CPI, WPI and the GDP Deflator Compared: Four Honest Readings

Each one prices a different set of transactions for a different set of buyers. The consumer price index (CPI) follows a household's fixed basket at the shop counter. The wholesale price index (WPI) follows goods changing hands before retail and holds no services whatsoever. The gross domestic product (GDP) deflator follows whatever the economy produced, fixed to nothing. For one Sankhya year they read 6.70, 4.62 and 5.00 per cent, and none is wrong.

The disagreement is stranger than it first looks. Three counters, one country, one twelve month stretch, and three answers to what looks like the same question. Nobody miscounted. Nobody is running a different economy. The three numbers differ because the question each measure was built to answer differs, and once the three baskets are laid out side by side the disagreement stops looking like a scandal and starts looking like arithmetic doing exactly what it was told.

A price is settled between one buyer and one seller. A price index is an attempt to say what happened to a great many of those settlements at once. The arithmetic of a consumer basket is set out under consumer basket construction, and what pushed those prices up in the first place is set out under the causes of inflation. Each of the three is worth building on its own terms before any of them are set beside the others, because the gap between the readings turns out to be nothing but the difference in what each one prices.

Every weight, price movement and reading below belongs to the Republic of Sankhya, a teaching invention. The figures were chosen so the sums close exactly. A working statistical system never behaves that way. Its groups are sampled, its weights are estimated, and its totals carry a residual nobody can remove.

What is a consumer price index actually pricing, and whose household is it describing?

Start with the simplest of the three and build it properly before either of the others is mentioned. A consumer price index takes a fixed list of things a household buys, attaches a share of total spending to each one, prices them all at the counter where a household actually pays, and repeats the exercise period after period. The list is the basketThe fixed list of items an index prices again and again. Only the prices are allowed to move, so one period can be compared with another.. The share attached to each item is its weightThe proportion of total spending assigned to one item or group. A price movement on it enters the total in proportion to how much of it gets bought.. The price is a retailThe last step in the chain, where a household hands money over for its own use. A retail price includes the transport, storage and shopkeeper margin stacked on top of what the producer received. price. It carries the transport, the storage and the shopkeeper's margin, not just what the producer got paid.

A single household month comes before a country. If rice, dal and vegetables take four rupees in every ten that leaves a household, then a twelve per cent rise in food prices is not a small annoyance to be absorbed, it is the single biggest thing that happened to that money this year. A household on a much larger income in the same street, where food takes two rupees in ten and the rest goes on school fees, a phone plan, fuel for a car and an insurance premium, meets the same twelve per cent, and the two households experience completely different years. A consumer index has to pick one set of shares for everybody, and the moment it picks, it has decided whose year it is describing.

The Sankhya consumer basket carries three groups. Food holds 40 per cent of the weight and its prices rose 12.0 per cent. Energy holds 10 per cent and rose 9.0 per cent. Everything else, the group usually called core, holds the remaining 50 per cent and rose 2.0 per cent. Multiply each weight by each price movement and add the three results and the basket reads 6.70 per cent. Strip out the food and energy groups and price only the core, and the same basket reads 2.00 per cent. Both numbers came out of the same collection exercise on the same day.

The weights are not a technical detail sitting underneath the index. They state whose household is being described, and that makes them the whole design decision. Hold the three price movements completely still and change only the shares, and the reading moves anyway. A Sankhya household spending 55 per cent on food reads 8.20 per cent. One spending 25 per cent on food reads 5.20 per cent. The spread between those two readings is 3.00 points, produced by nothing except who is being described. Every price in the country is identical across all three cases. A basket built for the middle of a distribution will describe the top and the bottom of it badly, however carefully the prices in it were collected.

What sits inside the wholesale measure, and what does it leave out entirely?

Put the consumer basket down completely. The wholesale measure is not a variation on it but a separate instrument built for a separate buyer. Goods are priced at the point where they change hands in bulk, before anybody has carried them to a shop, put them on a shelf or added a counter margin. The buyer it describes is a producer or a trader further back in the chain. The price recorded is the one that buyer actually pays, the factory gate price or the mandi price rather than the shelf price.

