Wednesday, July 11, 2012

Axiomatic Monetary Credibility

Credibly defined and extended

We spend a lot of time discussing the credibility of monetary policy, but there is a lack of firm axioms that define when monetary policy is credible or, more importantly, how we can tell when it's not. This post is an attempt to formalize some of these definitions, lemmas, and theorems, which may later lead to some interesting proofs.

One of the simplest investigations of this credibility problem is Kyland and Prescott's analysis of dynamic inconsistency. The model points out why monetary authorities always have incentives to  excessively inflate. If the private sector expects price stability, then a burst of unexpected inflation is likely to boost real output in the short run. The central bank then has an incentive to renege on its promise for price stability and inflate, even though it contradicts with the original goal of price stability! The central bank, at any given point, would want price stability for the future, but would want to inflate now. This is why the situation is called "dynamic inconsistency". In maximizing welfare, the central bank's current actions are inconsistent with its future planned actions. As a result, agents in the economy learn to not trust the central bank's promises of low inflation, breaking down the Philips curve relation as inflation is always rationally expected.

How does a central bank get around this credibility problem? Barro and Gordon show that, if the central bank keeps inflation low in good times, then private sector agents are more likely to believe that the central bank will always keep inflation low. Through repeated games, the private sector learns that the central bank is committed to the inflation target, and the central bank no longer has an incentive to renege. The repeated interactions shape private sector expectations of future inflation as well.

Barro and Gordon, in spite of their insightful analysis, do not provide a rigorous definitions. Later reviews characterize their view of credible policy as "policy which the private sector believes will be carried out in the context of a particular reason that might lead them to believe that it will not." But let us first define what the central bank is doing. Suppose that the central bank is targeting a policy variable, which has both a value and a time. This is the starting point for the following two definitions:

Definition: A policy variable is an economic indicator, whether level or rate, at a given point in time.

Definition: A target is the desired value or range of values for a policy variable.

Then credibility needs to incorporate the policy variable concept and expectations. I propose:

Definition: A credible policy is a policy that aligns expectations of the policy variable(s) with the target.

So a credible inflation target is one that aligns expected inflation over the course of a year with a point target, such as 2%, or an interval, such as between 1 and 3 percent. A credible nominal GDP level target results in expectations that NGDP next year will be at a level that meets a 4.5% trendline. A credible exchange rate floor aligns expectations of the instantaneous currency value with the floor value.

The Swiss case is a good example for credibility because the floor is holding in spite of increased asset purchases on part of the SNB. So short term fundamentals haven't affected the exchange rate. For inflation targeting, the stability of long run inflation expectations is a good example. Given credible inflation targeting, one would expect inflation expectations to resemble the Cleveland Fed figure below.

Inline image 1

Note that although the short term expectations are very high, they quickly converge back to around the long run target of 2%. In spite of the temporary shock to the price level, economic agents are confident that monetary authorities will push the price level back down to the long run target. In both of these examples, shocks have no effect on long term expectations. This suggests a lemma:

Lemma: If the central bank follows a credible policy with a predetermined policy target, current conditions can only move expectations of the policy variable within the policy target.

This lemma is just a trivial application of the definition. The credible policy guarantees that the expectation of the policy variable stays within the policy target. Because the policy target is predetermined and unchanged by current conditions, then the expectation of the policy variable still stays within the same policy target. However, current conditions may move the expectation within the interval.

Now we turn our attention towards how credibility is established. If credibility is established through Barro and Gordon's repeated game mechanism, then there must be a history of hitting the target for policy to be credible. How long does this history need to be? It seems that it is highly dependent on how often a central bank can prove itself. The Swiss National Bank has no problem convincing investors it'll defend the currency floor; forex markets tick every second of every day. But for a central bank to show that it can hit a NGDP target consistently, the task seems a bit more difficult. Nonetheless, it is probably true that the central bank needs time and repeated iterations to show that it can hit a target.

Proposition: Monetary policy credibility is obtained through the central bank repeatedly hitting its target.

The following is a proposition on the nature of policy variables, such as inflation, nominal GDP, or exchange rates

Proposition: Policy variables are occasionally subject to long lasting shocks in the absence of policy.

This implies that other factors beyond an individual central bank's policy affect policy variables. Inflation, in a world where it's not targeted, is subject to various pressures, whether trade balances, velocity fluctuations, or loose fiscal policies. A cursory look at any Fred graph shows that inflation can be volatile even with intervention, suggesting that the fluctuations would be larger without policy.

Theorem: If policy does not have a concrete mechanism, it can not be credible

Proof: Assume policy is credible without a mechanism. The volatility proposition implies the system will be subject to a shock. A shock to the system causes the policy variable to deviate from its planned path. Policy has failed to control its target. By repeated interations, policy is no longer credible. The contradiction implies the assumption is wrong.

