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.