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Sunday, August 3, 2014

What Does The NAIRU Tell Us About U.S. Inflation?

Chart: U.S. Unemployment Rate And NAIRU

The U.S. Employment Situation report released last Friday was somewhat weaker-than-expected, but the data follow the pre-existing trends. There is no sign that turmoil overseas has yet had an impact on the U.S. labour market, which is not too surprising - there is no reason to expect that U.S. labour market to lead international economic data. If the recovery is not derailed by the various existing imbalances, the unemployment rate would likely follow its post-2010 trend, and crash into the  nonaccelerating inflation rate of unemployment (NAIRU) at some point in 2015. In this article, I discuss various aspects of the NAIRU concept.

What Is NAIRU?

The NAIRU series above was calculated by the Congressional Budget Office (CBO), and is described in this document (written in 2001) which describes how it calculates "potential output". The document describes the NAIRU as (pages 11-12):

CBO's benchmark is an estimate of the natural rate of unemployment, called the nonaccelerating inflation rate of unemployment (NAIRU). It corresponds to a particular notion of full employment—it is the rate of unemployment that is consistent with a stable rate of inflation.The historical estimate of the NAIRU derives from an econometric estimate of a Phillips curve, which is an equation that relates the change in inflation to the unemployment rate and other variables, including changes in productivity trends, oil price shocks, and wage and price controls. The relationship between the unemployment gap (the difference between the unemployment rate and the NAIRU) and the change in inflation is strong and fairly stable. When the unemployment rate is below the NAIRU, inflation tends to rise, and when the unemployment rate is above the NAIRU, inflation tends to fall.
In the chart below, I show the post-1990 relationship between the "unemployment gap" (unemployment less NAIRU) and two measures of inflation: wage inflation, and CPI inflation. (I use the post-1990 period as inflation largely became anchored near 2%, and so the behaviour remains within a single regime.) If you eyeball the chart, a negative correlation appears, and you could possibly generate a weak regression relationship between the variables.
Chart: Unemployment Gap and Wage and CPI Inflation

The relationship between the unemployment gap and CPI inflation broke down in the 1990s, with the fall in the unemployment rate below NAIRU not causing a rise in CPI inflation. (Fed Chairman Greenspan's "Maestro" reputation was enhanced by his prediction of that outcome.) But this predictive failure caused many to question the concept of the NAIRU.

But the CBO notes in the document I referenced above that wage inflation reacted as expected, it was just CPI inflation that did not rise in response to the unemployment gap going negative. With regards to that episode, I believe that this defence is highly reasonable, for reasons I discuss further below.

The serious challenge to NAIRU is coming from the latest cycle. The unemployment gap "went off the chart" relative to previous values, yet the reaction from CPI and wage inflation was muted (but with the correct sign). There are a number of ways of explaining this result, which I discuss below.

NAIRU And Output Gaps

The NAIRU is related to the concept of "potential GDP", and the unemployment gap corresponds to the "output gap" (actual GDP relative to potential). The output gap is used more frequently in modern macroeconomic analysis, but it is a fuzzier concept to measure.* Since it would be unusual for the output gap and the unemployment gap to greatly diverge (directionally, at least), I will treat the unemployment gap as a proxy for the output gap.

I do not want to go into the theory of the NAIRU; the details of the area are subject to scholarly dispute. I will instead look at what are the broad directional predictions about inflation amongst various schools of thought.

I will assert that there are two basic principles we see in observed economic data ("stylised facts"):

  • The unemployment rate is a counter-cyclical variable: it rises during a recession, and falls during an expansion.
  • The (domestic) inflation rate is a pro-cyclical variable, it falls during a recession, and rises during an expansion. (I will explain why I add the qualifier "domestic" later.)

Broadly speaking, these observations are consistent with most reasonable theories of inflation that have been advanced. Some theories of inflation - notably the Quantity Theory of Money - can generate predictions that are at variance with these observations, and we are able to empirically reject them as a result.

You do not need a doctorate to look at the two observations above to generate a prediction that a falling unemployment rate is associated with rising inflation (and vice versa). This is because of the correlation between those variables and a third variable - economic growth. The NAIRU theory is an attempt to make the relationship stronger, attempting to force a stronger functional link between the two variables.

Post-Keynesian economists tend to reject the NAIRU formalisation for modelling inflation. However, they still use something resembling an output gap for explaining inflation, so the broad story is directionally similar to the more mainstream NAIRU view. I am in this camp; I think the concept is flawed, but it is not surprising that the observed data are often consistent with a NAIRU-based theory.

I will now go through a list of stories explaining why the high "unemployment gap" did not cause much of a fall in the rate of inflation this cycle.

