The RBI?s inflation forecasting- Getting the math right

By Indroneel Das

In what has now become a trend rather than an anomaly, the RBI’s inflation forecasts have been off their mark for a while now. The actual inflation data has been significantly lower than the RBI’s expectations, and the recent concerns raised by the RBI Deputy Governor Mr Viral Acharya, highlight what is fundamentally wrong with the inflation forecasting process in the country. To keep things simple, let us look at just one actual inflation data point from the recent past and compare it to the RBI’s forecasts while considering all the revisions of the forecast. The inflation we will mostly be referring to, throughout this article, is the headline inflation.

In October 2016, the RBI forecasted the March 2017 inflation to be 5.3%. An upward forecast despite the fact that, from July 2016 to October 2016, inflation had fallen from 6.1% to 4.2%. In December 2016, the forecast was revised to 5%, and finally to below 5% in February 2017 (which was only a month away from the period for which the inflation was being forecast- March 2017). The actual March 2017 inflation rate was well under 4%. The RBI had missed the one-month inflation forecast by about 110 bps. Missing the mark by such a huge margin, especially when the period for which inflation is being forecasted is only a month away, is both unexpected and worrying. Any discussion on why the RBI is unable to accurately forecast inflation is incomplete without a background of the model used by the RBI for the same. Therefore, it is important to delve into the econometric model used by the RBI to forecast inflation to understand the math before we discuss why it’s missing its mark much too often.

Sneak peek at the basket of models

The RBI uses a weighted combination of the outputs from multiple models. These models include- the relatively simple random walk model and a first-order autoregression model. It combines this output with outputs from much more complex, albeit more accurate models, such as- a moving average model, a Phillips curve model, a VAR model and a BVAR model, where the last two models are used with and without an exogenous variable, and the output from both variations of the model are used for forecasting.

The Random Walk model

The random walk model says what it sounds like- the variable being forecasted follows a random and unpredictable path, so that previous data points are rendered useless in forecasting the future values of the variable. Without going into the math, suffice it to say that the model totally excludes the possibility of any stable, mean-reverting level. The output is marred by its inherent instability and therefore, is believed to have too much ‘noise’ to be of any practical consequence, at least in isolation.

First Order Auto-Regressive  model

This model, theoretically, is more fundamentally sound in its predictive ability. Such a time-series model is based on the premise that any future value of the dependent variable (i.e. inflation) is a function of its own value in some previous period. There are some significant limitations though, including problems caused by the correlation between the two-time series (the time-series of the dependent variable and the time-series of the independent variable). Yet, with appropriate adjustments, it is a viable model to use.

Philips Curve model

That brings us to a very widely accepted model- the Phillips curve model. This is also a backward-looking model, forecasting a time series using more than one variable. There is solid statistical evidence to prove that the premise of this model- a perennial inverse relationship between the rate of inflation and the rate of unemployment in an economy, is solid. However, the concern here is that the model is episodic at best. This means that it has hardly ever improved upon the forecast of the univariate, random-walk models that we previously referred to. Therefore its additional, synergistic value in a basket of models, is close to zero. The other models are more complicated but provide more accurate outputs because of their inherent ability to take into account, a greater number of factors and also allows the RBI to introduce additional conditions, exogenous to the model.

Riddled with inconsistencies

The truth behind the façade is that the RBI is bluffing about ‘core’ inflation. To put things in perspective, the core inflation doesn’t include changes in the prices of food and fuel. The other metric of inflation is ‘headline’ inflation, which refers to the inflation as reported by the CPI, including the prices of commodities such as food, oil, and gas. The prices of such commodities tend to be very volatile and are subject to much more fluctuations in the short-term.  It is the core inflation that is a more critical input to the forecasting and policy making process. Given the consistently erroneous forecasts of core inflation and the lack of surety even on the RBI’s part, it is no surprise that even previously documented values of core inflation are off-the-mark.

Understanding elevator economics

The term ‘Elevator Economics’ is often used to describe the RBI’s method of arriving at forecasts of future inflation. If one goes through any of the previous Monetary Policy Reports, not once does one find the calculation (or even mention!) of ‘core’ inflation- the variable that the RBI somehow arrives at arbitrarily, based on ‘judgement’, which is then used to forecast inflation. The RBI, in its own reports, mentions that they use the previously specified basket of models to forecast inflation and use their own subjectivity and understanding of the economy, to adjust this forecast. Clearly, their own understanding has not been aligned with the direction that the economy is taking.

Also, there are other significant mathematical limitations that are common to almost all the models used for generating forecasts. Firstly, there is a requirement for correctly stated prior period and current period data. One of the most respected central banks in the world is expected to get this one right. But as we have inferred, as of now the RBI can’t really rely on its own current period and prior period values, it has to wait for the surveys to churn out the real numbers. Also, all the models will work only if there is a linear relationship between inflation and its explanatory variables- rarely the case in the real world. There are other requirements that are not possible to achieve in the real world either (such as covariance stationarity- the condition of having a finite and constant mean, variance and covariance across the time series)  and when these conditions aren’t satisfied, they have a compounding effect on the already accumulated error. An accurate forecast of inflation and consistent values for headline and core inflation are crucial to the entire monetary policy framework.

A fundamental shift

The current model threatens to have a slow, but spiralling effect on the economy and create undesirable outcomes, due to the gap between the monetary policy that the economy needs and the one the RBI comes up with. In an entirely statistical sense, no model is expected to be error free. But the essence of acceptable error generation lies in ensuring that the error is not too large, and over time, is equally distributed on both sides of the actual values (which translates to having a ‘zero’ expected value of what is known as the ‘error term’ in any forecasting model). The RBI’s model throws up forecasts that are significant in terms of the size of the error, and are always overstating inflation. This confirms that the model is biased and inaccurate. The reason is that inflation is not behaving like it has, historically. Our own historical data throws up a relationship that no longer holds. This is what is referred to as a ‘fundamental shift’.

While it is almost impossible to predict how variables will behave with respect to each other while a fundamental shift is playing out, the forecasting can be significantly and quickly improved if the forecasting models have access to real-time (and not lagged) data on prices. Even if it is possible, it is easy to see that it’ll be infeasible for the government or the RBI to develop such technology for data capture on their own. The only feasible solution then lies in involving enterprises who already have this capability, as feeders to the process.

Featured Image Credits: Livemint