## 26 June 2016

### The Trouble With Taylor Rules

Proponents of tight monetary policy like to show variants of the following chart
as evidence that the Federal reserve has kept interest rate too low since the financial crisis and that policy leading up to the financial crisis was too weak. To many this argument is compelling; as inflation is currently near target and output isn't too far from potential, the Federal Funds Rate should be higher, shouldn't it?

No. This analysis is flawed on multiple levels, most importantly its failure to acknowledge the nonneutrality of money. Of course no one who has shown this chart thinks that money is neutral, but they are nevertheless making a massive mistake. In reality, the interest rate implied by the Taylor Rule is affected by the actual level of interest rates. Say, for example, inflation is 2%, the output gap is zero, and the nominal interest rate is 3%. This implies an interest rate of roughly 4% in most specifications of the Taylor Rule, so the Federal Reserve raises interest rates by 1%. But now both output and inflation are lower, so the Taylor Rule suggests a lower interest rate. Thus, had the Fed raised interest rates back in 2011 when the Taylor Rule said it should have, since money is not neutral, inflation and output would have subsequently been lower, implying a lower rate suggested by the Taylor Rule.

Following a Neo-Wicksellian framework, any time inflation and/or output are above target, the interest rate either is currently or is expected to be below the natural rate. Given that both output and inflation are currently close to target, it is clear that the Wicksellian natural rate is about zero, or at least that the expected difference between all future interest rates and all future natural rates is about zero. Now is not the time to raise rates, then, as some Taylor Rules suggest.

Taylor Rules have the obvious problem of not taking the natural rate into account, or at least assuming that it is constant over time. This leads people to have mistaken expectations that interest rates should be at a certain level at full employment, not realizing that the level of interest rates determines whether or not we are at full employment; money is not neutral.

## 24 June 2016

### Why Wasn't it Greece?

Yesterday the United Kingdom voted to leave the European Union, or should I say England and Wales voted to leave the EU; Scotland and Northern Ireland (not to mention London and Cardiff) voted overwhelmingly to stay.

Some have argued that this is a good thing, or at least less of a bad thing because of how terrible the EU has been since 2010; the ECB clearly made a foolish mistake by raising rates in 2011 and post-2010 austerity has been a major drag on European, especially Southern European, countries. Britain leaving, therefore, sends a message to the undemocratic, inept EU and signals for either future reform or for the gradual collapse of the European Union.

Except the UK was affected by none of this. Britain wisely refrained from joining the Euro, so the Bank of England was free to hold rates constant while the ECB tightened monetary policy. Also British austerity was self imposed; no one in the EU forced George Osborne to slash deficits during the last government and the UK gave the Conservatives more support in 2015 than they gave them in 2010 -- the Conservatives came out of the 2015 general election with a full majority in the House of Commons.

So not only was the UK unaffected by the terrible policies of the EU over the last few years, it's populace handed a majority government to the very people who did impose austerity. Yesterday's result was not a victory for democracy, nor was it Britain's independence day; bar an early general election (which I would welcome), the UK is stuck with the same bad policy they supposedly voted to get rid of.

The people who should have been voting against EU membership yesterday are the millions of unemployed people in Spain, Portugal, Italy, Ireland, France, and Greece. In these countries, especially Greece, the electorate has denounced austerity with the rise of radical parties like Syriza in Greece, Podemos in Spain, and the National Front in France, yet the stability and growth pact dictates fiscal policy in these countries, not their legislatures.

On top of this Euro membership has removed any means of exiting recession with monetary stimulus; now countries hit harder by the financial crisis must go through an internal devaluation, in which their real exchange rate must fall, but their nominal exchange rate is pegged leaving prices and wages the only means of adjustment. Price stickiness and wage rigidity make this incredibly painful, hence the record unemployment.

Of all the member states of the European Union, the UK had the least reason to leave, but here we are. Yesterday should have been Grexit, but we got Brexit instead.

