Growth Expectations: How Forecasts Are Formed and Revised

A growth forecast is a total assembled from an estimate for each part of an economy, then checked against what capacity would allow. A forecast gets revised for three separate reasons, and only two of them are news about the future. The third reason is a correction to the past data the forecast started from. The correction moves the published rate and leaves the expected future untouched.

Underneath that answer sits a fact of arithmetic almost nobody says out loud. A growth rate is not a quantity. A growth rate is a relationship between two quantities, the size of output before and the size of output after, and a relationship moves whenever either end of it moves. Everyone reading a forecast watches the far end, the year that has not happened. The near end, the year that already happened and is still being counted, moves more often and gets watched by nobody.

A growth forecastA stated expectation of what a measured quantity will turn out to be, built from data and reasoning that the forecaster can be asked to show. is put together part by part, gets revised for three separate reasons, and only two of those reasons carry information about the year ahead. The arithmetic that turns a correction to the past into a fall in the published rate is short, and it is the part most often misread. How well a forecast was made and whether it turned out right are two different questions, and only one of them can be answered on the day the forecast appears.

Every rupee amount below belongs to the Republic of Sankhya, a country invented for this lesson, and every one of them starts from its year 3 output level of Rs 17,47,200 crore.

How is a growth forecast actually built?

In two moves, and the second one is not what most readers assume it is. The first move is to estimate what each part of the economy will contribute and add the parts together. The second move is to hold that total up against what the economy has the capacity to produce and ask whether the answer is even possible. The capacity comparison is a check, not a derivation.

Work it on the Republic of Sankhya. A forecaster there is building an expectation for year 4 and takes the spending side of the economy apart into four parts. Households come out at Rs 10,54,000 crore. Businesses putting money into new plant and stock come out at Rs 5,26,000 crore. Government spending comes out at Rs 2,00,000 crore. Sales abroad less purchases from abroad come out at Rs 37,088 crore. The four added together come to Rs 18,17,088 crore, and that total is the forecast, stated as a level of output rather than as a rate.

Now the check, and it needs one definition first because the word capacity is doing a lot of work. Capacity here means the level of output an economy could reach using the people, equipment and know how already inside it, at a rate of work it could keep up. Two things follow, and the second one surprises people. First, that level is not counted the way output is counted. Nobody has ever observed a year in which everything ran at exactly that rate. A capacity figure is therefore always an estimate, and two careful people can put it in different places from the same evidence. Second, the forecaster takes the figure as given. The check works the same way wherever the figure sits. Sankhya capacity for year 4 is put at Rs 19,05,626 crore, the year 3 figure of Rs 17,97,760 crore carried forward at a steady 6.00 per cent and rounded to the nearest crore. The assembled total of Rs 18,17,088 crore sits Rs 88,538 crore below that, a gap of 4.65 per cent of capacity. The total is not asking the economy to do something it cannot do. The check passes. Notice what the check did and did not do: it told the forecaster that the total is possible, and it told the forecaster nothing whatever about whether any of the four component estimates is right. A total can clear the capacity test with every one of its parts wrong, because four errors that happen to offset each other produce a perfectly plausible sum.

What actually goes into one component estimate?

Three things, and they are worth separating because only one of them explains why two careful people looking at the same economy publish different numbers. A component estimateThe forecast for one part of a total, such as household spending or business investment, built on its own and then added into the whole. rests on recent data, on a relationship that has held in the past, and on a judgement about whether that relationship still holds.

Take the Sankhya household line of Rs 10,54,000 crore. The recent data is what household spending has actually been doing over the last several quarters. Anybody can pull it. The past relationship is the way household spending in that economy has moved alongside household income. The record is public too, and anyone who bothers can estimate it. Two forecasters starting from those two inputs alone would land in more or less the same place. Then comes the third input. Does that relationship still hold this year, in this economy, with whatever has been going on inside it? The third input is a judgement, it cannot be looked up, and it is where the two forecasters part company.

The third input is the one doing the real work and it is the one that never appears in the published number. A forecast arrives as a figure. The figure carries no marking to say how much of it came from data, how much from a fitted relationship and how much from somebody deciding that the relationship was about to bend. The invisibility of that third input is why the assumptionA condition a forecast takes as given rather than works out. Stating one lets a reader test the forecast against it later, and leaving it unstated makes the forecast untestable. list matters more than the headline, and why a forecast published without one is close to unreadable. Think of a shopkeeper working out what next month will bring. Last month sales are the data. Sales usually rise in the run up to a wedding season is the relationship. Whether that pattern holds this year, with a new market opening two streets away, is the judgement, and it is the only part of the estimate the shopkeeper could not defend by pointing at a ledger.

