Be wary of how you use statistics

18 Sep, 2020 - 00:09 0 Views

eBusiness Weekly

Economists like to measure and they can do this better and better all the time and cannot just measure raw data but rates of change in data and the rate of change.

This is both necessary in the modern economy and can be useful, but the usefulness varies. The principal problem arises when data, trends and the change in trends is used not just to describe what happens, and that is what good data collection and data organised into a sensible form does superbly well, but what will happen.

A very good example is Zimbabwe’s inflation statistics. Many use these to state that Zimbabwe “is” facing high inflation”, which is not what the data and the trend lines say. What they say is that Zimbabwe “had” high inflation.

Drawing predictions from past events and past trends can of course be done, but it normally requires other factors to stay constant, or almost constant. If there are any sudden or major discontinuities in these other factors then predictions can be difficult, especially if the wrong conclusion is drawn from the raw data.

Inflation in Zimbabwe is an excellent example of what can be done, and what cannot be done, when using data and trends.

The annual inflation rate tells us one thing, and one thing only. It tells us how the cost of living, and by implication the value of money, has risen in the last 12 months. So it is an important reality check. It allows everyone to compare their changes of income, or revenues, their profits and their spending against the same figures for the previous year, feed in the adjustment for change of value, and see what has changed in something closer to reality.

So if there is a 600 percent annual inflation rate recorded in August, anyone and any business can go back to August last year, multiply the income, expenditure and asset figures by seven (remembering that 600 percent is seven-fold) and compare to the same figures in August this year. They will at least get a far better idea of well they have been doing, or not doing.

There are, of course, many other factors. Inflation measures the averages, it does not measure the particular personal circumstances. If for example annual inflation is 100 percent but the rise in medication is 200 percent and half your income goes on medical bills, then your personal inflation is something closer to 150 percent, because you do not fall in the central band.

But that is all an annual inflation figure tells you unless there is a long term trend line, without major changes in other factors, as in fact Zimbabwe had for a decade until the local currency suddenly collapsed totally, ending hyperinflation in one day.

In other words annual inflation is useful for prediction if there it can be described mathematically with a continuous function, but not if there is a discontinuous function, and regrettably a lot of economic data is discontinuous, even when trend lines tend to appear.

We can get a better picture of the last 12 months by looking at the monthly inflation rates. Here we do get a sort of continuous function, monthly inflation rising, and the rate of rising accelerating, until suddenly the July and August figures appear and there is an obvious major discontinuity.

Now we need to be smarter. What caused that inflation. IT was obviously not growth in the money supply of Zimbabwe dollars, and not even much in the total of deposits denominated in US dollars in nostro accounts, keeping the two sets of deposits separate for the moment. Thus demand pull factors cannot be the cause.

So we now start mapping the exchange rate. We get something resembling the inflation curve when we use the black-market rate, but to get a closer match we have to start making assumptions of the proportion of official rate US dollars and black-market US dollars used in our import mix. The main assumption is that the proportion of black-market dollars started increasing dramatically from April.

Feeding in that correction factor and we find a far closer match, with pricing pegged to the black-market rate, as anecdotal evidence suggests, bringing in a near perfect match. So we now know that monthly inflation curve was caused by cost-push inflation built around the parallel exchange rate. This in a sense makes the monthly inflation rates of historical interest, since the up-to-date figures were the daily black-market rates.

Then at the end of June we get our discontinuity, the arrival of the Reserve Bank of Zimbabwe auction system. And from the beginning of July prices largely stable. So even the July monthly inflation rate is not measuring a trend; it combines that the last week or two of the appalling accelerating rises in June and the first two or three weeks of the auction era. ZimStat take their measurements mid-month.

The August figure shows another huge drop. But the exchange rate was still stabilising in July and there was some catching up, in fuel costs if nothing else, but other business interests were still moving forward. Comparing the inflation rate to the exchange rate, but now feeding in official auction rate data rather than parallel market rate data, and you once again get a better match.

Out there in the real world some goods and services follow a different path, since the auctions only supply the higher priority imports. But there has been remarkable stability in the black market as well recently so the gaps are small.

But that major discontinuity caused by the auction has now made the annual inflation rate far less useful. Mapping the monthly inflation rate, or the mapping the exchange rate that is actually used, shows a rising exponential function suddenly going almost flat. You need two completely different mathematical expressions, trend lines if you like, to describe that curve, and that makes the trend line from the middle of last year (or even earlier) to the middle of this year totally useless to describe what is happening now. You have to start over again.

Obviously annual inflation rates will fall as the jumps in a month last year fall off the edge and the stability in a month this year are added in. But this does not tell you very much at all.

It is useful in some cases to take an extreme thought experiment. If prices are dead steady for a year,, suddenly jump 10 fold in one month, and then go steady again, you will have a zero annual inflation suddenly jumping to 900 percent, and then remaining at 900 percent for another 11 months, even though prices are steady, and then in one month dropping to zero gain as the jump month falls out of the calculation. But to say for those 11 months that inflation is 900 percent is accurate, but totally useless.

And it is useless, except as a way of comparing monthly figures a year apart, because the monthly graph has a huge discontinuity.

This is why trend lines are only useful when measuring a continuous trend. They are useless when describing a discontinuity. To describe that you have to go back a step to the raw data

In other words, assuming that the exchange rate curve will now move moderately, and the fundamentals suggest it will, the annual inflation rate becomes a far less useful figure for the next 10 months.

It measures, in a very limited way, what happened over 12 months but it does not tell you what is happening now.

Of course economists now need to start plotting exchange rates, in both markets if they wish, from the end of June and as the monthly inflation figures appear plot those.

Obviously and sudden major changes in an exchange rate need to be examined. But there is no longer a simple overriding figure to use because of that sudden June-end discontinuity.

The annual inflation rate tries to combine two mismatched trend lines into a single figure. But that no longer describes what is happening, only to a limited extent what happened.

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