Category Archives: Macroeconomic Theory

How Did the Gold Standard Work? Part 1: The Efficiency of the Gold Standard

Sebastian Edwards has written an interesting new book about FDR’s devaluation of the dollar and the legal and economic consequences thereof. This post is not about the book, although I do recommend it. What I would like to write about is motivated by some of the reaction to this book that I’ve seen and heard regarding gold and the gold standard. In recent years, I have become convinced that what I thought was the conventional wisdom on the gold standard is not widely understood. So I’d like to write a series of posts on the gold standard and how it worked. My tentative plan is as follows:

Part 1. The efficiency of the gold standard.
Part 2. The determination of the price level under the gold standard.
Part 3. The Monetary Approach to the Balance of Payments vs. the Price-Specie Flow Mechanism
Part 4. Gold standard interpretations of the Great Depression.

I don’t have a timeline for when these will be posted, but it is my hope to have them posted in a timely fashion so that they can get the appropriate readership. With that being said, let’s get started with Part 1: The efficiency of the gold standard.

Some people define the gold standard in their own particular way. I want to use as broad of a definition as possible. So I will define the gold standard as any monetary system in which the unit of account (e.g. the dollar) is defined as a particular quantity of gold. This definition is broad enough to encapsulate a wide variety of monetary systems, including but not limited to free banking and the pre-war international gold standard. Given this definition, the crucial point is that when the unit of account is defined as a particular quantity of gold, this implies that gold has a particular price in terms of this unit of account. In other words, if the unit of account is the dollar, then all prices are quoted in terms of dollars. The price of gold is no different. However, since the dollar is defined as a particular quantity of gold, this implies that the price of gold is fixed. For example, if the dollar is defined as 1/20 of an ounce of gold, then the price of an ounce of gold is $20.

This type of characteristic poses a lot of questions. Does the market accept this price? Or, is there any tendency for the market price of gold to equal the official, or mint price? This is a question of efficiency. If the market price of gold differs substantially from the official price, then the gold standard cannot be thought of as efficient and one must consider the implications thereof for the monetary system. What determines the price level under this sort of system? Does the quantity theory of money hold? What about purchasing power parity? In many ways, these questions are central to understanding not only of how the gold standard worked, but also the nature of business cycles under a gold standard. The price level and purchasing power parity arguments are equilibrium-based arguments. This raises the question as to what mechanisms push us in the direction of equilibrium. We therefore need to compare and contrast the monetary approach to the balance of payments with the price-specie flow mechanism. Finally, given this understanding, I will use the answers of this question to gain some insight into the role of the gold standard with regards to the Great Depression.

In terms of efficiency, we can think about the efficiency of the gold market in one of two ways. We could consider the case in which the dollar is the only currency defined in terms of gold. In this case, the U.S. would have an official price of gold, but gold would be sold in international markets and the price of gold in terms of foreign currencies is entirely market-determined. Alternatively, we could consider the case of an international gold standard in which many foreign currencies are defined as a particular quantity of gold. For simplicity, I will use the latter assumption.

This first post is concerned with whether or not the gold standard was efficient. So let’s consider the conditions under which the gold standard could be considered efficient. We would say that the gold standard is efficient if there is (a) a tendency for the price of gold to return to its official price, and (b) if market price of gold doesn’t different too much from the official price.

Under the assumption that multiple countries define their currency in terms of the quantity of gold, let’s consider a two country example. Suppose that the U.S. defines the dollar as 1/20 of an ounce of gold and the U.K. defines the pound as 1/4 of an ounce of gold. It follows that the price of one ounce of gold is $20 in the U.S. and £4. Note that this implies that $20 should buy £4. Thus, the exchange rate should be $5 per pound. We can use this to discuss important results.

Suppose that the current exchange rate is equal to the official exchange rate. Suppose that I borrow 1 pound at an interest rate i_{UK} for one period and then exchange those pounds for dollars and invest those dollars in some financial instrument in the U.S. that pays me a guaranteed rate of i_{US} for one period.