Why do forecasts get revised, and are all three reasons the same kind of news?

The three reasons are not the same kind of news, and running them together is the single most expensive habit a reader of forecasts can pick up. A revisionA change to a published number, either to a forecast of something still ahead or to an estimate of something already past. The word covers both, and the two get confused constantly. arrives from one of three places.

The first is that conditions changed. Something happened in the economy after the forecast was made, and the amount of output now expected is genuinely different. In Sankhya, picture a large standing export order placed with Sankhya producers being cancelled. Less will be produced than the forecaster previously thought, so the expected level itself comes down. A cancelled order is information about the year ahead.

The second is that the past data was revised. The starting level the forecast was built on was an estimate too, and a statistical office that receives fuller returns replaces its earlier estimate with a later one. Nothing about the year ahead has changed. The forecaster still expects exactly the same amount of output. But the published growth rate moves. A rate is measured from the starting level, and the starting level has just moved. Only the first and third reasons are news about the future, and the second is the commonest of the three.

The third is that the forecaster changed their mind. No new event and no new data: a relationship the forecast leaned on is judged to have stopped holding, and the component resting on it gets rebuilt. A rebuilt component is also information, of a quieter kind. The forecaster now reads the economy differently and has said so. A change of mind is the reason most likely to sit in a footnote and least likely to be reported anywhere.

Why does a revision to the past move a forecast about the future?

Because a growth rate is not a thing in itself. A rate is the distance between two levelsThe size of output itself, in rupees, at a point in time. A rate is worked out from two levels, so a rate can move when either level moves. expressed as a proportion of the earlier one, and it moves whenever either level moves. Moving the far one changes the view of the future. Moving the near one changes nothing except the ruler.

Work it on the Republic of Sankhya, one level at a time. Year 3 output was published at Rs 17,47,200 crore. A forecaster expects Rs 18,17,088 crore in year 4. The gap between the two is Rs 69,888 crore, and Rs 69,888 crore as a proportion of Rs 17,47,200 crore is 4.00 per cent exactly. So the forecast goes out as four per cent growth, and four per cent is what everybody quotes and remembers.

Some months later the statistical office replaces its year 3 estimate. Fuller returns have come in and year 3 output is now put at Rs 17,60,000 crore, Rs 12,800 crore higher than the first estimate. The forecaster looks at the year 4 work again and changes nothing at all: the four component estimates stand, the capacity check still passes, and the expected level for year 4 is still exactly Rs 18,17,088 crore. But the gap is now Rs 57,088 crore rather than Rs 69,888 crore, and Rs 57,088 crore as a proportion of Rs 17,60,000 crore is 3.24 per cent. The published forecast has fallen from 4.00 per cent to 3.24 per cent and not one thing about year 4 has changed. That fall is a base effectA change in a growth rate caused by movement in the earlier of the two levels it is measured between, rather than by anything happening in the later one., and it is the single most misread event in this whole area.

Here is the household version. A salaried worker tells a friend that this year's salary will be about eight per cent higher than last year's. Going back over last year turns up a bonus that had not been counted, so last year was larger than stated. The coming year's salary is exactly what it was always expected to be, rupee for rupee. The quoted rise drops to five per cent. Nothing about this year moved. The measurement simply started from a taller point.

What do all three revisions look like worked through on one set of levels?

Here is the whole worked instance in one place, and every rate in it can be recovered from the two levels sitting beside it. One Sankhya forecast, revised three times for the three different reasons, ending lower each time.

Check two of them yourself. Rs 18,17,088 crore divided by Rs 17,60,000 crore is 1.0324364, so 3.24 per cent after rounding. Rs 17,95,200 crore divided by Rs 17,60,000 crore is 1.02 exactly, so 2.00 per cent. Every one of the three revisions lowered the headline, and only the second and third of them altered what anybody expects Sankhya to produce in year 4. A reader watching only the rate saw a forecast fall from four per cent to one and a half and would describe the whole 2.50 point fall as a worsening outlook. Slightly over three tenths of that fall, the first 0.76 of a point, was the statistical office finishing its arithmetic on a year that had already ended.

Why do forecasters end up so close to each other?

Not usually because they all found the same evidence. There is a pull toward the middle of the range that operates on any forecaster whose name is attached to a published number, and it has nothing to do with what the data says.

