Why Nominal GDP Targeting Solves the Credibility Problem

Monetary easing at the zero lower bound seems to work in practice. But does it work in theory?

In his recent BIS speech, Rajan argues that monetary policy at the zero lower bound requires an impossible commitment. For the Fed to get real rates low enough for the economy to "lift-off", the only option is to raise expectations of future inflation. But what happens when that future arrives? Now that the economy has escaped the zero lower bound, the Fed is tempted to renege and stick to the original inflation target. Market participants, knowing this, then refuse to believe the original commitment, leaving the Fed stuck.

The same argument was made in reverse to explain why the Fed could not escape the high inflation equilibrium of the 1970's. As argued by Barro and Gordon, the Fed declares that it wants low inflation. If this is credible, then agents lower their expectations of inflation. However, this tempts the Fed into actually delivering high inflation to exploit the Philips curve relation and lower unemployment. As a result, the Fed is stuck at high inflation.

But the Fed escaped. The last release of the PCE price index came in at just 1.0% year over year, suggests that, if anything, the Fed lowered inflation too much. How did policy do this? In the case of moving from high inflation to low inflation, the solution was simple: adopt an inflation target. If the Fed only has to keep inflation from deviating from a target, then of course it will not cheat with any kind of surprise inflation. This kind of target can also be self reinforcing through a reputation mechanism, as the Fed knows that if it cheats now it will hurt more in the future. This removes the temptation to renege as unemployment deviations no longer matter. In the end, the Fed was successful. It managed to lower inflation from around 8% in the 1970's to the 2% levels we see today.

The target is just as important today. If the entire goal is to keep inflation at 2%, then of course there can be no commitment to forward guidance! But that is a criticism of inflation targeting, not forward guidance. Therefore the Fed needs to change its policy target. If the Fed decides its operating procedure no longer is to keep inflation at 2%, but rather to keep nominal GDP on a 5% trend, this drastically changes the perception of what is credible. The Fed no longer needs to "credibly promise to be irresponsible" -- it can just change the definition of responsibility.

If it seems magical that the Fed can change this definition so easily, it's because the loss functions that underpin these models of time inconsistency are arbitrary. In the Barro and Gordon case, the reason low inflation was time inconsistent was because unemployment deviations were included. Once the Fed ignored unemployment, its actions were time consistent. In the current forward guidance case, the reason high inflation is inconsistent is because the inflation rate is in the loss function. Therefore replacing inflation with a nominal GDP term would solve the time inconsistency problem now. The Fed gets to determine these costs. With the right loss function, credible policy becomes almost obvious.

The government can take steps towards this in many different ways. On the Fed side, they could come out with announcements saying that they are more concerned about stabilizing certain level variables -- for example nominal GDP. This would show that the Fed's loss function is changing, and therefore the expected policy adjusts. On the congressional side, they could pass a law that defines the dual mandate in terms of a nominal GDP target. This institutional reform would make Fed commitments to low future rates credible and help pull them out of the zero lower bound.

When nominal GDP targeting is cast as a framework for making future paths of interest rates credible, the implementation details of a nominal GDP target also become self evident. It's no longer a "whatever it takes" target, rather it becomes a template for adjusting the nominal interest rate. Raise the policy rate if nominal GDP is above trend, lower the rate if it's below. And if nominal GDP is so far below trend that your interest rate is stuck at zero, then provide forward guidance that the interest rate will be at zero until nominal GDP normalizes. Even though this is about future policy, there is no commitment problem. The promise is already optimal.

Therefore, nominal GDP target can make policy on the monetary instrument even more rule based. A well-defined target may make unconventional policies such as quantitative easing unnecessary -- forward guidance would be able to deliver similar results. As evidence, the recent whispers of Fed tapering have shown up most strongly in the forecasts of future interest rates. While this might seem peculiar because the Fed has not said anything about future rates, it is natural if QE is seen as a signal of the Fed's stance on future rates. Gavyn Davies notes:

There is evidence that this signalling effect of Fed balance sheet changes might be very powerful. If the Fed is not willing to “put its money where its mouth is” by buying bonds, then the market might take its promises to hold short rates at zero less seriously than before. According to this recent research by the San Francisco Fed, it is possible that a sizeable proportion of the total effect of QE on bond yields came from these signalling effects rather than the portfolio balance effects which have usually been emphasised by the central banks.

