## Sunday, April 19, 2009

### The policy rate, expressed in real terms

Economists are very clear that the interest rate that matters is one that is expressed in real terms. If I borrow Rs.100, and am obligated to pay back Rs.110 a year from now, the true cost of borrowing that weighs in my mind is not 10%; it is lower to the extent that I expect the rupee will be worth less owing to inflation, a year from now. Hence, what matters is the real rate: the difference between the nominal interest rate, and expected inflation over that identical horizon. This perspective matters greatly for thinking about monetary policy. What matters is not the short-term interest rate which we apparently see on the money market; what matters is this rate after subtracting out expected inflation over the same time horizon

In good countries, inflation has become boring, owing to the success of inflation targeting central banks, and the distinction between the real rate and the nominal rate has become less prominent. But in India, inflation volatility is immense, and it is particularly important to look at the policy rate in real terms.

In the recent article India in the Great Recession, which appeared in Financial Express on 15 April, of particular interest to a lot of people was the graph of the time-series of the policy rate, expressed in real terms. (This is inside section VII of the article). Lots of people asked for details about how this was done. Here goes:

1. Start with the time-series of the level of WPI
2. Convert this into seasonally adjusted levels [methodology]
3. Shift to a time-series of inflation measured as point-on-point changes of the seasonally adjusted series.
4. Now run through the time-series, starting from the beginning. At each point in time, only use data visible upto that point. Fit an ARMA model to the inflation time-series. Use that model to make forecasts for inflation for the next 3 months. Average those forecasts and you have a forecasted inflation over the next 90 days.
5. Define the 90-day treasury bill rate (on the market) as the policy rate in nominal terms. This helps us get away from the fog of multiple instruments that RBI uses. The argument here is: in the bottom line, monetary policy is about the short rate, and the 90-day rate is the short rate. RBI uses various levers such as CRR, the repo rate, the reverse repo rate, the bank rate, etc. to try to influence the short term rate. The 90-day treasury bill rate shows the summary statistic of what is happening in monetary policy at a point in time.
6. So now you are holding: a time-series of the policy rate in nominal terms (i.e. the 90-day treasury bill date) and a time-series of forecasted inflation at every point in time (i.e. the forecasts of point on point changes to seasonally adjusted WPI, made carefully to only use information available at time t when forecasting for months t+1, t+2 and t+3). Subtraction yields the time-series of the real rate.
7. Smooth this series so as to get away from the month to month fluctuations to some extent. In the graph below, the deep line is smoothed and the light (dashed) line is the underlying unsmoothed data. The smoothing here is done using the smooth(x, kind="3R") function in R, which is a simple non-parametric smoother.

This time-series (click on the picture to see it more clearly) shows some signs of procyclicality:

1. The Asian crisis broke in August 1997 and India tested nuclear weapons in May 1998. India's downturn ran from 1998 till 2002. Early in that period, monetary policy tightened by around 600 basis points.
2. From 2001 onwards, the greatest business cycle expansion in India's history commenced. Monetary policy responded to this by cutting rates from 2001 till 2004. In good times, monetary policy made it better. Then tightening took place from 2004 till 2007 but in the great inflation of 2008, the real rate again dropped.
3. The happy days ran from 2002 till mid-2008. When bad times were clearly upon us (from 9/2008 onwards), monetary policy seems to have tightened.

While on this subject, do read about the Taylor Principle which gives a simple conceptual framework for thinking about how the real rate should respond to changes in expected inflation. Now all this is vulnerable to the difficulties of measurement that bedevil the WPI. So it's worth doing this by the CPI (IW) also. Here's the graph that it yields (click on the picture to see it more clearly):

How good is this estimator of the real rate? Only as good as the inflation forecast.

What would be great is to have a liquid market for inflation indexed bonds and a liquid market for nominal bonds; the difference between these would be a market-based estimator of expected inflation. This would take into account myriad factors that affect inflation. In contrast, forecasting inflation using ARMA models is quite lame. It only uses the time-series structure of inflation and fails to take into account all the other factors that affect inflation. This can and should be done better by going to a multivariate setting.