If The Predictions Are Off, Redefine NAIRU

In order to generate useful predictions, NAIRU has to be roughly constant. (It could possibly change depending on the "regime", and would presumably be different for different countries as a result of measurement and structural differences.)

But what we see is that the estimated NAIRU is shifting up and down over time, at a rate that seems suspiciously high for a "structural" parameter.

The problem with redefining NAIRU or potential GDP to fit the data (which is exactly what happens), is that the "theory" cannot be refuted. As Karl Popper argued, a theory that cannot be refuted has no theoretical content. A less academic explanation of this weakness is that if we want to do inflation forecasts, we have just replaced predicting inflation with predicting the unobservable NAIRU, which is presumably harder to do.

This solution largely preserves the NAIRU theory as-is, and so it makes it attractive to some. It also has the most hawkish implications for monetary policy. If the only way to explain the stability of inflation post-2008 is a rise in NAIRU, we are presumably very close to it already (that is, the CBO estimate is too low). The justification for the rise in NAIRU is that the destruction within some sectors of the economy has meant that many workers who were previously employable no longer has useful skill sets. Therefore, the fear is that any further falls in the unemployment rate will cause accelerating inflation. To be clear, I disagree with that assessment, but I cannot be certain.

Domestic Versus Imported Inflation

The distinction between "domestic" inflation and CPI inflation is important, but it is missed by single-good economic models. (I noted the problems with single-good economic models here.)

In the 1990s, the inflation rate did not react to the "unemployment gap" going negative. This can be explained by the structural reduction in prices as the result of manufacturing being outsourced to low-wage developing countries, and the collapse in energy prices in response to the Asian Crisis. (Even though I show core - ex-food and energy inflation - energy is an input throughout the production chain, and so its price influences core prices as well.)

Going in the other direction, people in Iceland had increasingly moved towards consuming imported goods before the financial crisis. The collapse in the Krona during the financial crisis led to high inflation, despite the collapse in domestic activity. Developing countries have had similar problems with imported manufactured goods.

The main developed countries have consumption baskets that are weighted more towards domestic goods and services, but one could imagine a scenario where global supply chains are disrupted and goods price inflation takes off, regardless of what is happening in the domestic economy. Such an event appears to be hard to forecast within an economic model.


Chart: U.S. Inflation Expectations Versus Realised

Modern economic theory emphasises the role of expectations in the generation of inflation. This emphasis is reasonable, but I question its practical usefulness for inflation forecasting. The points I note:

  • Tautological. There are very few "flexprice" markets (markets exhibiting rapid price responses to supply and demand trends) in modern economies; only things like commodities and stock markets. Other prices - the bulk of the CPI basket, as well as wages - are administered and are fixed for periods of time. If a business expects input prices to rise from their current level over the next "period" for which its administered selling prices are fixed, it will raise the price now. Therefore, the expectation of higher prices mechanically implies higher current prices. It is only because economic models have wildly unrealistic price setting behaviour that the role of expectations appears revolutionary.
  • Estimation. How exactly do we measure inflation expectations? Survey and financial market measurements do not appear to be very reliable.
  • Causality. It is unclear to me whether rising prices occurs before or after survey-based inflation expectations rise. But realised inflation and survey-based inflation expectations tracked each other well during the 1970-1990 inflation cycle, which means that estimated models will put a high weight on inflation expectations as an explanatory variable. But that just means we now have to explain expectations, and not inflation, and it is unclear whether we are any further ahead.
Although expectations obviously matter, I do not see what will cause them to become "unmoored" from 2%, other than CPI inflation rising well above 2%. But that is presumably precluded by "moored" inflation expectations. This logic appears to make a large rise in inflations impossible, regardless of the state of the economy, which appears to be a fairly bizarre conclusion.

Central Bank Probity

One strand of theory is that realised inflation is the conscious decision of policy makers. The literature resembles a morality play, in which virtuous "sound money" central bankers face off against (naughty) politicians that want inflation in order to "finance" spending (without raising taxes). The desire for central bank independence comes from this theory.

Since this theory assumes that realised inflation is the result of a conscious choice of policy makers (plus some random "noise"), it is impossible to refute empirically. The only place of debate is in the abstract area of policy rules. Since there is no way of telling what policy rule is being followed with a finite run of data, this is also non-testable.

This theory comes closer to being testable if we assume that inflation expectations are driven by policy rules. But I have my doubts whether this really can be done, other than by assuming the conclusions in advance (policy makers in the 1970s were "naughty", but they followed "sound policy" in the 1990s). And if you are an investor, the theory offers no useful guidance. If you spent your time over the last few years scrutinising central bank rhetoric and obsessing about their tolerance for inflation, my guess is that you would have ended up losing money on the "inflation is coming" trades that buried a lot of investors.

