[Update: Or maybe this is a more general way of stating the intuition: The IT central bank must create a big enough output gap to make the sample of firms that want to pay the menu cost an unbiased sample, so on average they leave prices the same. An NGDPT central bank can allow a biased sample of firms to change prices, provided it offsets it with a (smaller than under IT) output gap.]

The intuition is that an inflation targeting central bank must create a big enough output gap to dissuade the firms that most want to deviate from the inflation target from doing so. An NGDP targeting central bank can allow those firms to deviate from the implicit inflation target, provided it creates an output gap just big enough to keep NGDP on target. The smaller the percentage of firms that want to deviate, the smaller the output gap needed to keep NGDP on target.

The only important difference from a standard New Keynesian model is that I've ditched Calvo's fairy, because she keeps on insisting that the firms that change prices are a representative sample of all firms . I've replaced her with a coordination game with menu costs, a bit like Ball and Mankiw (pdf) . Relative shocks are skewed, so those firms that most want to change prices are not representative of all firms. I think that's much more realistic than the random flight of Calvo's fairy.

Tony Yates complains that Market Monetarists don't have a model to justify their support for NGDP targeting. So I decided to build him a little model. It's a cruddy little one-period model, and it's really only a sketch of a model, but any competent grad student should be able to do the math to finish it.

To keep it simple, there are only three firms: call them A for apples, B for bananas, and C for carrots. (I can't have two firms because then I couldn't have skewed shocks. And NGDP targeting would perform even better with more than three firms.)

This is the order of moves:

1. The central bank announces either an inflation target, or an NGDP target.

2. The firms announce their (provisional) initial prices.

3. Nature rolls a 3-sided die, and announces whether it lands on A, B, or C.

4. Nature then flips a coin, and announces heads or tails.

5. The die and coin cause a shock to preferences. "A-tails" means that consumer preferences shift away from apples, towards bananas and carrots equally. "A-heads" means that consumer preferences shift towards apples, away from bananas and carrots equally. For simplicity the preference parameters are rigged so that preference shocks would have no effect on aggregate output if prices were perfectly flexible. Call that level of output Y*.

6. The central bank does whatever it needs to do to ensure its previously announced target will be hit.

7. Each firm chooses whether to pay a menu cost for permission to adjust its price now that it has observed the preference shock and the central bank's response.

The key to understanding the model is to understand that (if the die lands on A) firm A has a bigger incentive to pay the menu cost and change its price than do firms B or C. Because the relative demand shock is twice as big for firm A than it is for firm B or firm C. There may (or may not) be multiple equilibria, because if they observe "A-tails", firms B and C might choose to pay the menu costs and raise their prices if they expect that firm A will refuse to pay the menu cost to cut its price. But we are unlikely to observe such equilibria, because the driver commonly known to have the most to lose in a head-on crash will be more likely to swerve in a game of "chicken".

What will the equilibrium look like?

Let's start with inflation targeting.

All firms set a provisional initial price that hits the inflation target.

Suppose the preference shock is "A-heads".

If menu costs are very small, all three firms will pay the menu cost, firm A will raise its price, firms B and C will cut theirs, and the inflation target is hit and output is at Y* (the flexible price equilibrium).

If menu costs are very large, no firm will pay the menu cost, provided the central bank does not let Y deviate too far from Y*. Inflation stays on target, but output is indeterminate within that range (the central bank can manipulate output within that range without causing inflation to miss the target). [Update: but if firms expected the central bank to manipulate output away from Y*, they would want to set higher or lower initial relative prices, so there is no equilibrium where inflation is on target. So the central bank would commit not to do this.]

If menu costs are medium-sized, only firm A would pay the menu cost and raise its price if the central bank sets Y at Y*. But then inflation would rise above target. But the central bank knows this, and would have to ensure that Y is far enough below Y* to dissuade firm A from paying the menu cost. Inflation targeting causes a recession. (And inflation targeting causes a boom if the coin comes up tails.)

Now let's look at NGDP targeting.

All firms set an initial price that hits the NGDP target at Y*.

Suppose the preference shock is "A-heads".

If menu costs are very small, all three firms will pay the menu cost, firm A will raise its price, firms B and C will cut theirs, and the NGDP target is hit and output is at Y* (the flexible price equilibrium).

If menu costs are very large, no firm will pay the menu cost, provided the central bank does not let Y deviate too far from Y*. And since it targets NGDP, the central bank will not let Y deviate from Y*.

If menu costs are medium-sized, only firm A would pay the menu cost and raise its price if the central bank sets Y at Y*. But then NGDP would rise above target. But the central bank knows this, and would have to ensure that Y is far enough below Y* that the NGDP target is hit. But the recession would be smaller than under inflation targeting. Because under inflation targeting the central bank would have to create a recession big enough to dissuade firm A from paying the menu cost to raise its price. Under NGDP targeting the central bank can let firm A raise its price, provided it cuts Y by one third (because there are three firms) of the percentage that firm A raises its price. (There would be a boom if the coin came up tails, but a smaller boom than under inflation targeting.)

With three firms, NGDP targeting beats inflation targeting, because it leads to smaller output gaps. The larger the number of firms, the better NGDP targeting will perform. In the limit, as the number of firms gets very large, NGDP targeting will perform perfectly, though that is only true in this special model where only one firm gets chosen by the die. But NGDP targeting will outperform inflation targeting provided the shocks are skewed. Real world shocks will nearly always be skewed, to some extent.