The Sankhya wholesale basket carries three groups and its own weights, and neither the groups nor the weights match the consumer basket. Primary articles, the group covering farm output and raw material, hold 22 per cent. Fuel holds 15 per cent. Manufactured goods hold the remaining 63 per cent. No group in either basket is heavier. Something has already happened in that distribution. Food related prices carry 40 per cent of the consumer basket and 22 per cent of the wholesale one, so the identical farm price movement enters the two measures with almost half the force in the second.

Then comes the part that surprises most readers the first time. The wholesale measure contains no servicesOutput that cannot be stacked in a warehouse: a haircut, a bus ride, a school term, a doctor consultation, a phone connection. A haircut is produced and consumed in the same moment, so it never changes hands in bulk. at all. Not a reduced weight for services, not a partial sample of them. None. No haircut, no bus fare, no school fee, no rent, no doctor's consultation and no phone plan enters it anywhere. A service is produced and consumed at the same moment and never travels through a wholesale stage, so there is no bulk transaction for a wholesale collector to observe. The absence of services is a narrow question being asked deliberately rather than a gap somebody forgot to close, and it stops being harmless the moment services become a large share of what people actually buy.

Leaving services out explains most of what the wholesale reading does. In the Sankhya year, manufactured goods rose only 1.0 per cent while the household core rose 2.0 per cent, and the difference between those two is largely the retail margin and the services buried in the household core. So the wholesale basket puts its heaviest weight, 63 per cent, on the calmest prices in the country. The wholesale measure therefore reads low, and it will keep reading low in any year where factory gate goods are quiet, whatever is happening in a barber's shop or a school office.

Why does the GDP deflator have no basket at all?

Put both baskets down now. The third measure is not built the way either of them is built. There is no list of items, no set of shares and no price collector standing in a shop or at a factory gate. The deflator is a ratio. Take everything the economy produced in a year and value it at that year's prices. Then take the same output and value it at the prices of a base yearThe year an index is set equal to 100. Every later reading states how much prices have moved since then. Choosing a different base year changes every printed level without changing a single underlying price.. Divide the first by the second, multiply by a hundred, and that is the deflator for the year.

Read what that construction implies. The deflator is unlike either basket. The deflator's composition is whatever the economy actually made that year, in whatever proportions it happened to make them. If Sankhya built more cement and fewer bicycles this year than last, the deflator quietly reweights towards cement, and nobody chose that. There is no revision meeting, no decision about whose spending to describe, and no fixed list going stale. The measure simply inherits the shape of production.

Not holding anything fixed is the deflator's distinguishing feature and its central difficulty at the same time. A movement in it mixes prices changing with what the economy produced changing, and nothing inside the measure can separate the two. A basket index can promise that only prices moved, because everything else was nailed down by construction. The deflator can make no such promise. The deflator offers instead the kind of coverageWhich transactions a measure is built to observe. Wide coverage means few things are excluded; narrow coverage means the measure deliberately watches one slice of the economy. that neither basket comes close to: everything produced, priced at whatever it fetched, with nothing left outside because it was not on a list somebody drew up years ago.

One consequence catches people out. Because the deflator is built from output, it prices what the economy makes rather than what its households buy. Things Sankhya produces and sells abroad are inside it. Things Sankhya households buy that were made elsewhere are not. A consumer index takes the exact opposite view of both. Neither view is a mistake, and a reader who assumes the two are approximations of one another will keep being surprised by the gap between them.

How do the three measures line up once each one is built?

All three are now built, each on its own terms, so they can finally be put beside one another. A reading is only interpretable once four questions have been answered, and all four are worth asking every time a price number turns up. Whose prices are these? Which items are being priced? Is the list held still? And what question was the instrument built to answer?

On the first, the consumer measure asks about a household at the counter, the wholesale measure asks about a buyer of goods in bulk before retail, and the deflator asks about everybody at once because it covers everything produced. On the second, the consumer basket carries goods and services both, the wholesale basket carries goods only, and the deflator carries whatever got made. On the third, both baskets are held still until somebody revises them. The deflator holds nothing still, ever. Each measure was built to answer a different question. The right one therefore depends entirely on whose prices are being asked about, not on which instrument is the most accurate.

The instinct to rank the three is very strong, so the point deserves saying plainly. There is no ranking. The wholesale measure is not a crude version of the consumer measure, and the deflator is not a superior version of either. Asking which is most accurate is like asking whether a kitchen scale is more accurate than a bathroom scale. Both are accurate. The two scales weigh different things, and using one where the other belongs gives a wrong answer that looks perfectly reasonable written down.