Correspondingly, this literature is useful only if you are a fan of economic theology.

That Darned Zero Bound

There has been some movement away from a single (composite) good economy in analysis. One effect that has been noted that there is a tendency to avoid price or wage decreases - that is, there is a floor for price changes at 0% -  which has been empirically observed in micro-data. (Note that this holds for administered prices, not flexprices, which are rare within the CPI basket.) This creates a skew in price increases towards higher prices at low inflation rates.

The modelling principle is that individual price increased are randomly distributed around a central tendency. Under normal circumstances, the mean price change is (roughly) equal to the central tendency. This central tendency is what is to be predicted with the NAIRU-based model. But when the central tendency is too close to zero, many individual prices will hit the 0% barrier. This drags up the average price rise above the central tendency.

For example, assume that:
  • 50% of price changes observed are 2% above the central tendency;
  • 50% of prices changes observed are 2% below the central tendency (but floored at 0%). 

If the central tendency is 2% or higher, the observed inflation rate equals the central tendency. But if the central tendency drops to 1%, the observed price changes will be 0% and 3%, creating an average price change that is 1.5%, which is higher than the central tendency.

In summary, you build a model similar to the existing NAIRU-based models, but you are now initially forecasting the unobserved "central tendency". You then apply a nonlinear transformation to the "central tendency" to generate a predicted inflation rate, where the nonlinear transformation is increasingly insensitive to a falling "central tendency" as it goes to zero (or even negative). This change should be able to generate the muted inflation reaction seen in the latest cycle, but acting more normally in earlier cycles.

It is clear that if there is significant dispersion of individual price changes, it will be hard for the observed inflation rate to drop below 1%. This leads to an observation that will not be too popular with central bankers - they have only been able to hit their inflation targets reliably as a result of this effect. All you need to do is keep the economy operating with considerable slack, and you will always be close to a 2% inflation target. This observation contradicts the alleged fact that inflation-targeting leads to "optimal" societal outcomes. But it also means that central banks will not be able to reliably hit an inflation target which is further away from zero (there are calls for inflation targets to be raised to 3-4%). Since they could not rely on this skew effect to keep inflation near the target, people will become even more skeptical about their ability to steer the economy.

I believe that this effect is observable in the data. But I would also note that it calls into question the "microfounded" DSGE models with composite goods. If a significant proportion of the economy is not setting prices in line with the expected value that this desired by the central bank, what are those agents with "model consistent rational expectations" thinking?

(UPDATE: This article explains how I incorporated nominal rigidity into a wage inflation model to improve the recent fit.)

Effect Of Multiple Sectors In A Welfare State

My preferred theory is that we need to dis-aggregate the welfare state. I have only read Minsky's description of this model, but it is based on earlier work by Baumol. (I discussed this in a recent article on fiscal policy, and the model is described in the book of articles I reviewed here.)

Since I covered this ground recently, I will only do a brief summary here. What we do is divide the economy into two sectors, a high-productivity "high pressure" economy, and a low productivity "low pressure" economy. We correspondingly have to divide the labour force into two groups; the highly skilled labour force needed by the high pressure economy versus the less skilled that work in the low pressure economy. Minsky argued that mechanisms of the conventional welfare state (in in particular, "military Keynesianism" that relied on infrastructure and military spending) stimulated the "high pressure" economy without reducing labour market slack in the "low pressure" economy. This leads to the possibility of high inflation, despite high unemployment rates.

Aggregate economic data is the weighted average of these two sub-economies. Even if each sub-economy acts as if there is a NAIRU that exists for it, the aggregate behaviour need not exhibit a well-defined NAIRU if there is considerable divergence in conditions between the sub-economies (and if the models incorporate some nonlinearities, such as the skew effect at low inflation rates).

I would interpret the recent cycle as being the case that the "high pressure" economy is running near capacity and generating the inflation we see, despite the slack that remains in the "low pressure" economy. (The observation that economic activity is very unequally distributed is well known, which is consistent with the model.)

The obvious weakness with the theory is that we cannot directly measure the "high pressure" and "low pressure" sub-economies; people do not run around with "H" or "L" superscripts tattooed on their foreheads. We can try to estimate this from industrial breakdowns, but the problem is that the sectors which are classified as "high pressure" presumably changes over time.

A reasonable way forward is to create a theoretical model for such a divided economy, and see what predictions are generated about aggregate behaviour. These rules can then be applied to observed aggregate behaviour. I am aware of models within the stock-flow consistent (SFC) literature that could be adapted for this purpose (models of multiple economies sharing a currency), there may be explicit models of this form as well.