The cost of my borrowing when we reach the next period is (1 + i_{UK})\pounds 1. But remember, I exchanged pounds for dollars in the first period and 1 pound purchased 5 dollars and invested these dollars. So my payoff is (1+i_{US})\$5. I will earn a profit if I sell the dollars I received from this payoff for pounds, pay off my loan, and have money left over. In other words, consider this from the point of view in period 1. In period 1, I’m borrowing and using my borrowed funds to buy dollars and invest those dollars. In period 2, I receive a payoff in terms of dollars that I sell for pounds to pay off my loan. If there are any pounds left over, then I have made an arbitrage profit. Let f denote the forward exchange rate (the exchange rate in period 2), defined as pounds per dollar. It follows that I can write my potential profit in period 2 as

(1+i_{US})f\$5 - (1+i_{UK})\pounds 1

We typically assume that in equilibrium, there is no such thing as a perpetual money pump (i.e. we cannot earn a positive rate of return with certainty with an initial investment of zero). This implies that in equilibrium, this scheme is not profitable. Or,

(1+i_{US})f\$5 = (1+i_{UK})\pounds 1

Re-arranging we get:

(1+i_{US})f\frac{\$5}{\pounds 1} = (1+i_{UK})

This is the standard interest parity condition. Note that f is defined as pounds per dollar. If the gold standard is efficient we would expect the forward exchange rate to equal to official exchange rate (we should rationally expect that the gold market tends toward equilibrium and the official prices hold). Thus, one should expect that f = .20. Plugging this into our no-arbitrage condition implies that:

i_{US} = i_{UK}

In other words, the interest rate in both countries should be the same. There is a world interest rate that is determined in international markets.

However, remember that this is an equilibrium condition. Thus, at an point in time there is no guarantee that this condition holds. In fact, in our arbitrage condition, we assumed that there are no transaction costs associated with this sort of opportunity. In addition, under the gold standard, we do not have to exchange dollars for pounds or pounds for dollars. We can exchange dollar or pounds for gold and vice versa. Thus, under the gold standard what we really care about are market prices of the same asset in terms of dollars and pounds. For example, consider a bill of exchange. The price paid for a bill of exchange is the discounted value of the face value of the bill.

e = \frac{\frac{\pounds 1}{(1 + i_{UK})}}{\frac{\$5}{(1+i_{US})}} = \frac{\pounds 1}{\$5} \frac{1+i_{US}}{1+i_{UK}}

So if the ratio of the prices of these bills differ from the official exchange rate, there is a potential for arbitrage profits. As the equation above implies, this can be reflected in the ratio of interest rates. However, it can also simply be observed from the actual prices of the bills.

Officer (1986, p. 1068 – 1069) describes how this was done in practice (referencing import and export points as what we might call an absorbing barrier under which it made sense to engage in arbitrage, given the costs):

In historical fact, however, cable drafts in the pre-World War I period were dominated by demand (also called “sight”) bills as the exchange medium for gold arbitrage. Purchased at a dollar market price in New York, the bill would be redeemed at it pound face value on presentation to the British drawee, with the dollar-sterling exchange rate give by the market price/face value ratio. When this rate was greater than the (demand bill) gold export point, American arbitrageurs (or American agents of British arbitrageurs) would sell demand bills, use the dollars thereby obtained to purchase gold from the U.S. Treasury, ship the gold to London, sell it to the Bank of England, and use part of the proceeds to cover the bills on presentation, with the excess amount constituting profit.

[…]

When the demand bill exchange rate fell below the gold import point, the American arbitrageur would buy demand bills, ship them to Britain, present them to the drawees, use the proceeds to purchase gold from the Bank of England, ship the gold to the United States, and (if not purchased in the form of U.S. coin) convert it to dollars at the U.S. mint.

