I. Marx vs. Smith and food banks
When Heinz produces too many Bagel Bites, or Kellogg produces too many Pop-Tarts, or whatever, these mammoth food-processing companies can donate their surplus food to Feeding America, a national food bank. Feeding America then distributes these corporate donations to local food banks throughout the country.

What's the economically optimal way to allocate the donations across the country?

Option one is what you might call "full communism." Under full communism, Feeding America collects the food donations and then top-down tells individual food banks what endowments they will be receiving, based on Feeding America's own calculation of which food banks need what.

Prior to 2005, this was indeed what occurred: food was distributed by centralized assignment. Full communism!

The problem was one of distributed versus centralized knowledge. While Feeding America had very good knowledge of poverty rates around the country, and thus could measure need in different areas, it was not as good at dealing with idiosyncratic local issues.

Food banks in Idaho don't need a truckload of potatoes, for example, and Feeding America might fail to take this into account. Or maybe the Chicago regional food bank just this week received a large direct donation of peanut butter from a local food drive, and then Feeding America comes along and says that it has two tons of peanut butter that it is sending to Chicago.

To an economist, this problem screams of the Hayekian knowledge problem. Even a benevolent central planner will be hard-pressed to efficiently allocate resources in a society since it is simply too difficult for a centralized system to collect information on all local variation in needs, preferences, and abilities.

This knowledge problem leads to option two: market capitalism. Unlike poorly informed central planners, the decentralized price system – i.e., the free market – can (often but not always) do an extremely good job of aggregating local information to efficiently allocate scarce resources. This result is known as the First Welfare Theorem.

Such a system was created for Feeding America with the help of four Chicago Booth economists in 2005. Instead of centralized allocation, food banks were given fake money – with needier food banks being given more – and allowed to bid for different types of food in online auctions. Prices are thus determined by supply and demand.

At midnight each day all of the (fake) money spent that day is redistributed, according to the same formula as the initial allocation. Accordingly, any food bank which does not bid today will have more money to bid with tomorrow.

Under this system, the Chicago food bank does not have to bid on peanut butter if it has just received a large peanut butter donation from another source. The Idaho food bank, in turn, can skip on bidding for potatoes and bid for extra peanut butter at a lower price. It's win-win-win.

By all accounts, the system has worked brilliantly. Food banks are happier with their allocations; donations have gone up as donors have more confidence that their donations will actually be used. Chalk one up for economic theory.

II. MV=PY, information frictions, and food banks
This is all pretty neat, but here's the really interesting question: what is optimal monetary policy for the food bank economy?

Remember that food banks are bidding for peanut butter or cereal or mini pizzas with units of fake money. Feeding America has to decide if and how the fake money supply should grow over time, and how to allocate new units of fake money. That's monetary policy!

Here's the problem for Feeding America when thinking about optimal monetary policy. Feeding America wants to ensure that changes in prices are informative for food banks when they bid. In the words of one of the Booth economists who helped design the system:

"Suppose I am a small food bank; I really want a truckload of cereal. I haven't bid on cereal for, like, a year and a half, so I'm not really sure I should be paying for it. But what you can do on the website, you basically click a link and when you click that link it says: This is what the history of prices is for cereal over the last 5 years. And what we wanted to do is set up a system whereby by observing that history of prices, it gave you a reasonable instinct for what you should be bidding."

That is, food banks face information frictions: individual food banks are not completely aware of economic conditions and only occasionally update their knowledge of the state of the world. This is because obtaining such information is time-consuming and costly.

Relating this to our question of optimal monetary policy for the food bank economy: How should the fake money supply be set, taking into consideration this friction?

Obviously, if Feeding America were to randomly double the supply of (fake) money, then all prices would double, and this would be confusing for food banks. A food bank might go online to bid for peanut butter, see that the price has doubled, and mistakenly think that demand specifically for peanut butter has surged.

This "monetary misperception" would distort decision making: the food bank wants peanut butter, but might bid for a cheaper good like chicken noodle soup, thinking that peanut butter is really scarce at the moment.

Clearly, random variation in the money supply is not a good idea. More generally, how should Feeding America set the money supply?

One natural idea is to copy what real-world central banks do: target inflation.

The Fed targets something like 2% inflation. But, if the price of a box of pasta and other foods were to rise 2% per year, that might be confusing for food banks, so let's suppose a 0% inflation target instead.

