# Monthly Archives: December 2017

## The Quantity Theory of Money: Lessons from Sweden’s Age of Freedom

Throughout the 17th and early 18th century, Sweden had a significant empire in northern Europe. In 1700, an alliance of Denmark-Norway, Russia, and others attacked the Swedes. While Charles XII, then the king of Sweden, had initial success against this alliance, he was eventually wounded and the Swedes never really recovered. Charles died in 1718. Charles had taken power at the age of 15 and spent virtually his entire adult life at war. He never married nor did he have children. When he died, there was uncertainty about who had the rightful claim to the throne. Charles’s sister Ulrika claimed that she was the rightful heiress since she was the closest living relative. Ultimately, the Swedish Riksdag agreed to recognize Ulrika in exchange for eliminating the absolute monarchy and setting up a parliamentary system. In this new system, the political power was concentrated in the Riksdag. The period from 1721 – 1772 is therefore known as “Frihetstiden”, or the Age of Freedom.

During the Age of Freedom, the Riksdag was dominated by two political parties that were referred to as the Hats and the Caps. The Hats controlled power for nearly 30 years beginning in 1738 and were mercantilists (their motto was “Svensker man i svensk drakt”, or “Swedish men in Swedish clothes”). In 1739, The Hats used the Swedish central bank, the Riksens Standers Bank (what is now known as the Riksbank), to give loans to private industry. These loans were funded with the creation of bank notes. In addition, the Hats started an ill-fated war with the Russians over parts of Finland. During this time, Sweden was effectively on a copper standard, but the expansion of bank notes for the provision of private lending and the use of the bank to finance the war ultimately led to the suspension of convertibility into copper in 1745. The increase in the provision of private credit by the central bank continued. In the 1750s, Sweden entered the Seven Years War to fight alongside their French allies. Sweden was particularly involved in the Pomeranian War with Prussia over land that they had lost in the Great Northern War under Charles XII (discussed above). The Hats were hesitant to levy any new taxes to pay for the war because to do so would require calling the Riksdag and therefore divulging the state’s budget. As a result, loans to the Crown increased substantially during the war and the supply of bank notes increased correspondingly.

The Hats seemed to view the money supply as a limiting factor in development. They thought that an increase in the money supply would increase aggregate demand, which would encourage greater production and entrepreneurship. Increases in the money supply could apparently have a permanent effect on output. The opposition party, the Caps, countered that this increase the supply of bank notes was excessive and that the excess supply of money was causing rising prices and a depreciation of the exchange rate. By 1765, the public voted the Caps into power and the Hats become the main opposition party. Upon taking power the Caps decided to decrease the money supply in order to restore the price level and the exchange rate to what it had been prior to this expansion. What followed was a major decline in the supply of bank notes and a very costly deflation. The deflation was so costly that it pushed the Caps out of power and returned the Hats to power. Ultimately, a coup ended the parliamentary system and restored the monarchy. Shortly thereafter, Sweden adopted a silver standard.

So why give you all of this history? The reason is that this series of events represents a sort of quasi-natural experiment regarding monetary policy. The Hats engaged in a deliberate increase in the money supply to increase economic activity and finance a war. What followed were significantly higher prices and a depreciation of the exchange rate. The increase in the money supply can be considered exogenous in the sense that the change in the money supply was brought about through deliberate policies by the Hats and is therefore immune to claims that higher prices were causing an increase in the supply of bank notes. The subsequent reduction of the money supply by the Caps brought about a significant deflation. Again, this was a deliberate attempt by the Caps to reduce the money supply and is therefore immune to claims of reverse causation. As Johan Myhrman notes “it is almost like a controlled experiment.” Below is a line graph of the monetary base and the price level during the period in question (the source is Riksbank historical statistics). I have also plotted the best linear fit of the data. As shown in the figure, there is a standard quantity theoretic interpretation of the data. Given the quasi-experimental nature of the period, this would seem to provide strong evidence in favor of the quantity theory of money under an inconvertible paper money.

## The Phillips Curve, Again

The Phillips Curve is back. In saying so, I do not mean to imply that being “back” refers to a sudden reappearance of a stable empirical relationship between unemployment (or the output gap) and inflation. The Phillips Curve is back in the same way that conspiracy theories about the assassination of JFK are back after the recent release of government documents. In other words, the Phillips Curve is something that people desperately want to believe in, despite the lack of evidence.