What does the wholesale reading look like built step by step from its own basket?

Most treatments print the wholesale number, print the consumer number, note that they differ and move on. The impression left is that the two measures drifted apart for some accidental reason nobody can quite name. Nothing accidental happened. Every point of separation is put there by weights that can be read off directly, and the only way to believe that is to watch the wholesale reading assemble itself.

Take the three Sankhya wholesale groups in turn. Primary articles hold 22 per cent of the basket and their prices rose 12.0 per cent, so they push the reading up by 0.22 times 12.0, or 2.64 points. Fuel holds 15 per cent and rose 9.0 per cent, adding 0.15 times 9.0, or 1.35 points, for a running total of 3.99. Manufactured goods hold 63 per cent and rose 1.0 per cent, adding 0.63 times 1.0, or 0.63 points. Add the three contributions and the wholesale measure reads 4.62 per cent for the year.

Look at which group did the least work. The group holding almost two thirds of the basket contributed 0.63 points out of 4.62, and a group holding under a quarter of it contributed 2.64. That is not a flaw in the measure and nobody weighted it badly. A basket does exactly this when its heaviest group is sitting on the calmest prices in the country. Run the same three price movements through the consumer weights instead and the answer changes completely. There the heavy weight sits on food.

Set the consumer basket out the same way and the contrast is immediate. Same country, same twelve months, same collectors going out on the same mornings.

Food alone contributes 4.80 points to the consumer headline. Food's contribution alone is larger than the entire distance between the highest and the lowest of the four readings. The wholesale basket takes the identical 12.0 per cent farm price movement and weights it at 22 per cent instead of 40, converting it into 2.64 points rather than 4.80. Nothing else needs to happen for the two measures to separate by two full points.

Where did the Sankhya deflator reading of 5.00 per cent come from?

A reading that appears from nowhere is a reading that cannot be checked, so this one is worth tracing. The deflator figure used here was not assumed and it was not chosen to make a point. The figure was already sitting in the Sankhya output figures before any of these baskets existed, and it comes out of them by division.

Sankhya's output was measured twice in each of two years. In year 2, output valued at that year's prices came to Rs 17,64,000 crore while the same output valued at base year prices came to Rs 16,80,000 crore. Divide the first by the second and multiply by a hundred and the deflator for year 2 is 105.00. In year 3 the same pair of valuations gave Rs 19,26,288 crore and Rs 17,47,200 crore, so the deflator is 110.25. The price movement between those two years is 110.25 against 105.00, a rise of exactly 5.00 per cent.

The deflator reading is therefore not a fourth assumption sitting beside three baskets, it is the price level that the output figures already implied, and the fact that it lands on a clean 5.00 per cent is a property of those figures rather than a convenience. That is also why no slider in the calculator can move it. Nothing in either basket feeds it. For the deflator to change, the economy has to produce something different or sell it at a different price, and neither of those is a weight anybody sets.

How can four honest readings of one year disagree by 4.70 points?

Now put all four on one line. For the same Sankhya year, the consumer headline reads 6.70 per cent, the deflator reads 5.00, the wholesale measure reads 4.62 and the consumer core reads 2.00. The distance from the top of that list to the bottom is 4.70 points. The 4.70 points is not a rounding disagreement or a sampling wobble. The spread is larger than most of the individual readings themselves.

Account for the gap one contribution at a time and it stops being mysterious. Food holds 40 per cent of the consumer basket and rose 12.0 per cent, so that one line alone contributes 4.80 points and the headline sits highest. The consumer core removes food and energy entirely and prices only the group that rose 2.0 per cent, so it sits lowest. The wholesale measure sits low because the group holding 63 per cent of its basket rose only 1.0 per cent, and because it never sees a service or a retail margin. The deflator sits in the middle because it covers everything the economy made and is dragged neither by the food weight of a household basket nor by the manufactured weight of a wholesale one.

Every one of those four numbers is defensible and none of them is wrong. The entire 4.70 point spread is produced by what sits in each basket and whose prices they are, not by anybody measuring badly. When two people quoting inflation figures disagree by two points, the first question is almost never who made an error. The question that pays is which measure each one is holding.

Which measure fits which question?