It turns out inflation targeting is not a good idea! In the presence of the information frictions described above, inflation targeting will only sow confusion. Here's why.

As I go through this, keep in the back of your mind: if households and firms in the real-world macroeconomy face similar information frictions, then – and this is the punchline of this entire post – perhaps inflation targeting is a bad idea in the real world as well.

III. Monetary misperceptions
I demonstrate the following argument rigorously in a formal mathematical model in a paper, "Monetary Misperceptions: Optimal Monetary Policy under Incomplete Information," using a microfounded Lucas Islands model. The intuition for why inflation targeting is problematic is as follows.

Suppose the total quantity of all donations doubles.

You're a food bank and go to bid on cheerios, and find that there are twice as many boxes of cheerios available today as yesterday. You're going to want to bid at a price something like half as much as yesterday.

Every other food bank looking at every other item will have the same thought. Aggregate inflation thus would be something like -50%, as all prices would drop by half.

As a result, under inflation targeting, the money supply would simultaneously have to double to keep inflation at zero. But this would be confusing: Seeing the quantity of cheerios double but the price remain the same, you won't be able to tell if the price has remained the same because
(a) The central bank has doubled the money supply
or
(b) Demand specifically for cheerios has jumped up quite a bit

It's a signal extraction problem, and rationally you're going to put some weight on both of these possibilities. However, only the first possibility actually occurred.

This problem leads to all sorts of monetary misperceptions, as money supply growth creates confusions, hence the title of my paper.

Inflation targeting, in this case, is very suboptimal. Price level variation provides useful information to agents.

IV. Optimal monetary policy
As I work out formally in the paper, optimal policy is instead something close to a nominal income (NGDP) target. Under log utility, it is exactly a nominal income target. (I've written about nominal income targeting before more critically here.)

Nominal income targeting in this case means that the money supply should not respond to aggregate supply shocks. In the context of our food banks, this result means that the money supply should not be altered in response to an increase or decrease in aggregate donations.

Instead, if the total quantity of all donations doubles, then the price level should be allowed to fall by (roughly) half. This policy prevents the confusion described above.

Restating, the intuition is this. Under optimal policy, the aggregate price level acts as a coordination mechanism, analogous to the way that relative prices convey useful information to agents about the relative scarcity of different goods. When total donations double, the aggregate price level signals that aggregate output is less scarce by halving.

It turns out that nominal income targeting is only exactly optimal (as opposed to approximately optimal) under some special conditions. I'll save that discussion for another post though.

Feeding America, by the way, does not target constant inflation. They instead target "zero inflation for a given good if demand and supply conditions are unchanged." This alternative is a move in the direction of a nominal income target.

V. Real-world macroeconomic implications
I want to claim that the information frictions facing food banks also apply to the real economy, and as a result, the Federal Reserve and other central banks should consider adopting a nominal income target. Let me tell a story to illustrate the point.

Consider the owner of an isolated bakery. Suppose one day, all of the customers seen by the baker spend twice as much money as the customers from the day before.

The baker has two options. She can interpret this increased demand as customers having come to appreciate the superior quality of her baked goods, and thus increase her production to match the new demand. Alternatively, she could interpret this increased spending as evidence that there is simply more money in the economy as a whole, and that she should merely increase her prices proportionally to account for inflation.

Economic agents confounding these two effects is the source of economic booms and busts, according to this model. This is exactly analogous to the problem faced by food banks trying to decide how much to bid at auction.

To the extent that these frictions are quantitatively important in the real world, central banks like the Fed and ECB should consider moving away from their inflation targeting regimes and toward something like a nominal income target, as Feeding America has.

VI. Summing up
Nominal income targeting has recently enjoyed a surge in popularity among academic monetary economists, so the fact that this result aligns with that intuition is pretty interesting.

To sum up, I'll use a metaphor from Selgin (1997).

Consider listening to a symphony on the radio. Randomly turning the volume knob up and down merely detracts from the musical performance (random variation in the price level is not useful). But, the changing volume of the orchestra players themselves, from quieter to louder and back down again, is an integral part of the performance (the price level should adjust with natural variations in the supply of food donations). The changing volume of the orchestra should not be smoothed out to maintain a constant volume (constant inflation is not optimal).

Central banks may want to consider allowing the orchestra to do its job, and reconsider inflation targeting as a strategy.

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