The Phillips Curve is all the rage among central bankers. Since the Federal Reserve embarked on quantitative easing, they have been ensuring the public that QE would not be inflationary because of the slack in the economy. Until labor market conditions tighten, there would be little threat of inflation. Then, as the labor market tightened, the Federal Reserve warned that they might have to start raising interest rates to prevent these tightening conditions from creating inflation.

What is remarkable about this period is that the Federal Reserve has undershot its target rate of inflation throughout this entire period — and continues to do so today. So what does this tell us about the Phillips Curve and what can we learn about monetary policy?

If one looks at the data on unemployment and inflation (or even the output gap and inflation), you could more easily draw Orion the Hunter as you could a stable Phillips Curve. Fear not, sophisticated advocates of the Phillips Curve will say. This is simply the Lucas Critique at play here. If a Phillips Curve exists, and if the central bank tries to exploit it, then it will not be evident in the data. In fact, if you take a really basic 3-equation-version of the New Keynesian model, there is a New Keynesian Phillips Curve in the model. However, when you solve for the equilibrium conditions, you find that inflation is a function of demand shocks, technology shocks, and unexpected changes in interest rates. The output gap doesn’t appear in the solution. But fear not, this simply means that monetary policy is working properly. The Phillips Curve is apparently like the observer effect in quantum mechanics in that when we try to observe the Phillips Curve, we change the actual result (this is a joke, please do not leave comments about why I’ve misunderstood the observer effect).

However, I would like to submit that even this interpretation is problematic for thinking about monetary policy and defending the Phillips Curve. In the New Keynesian model, we get an equation that looks like this:

$\pi_t = \beta E_t \pi_{t+1} + \kappa y_t$

where $\pi$ is the rate of inflation, $y_t$ is the output gap, and $\kappa$ and $\beta$ are parameters. This equation is an equilibrium condition of the model. Since it is an equilibrium condition, it always holds. This equilibrium condition can be derived by (1) having a monopolistically competitive firm solve a profit-maximization problem with a Rotemberg-esque quadratic adjustment cost associated with prices, (2) solving for a symmetric equilibrium, and (3) log-linearizing around the steady state. So this is an equilibrium condition for the aggregate economy. When you look at this equation, you would think that you can use this equation for some intuition about the evolution of inflation. To demonstrate how silly it would be to do so, let’s assume that people in the economy are sufficiently patient that we can re-write this equation as:

$\pi_t = E_t \pi_{t+1} + \kappa y_t$

So you look at this equilibrium condition and you get a very New Keynesian interpretation of the world. It looks as though inflation is explained by changes in expected inflation and changes in the output gap. However, this interpretation is wrong. This equation is an equilibrium relationship. Thus, I could just as easily re-write this equation as

$y_t = \frac{1}{\kappa} (\pi_t - E_t \pi_{t+1})$

Hmm. Now we have something that looks like an expectations augmented Phillips Curve with the direction of causation moving in the opposite direction. Now, it looks as though unexpected changes in inflation are causing changes in the output gap.

So what is a central bank to do?

Actually, using this equation alone, we can’t say anything at all! This equation is just an equilibrium relationship. Without knowing anything else about the economy, this tells us nothing. We have one equilibrium equation with two unknowns. In addition, we have a rational expectation about inflation, which implies that the expectation is model-consistent. In order to know what a model consistent expectation is, we need to have a model from which we can form expectations. In other words, this equation tells us absolutely nothing in isolation from a bigger model.

For example, suppose that we are in a world with the gold standard. Let $p_t$ be the log of the price level. A reasonable assumption would be that $p_t$ follows a random walk:

$p_t = p_{t-1} + e_t$

or

$\pi_t = e_t$

Combining this with our Phillips Curve would give us

$y_t = \frac{1}{\kappa} \pi_t = \frac{1}{\kappa} e_t$

So output and inflation are driven by shocks to the price level. There is no exploitable relationship between inflation and the output gap, despite the fact that (a) regressing the output gap on inflation would yield a positive coefficient, and (b) the model features a New Keynesian Phillips Curve. This is important because the best evidence that we have when it comes to the Phillips Curve is from the gold standard era.

In addition, if the quantity theory holds, then the rate of inflation and the expected rate of inflation would be determined by the path of money supply. Output would then adjust to fit the equilibrium condition that looks like a Phillips Curve. This was the view of Fisher and Friedman, for example.

What all of this means is that even given the fact that the New Keynesian model features an equation that resembles the Phillips curve, this does not imply that there is some predictive power that comes from thinking about this equation in isolation. In addition, it certainly does not imply that changes in the output gap cause changes in the rate of inflation. There is no direction of causation implied by this one equilibrium condition.