Nominal GDP is just one of an infinite number of variables that monetary policy might target. The probability that NGDP is exactly the best target variable is infinitesimal. I nevertheless support NGDP targeting, because I think it is probably reasonably close to that unknown best target variable; and I think NGDP level path targeting is probably better than reasonable alternatives like inflation or price level targeting.
Here are three reasons why I believe that:
There are lots of long-term contracts with payments fixed in nominal terms. Not just long term bonds, but things like pension plans and government transfer payments. We aren't very good at forecasting what real GDP wil be 10 or 30 years from today. Inflation or price level targeting gives the creditor full insurance against unforeseen changes in future real GDP, and puts all the risk upon the debtor. This doesn't seem to be an efficient or a fair way to allocate aggregate risk. NGDP targeting provides a 50-50 aggregate sharing of aggregate risk between creditors and debtors. If real GDP falls 10% below what was expected, the price level rises 10% above what was expected. The real incomes of both creditors and debtors fall by the same 10%. It is unlikely that 50-50 sharing of that risk would be exactly first best in all circumstances, but it is probably better than a 0-100 allocation of that risk.
Sure, debt contracts can always be renegotiated. But the whole point of having a long-term contract is because you don't want to renegotiate it every year or every day when circumstances might change. If the expectation of renegotiation weren't a problem, we wouldn't have agreed to a long-term contract in the first place. "Here's $100; let's leave it open for future negotiation how much you pay me." That's not a contract. I might say that to my kids or close friends, but I wouldn't do business on that basis.
2. Divine Coincidence Failure. The Old Keynesians wanted to target real GDP. They wanted monetary (and/or fiscal) policy to target "full-employment output". It sounded like a good idea at the time. After all, real Y is what really matters. P doesn't matter at all. The rate of change of P (the inflation rate) only matters a little (unless it gets very big or very negative). But Friedman and Phelps, and the policy failures of the 1970's, taught us it couldn't work. A Y target lacks a nominal anchor.
So we switched to targeting P, or the rate of change of P.
Since NGDP=P.Y, you can think of NGDP targeting as a 50-50 compromise between the Old Keynesian Y target and the New Keynesian P target. It is probably a reasonably good compromise.
Many New Keynesian models assume Divine Coincidence. They assume that if monetary policy is successful in keeping P on target it will also, as a happy side-effect, keep Y on target too.
If there are only AD shocks, diving coincidence holds trivially; if monetary policy can prevent the AD curve fluctuating, P will stay on target, and Y will stay on the LRAS curve too. But if there are supply shocks, Divine Coincidence may or may not hold. It all depends on the model.
Suppose that a negative supply shock causes the LRAS and SRAS curves to shift left by exactly the same amount. In that case Divine Coincidence holds. Keeping P on target will keep Y equal to LRAS. I do not understand SRAS shocks very well at all, but I don't think the world is like that. I think that a typical supply shock shifts the SRAS curve left (or right) by a much greater amount than it shifts the LRAS curve left (or right). And if I'm right on that point, then NGDP will be a better target variable than P (though NGDP will only be exactly optimal under very special parameter values). That's because an unchanged target for P will cause Y to fall by the full amount of the leftward shift in SRAS, when we only want Y to fall by the amount of the leftward shift in LRAS. An unchanged target P.Y will allow P to rise so Y won't fall as much.
It is possible to build models in which real shocks cause SRAS to shift sideways by more than LRAS shifts sideways (or even make the two curves shift in opposite directions). A model with sticky nominal wages and flexible prices is one, because a negative productivity shock would usually require equilibrium real wages to fall, which can only happen if P rises. The Ball-Mankiw model(pdf) of skewed relative price changes plus menu costs is another. I am less than fully convinced by those models, but they do seem to match what I think I see usually happening. Things like oil price shocks, or changes in indirect taxes, seem to cause the SRAS curve to shift vertically up or down, without seemingly shifting the LRAS curve much at all.
Plus, SRAS shifts can also be the consequence of past failures to prevent AD shifts. When monetary policy fails, an AD shock plus nominal rigidity has real effects that persist for longer than the AD shock and nominal rigidity. We call this "hysteresis". I suspect that hysteresis acts much like other supply shocks, and causes the SRAS curve to shift by more than the LRAS curve shifts. The failure of inflation to fall significantly in the recent recession is one reason I believe this. Though I do not understand this anywhere nearly as well as I would like.
3. Self-stabilising AD. It is reasonably well understood that Price Level Path Targeting has a desirable property that Inflation Targeting lacks. Central banks are imperfect and not omniscient and will sometimes make mistakes. Suppose there's a negative AD shock, and that P falls relative to target. Under PLPT people will expect a temporarily higher than normal inflation rate going forward. This will automatically lower the real rate of interest relative to the natural rate of interest and make AD higher than it would otherwise be, so the fall in AD is less than it would be under inflation targeting.
PLPT beats IT in this case because it helps anchor expected future P. Anchoring expected future Y, if that were feasible, would also prevent AD from falling as much for exactly the same reason. The natural rate of interest is an increasing function of the expected growth rate of Y. The higher is expected future Y, the greater will be investment and consumption demand.
When a negative AD shock hits, both P and Y will fall. When AD recovers both P and Y will rise. But we know very little about how that rise in AD will be divided into a rise in P and a rise in Y. It depends on the slope of the SRAS curve, about which we know little. And we know even less about how people will expect any recovery to be divided between a rise in P and a rise in Y.
Relying on the self-stabilising properties of PLPT puts all our eggs into one basket. If the SRAS curve is fairly flat, P will fall little when AD falls, and will be expected to rise by little when AD recovers, and the self-stabilising properties will be weak. NGDP Level Path Targeting means convincing people that if PY falls then PY will rise back up again. And this means putting our self-equilibrating eggs into two baskets that are negatively correlated, which makes our portfolio of self-stabilisation much safer. When a negative AD shock hits, people will know for sure that PY will rise, and so will know for sure that either P will rise or that Y will rise, and either way they know for sure they should invest more and consume more now.
4. Scott Sumner. Not really a reason, but definitely influential in slowly changing my mind.