Thus, we can think of interest rate differentials as opportunities for arbitrage directly, or as reflecting the current market exchange rate. In either case, the potential opportunities for arbitrage profits ultimately kept gold near parity. In fact, Officer (1985, 1986) shows that gold market functioned efficiently (and in accordance with our definition of efficiency).

With this in mind, we have a couple of important questions. This discussion focuses entirely on the microeconomics of the gold standard. In subsequent posts, I will shift the discussion to macroeconomic topics.

The Phillips Curve and Identification Problems

Frequent readers of the blog (can you be frequent if I only write about 5 or 6 times a year?) will know that I often criticize the Phillips Curve. One counterargument that I receive to my complaints about the Phillips Curve is that my critiques are unfair because they ignore the role of countercyclical monetary policy. For example, suppose that the following two things are true:

1. The central bank responds to a positive output gap by tightening monetary policy.
2. Inflation is caused by positive output gaps.

If these two things are correct, the critics say, then you might fail to see an empirical relationship between inflation and the output gap (or even a negative relationship). However, this violates point (2) which we’ve assumed to be true. Thus, we have an identification problem. The failure to find an empirical relationship might be because countercyclical policy is masking the true underlying, structural relationship. (I could make a similar argument about the quantity theory that, for some odd reason, is not as popular as this story.)

Well, if identification is the problem, then I have a solution. During the period from 1745 to 1772, Sweden’s central bank, the Riksbank, issued an inconvertible paper money. What we would now call monetary policy was carried out through discretionary means. For example, the Hat Party, which controlled the Riksdag and the Riksbank from 1739 to 1765, expanded the bank’s balance sheet in an attempt to increase economic activity. However, while monetary policy was determined through discretion, there is no evidence whatsoever that the central bank used countercyclical policy. In fact, the Hat Party explicitly thought that monetary expansions would boost economic activity. The closest thing to a countercyclical policy occurred when the Cap Party took over and reduced the money supply in an attempt to bring down the price level. However, they did this so dramatically that any good advocate of the Phillips curve would believe that this would result in a negative output gap and deflation such that the relationship would still hold.

So, what we have here is a period of time in which the identification problem is not of any significance. As a result, we can have a horse race between the quantity theory of money and the Phillips Curve to see which is a better model of inflation.

Here is a figure from my recent working paper on the Riksbank that looks at the relationship between the supply of bank notes and the price level from 1745 – 1772. The solid line represents the best linear fit of the data. This graph seems entirely consistent with the quantity theory of money.

Now let’s look at a Phillips Curve for the same period. To do so, I construct an output gap as the percentage deviation of the natural log of real GDP per capita from its trend using the Christiano-Fitzgerald filter (the trend is computed using data from 1668 to 1772). Here is the scatterplot of the output gap and inflation.

Hmmm. There doesn’t seem to be any clear evidence of a Phillips Curve here. In fact, note that the relationship between the output gap and inflation should be positive. Yet, the best linear fit is negative (but not statistically significant). Maybe its the filter. Let’s replace the output gap with output growth (a proxy for the output gap) and see if this solves the problem.

Hmm. The Phillips Curve doesn’t seem to be there either. In fact, the slope is steeper (i.e., going in the wrong direction) and now statistically significant.

So here we have a period of time in which the central bank is using discretion to adjust the supply of bank notes and there is no role for countercyclical policy. The data is therefore immune to the sorts of identification problems we would see in the modern world. In this context, there seems to be a clear quantity theoretic relationship between the money supply and the price level. And yet, there does not appear to be any evidence of a Phillips Curve.