If this is the case, then the credibility effect of a nominal GDP target on forward guidance would be enough. Long rates across the board -- MBS, treasury, corporate debt -- could be lowered merely by the expected future path of rates without direct Fed intervention into those markets. Note that because inflation targeting would suffer from credibility issues when it comes to forward guidance, it can get stuck with a persistently negative output gap. This may end up forcing policy makers to deviate from the rule. So surprisingly, nominal GDP targeting would actually be more rule-based as a result.

Credibility is no problem at the zero lower bound. A nominal GDP target would go a long ways towards securing it -- in both practice and theory.

Cochrane: "Woodford Needs to Fight Harder!"

When reading John Cochrane's critique of Woodford's call for NGDP targeting, I felt it was actually a great justification for why Woodford needed to write that paper, and for why the market monetarist project is something that we need to continue to fight for.

Cochrane's largest argument rests on a credibility argument -- that there's no way for the Federal Reserve to credibly commit to a permanent expansion of the monetary base, because the market expects that the Fed will tighten to reach 2% inflation in the future. As a result, because there's no way to effectively change expectations of the future monetary base, there's no way to change the level of present NGDP.  In the words of Cochrane:

How can the Fed promise today to do something it will very much regret tomorrow, and get people to believe that promise?  More deeply, how does the Fed commit to allowing "just a bit" of inflation in the future, and not starting down the path of the 1970s again?

Cochrane must know that hose are two very different questions! When we call for a 5% NGDP target, we're not calling for the path of the 1970's -- to say so is a complete straw man. Thus, the real question is how do we convince people that the Fed won't tighten in response to mild inflation. And to me, the answer is simple: declare that the Fed is targeting NGDP.

Why? Because all of the current analysis on credibility and promises implicitly assumes that the Fed is targeting inflation! Of course, an inflation targeting Fed's promise to hold rates low until an NGDP target is hit is not credible because everybody knows the Fed will tighten in response to the higher level of inflation. If, on the other hand, if people know that the Fed is willing to tolerate higher levels of inflation because it is in their mandate, the credibility problem will go away.

The problem is that everybody is looking at the standard loss function for inflation and arguing that NGDP targeting doesn't minimize the function. If you're just trying to minimize the squared deviations from 2% inflation, of course an NGDP target is nonsensical; an NGDP target actively encourages deviations from 2% inflation to correct for past mistakes. However, if the loss function is seen as the squared deviation of actual NGDP from trend NGDP, then the promise to target NGDP is much more logical.

Formally, if the Fed's optimal policy is described by minimizing this:

(π - 2)²

Of course the Fed won't manage to minimize this:

(Y-Ytrend)²

This is why Woodford's paper is so important. It's the first step towards convincing economists and market participants that the Fed's loss function is changing. Given that Woodford presented the paper at Jackson Hole, the premier meeting on monetary policy, the paper is a key step in signalling that NGDP targeting is gaining legitimacy.  If successful, people will realize that the Fed's new policy will tolerate a temporary inflation increase in order to bring NGDP back to trend. No longer does the Fed have to "credibly promise to be irresponsible", it can just change the definition of responsibility. 

So when Cochrane argues that NGDP targeting is flawed because the Fed can just go back to inflation targeting, what he's actually saying is that academics should fight extremely hard to legitimize NGDP targeting. When a monetary policy that targets NGDP becomes as self-evident as one that targets inflation, it will be no difficulty to credibly commit to a new monetary regime.

Monetary Axioms II: The Movement of Expectations with Respect to Shocks

Pity that these concepts are "counter-intuitive"

I quite enjoyed my last definition/proposition/lemma/theorem post, and although many of the statements were axiomatic or self-evident, they led me to an interesting realization about current nominal GDP growth, credible monetary policy, expected future nominal GDP growth,  and interest rates.

While we often talk about nominal GDP gaps, I would like to start the drawing and theorem process by looking at graphs of nominal GDP growth. Below is a graph of log nominal GDP (right) and continuously compounded annual rates of nominal GDP growth (left), both reported quarterly.

In terms of calculus, nominal GDP is the level of the variable, whereas the growth rate is the instantaneous derivative. Note that although the level falls significantly from its previous trend, the growth rate returns to a value that's similar to its pre-crisis trend. However, even a temporary shock in the growth rate can cause a permanent fall in the level if there is not a restoring amount of growth after the shock.