And we do have a real world example - the euro area. The national economies can be easily divided into "high pressure" and "low pressure" economies. However, the euro area natural experiment has been a bit of a disaster as a result of the lack of a common fiscal policy, which should aim to equalise the activity between the "high pressure" and "low pressure" economies.

(As an aside, the analogy between the euro area and sub-economies suggests that arguments in favour of investing in infrastructure using Net Present Value calculations are misleading. Infrastructure investments in Germany would probably have the greatest financial pay-off for governments, since they would be enhancing a dynamic economy that is already generating a lot of tax revenue. But such spending would be entirely useless as a stabilising tool, as it would just act to stimulate an economy that is already near overheating.)

Future Trends?

Assuming the U.S. economy is not derailed by a recession in the next few years (which I believe would originate from elsewhere, and I find hard to forecast as a result), the unemployment rate will probably power through the NAIRU. I still believe that there is sufficient aggregate slack in the labour market to keep domestic inflation under control.

Chart: Not In Labor Force, Want Job Now
There are a lot of people who dropped out of the labour force, but who will come back if hiring picks up, and becomes less discriminating. (Employers can get away with being very choosy now.)

Chart: Unemployment Rate, 20-24 Year-Old Cohort
Additionally, although the fall in the Unemployment Rate does reflect an ageing population, the unemployment rate is very high if we control for ageing by looking at a fixed age cohort. Youth unemployment remains high, being near the cyclical peaks of the pre-1970s era.

There appear to be valid reasons to be cautious about the inflation performance over the coming years. My instinct is that inflationary pressures in the high pressure economy will not accelerate further, and so aggregate inflation will only inch up as the low pressure economy slowly recovers. But my suspicion is that the Fed would overreact to core PCE inflation rising above 2%, and so my doveish view on inflation may not translate into lower bond yields.


* In an economy that is heavily driven by services, the notion of "capacity" is fuzzy. As an extreme example, if the mix of electronic books switched from books costing an average $4/book switched towards $5/book, the nominal value of books sold could rise by 20% without a change in volumes downloaded, and with prices for specific books remaining fixed. Other consumer goods and services also show very wide price divergences between products which have relatively similar real inputs required in their production.

See Also:

(c) Brian Romanchuk 2014


  1. The 'high' and 'low' pressure economies tend to relate to the primary and secondary job markets that Bill Mitchell talks about a lot.

    'Primary' are usually full time jobs that are relatively well paid with very low substitutability and low supply. 'Secondary' are the more casual jobs with high substitutability and high supply. They relate to skill level.

    The primary market has relatively more wage pricing power than the secondary market.

    1. Yes. I read Minsky's book on the labour market more recently, and so it is more fresh in my mind. I think you end up with similar conclusions, although I think the line between the two "sectors" may need to be blurry. The breakdown could be part-time vs. full-time, it could be by industry, or it could be geographic. For example, even casual labourers are doing well (based on anecdotes) in Fort MacMurray Alberta - the centre of Canada's tar sands boom.

      Policy needs to be careful about targeting stimulus along all of those axes, which is arguably challenging.

  2. This is a very interesting post. Thanks. I like your style. Your charts are great too.

    On the NAIRU, I actually don't mind discussion that use the NAIRU as a reference point. Where I get irritated is when officials use it to justify blind policy moves. Cautious experimentation is the way to go. The 90s in the US (NOT in Canada) were actually a good example.

    1. Thanks.

      In terms of the modelling history, I was purposefully vague about attributing as to who said what. I think there was a half dozen famous models out there that all blended into the same thing from my point of view (I could simulate most of them by just switching out input variables). My job was developing "proprietary models", so I did not want to replicate the existing literature...

      As for policy, I am also in favour of caution, except when it was impossible (WWII wartime economics, but I hope to avoid we avoid similar situations...). The "true" models are probably too complicated to correctly estimate, so we have to work with partial models. But I can see the obvious complaint about NAIRU if you want to implement a jobs programme like the Job Guarantee - the NAIRU concept implies that inflation would spiral out of control. But since that represents a structural change, it seems unlikely a partial model would be successful.

      As an aside, I should do a follow up post "shortly" and show how my the "skew" effect at 0% makes a simple NAIRU-based model much better.

  3. My last sentence was probably unclear. I mean 'cautious experimentation' to mean going beyond the NAIRU level to 'test the waters'. I think the Fed did a good job here, as far as real world policymaking goes.

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  5. Just to point out that NAIRU is awful English. An increase in the rate of inflation is not an acceleration. It' s true the price level accelerates but it's simply an 'increase' in the rate of inflation.

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