Paradox of predicting inflation

At an abstract, elemental level, inflation is the product of our ability to make contracts and deliver on promises. If we were a totally untrustworthy people, who never delivered on promises, we would not have inflation. Of course, we would also be crushingly poor and living in primitive conditions. But, if that is any comfort, there would be no inflation.

While we think of promises mostly in bilateral terms, the most important ‘economic' promise — one that has made modern civilisation possible — is the mysterious promise represented by money — the note in your wallet or the bank balance in your account, which in itself is of no value but is a record of work you did for which you are yet to redeem goods and services. Money is nothing but a generic promise from society — government being the most important representative of that — that you will be able to change these useless bits of paper for actual goods and services in the future.

Twin-tasking

Before turning to the subject of macro demand management, I want to draw the reader's attention to another intriguing problem with inflation management. There are agencies, in every nation, that are entrusted with the task of both forecasting inflation and trying to adopt policies that keep inflation under control. A nation's central bank tries to do this as does the Treasury or Ministry of Finance.

But this twin tasking gives rise to an intriguing conundrum, which is specific to the social and economic sciences and has few parallels in engineering and the natural sciences, even though Heisenberg's famous uncertainty principle could be thought of as a counterpart to this from the natural sciences.

Discussing the effort of Herbert Hoover, the US President, to boost confidence in the economy in the aftermath of the Great Crash of 1929, Ahamed (2009, p. 363) observes, “To some extent he was caught in a dilemma that all political leaders face when they pronounce upon the economic situation.

What they have to say about the economy affects its outcome — an analogue to Heisenberg's principle. As a consequence, they have little choice but to restrict themselves to making fatuously positive statements which should never be taken seriously as forecasts.”

This is an interesting observation, worth elaborating upon. I shall point out how, drawing on another mathematician-philosopher-scientist, L. E. J. Brouwer, we can rescue ourselves from Ahamed's trap of forecasts “never be taken seriously.”

It is widely believed and is arguably true that when a well-informed responsible government or quasi-government agency makes an inflation forecast that, in itself, can cause the course of inflation in the future to change. This is because, at least in the short run, the actual inflation rate depends, in part, on what people expect the inflation rate to be. Inflation can get worsened by the very fact of higher inflationary expectations and likewise prices can be stabilised, to a certain extent by virtue of leading people to expect that prices will be stable.

Thus, we often hear about how a policymaker stoked inflation by saying in public that inflation will go up.

Usually, behind such an observation is the critique that no one should be so irresponsible as to fuel inflation by making such statements. But this immediately places the central bank and the Treasury in a dilemma that Ahamed (2009) alludes to and may be logically impossible to resolve.

Treasury forecasts

To understand this, suppose that if no public forecast is made by the Treasury about future inflation, inflation will be 5 per cent per annum. This is shown by the horizontal line A'.

Now suppose, if the Treasury forecasts an inflation number, then this will influence human expectations and behaviour in such a way that actual inflation will turn out to be halfway between 10 per cent and what the Treasury forecasts.

This is shown in the Figure by the upward-sloping line, B. In this figure, the horizontal axis refers to the forecast made by the Treasury and the vertical axis the actual inflation.

For every inflation forecast of the Treasury, we can read off the actual inflation that will occur from line B. Let me, in brief, call all such graphs that plot the relation between forecasts and actual inflations as the “forecast function.” A more complex model with dynamic features would allow for adjustments to this forecast function based on the forecaster's past record of forecast accuracy. But I shall stay away from this here.

Forecast function

What is of interest here is note that the fact that the actual inflation moves with the forecast does not, however, mean that we can never make an accurate forecast. What we need to do is to look for the ‘fixed points' of this forecast function.

Assuming that the forecast function in the economy under consideration is depicted by line B in the figure, let us ask what the Treasury should do. Assume for simplicity that inflation forecasts can only be a non-negative number.

In this model, when the Treasury tries to forecast inflation, it has to treat its own forecast as one of the determinants of the inflation. If, for instance, it makes a forecast of zero inflation, actual inflation will be 5 per cent.

If it forecasts inflation to be 5 per cent, actual inflation will be 7.5 per cent. It is now easy to see that, if the Treasury wants to forecast inflation correctly, it has to make a forecast of 10 per cent inflation. No other forecast will be borne out in practice. Basically, an accurate forecast is a search for the fixed points of the forecast function.

Expectations and policy

Now suppose that the Treasury takes its job of holding inflation down seriously. Then, keeping in mind that its own forecast of inflation is one of the causes of inflation, what forecast should it make. Clearly, it should forecast inflation to be 0 per cent. The forecast will turn out to be false but inflation will be as low as possible, to wit, at 5 per cent. So, the objective of accurate forecasting and the objective of inflation control, pull in different directions.

Therein lies the dilemma. It is not always possible to carry out both tasks that the Treasury is entrusted with, namely, accurately forecasting inflation and minimising inflation. There are situations, where an internal consistency problem arises between the two tasks. Do one task perfectly, the other gets thrown out of gear. Do the other task diligently, and the former gets out of control. This is not a problem specific to India or China or the US.

This is a problem with the way the world is. There is no way to resolve this; all policymakers in a position to make publicly-observed forecasts have to live with this dilemma.

In case the forecast function is non-linear and has more than one fixed point (that is, it cuts the 45-degree line in multiple places), then each fixed point would be an accurate forecast.

In such a situation, the task of predicting inflation accurately and trying to keep inflation low can have significant content. It will simply mean that we should forecast the lowest value of inflation, which is also a fixed point of the forecast function.

Lower deficits

Before moving away from this topic, it is worth digressing briefly on an interesting connection between expectations and government policy. In the above discussion, I did not elaborate on why greater inflationary expectations lead to greater actual inflation.

One class of analysts has argued that widespread expectations of inflation lead the government to behave in ways — such as running large deficits — that in fact help fulfil those expectations.

One way to break this link is for the government to visibly alter its rules of behaviour, such as making an open and credible commitment to maintaining lower deficits in the foreseeable future.

(To be concluded)

(Kaushik Basu is Chief Economic Advisor.)

(Excerpts from the Tenth Gautam Mathur Lecture)

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