However, I do think that this is a useful first cut, and it's more useful to look at this rendition of the real rate as compared with only looking at the policy rate expressed in nominal terms, as is currently done in India.

1. 1. The methodology depends on the final aim of the exercise. ARMA forecasting of inflation is lame as you rightly point out. As is any other multivariate forecasting. And it is not even a good first cut.

Forecasting inflation using a model is different from knowing how people at large are forecasting inflation.

Unless we can show that the output of any forecasting model proxies inflation expectations, the methodology does not serve the economic purpose.

The TIPs vs. nominal market is only one indicator and not totally reliable. And even that can be problematic because nominals are more often than not, more liquid. Also, there is the inflation risk premium which biases the estimates from inflation-linkers.

We need good survey based measure of long-term expected inflation.

2. Even if we assume that the ARMA model is a good approximation of the people’s expectation formation process, 3-month expectations are not what policy makers worry about.

Monetary policy is mainly about stabilizing long-term expectations of inflation.

The key to counter-cyclical policy is that when the central bank reduces short-rates, the entire term structure should descend. If the central bank’s actions lead to a rise in inflation expectations and the long-end sells off, policy would be ineffective.

3. Conducting this exercise with headline inflation is even more useless. When inflation expectations are stabilized, pass-through from a temporary rise in prices (oil, primary etc) to core measures is limited.

Your comments: “In good countries, inflation has become boring, owing to the success of inflation targeting central banks, and the distinction between the real rate and the nominal rate has become less prominent. But in India, inflation volatility is immense, and it is particularly important to look at the policy rate in real terms.”

Headline inflation is quite variable everywhere in the world. Headline PPI is even more volatile. Central banks globally look at some core measure of inflation. Core is relatively stable and that is what should be looked at for policy purposes.
Comparing WPI to core PCE deflator is like comparing apples to oranges.

4. Using the Taylor Rule for India has no economic rationale.

How do you theoretically define an output gap and a natural rate of interest for an economy with infinite supply of labor on the margin?

I could argue that India can grow as fast as it can accumulate capital. Inflation may be determined by capacity utilization, but in an open economy even that becomes immaterial since you can import. The country imports global inflation. Potential growth in this schema is determined by the sustainable level of current account deficit for a given level of capital efficiency. Constant returns to scale growth is possible and the natural rate in this case is determined by the efficiency of capital.

I could be totally wrong. All I am saying is that let’s not trivialize extremely complex issues. But I have to see good theoretical arguments and econometrics devoid of economics cannot be a good first cut for policy-making in my book.

We need solid theory before we can make these claims.

2. I will stick to my basic points.

* In interpreting what monetary policy is doing, it is the real rate that matters and not the nominal rate.

* A lame estimator of the real rate is better than the nominal rate.

Yes, of course, we should build better estimators of the real rate. What I would like most is to see a half decent bond market, featuring both nominal and real bonds, so that inflationary expectations can be backed out. Yes, of course, multivariate models will do better than ARMA models. Yes, all those good things should be done.

Until they're done, this lame approach is the best measure for understanding what monetary policy is doing.

3. "* In interpreting what monetary policy is doing, it is the real rate that matters and not the nominal rate."

My comments: I agree.

"* A lame estimator of the real rate is better than the nominal rate...

Until they're done, this lame approach is the best measure for understanding what monetary policy is doing."

My comments: I do not agree. For the reasons mentioned in my previous post, this particular lame estimator cannot be used for gauging whether policy is expansive or contractionary.

Instead the following lame estimator may be less lame:

r = i - 5-year average of inflation

4. In my opinion, interest rates can be much better modelled as mean reverting than equities. And of course add it with the apparent transparency of the interest rate discovery to the entire process, I am glad that this is happening.

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