## 16 June 2015

### In Theory, Monetary Offset Doesn't Work

Monetary offset, one of the major aspects of Market Monetarism, is severely hindered by the application of some basic macroeconomic theory. Take the bond pricing equation at the heart of most of modern macro:

$$c_t = \left[\frac{(1 + \rho)(1+E_t \pi_{t+1})}{1 + i_t}\right] E_t c_{t+1}$$

$c_t$ is current consumer spending, which is chosen in order to maximize all expected future consumption. When the real interest that can be earned on saving or investment increases above its natural rate, $\rho$, current consumer spending falls. In normal times, the central bank targets an inflation rate, $\pi_t$, which anchors inflation expectations to that target, so any adjustment in the nominal interest rate, $i_t$, directly changes current consumption. If the government decides to actively reduce its budget deficit which depresses GDP, the central bank can lower the nominal interest rate to offset this change. This is the theoretical explanation for monetary offset.

When the nominal interest rate is at zero, the central bank can no longer lower the nominal interest rate to counteract the effects of austerity. It only has two options: somehow increase inflation expectations or promise to keep future interest rates low. This is exactly what the Federal Reserve has resorted to in the last few years. Quantitative easing has increased inflation expectations and forward guidance has given the promise of an extended period of low rates. Perhaps expanding the monetary base like there's no tomorrow can have some effect in both keeping rates low and increasing inflation expectations. Nevertheless, neither of these policies are proven to work either in theory or in practice. Central banks are, for all intents and purposes, ineffective at increasing consumption at the zero lower bound.

Central banks slowly lose what small ability to control the economy they have as the economy returns to its natural state on its own. Inflation expectations are bound to fall as consumption returns to its natural level. At the zero lower bound, the steady state expected inflation rate falls $\frac{1}{1+\rho}-1$. This at least partially explains the multi-decade long period of low inflation and zero nominal interest rates in Japan. As the economy returns to equilibrium, the central bank will be progressively more powerless to offset shocks, fiscal or otherwise.

The key problem with Market Monetarism in general is that it isn't grounded in any kind of model outside of conjecture around a simple version of AD-AS in which the central bank has the ability to achieve any inflation or nominal GDP target it chooses. The reality is, central banks are not omnipotent and aggregate demand is more than just a negative function of the price level.

## 06 June 2015

### Graphs!

I recently decided to learn how to do more things than just simulate macroeconomic models in Octave (an open source version of Matlab) using Dynare (DSGE simulation tool for Matlab and Octave). The result was a whole lot of fun graphs:

First, I made the graph for a small labor market:

Next, I figured out how to make a Cobb Douglas Production Function:
Next, I made a drastically simplified money market:

Then I made a simple linear Utility Function with two consumption goods:
And finally, I made a graph showing utility maximization with a budget constraint (still working on this one):