Every month for more than half a century, the University of Michigan Survey Research Center has been asking consumers 50 questions about their personal finances, business conditions and buying plans, both current and future. The results are compiled into two indexes, one reflecting current conditions, the other expectations about the economy. The Index of Consumer Expectations is one of 10 components of the Index of Leading Economic Indicators, so it tells you just how important consumer sentiment is.

One of the monthly survey questions is about expected inflation: next year and five-to-10 years from now. The index of one-year inflation expectations averaged 3.2 percent over the past year and 3.1 percent over the past five years, which captures the post-Lehman panic and financial crisis.

The readings for longer-term inflation expectations are pretty similar: an average of 2.9 percent in the past year and 3 percent over the last five years. Where have these folks been? The Federal Reserve has been targeting inflation of 2 percent, first implicitly and then explicitly, for a long time. Even if they haven't been paying attention, haven't they observed the real-world results? Inflation has been running at 1.5 percent, on average, over the last five years.

Consumers either don't listen, don't care or derive their expectations from their own shopping cart. Food and gas comprise a big part of the household budget, and energy prices, at least, have been rising much faster than inflation. Just as consumers vote their pocketbook, they use their pocketbook to make judgments on where inflation is today and where prices are headed.

Various academic economists, including Ken Rogoff and Greg Mankiw of Harvard, have pushed the Fed to adopt an inflation target of 4 percent or 6 percent to goose the economy. The goal would be to reduce real short-term rates since the Fed can't lower the nominal funds rate when it's already close to zero.

I've pointed out the short-sightedness of this approach, which would damage the Fed's hard-won credibility. Nominal long-term rates would rise to incorporate higher-inflation expectations -- and probably a bigger term premium. There is no reason to think real long-term rates, which drive investment, would fall.

It's true that when the Fed talks about the public, it really means financial markets. (Like corporations, markets are people.) Expectations about the economy and interest rates are incorporated into asset prices. Consumers get the message through an increase in their wealth, be it the value of their home or their 401k account, and spend more.

In all this time, the broader public hasn't grasped the Fed's commitment to 2 percent inflation, either in words or from results. At the same time, markets haven't grasped that tapering isn't tightening. The conclusion isn't that the Fed has been unclear or miscommunicated. It's that people and markets form their own expectations, often independent of the institution that's trying to shape them.

(Caroline Baum is a Bloomberg View columnist. Follow her on Twitter.)