## How Do We Predict Inflation?

Ken Houghton notes that playing with data is dangerous.

Predicting the future tends to be easy. There are several ways to do it. First, you can predict that everything will grow as it did this year—or last year, or the mean of the past x years. Or you can predict that it will be great if a Republican is in office, but horrible if a Democrat is. (Call this The Kudlow Effect.)

Or, you can just predict that everything next year will be the same as it is this year.

This appears to be fairly close to what consumers do, judging by this scatterplot of annual inflation (i.e., inflation over the previous twelvemonth) against the University of Michigan’s median expectation from consumer surveys.

So the “Rational Agent” believes that nothing will change. Comments?

It is a property of randomness or random walk. The best estimate of the future price is the current price. It is also called the naive forecast. Sometimes it is the current price with a drift component (a constant growth factor). It is also a fundamental component of efficient markets that the best estimate of the future price is the current price. Basically, you have shown that agents are rationale and inflation prediction markets are efficient markets. (That is if your judgment of the scatter plot holds up statistically.)

One of the best estimates of tomorrow’s weather is today’s weather and that forecast will beat many meteorologists” model forecasts. Likewise, for securities prices and many other economic variable forecasts that have random movements around a trend line.

Heteroskedasticity?

We actually know that inflation is very persistent. Assuming there is some cost with actually forming a complex forecast about future inflation and given that inflation is so persistent (one of those issues economists are actually trying to figure out) then a sample of people whose need to forecast inflation is low will have simple forecasts for inflation. Its is fully rational to not derive such forecasts. Now why economists almost always drop such costs when modeling is another issue.

Does not bias the estimates.

Cantab,

Right. I didn’t say it did. Just an observation and a question based on an eyeball analysis. It raises questions about conditional heteroskedasticity and how that affects risk perceptions. In other words, something like a GARCH-in-Mean forecast.

Methinks we need an f-test. The plot out to 6% or so looks a great deal flatter than the fitted line. If so, what we may be seeing is that in periods of relatively good control of inflation, people believe the Fed will continue to do a good job, raising inflation when it is low, lowering it when it is high. Up to around 3% measured inflation, expected inflation tends to be higher than measured inflation.

Below about 6%, dat ole devil heteroskedasticity don’t show up much, either. What we are seeing is the consequences of policy error in the formation of inflation expectations. Confidence suffers when inflation gets out of hand. We already knew that, but it shows up clearly in the plot.

It also suggests that naive observers are not all that naive. They expect inflation around 3% when inflation runs from 1% to around 4%-5%, but begin to growth less confident when the Fed messes up.

Before we decide this plot is evidence of irrationality (whatver that means), we need an f-test.

Well, simple enough: look at the chart.

On the left side you’ve got clusters around 3 percent and on the bottom the major cluster to the left side is centered on 3 percent. Looks about right to me. Guessing 3 percent is always pretty much right.

basic statistics. the present is the weighted average of the past. since we know nothing about the future, the best guess would be, as always, the average of the data collected to date.

J.Goodwin:

And you would be correct. A time series plot with a trend line did confirm such for me from the data I was able to find.