Because none of the three ranks above the others, the choice is decided entirely by whose prices the question is about. Three cases cover almost everything a reader will meet. If the question is what has happened to the cost of running a household, whether that is a pension being reviewed, a wage discussion or a personal budget, the consumer measure is the one built for it, and it alone prices at the counter where a household actually pays. If the question is what has happened to the cost of the goods a producer buys, the wholesale measure is the one built for it, and it prices at exactly the stage where those goods change hands. And if the question is how to convert an output series from nominal to real, the deflator is the one built for it. The deflator was derived from that same output, and nothing else will divide out cleanly.

The third case is worth a sentence more. Deflating an output series with the deflator undoes the price movement that the output figures themselves contained. Any other index was built on a different set of transactions, so it will leave a residue. The result will look as though it worked. The number will be plausible and nothing will fail to calculate.

All three numbers are called inflation and all three come with a per cent sign attached, so reaching for the wrong measure is both the most common error in this area and an almost invisible one. Nobody announces that they have swapped one for another. The chart still draws, the ratio still divides, and the answer is quietly wrong by whatever the gap between the two measures happened to be that year. In the Sankhya year that gap was 2.08 points between the consumer headline and the wholesale reading.

Is there any clean answer to the fixed basket problem?

No, and it is worth being honest about that rather than presenting one option as the sensible one. Both baskets are held still on purpose. Holding the list fixed is exactly what allows this year to be compared with last year: if only the prices are permitted to move, then a movement in the index is a movement in prices and nothing else. A basket index promises exactly that, and the promise is a real one.

The trouble is that households do not hold still. Set a basket today and in ten years it describes spending that has quietly stopped happening. Items whose share has halved are still carrying their original weight. Items that households have since started buying in quantity are not on the list at all, so their prices are invisible to the index no matter how hard they move. The index is now measuring a household that no longer exists, with complete internal consistency.

The obvious repair is rebasingResetting an index to a new base year, usually with refreshed weights and a refreshed list of items. Later readings then describe current spending rather than spending from years ago.: refresh the weights, add what people now buy, drop what they no longer do. Rebasing fixes the staleness and immediately creates a different problem. Every comparison spanning the revision is now a comparison between two different lists, so a change read across that join mixes a price movement with a change in what was being priced. The series is more relevant afterwards and less continuous through the middle.

No version of this is simply correct, so the practical instruction is not to pick a side. A basket's last revision date is exactly where the two problems trade places, so establish that date before comparing an index across a long stretch. A five year comparison inside one basket is measuring prices. A twenty year comparison across two revisions is measuring something more complicated, and it is worth knowing which of the two is happening before the sentence gets written.

Why does an analyst check which measure a contract is indexed to?

Everything above has been about reading a number. A contract clause is about a number that moves money. There the difference between the measures stops being a matter of interpretation. Long contracts frequently carry an indexationA clause tying a payment to a published index, so the amount payable rises or falls automatically with that index instead of being renegotiated each period. clause: a supply agreement whose prices step up with a wholesale index, a wage agreement whose pay steps up with a consumer index, a rent whose escalation follows a published series. In a calm year the three land within a few tenths of one another, so nobody in the room usually thinks of them as different.

Take a Sankhya manufacturer with an input bill of Rs 4,00,00,000/- indexed to the wholesale measure and a wage bill of Rs 2,00,00,000/- indexed to the consumer measure. In the Sankhya year the input line steps up by 4.62 per cent, or Rs 18,48,000/-, and the wage line steps up by 6.70 per cent, or Rs 13,40,000/-. Total uplift, Rs 31,88,000/-. Had the input line been written against the consumer measure instead, as a drafter working at speed might easily have done because it is the familiar one, it would have stepped up by Rs 26,80,000/- rather than Rs 18,48,000/-, a difference of Rs 8,32,000/- on that line alone.

The measures separate when food and fuel move hard, and those are the years a business is already under cost pressure. Two contracts indexed to two different measures therefore diverge most in exactly the years when the divergence hurts most. That is the practical reason an analyst reads the indexation clause rather than assuming it: not because the wrong index was chosen dishonestly, but because in the quiet years nobody found out it mattered. A lender modelling covenant headroom, an investor modelling margin and a household signing a rent escalation are all in the same position. Which series the clause names is the first question. What that series is built from is the second, and only the second says how the clause behaves in a bad year.