This is a reason why central banks during the gold standard could credibly promise to bring prices down, but could not promise to always bring prices up. The interest rate has no upper bound, so central banks could always pull money out of the economy. But once the central bank started lowering interest rates to boost prices, gold outflows would devastate its balance sheet. The gold standard example is particularly illuminating because it shows how credible policies in certain areas lead to "incredible" policies in others. Because the gold peg was credibly sustained, price stability could not be credible. Shocks to the price level could not be controlled because there was no longer a specific mechanism to control prices. By similar logic, India's attempts to stop the devaluation of the rupee are not credible because there's no infinite forex intervention that can stop the rupee's slide without also contracting monetary policy. Given that the Reserve Bank of India has shown no signs it wishes to tighten monetary policy, the forex intervention is not credible because the mechanism is not infinite.

These credibility problems extend across all "impossible trinities", whether it's Fleming's capital mobility, independent monetary policy, exchange rate peg trinity, or Rodrik's deep integration, sovereignty, and democracy trinity. Those trinities are impossible because there is no mix of mechanisms that can control all three of those at the same time. To take Fleming's example on the conduct of international monetary policy, if a currency peg, as a side effect, keeps domestic monetary conditions stable, then the currency peg mechanism is not conflicting with the independent monetary policy mechanism. As a result, a policy with all three is credible. Now that we're talking about combinations of policies, let us establish some definitions.

Definition: A policy bundle is a set of policies that each try to hit their own targets.

Definition: A credible policy bundle contains a set of credible policies.

This leads to a lemma:

Lemma: If a target is added to a policy bundle, if the mechanism for the new target prevents the functioning of a previous mechanism, the policy bundle is not credible.

Proof: Once a new mechanism negates a previous mechanism, that policy is no longer Fully Credible. Then by definition, the Policy Bundle is no longer credible.

This listing of ostensibly obvious statements provides a framework of more rigorous treatments of market monetarism. Given the major criticism of market monetarism as policy without a well defined model, working our way up from these basic propositions forces us to outline our collective assumptions that can form the basis of larger models.


  1. Excellent post. What part of market monetarism do you think is not well-defined?

    1. Scott, I think the main issue now is to fine tune the implementation of such a policy and what key indicators we should be looking for/at. That's why I've been thinking about these key market monetarist arguments in a more axiomatic fashion. While a lot of the expectations game has to do with non-linear causality, I don't think it's any reason for our explanations and lines of thoughts to be as nonlinear. I think you've done a very good job with showing how market monetarism would help policy now, and I just want to work around the edges to highlight some interesting theoretical results of market monetarism.

      The lack of a rigorous mathematical DSGE model is also, for better or for worse, a rather big deal. I remember Krugman talking about his trade models and noting that increasing returns didn't start playing a large part in trade models until there was Dixit-Stiglitz and a way to model monopolistic competition. But to build a model, we likely need to define a few "obvious" assumptions and, from there, work our way up to the common market monetarist arguments we hear about tight/loose monetary policy, interest rates, and expectations of the future.

  2. Fascinating stuff. But there's a factor I don't see accounted for. Expectations are created when the game is repeated and there's a history of consistently hitting the target by the Central Bank in question. Agree with that. But one huge whole in the theory is the actual METHOD of measuring of inflation. You are assuming that the methodology of measuring inflation is static -does not change and is universally accepted. In fact, that is not true. The substitution effect, the hedonics component, and changes in the weights of the CPI basket are characteristics that distort -or accommodate, depending on what is your perspective- the "actual" level of inflation, which are used by the central bank to make the "actual" level of inflation approach the stated target and increase their "batting average" and therefore their credibility.

    Something to think about.

  3. I love the taste of ice cream, but I want to avoid getting fat. Shall I eat some ice cream now? There will be an immediate positive result (taste), and a long-run negative result (body fat). But this is hardly more than an ordinary trade-off; why glorify it with the pretentious term ‘dynamic inconsistency’?

    Same question for the central bank’s trade-off concerning inflation.

    1. Philo, I think it's the nature of the social sciences to come up with jargon for ostensibly simple concepts, and Economics is no exception. From what I can see the term "dynamic inconsistency" came about because of the inconsistency that the central bank faces in the process of dynamic optomization by manipulating the inflation rate, with the problem as I described in the post. In your example, the inconsistency would be the reason why the person would have a hard time committing to a diet. Any given ice cream cone isn't going to make him fat, but if he ate all of them he would never fulfill the diet. That's why rule based systems (in this case, weight watchers), are created. Your ice cream example is great, it's just "temptation" sounds almost biblical and "Ice cream inconsistency" doesn't sound like something you'd put in an academic journal.

  4. Economic conditions are getting worse because of the monetary policy as stated by Ed Butowsky in his article posted in Fox News, "Obama Chose Monetary Policy - And You're Feeling It".