The Optimal Rate of Inflation

Notes on the Optimal Rate of Inflation

(Work in progress)

Background reading: Schmitt-Grohe and Uribe, "The Optimal Rate
of Inflation," 2010.

Here are four macroeconomic issues that you may wish to think about
when asking about the optimal rate of inflation.

Suppose throughout that the central bank can choose the inflation rate,
at least on average, over the medium run. What should that inflation rate be?

Arbitrage considerations
First, let's look at the optimal rate of inflation from the perspective
of asset pricing. For every dollar you have in cash or in a checking
account, you are foregoing buying a risk-free bond and earning some
interest. That foregone interest is one cost of holding cash. Suppose
that the bond earns real return r. The optimal rate of inflation that
removes the difference between bond returns and cash returns sets
inflation = -r. That is, the optimal rate of inflation is actually
deflation at the rate of r% per year. With r = 0.02 or so, the optimal
rate of deflation is 2% per year. At that deflation rate, you are no
worse off holding cash than holding bonds. So the central bank should
aim for mild, gradual deflation. This argument was originally presented
in a Milton Friedman paper and has become known as the "Friedman rule."

Price Stability considerations
Second, let's look at the optimal rate of inflation from the perspective
of menu costs. Firms face costs in changing their prices. When a firm
changes the prices it charges for its products, it must update its online
catalog, must replace the sticker prices on the shelves, etc. These costs
are known as "menu costs," the idea being that you have to print up a
new menu when you change the price of a good. There is some evidence that
menu costs are actually quite large; Mankiw has a few papers on this.
We'd like to establish a macroeconomic environment where firms don't have
to change their prices solely due to inflation. (They'll still change
their prices in response to variations in local demand, local cost shocks,
etc. But they won't have to change prices solely due to aggregate inflation.)
To minimize on these costs, we should set the inflation rate to 0%, which
removes any need to update menus purely due to inflation.

Inflation and taxes
Third, we will simply never index the tax code properly. Inflation distorts
the real after-tax return on investment; minimizing these distortions guides
us towards an optimal inflation rate of 0%.

Business cycle considerations
Fourth, let's look at how inflation interacts with the nominal interest
rate and with the broader business cycle. During a recession, output
falls and unemployment rises. In response, the central bank usually cuts
the nominal interest rate in an attempt to return output and employment
to normal levels. However, the nominal interest rate cannot go below
zero. Suppose the normal inflation rate is 4% and the normal nominal
interest rate is 6%. Then if we enter a recession, the central bank can
cut interest rates by 600 basis points before hitting the zero lower bound.
But if the normal inflation rate is 2% and the normal nominal interest rate
is 4%, then the central bank only has 400 basis points worth of cuts before
it hits the zero lower bound. If the normal inflation rate is 0% and the
normal nominal interest rate is 2%, then the central bank can only cut
interest rates by 200 basis points before hitting the zero lower bound.
Hence a higher inflation target gives the central bank more room to maneuver
during recessions.

Furthermore, although the Friedman rule says we might like deflation
on average, it is also true that deflation during recessions can be dangerous.[1]
In a recession, deflation has various unpleasant effects, most prominently
that it increases real debt burdens of debtors, causing debtors to cut
back on spending, which can exacerbate the decline in output that's already
occurring.

So we have four guidelines. The Friedman rule says that to compensate you
for the interest you lose when you hold money, the inflation rate should
be slightly negative. The sticky-price rule says that to minimize the cost
of changing prices, the inflation rate should be 0%. Inflation's interaction
with the tax code suggests an inflation target of about 0%. The recession-fighting
rule says that we should aim for slightly positive inflation, so as to have
room to cut interest rates in a recession; maybe target an inflation
rate of 4% or so.

Modern central banks weigh these considerations and tend to target
a slightly positive inflation rate over the medium term. 2% is a common
benchmark.

See these examples:

Bank of Canada: "The target aims to keep total CPI inflation at the 2 per
cent midpoint of a target range of 1 to 3 per cent over the medium term.
'The Bank raises or lowers its policy interest rate, as appropriate, in
order to achieve the target typically within a horizon of six to eight
quarters—the time that it usually takes for policy actions to work
their way through the economy and have their full effect on inflation."

Swedish Riksbank: "The inflation target has since been defined as
keeping the annual rise in the CPI at 2 per cent." See also their website:
http://www.riksbank.se/en/Monetary-policy/Inflation/Adoption-of-the-inflation-target/

US Federal Reserve: "The inflation rate over the longer run is
primarily determined by monetary policy, and hence the Committee
has the ability to specify a longer-run goal for inflation.  The
Committee reaffirms its judgment that inflation at the rate of
2 percent, as measured by the annual change in the price index
for personal consumption  expenditures, is  most  consistent
over the longer run with the Federal Reserve’s statutory mandate."

Bank of England: "The Bank’s monetary policy objective is to deliver
price stability -- low inflation -- and, subject to that, to support
the Government’s economic objectives including those for growth and
employment. Price stability is defined by the Government’s inflation
target of 2%."

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