You know, Stephen, you would be doing a great service to economists as well as the general public if you would finally answer the question asked of you many times, in many ways, how can we get inflation -- in the US, right now, in our current situation, with our current employment level, inflation level, etc. -- without also getting an increase in employment and real GDP.Here's my stab at an answer.
The key question here is: "how can we get inflation ... without also getting an increase in employment and real GDP." The question is a bit odd, as we usually ask it the other way around. Monetary policy seems to be about manipulating nominal quantities, so how on earth can that have anything to do with real quantities like employment and real GDP? As for many economic questions, it is useful to start with the simplest case and then make it more complicated. An uncontroversial notion in macroeconomics is that money is neutral in the long run. If the central bank increases the level of the quantity of outside money - currency and reserves - in a one-time fashion, in the long run all nominal quantities, including prices and wages, will increase in proportion to the money supply increase, and there are no real effects.
Now, think about something more complicated. Imagine that the central bank permanently increases the rate of growth rate in the stock of outside money. Would this be neutral in the long run? Well, clearly not, as otherwise why do we care about inflation? If increasing the level of the money stock increases the price level, then increasing the rate of growth in the money stock increases the inflation rate in the long run. Leave aside the question of what these long-run nonneutralites from changes in money growth are (more on that later when I have time), but suffice to say that a higher money growth rate implies a higher inflation rate in the long run, and this relationship is roughly one-for-one.
Another complication is thinking about what the short-run non-neutralities of money are. This is much more controversial. There are many different ideas about short-run nonneutralities, and the implications for monetary policy. Among these are:
1. Lucas (1972 "Expectations and the Neutrality of Money"): Monetary policy has short run effects because monetary intervention confuses price signals for private sector producers. I am producing a product for which the market price goes up. I produce more thinking that this is because my price went up relative to other market prices, but I was fooled into thinking so. Actually, what happened was that the Fed increased the money supply and all prices went up. All producers are in fact doing the same thing. Policy conclusion: The Fed should behave in a predictable fashion. This monetary intervention may move output around, but those fluctuations are inefficient. Is this theory any good? I don't think many economists pay much attention to it any more, principally because it seems the information friction in this type of model is not plausible.
2. Sticky prices: The New Keynesian story is that only some firms can or wish to change their prices in the short run. If I am a sticky-price firm, I produce more when demand for my product rises. Demand for the products of all firms can rise in the present due to monetary intervention which reduces the nominal interest rate, which also reduces the real interest rate (remember the prices are sticky), and therefore induces intertemporal substitution of goods, increasing the demand for goods in the present. Policy conclusion: It need not be efficient for the central bank to increase output, even though it can. However, there is a role for monetary policy in minimizing the welfare losses from the relative price distortions induced by sticky prices. A key flaw in the theory is the link between monetary policy and output. We have to think that is somehow less costly for the firm to hire more factor inputs and produce more output in the face of higher demand than to increase its price.
3. Sticky wages: In modern macro, this works much like (2), with the same caveats.
4. Market segmentation: Early models of this type were Grossman and Weiss and Rotemberg. Lucas worked on this, as did Fernando Alvarez, Andy Atkeson, Pat Kehoe, and Chris Edmond, among others. The idea here is that different people, firms, and financial institutions have different degrees of participation in financial markets. Some hold stocks, others don't; some trade frequently in sophisticated asset markets, others don't; some have transactions accounts with banks, but others don't. What this leads to is a distributional wealth effect from monetary policy actions. For example, an open market operation will have its first round effects on the economic agents who trade frequently in financial markets, and thus have initially large effects on asset prices, e.g. nominal interest rates. Over time, the effects become more diffuse, affecting everyone in the economy. These models never gained much traction, though Christiano and Eichenbaum did some empirical work in the early to mid-1990s on this stuff. I think they are interesting, but I don't think this mechanism will give you much in terms of effects on aggregate output and employment.
5. New Monetarist Models (shameless advertising): You can read about that stuff here, here, and here. One idea in here is that asset liquidity and liquidity premia are determined by how assets are used in exchange, and monetary policy actions can have subtle effects on asset prices and output that we can understand by being explicit about the exchange process in retail markets and financial markets.
6. Models with Illiquidities: Here, I am thinking of work by Mark Gertler, Nobu Kiyotaki, and John Moore, among others. This is somewhat related to (5), but is less explicit about the financial frictions. Interesting ideas though.
Where does that leave us right now? I more or less dismissed (1) as a useful theory of monetary policy. What does (2) tell us about what the effects of QE2 will be? This theory tells us that, once we are at the zero lower bound on the nominal interest rate, there is nothing the central bank can do. We can lower the interest rate on reserves from 0.25% to zero, but that won't do much, according to the theory. Of course there are some nominal interest rates - the yields on long maturity bonds - that are positive, but New Keynesian models are silent about how the quantities on the central bank's balance sheet can move those long-term interest rates. Ditto for (3).
Now, market segmentation might be able to tell us something here. Indeed, old-fashioned "preferred-habitat" models (though I don't want to call these things models - they are really just stories) are essentially about market segmentation. Given enough market segmentation, the Fed could in principle reduce long bond yields by purchasing long bonds. Also, (5) and (6) may have something to say as well. Exchanges of outside money for long-maturity Treasury bonds by the Fed could indeed increase the average liquidity of the outstanding debt of the Treasury and Fed combined. To the extent that the marginal value of liquidity in financial markets is high, this will matter, and could reduce long bond yields.
Now, how much will any of these things matter for real activity in the short run given the size of the QE2 operation? I think not much. With short-term nominal interest rates close to zero, and the market already flooded with liquidity from the previous large-scale asset purchases conducted by the Fed, I can't see that it will matter much, for real activity. It can certainly matter for inflation though, and this depends on the extent to which the outside money injections are not just held as reserves. One way you can think of the price increases happening without any increase in output is that price increases feed through the chain of supply. The price increases start in the markets for commodities - a storable commodity is just another asset, and we can think of this fitting into the array of available assets. Even if there are few good investment projects to fund, monetary policy actions can have the effect of bidding up the prices of commodities. These commodities are used in production processes, and increases in their prices increase the costs of production, and therefore lead to increases in final goods prices and in wages. All prices and wages go up together with little or no real effects.