Beliefs and the Monetary Transmission Mechanism

In my last post, I urged the Fed to raise the interest rate at its next meeting. In response to that post, David Andolfatto asks, 

Suppose a CB was to raise its policy rate permanently in an attempt to raise the inflation rate (without the corresponding policies you favor [in your post]). You claim that this would ultimately raise the rate of inflation (possibly after a recession). Can you describe the economic mechanism that would work to produce this result? (I mean, an explanation that extends beyond simply stating that the Fisher equation must hold.)

Here is my necessary, (but Wonkish) response. 

If we write a 'Fisher like equation' of the form

EQ 1) i - rho = E[Pi_t+1] + E[y_t+1] - y_t

Here, i is the money interest rate, y_t is GDP, Pi_t is inflation between dates t-1 and t and rho is the real rate of interest. E[ ] is the subjective expectation formed at date t. An equation like this would arise in a representative agent model with logarithmic preferences.

Now we can agree, I think, that if the Fed sets i equal to some constant rate, if we impose rational expectations, and if we write down a process that determines {y_t}; then an increase in i will lead to an increase in inflation. You want to know the adjustment mechanism from one steady state rational expectations equilibrium to another.

Let's assume that the Fed operates an interest rate peg, and that at some date, it announces an increase in that peg. At date t, one of two things can happen. Either, the increase in i can lead to an increase in E[Pi_t+1] + E[y_t+1], OR it can lead to a fall in y_t. If expectations are slow to adjust, the increase in the peg will lead to a fall in current GDP.

In my view, the equations needed to close this model are equations that determine E[Pi_t+1] and E[y_t+1], as functions of Pi_t, y_t i_t, and, other observables. Those equations are fundamentals that behave like preferences. It is the fact that expectations are 'sticky' that leads to nominal shocks, such as an increase in a purely nominal variable, like i, to have real effects.

In a slightly more complicated model, where the coefficients on output growth and inflation in equation 1, are different, the following expectations rule works well at explaining data

EQ 2) E[Pi_t_1] + E[y_t+1] - y_t = Pi_t + y_t - y_t-1

in words, expected nominal income growth is a martingale. By closing a three-equation model with that specification of the belief function, and by writing down a slightly more sophisticated version of a Taylor rule (not just a simple interest rate peg) I showed here that a model closed with a belief function, outperforms the NK Phillips curve model.

The idea of making the belief function 'fundamental' is consistent with equilibrium and rational expectations because of my assumption that the labor market operates as what I call, in my forthcoming book, Prosperity for All,  a 'Keynesian search market'. Employment and GDP growth are not uniquely pinned down in the steady state: they depend on initial conditions and the entire history of shocks.