By looking at the growth rate, we can determine the size of the output gap by integrating, or looking at the area. The integral of the growth rate minus the integral of the trend rate is the size of the output gap, as shown in the stylized diagram below in which trend growth is simplified, without loss of generality, to 0%.

From this, we can see that growth rate targeting can leave large gaps in the actual level. Since the central bank moves the growth rate to the precrisis rate of 0, it leaves the output gap. This can be corrected by level targeting, which tries to get the level of the variable back to pre-shock trend growth. This entails a period of growth above 0 to balance the output gap. How much higher? For how long? Mathematically, the integral of the curve over this time period should be zero. Graphically, it means that the higher rate must be sustained until the blue area (positive growth) minus the red area (negative growth) equals zero. This means the red and blue areas should be the same.

By the calculus definition, the average of a function over an interval is the integral of the function over the interval divided by the size of the interval. In this context, it means that the average growth of nominal GDP over the entire period is zero, the original trend growth rate. We have therefore successfully targeted the level of nominal GDP.

To start looking at credible nominal GDP targeting in this framework, let's define some time lengths:

Definition: The crisis time (c) is the period of time starting with the formation of the output gap to the conclusion of the policy response.

Definition: The expectation horizon (e) is the period of time that economic agents forecast and use to determine their expectation of future nominal GDP growth.

For the discussion below, I will assume that before the negative shock, economic agents were unable to forecast the shock; this is the reason why the credible level targeting didn't solve the shock before it happened. However, once the shock takes place, economic agents are fully aware of the time path of nominal GDP growth that occurs as a result of the shock and policy response. Importantly, agents know that the central bank is committed to level targeting, and that this declaration is credible. This means that the private sector knows the areas, red and blue, will be the same in the end. 

In reality, these would all be expectations. But I will accept the rational expectations hypothesis that expectations match the reality for the purposes of this benchmark model.

Let us start with a special case, in which the expectation horizon is equal to the crisis time, as pictured below.

What is the expectation of economic agents of average nominal GDP growth over the expectation horizon at time to? As both areas are equal to each other, the integral over the expectation horizon is zero, so average expected nominal GDP growth is also zero. No surprise there. But what about at some time in the middle of the output gap, say at tm? The integral is then positive! The integral is represented in the graph below by the blue area minus the pink area (note that trend growth is zero after the policy response). As you can see, the blue area is larger, making the integral positive. Because  expected average nominal GDP growth is the interval divided by the expectation horizon e, the expectation of nominal GDP growth also becomes positive.

As a result, if monetary policy is perceived as credible enough to solve the shock in the same interval as the expectation horizon, a current negative nominal GDP shock manifests itself in increased expectations of nominal GDP growth over the expectation horizon. The graph would look something like this:

A similar result is obtained if the expectation horizon is greater than the crisis time (e>c). Just move to+e to the right, and both the nominal GDP growth and the expectation curves return to zero at to+c.

This result might seem puzzling, as this hardly seems like what happens in real life. To get to "real life" monetary policy, imagine a world with highly inertial policy, such that the crisis period is longer as policy takes more time to respond and the output gap lasts longer as a result. We would be in a world such as that below:

From here, the growth expectation at time to is the value of the pink area divided by e. Although e is chosen such that to+e is to the left of the policy response, as long as e is less than c, the expectation will start out negative. The expectation curve moves forward in a different manner compared to the e=c case. The expectation does become positive when the [to, to+e] interval only covers the blue portion. As a result, the expectation over the period looks like this:

Note that the exact curvature is dependent on the function for the shock and the expectation horizon. But it should be noted that the max/min of the expectation curve should not go past the max/min of the actual path for nominal GDP growth.

Flipping the directions of the output gap and policy response gives us the result for a positive aggregate demand shock, and they are, predictably, the opposites of the ones we obtain for a negative shock.

This long and winding road then allows us to conclude the following:

Theorem: Given a monetary regime that has a credible nominal GDP level targeting policy:

1. If the crisis period is greater than the expectation horizon, expectations of nominal GDP will be procyclical to current nominal GDP growth.
2. If the crisis period is less than or equal to the expectation horizon, expectations of nominal GDP with be countercyclical to current nominal GDP growth.