## 22 June 2016

### Market Monetarism and Multiple Equilibria

I have consistently taken issue with the likes of Sumner because of what I view as his confusion of policies and the results of policies, or rather his confusion of policies and observations. Case in point would be the post I was just reading, in which Sumner says
But how did the Swiss authorities make sure this decrease in interest rates had a contractionary impact? The answer is simple; they did a simultaneous, once and for all, massive appreciation in the SF.
This idea that the exchange rate is just something that the SNB can set (while setting interest rates) is terrifyingly stupid from a conventional viewpoint. In general monetary policy can be seen through one of two lenses: 1) the central bank sets the monetary base and everything else is endogenous or 2) the central bank sets the short term risk free interest rate and everything else (including the monetary base) is endogenous.

Sumner regularly flaunts this view by suggesting that a central bank can, for example, set the interest rate and set the exchange rate at the same time. This is where my epiphany comes in. What's really going on is that there are multiple equilibria. A cut in the nominal interest rate can either occur through an increase in the money supply (ceterus paribus) or a negative shock to money demand (ceterus paribus), but which occurs in a given scenario? Obviously it's almost always a combination of both -- the monetary base is rarely constant and neither is money demand, but absent the presence of a more complete model, what I just outlined has many possible equilibria.

Sumner's solution to this problem is, rather than more completely specify the model, to simply choose the equilibrium that is consistent with the facts and assert that the central bank is responsible for bringing that equilibrium about. Do I think this approach is valid? Not exactly. Nevertheless I am much more sympathetic to it than what I previously perceived from Sumner. Furthermore even some full models exhibit multiple equilibria -- like New Keynesian models in which the Taylor Principle is not followed -- meaning that Sumner's approach to, e.g., Neo-Fisherism, while not as 'correct' as a more analytical description of the possible equilibria is at most equally egregious to Cochrane's dubious equilibrium selection.

To put this in terms more conducive to Sumner's typical line of reasoning, low interest rates can either be consistent with high NGDP or low NGDP. In his view the central bank chooses which equilibrium prevails and that equilibrium selection is the 'stance' of monetary policy. I personally don't think that assuming central banks are capable of equilibrium selection without explicitly modeling it is a good thing, but at least it's better than just assuming central banks are capable of pegging whatever nominal variable to whatever they want regardless of the circumstances.

## 10 June 2016

### Either the Model is Wrong or Market Monetarism is Wrong

The idea that the zero lower bound is not actually a significant constraint on the ability of monetary policy to raise nominal GDP is integral to Market Monetarism. If the zero lower bound actually represents that constraint that mainstream macro says it does, then nothing Scott Sumner has said about monetary offset in the last 8 or so years is right.

Thus the stakes are quite high and, ignoring the extremely clear evidence that open market operations are useless at the zero lower bound (just look at the velocity of the monetary base in any country at the zero lower bound), if we can demonstrate that monetary policy is impotent at the zero lower bound, then the battle is won.

Unfortunately Market Monetarists refuse to believe that plummeting base velocity is tantamount to proof that further monetary expansion is next to useless at the zero lower bound, so the only possible argument is theoretical and therefore necessarily inconclusive. Nevertheless, I can at least prove that whatever model Sumner et al. are appealing to is not mainstream in the least when it comes to liquidity traps.

The most potent example of this is the consumption Euler equation, written in log terms like this:
$$c_t = E_t c_{t+1} - \theta(i_t - E_t \pi_{t+1} - r^n_t)$$
Assuming $\theta=1$ and, in line with most of the New Keynesian literature, that there is no investment or government spending, it can be rewritten in terms of nominal GDP:
$$n_t = E_t n_{t+1} -(i_t - r^n_t)$$

This simple relationship shows exactly how the Market Monetarist policy prescription of nominal GDP level targeting fails to alleviate periods in which $r^n_t$ -- that is the real natural rate of interest -- is negative. If the central bank targets zero nominal GDP growth, for instance,  then any time $r^n_t < 0$ either current nominal GDP must fall below target or future nominal GDP must go above target. The only two ways to avoid recession are to either abandon nominal GDP level targeting or to use expansionary fiscal policy.

Since the Market Monetarist position is clearly at odds with this interpretation, it is evident that whatever model each Market Monetarist appeals to (whether it is Sumner's Musical Chairs 'model' or whatever Nick Rowe is currently using to tell everyone recessions are excess demand for the medium of exchange) is not consistent with the basic assumption of utility maximization and a budget constraint needed to derive the consumption Euler equation and, in the interest of having an argument in which we all aren't yelling past each other, that model should be made clear; what specifically is wrong about the Euler equation?