A Theory of Tariffs as a Method of Promoting Long-Run Free Trade

Tariffs have been in the news lately. As is typically the case, economists have come to the rescue on social media and op-ed pages to defend the idea of free trade and to discuss the dubious claims that politicians make about protectionist policies. I have no quarrels with these ardent defenses of free trade (although I would note that claims about the supposed importance of New Trade Theory and New New Trade Theory and claims about the global optimality of free trade are potentially contradictory; perhaps economists don’t like NTT or NNTT as much as they claim, but I digress). Despite my general support of free trade, I also think we should take a step back and try to understand the motivations of politicians who embark on protectionist policies. In addition, I think that we should start with the basic premise that politicians are rational (in the sense that they have some objective they want to pursue and their actions are consistent with such a pursuit) and potentially strategic actors. In doing so, we might obtain a better understanding of why politicians behave the way that they do. Once upon a time, this type of analysis was referred to as public choice economics. What follows is a short attempt to do so.

Let’s start with the following basic assumptions:

1. We will refer to the country of analysis as the Home country and a trading partner as Country X.
2. Country X has imposed trade barriers on the Home country that are costly to a particular sector in the Home country.
3. Free trade is unequivocally good and is the long-run goal of all of the politicians in the Home country (I make no assumptions about the goals of Country X).

With these assumptions in mind, I would like to make the following claim:

Given that Country X is imposing a costly trade restriction on an industry in the Home country, the politicians in the Home country would like to reduce this trade restriction. They could try to negotiate the trade restriction away. However, if the Home country does not have trade restrictions of their own that they can reduce, they do not have much to offer Country X. As a result, the Home country might impose trade restrictions on Country X. By doing so, the Home country might be able to induce Country X to reduce their trade restrictions in exchange for the Home country getting rid of its new restriction.

So what is the basis of this claim? And why would politicians do this given the assumption that I made that free trade is unequivocally good and therefore all trade restrictions are bad?

Here is my answer. Without having trade restrictions on Country X, the Home country does not have anything to bring to the bargaining table to induce Country X to reduce trade restrictions (setting aside other geopolitical bargaining). So the Home country needs to create a bargaining chip, but the bargaining chip needs to be credible. For example, one way to create a bargaining chip would be to impose trade restrictions on Country X. However, for this to be a credible threat, these restrictions have to be sufficiently costly for the Home country. In other words, politicians in the Home country have to be willing to demonstrate that the trade restrictions imposed by Country X are so costly to the Home country that the politicians are willing to punish Country X even if their own constituents are harmed in the process. By demonstrating such a commitment, they now have a bargaining chip that they can use to negotiate away trade restrictions and end up with free(r) trade in the long run. At the same time, politicians in the Home country cannot broadcast their strategy to the world because this would undermine their objective. So the politicians will likely adopt typical protectionist rhetoric to justify their position.

The problem, of course, is that this is not a foolproof plan. Once the Home country imposes trade restrictions on Country X, this could turn into a war of attrition. If the Home country is not willing to commit to these trade restrictions indefinitely, then they might eventually unilaterally remove these restrictions without any benefit. Not only that, but by doing so, Country X might now see this as evidence that they can impose additional trade restrictions on the Home country without subsequent retaliation. So make no mistake. This sort of policy can be a gamble because it requires winning a war of attrition. However, some politicians might be willing to make that gamble in order to achieve the long run benefits.

On Prediction

Suppose that you are a parent of a young child. Every night you give your child a glass of milk with their dinner. When your child is very young, they have a lid on their cup to prevent it from spilling. However, there comes a time when you let them drink without the lid. The absence of a lid presents a possible problem: spilled milk. Initially there is not much you can do to prevent milk from being spilled. However, over time, you begin to notice things that predict when the milk is going to be spilled. For example, certain placements of the cup on the table might make it more likely that the milk is spilled. Similarly, when your child reaches across the table, this also increases the likelihood of spilled milk. The fact that you are able to notice these “risk factors” means that, over time, you will be able to limit the number of times milk is spilled. You begin to move the cup away from troublesome spots before the spill. You institute a rule that the child is not allowed to reach across the table to get something they want. By doing so, the spills become less frequent. You might even get so good at predicting when the milk will spill and preventing it from happening that when it does happen, you and your spouse might argue about it. In fact, with the benefit of hindsight, one of you might say to the other “how did you not see that the milk was going to spill?”