This gives us a yardstick to judge if a monetary policy is credibly level targeting for a variety of expectation horizons. Most importantly, if treasuries of varying maturities are correlated with expected nominal GDP growth over the treasuries' time periods, then we can look at the movement of treasuries to judge forecasts of crisis lengths in credible level targeting regimes. The treasuries with yields that rise have maturities beyond the crisis period, while the treasuries with yields that fall have maturities within the crisis period. This also solves the data problem, as we now can find out the market's observations about current GDP growth by looking at its expectations of future NGDP growth.

Although the model outlined above discusses level targeting, it can be extended to rate targeting as well. Think of rate targeting as a form of level targeting whose "policy response" is to hope a positive shock comes the other way in the future. In effect, rate targeting is level targeting with an extremely long crisis period. As a result, shocks to nominal GDP growth in a rate targeting regime almost fall into the first case of the theorem for most expectation horizons. By this theory, current yields on long term treasuries betray a very negative outlook on future nominal GDP.


As this model uses interest rates as a way of gauging expectations, they work the best when interest rates are allowed to float and communicate information. If these interest rates were targeted, the central bank would be suppressing a key source of information. This is another advantage of a NGDP futures level targeting regime versus an interest targeting regime. High interest rates won't be confused for "tight money" if the interest rate is determined by the market.


This post should remind us that Market Monetarism is a world of non-linear causality and counter-intuitive movements in both expectations and interest rates. Except they wouldn't be counter-intuitive and these arguments would be self evident if policy actually targeted the level of nominal GDP. Alas, the Fed does not. A great shame, for both both our learning of intuition and suffering in this nation.

Edit (7/13/2012): Fixed the grammar in the last three paragraphs, no substantive change in the message.

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.

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.

NGDP Targeting: What if it fails?

Recently in the economics blogosphere, the monetary paradigm of nominal GDP level targeting (NGDPLT) has been gaining steam.  NGDP targeting takes a departure from the classic regime of inflation targeting by the growth rate in NGDP, allowing for balance between employment and inflation.  This then leads to a wide variety of benefits, as the new regime is robust to supply shocks, can craft stable expectations of overall future growth, and can reduce fears of any specific industry going through a crisis.  It's particularly attractive for financial crises, as if NGDP growth is stable, previously sustainable levels of debt are less likely to become unsustainable.  If the economy's productive capacity is constant, there's no reason for it to be less able to service its debt.

However, this view seems almost too simplistic.  Even though the US economy was incredibly stable during the over the 20 year Great Moderation, it all came down to a screeching halt with the 2008 financial crisis.  Similarly, even though Britain managed to stay out of a major recession for 16 years, NGDP fell by about 4.7% during the crisis.  Given that there had been such a long legacy of stability, how did expectations suddenly become unanchored?  Even if the US Federal Reserve made a bad policy decision at that point to focus on oil prices and other supply shocks to the detriment of nominal stability, why did the expectations of prudent policy in the future not "solve back" the concerns?  In the end, the crisis culminated into the worst disruption since the Great Depression: hardly a desired result for a responsible regime.

The unhappy ending in 2008 seems to suggest that responsible policy can break down into chaos given a large enough of an exogenous shock.  This problem is very close to what Nicolas Nassim Taleb discusses in The Black Swan: in exchange for low volatility, the economy goes along with high fragility, such that one large shock can cause non-linear, disproportionate harm.  So in the end, the question is about credibility.  How is it established?  How is it maintained?  If decades of prudent monetary policy were not enough to anchor expectations, why should we expect the Federal Reserve to be considered "credible" when the next large financial bubble appears?  If shadow banking markets start to grow shadows and systemic risk goes through the roof, why should we expect the Federal Reserve to be considered "credible"?  Especially if non-monetary factors as posited by Bernanke play a key role in recessions, why would nominal stability be enough?  And when everything crashes down, how will we deal with the mess of debt and contracts that were only sustainable under the old regime?  NGDP targeting seems to play on circular logic.  Boost aggregate demand to hold the expectation; with the expectation there's no need to boost aggregate demand.

So when a policy maker messes up, and lets a NGDP crisis unfold, the crisis emerges.  This is where the black swan hides, cloaked by the rhetoric of stable expectations and the "perfect" monetary policy.