Calculating Real Interest Rates Under Price Level Shifts

"You take the blue pill—the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill—you stay in Wonderland, and I show you how deep the rabbit hole goes. Remember: all I'm offering is the truth." - Morpheus, The Matrix (1999)

As a follow up to yesterday's post on interpreting measured deflation, someone on Twitter remarked that since inflation is negative, real interest rates would be high, so BNM should cut the OPR. A Bloomberg Opinion article said roughly the same thing. I could respond by saying that since this analysis is based on the false premise that Malaysia is in a deflationary environment, that policy prescription would also be false. But the question is interesting enough that it bears both examination and explanation.

What is a real interest rate, and why does it matter?

As inflation is a measure of a decline in purchasing power over time, and since investments make returns over time, the "real" value of any return has to be inflation adjusted. For example, a bond yielding 4% in an environment of 2% inflation would have a real return of 2% after a year. For any given rate of interest (or any rate of return on investment for that matter), the higher the rate of inflation, the lower the real rate of return. In a deflationary environment, the opposite would therefore be true - low or negative inflation implies a higher real rate of return.

For obvious reasons, a higher real rate of return is great for investors but lousy for borrowers. Deflation actually raises the real burden of debt. A higher real rate would, all things equal, reduce borrowing, reduce investment, and slow down economic growth. So far so good.

But, as per my analysis yesterday, a price level shift is fundamentally different from a true deflationary environment. Just as base effects distort the measurement of inflation, so do they distort measurement of the real rate.

A little thinking from first principles should show why. Let's say for example I put in a fixed deposit yielding 4% in June last year (you can use a fixed term loan, it doesn't really make a difference to this analysis). Inflation is assumed to run a steady 2% per annum. The real rate would therefore be 2%.

Now assume that the country falls into a true deflation of -1% per annum. The real rate then jumps to 5% (4% - (-1%) = 5%), which benefits me as a depositor, but penalises borrowers.

Next assume that there is a price level shift downwards, such that measured deflation is also -1%, but there is no change in the slope of the CPI (you can refer to yesterday's figure for a visual representation):

The calculated real rate is still 5%, but there is one crucial difference. If I were to put in a deposit right after the discontinuity in the curve, my real rate of return remains 2%, not 5%. Since the slope hasn't changed (chart 2 in the figure above), there is effectively no change in the real financial return I would expect to get a year from now (since we're looking at annual returns), than I would have expected before the curve shifted. Similarly, if I were to borrow right after the point where the curve shifts, there is also no difference in the expected real financial cost to me after a year, than if I had borrowed before the shift.

Alternatively, try calculating the before and after real return on a monthly basis rather than an annual basis. If the slope of the CPI hasn't changed, neither will the real interest rate that faces economic agents. There is a real effect on returns and costs from the price level shift, but since it's instantaneous and not continuous, there's no change in real economic and financial incentives facing investors or borrowers before or after the shift.

To put it bluntly, it would be an extremely foolish central bank that responds to one-off shifts in the price level.