Now suppose that there was an outside observer who studied the spilling of milk at your house. They are tasked with difficult questions: How good are you at successfully predicting when milk is spilled? Were any of your methods to prevent spilling actually successful?

In theory these don’t sound like hard questions. For example, if the observer notices that you are taking preemptive action and the spilling is becoming less frequent, then isn’t this evidence that you are doing a good job at both predicting and preventing spills? Not necessarily. Your child might be maturing and gaining more experience with drinking out of a cup with no lid and therefore less likely to spill their milk. In addition, we would need to know the counterfactual of what would have happened if you had not taken action or created a particular dinner rule for your child. In other words, we need to know whether your child would have spilled the milk if you had not taken the action that you did.

Now, let’s imagine a scenario in which the observer studying your dinner table is naive and just records what happens. Based on their observations, the observer then has to explain why the milk spills. Since the naive observer sees you take action (perhaps even frequently), but also records instances where the milk spills, the observer might come away with the conclusion that you know how to prevent spills (they see you taking such actions), but that you don’t do a good job predicting spills. Their recommendation would be that you need to get better at predicting spills.

As you have certainly realized by now, this post is not meant to be about milk or the weird person observing your dinner habits. It is really about business cycles and countercyclical policy. Naive critics of macroeconomics often point to recessions (especially severe recessions) and say “why didn’t macroeconomists see this coming?” This is an incredibly naive and silly critique in the same way that concluding that you could prevent all of your child’s spills if you were just better at prediction. This view is naive for several reasons. First, we do not have the counterfactual. What would have happened if we had done things differently? It is possible that it might have prevented what we observed, but we need to have a model of how things would have played out differently. It is also possible that there was nothing that we could do or that our actions could have made things even worse. Second, even if we live in a world in which there is some Pareto-improving policy that would have prevented the recession and everyone knows it, this doesn’t mean that we would never have recessions. In fact, in a world of a commonly known Pareto-improving policy, recessions would only occur when they were not predicted. In other words, virtually by definition, recessions would be unpredictable events in that world. To the naive observer, however, they only see the data. They do not have the counterfactuals. Thus, they are likely to conclude that macroeconomists are terrible at their jobs because they never see the recession coming. Put differently, their criticism of macroeconomics would be that macroeconomists fail to predict unpredictable events. That critique is as silly as crying over spilled milk.

Allan Meltzer

Earlier this month, I had the privilege of speaking at a conference in honor of Allan Meltzer. It was a great conference with a number of excellent speakers (how I got on the list is anyone’s guess). Meltzer had an incredible influence on the profession through his work on monetary policy and the history of the Federal Reserve.

I was on a panel discussing Meltzer’s views on the monetary transmission mechanism. Anyone who is familiar with Meltzer’s work knows that this was a topic that he thought was of the utmost significance. For those not familiar with economic jargon, this line of research examines the various possible channels through which monetary policy affects economic activity. On the one hand, this research has been pretty influential in the sense that Ben Bernanke often sounded quite Meltzer-esque in his discussion of monetary transmission when justifying the Federal Reserve’s large scale asset purchases. On the other hand, much of the current literature on monetary policy fails to take into account many of Meltzer’s insights because this recent literature focuses too narrowly on the short term nominal interest rate.

I understand that they are putting together a book that collects the contributions of each of the speakers, but some of the material is already available online. I know of 3 papers that have been posted online, including my own (I’ll update this if I hear of others before the book comes out). These papers are linked below. I hope that those interested will take the time to wrestle with Meltzer’s arguments.

Allan Meltzer: How He Underestimated His Own Contribution to the Modern Concept of a Central Bank by Robert Hetzel

Allan Meltzer’s Model of the Transmission Mechanism and Its Implications for Today by Peter Ireland

and my paper:

Monetary Policy and the Interest Rate: Reflections on Allan Meltzer’s Contributions to Monetary Economics

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.

Money and Prices

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.