The mechanism is an asymmetry in what it costs to be unusual. Suppose a forecaster publishes a number a long way from where everyone else is. If it turns out wrong, the forecaster is wrong alone, visibly, and everybody can see that standing apart was a choice. If it turns out right, there is some credit, but nothing like the mirror image of the damage. Suppose instead the forecaster publishes a number in the middle of the pack. If the middle turns out wrong, everybody is wrong together, and being wrong in company costs almost nothing at all: nobody could have seen it, the reasoning was widely shared, the same thing happened to everyone. The penalty for being wrong alone rises far faster with distance from the middle than the reward for being right alone does, and that gap is enough to pull published numbers together without any forecaster ever deciding to copy anyone.

One consequence is worth carrying away. When a consensusThe middle of a set of published forecasts, often quoted as though it were a single view. A consensus is an average of numbers, not an average of the reasoning behind them. shows estimates tightly bunched, the tightness is not evidence that the estimates are good. Tight bunching is also what a group of people who each know what the others published, and would rather not be conspicuous, would produce. A wide range at least says the underlying question is genuinely open, and openness is information. A narrow one may say the same thing about the evidence, or it may say nothing except that standing apart is uncomfortable. There is a version of this in a street of shops that all price a bag of rice within two rupees of each other. The narrow band may reflect a real cost structure the shops share, or it may reflect nobody wanting to be the odd one out, and the prices alone do not say which.

What is the difference between a forecast being wrong and a forecast being badly made?

Being wrong and being badly made are two separate questions, and treating them as one is what makes people distrust forecasting for the wrong reason. Hold them apart as two axes rather than as ends of a single scale.

The first axis is how the forecast was made. Were the assumptions stated? Was the reasoning shown? Did the components add up, and was the total checked for possibility? Was the judgement in it visible enough to argue with? How a forecast was made can be read the day it is published, by anybody, without waiting for anything.

The second axis is whether the forecast turned out right. Whether it turned out right cannot be read at publication at all. The year has not happened. And when it finally can be read, it arrives too late to help the person who had to use the forecast. The only axis a reader can actually assess at the moment a forecast is published is how it was built. The assumption list therefore matters more than the headline figure. The two axes really are independent. The future is not obliged to resemble the past, so a forecast can be honestly built, transparently assumed, carefully checked and still wrong. There are only so many plausible numbers, and luck distributes itself evenly, so a forecast can also be lazily built on a number somebody half remembered and turn out right. Being right by accident leaves nothing behind that anyone can reuse. There was no reasoning to inspect.

How should a forecast that has just been handed over be weighed?

With four questions, asked in this order, before the number is allowed to influence anything. Which assumptions did it state? Which conditions would have to hold for it to be right? Which events would make it wrong? And were any of those assumptions stated at all, or must they be guessed at?

The first three are answerable only if the fourth one is. A forecast that arrives as a bare figure offers nothing to test, nothing to disagree with and nothing to check against later. Whether it clears its own capacity check cannot be told. Which component carries the weight cannot be told. Whether it will move when the past data is next replaced cannot be told either, and the arithmetic above has already shown how large that movement can be. A forecast with no stated assumptions cannot be assessed at all and should be read as an opinion rather than as work, however precise the number sounds. Precision is not evidence of care: a figure quoted to two decimals is exactly as untestable as one quoted to none if nobody says what it rested on.

There is a fifth question worth adding for anything expressed as a rate, and it is the one most often skipped. Which two levels is this rate measured between, and how firm is the earlier of the two? If the starting level is still an early estimate that a statistical office may yet replace, then the rate has a moving part in it that has nothing to do with the year being forecast.

What does an analyst actually take away from a published forecast?

Not the number. The number is the part everybody quotes, and it will have moved by the time anybody acts on it. The useful part is the list of what it assumed.

Consider what that list actually is. Somebody who spends every working day on one economy has sat down and written out which questions they think are open, which relationships they think are load bearing, and which conditions they think the year turns on. The list is a map of the problem drawn by somebody with far more time on it than most readers have, and the map stays useful even if their number turns out to be nowhere near. An analyst covering companies in that economy takes the assumption list and asks a different question of it: which of these assumptions, if it broke, would show up in the specific line being modelled? A lender sizing whether a borrower can service what it has borrowed does the same thing from the other side, asking which of the stated conditions would hurt that borrower first. Neither of them needs the headline rate to be right. Both need to know what somebody serious thinks the questions are.

There is a second practitioner move, and it is defensive. When a published forecast changes, establish which of the three reasons produced it before touching anything downstream. A revision driven by a correction to the past data should change nothing at all in a model whose inputs are levels rather than rates, and a great deal of work gets redone every year for no reason because nobody asked which kind of revision had arrived. A household version: for a monthly budget kept in rupees rather than in percentages, a correction to last year's supposed earnings changes the commentary and not the budget.