads the pair the same way for a different purpose. Wide improvement across many small borrowers with total output falling tells a lending desk something about which of its borrowers are moving, and it is a different piece of information from either number alone. A household version: if most shops on a street report a better month while the one large showroom that generates most of the street's takings reports a worse one, the street's total takings can fall while most shopkeepers are more cheerful. Both statements are true, and either one alone is misleading.