A Reply to Steve Williamson -- Why Dynamic Stories are Important

Steve Williamson caused a firestorm in the blogosphere over his modeling results that helicopter drops in liquidity traps reduce the inflation rate. While hist first few posts were filled with mathematical equations, he was gracious enough in a recent post to present a story of what's going on in the model (my emphasis is bolded)

Next, conduct a thought experiment. What happens if there is an increase in the aggregate stock of liquid assets, say because the Treasury issues more debt? This will in general reduce liquidity premia on all assets, including money and short term debt. But we're in a liquidity trap, and the rates of return on money and short-term government debt are both minus the rate of inflation. Since the liquidity payoffs on money and short-term government debt have gone down, in order to induce asset-holders to hold the money and the short-term government debt, the rates of return on money and short-term government debt must go up. That is, the inflation rate must go down. Going in the other direction, a reduction in the aggregate stock of liquid assets makes the inflation rate go up.

Translated further, Steve's story is as follows:

1. The central bank prints more money
2. People don't want to hold onto that money
3. To make sure people hold onto that money, the inflation rate must fall (to make holding money more attractive)
4. Hence, printing money lowers the inflation rate.

Any cursory scholar of monetary economics should find that counterintuitive. I would suggest that it's counterintuitive because it's, well, wrong. In particular, the jump from (2) to (3) isn't clear at all. If everybody receives a helicopter drop, and nobody wants to spend it, then how does inflation fall? Or in the words of Paul Krugman: "How does this requirement translate into an incentive for producers of goods and services — remember, we’re talking about stuff going on in the real economy — to raise prices less or cut them?"

On the other hand, a much more realistic view would be a "monetary disequilibrium" or otherwise stated as David Hume's price specie flow mechanism as described by David Hume in his essay "On Money". At the moment that people get more money, the inflation rate is fixed. Hence the rate of return isn't high enough to hold money, and so people spend that money. This causes prices to rise and generates inflation.

Here's the fundamental problem with Steve's model: he acts as if equilibrium conditions are enough to explain causality. Sure, in equilibrium it must be that the inflation rate must equal the liquidity value of holding onto money. But that can happen in two ways. Either the inflation rate could fall (Steve's story), or people could hold less cash lower real cash balances, thereby raising the marginal value of their liquidity holdings. Dynamic stories matter, and if you can't explain how you get to equilibrium, you may end up on the wrong side of truth.

Edit: Adjusted for a few comments from Nick Rowe