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Sunday, February 19, 2017

NAIRU And The Santa Claus Test

Chart: U.S. NAIRU (CBO) and the Unemployment Rate

Although economic squabbling is fun to follow, a lot of it is the result of the use of fuzzy language. As a result, there is no way of advancing the conversation; arguments are just people clinging to different definitions. The use of mathematics in economics is supposed to eliminate this squabbling; unfortunately, the mathematical models themselves rarely fit reality. However, we need to translate the debates into operational discussions, to see whether they can be applied to the real world. If we turn to my previous article about NAIRU, we need to ask ourselves -- does the definition of NAIRU we are using pass the Santa Claus test?

Defining the Santa Claus Test

The Santa Claus Test for a concept is straightforward: can we replace the original phrase with "Santa Claus" (or perhaps an acronym -- SCAKAFC -- Santa Claus, Also Known As Father Christmas) without losing important information?

One defense of NAIRU is that the concept is OK, but we just have a hard time measuring it. This fails the Santa Claus Test. It is essentially saying:
If the unemployment rate is below some unknown value, inflation will start to accelerate higher.

This statement conveys no more useful information than saying:
If a country is on Santa Claus' naughty list, inflation will start to accelerate higher.

It should be noted that NAIRU was not supposed to be a hand-waving concept, like those darned post-Keynesians throw around.* Instead, NAIRU is a well-defined time series, as shown at the beginning of this article. When I am referring to "NAIRU," it is that family of well-defined time series. And as was discovered in the 1990s, NAIRU offered concrete predictions -- and failed. (I discussed this in Section 3.4 of Interest Rate Cycles: An Introduction.)

I have a low opinion of the value of mainstream research, and so I no longer attempt to follow it closely. My understanding is that modern researchers have given up on NAIRU -- in much the same way that the NAIRU replaced the analytical failure that was the "natural rate of unemployment." These new measures may be qualitatively similar, but are calculated in a different fashion. Since they are generated by different modelling techniques, I feel makes no sense to refer to them as "NAIRU models." Whether or not they are useful depends on analysing each model.

Why 4%?

I want to get back to a passage from Simon Wren-Lewis that I previously quoted.
 If we really think there is no relationship between unemployment and inflation, why on earth are we not trying to get unemployment below 4%? We know that the government could, by spending more, raise demand and reduce unemployment. And why would we ever raise interest rates above their lower bound?
I’ve been there, done that. While we should not be obsessed by the 1970s, we should not wipe it from our minds either. Then policy makers did in effect ditch the NAIRU, and we got uncomfortably high inflation.
I did want to be critical in my original article, but I think I need to offer a longer explanation why this passage represents questionable analysis.
  1. Where did this magical 4% number come from? (My guess is that he is referring to the United Kingdom.) That is exactly like the magical levels of the unemployment rate that hawks said would cause accelerating inflation in the 1990s. (Those levels were repeatedly revised lower in response to inflation stability.)
  2. Just because policymakers made a mistake in the 1970s, does not mean that policy could be done correctly. The Old Keynesians either did not understand, or they did not care about the inflationary bias of their policies.
For example, if the government actually cared about reducing underemployment, it could do the following policy changes.
  1. A programme of direct employment at a relatively low wage; in the limit, a Job Guarantee programme.
  2. Raising income tax rates.
  3. Tweaking other spending programmes to eliminate the tendency of price rises to be propagated (indexation).
The objective of the first step is to raise incomes for those at the bottom of the income distribution. This could easily cause a one-time shock to the price level, as businesses that rely on underpaid labour get wiped out. This is why the last step is necessary -- to prevent that one-time shock turning into a sustained inflation.

I am not saying that calibrating the size of tax hikes to keep inflation in check would be an easy task; my feeling is that the initial tax changes would be a guesstimate. However, once the dust settles, the country could have an unemployment rate below the magical 4% level while at the same time having a stable inflation rate.

NAIRU With Dead Zones

Figure; Standard NAIRU

The possibility that we can use NAIRU with a "dead zone" was raised in the comment section. Although this is certainly a reasonable idea, I feel that it has problems when put into practice.

The figure above shows the standard conception of NAIRU; it plots the effect of the unemployment rate on "inflation acceleration" (technically, the acceleration of the price level). 
  • If the unemployment rate is greater than NAIRU (UR* in the figure), there is a "negative acceleration in inflation" (falling inflation rate) -- all else equal. (Throughout this article, I am ignoring the fact that most NAIRU models have other variables that affect inflation, such as inflation expectations. Each method to estimate NAIRU uses different variables; and we often have no idea of how to forecast them in the first place.)
  • If the unemployment rate is below UR*, inflation is rising.
The slope of the line (theta) is a second free parameter if we want to fit this model to data. If we allowed for a nonlinear relationship between the plotted variables, we would end up with extra free parameters that define the nonlinearity.

It should be noted that this figure only shows what is happening at a given point in time; the NAIRU level (UR*) is allowed to move around over time (as seen in the chart at the beginning of this article). The fact that this value is mobile means that a NAIRU model can always be fit to data (and hence there is no way of rejecting it). This inability to reject the model explains why it was useless for policymakers in the 1990s: in order to forecast inflation, you needed to forecast UR* as well as the unemployment rate. Even though they got their forecast of the measurable unemployment rate right, the unmeasurable UR* moved on them, and hence their inflation forecast was still wrong.

Figure: NAIRU with dead zone

The figure above is a somewhat more sensible model. In it, there is a flat part of the curve in which movements in the unemployment rate have no effect on inflation. (In economist jargon, this is known as a flat Phillips Curve. However, Phillips actually plotted different variables on his curve, so I dislike using that name.) The flat part of the curve is referred to as a dead zone in the engineering literature.

There are now three (possibly four) free parameters to this model.
  • UR_LO: the level beyond which low unemployment generates upward inflationary pressures.
  • UR_HI: the level beyond which high unemployment generates downward pressure on inflation.
  • The slope of the lines (theta). If we allowed two different slopes, we would have a fourth free parameter.  
There are good precedents for a model with a dead zone. It should be noted that such a relationship is not part of the standard NAIRU definition -- the "R" in NAIRU stands for "rate" and not "region."
Figure: Ambiguity of NAIRU with a dead zone
The problem with this characterisation is that we have too many parameters, which are presumably all time-varying. The figure above shows a few curves that would be impossible to disentangle in practice.
  • A baseline curve (solid line).
  • A curve with no dead zone, but lower slope (dashed line).
  • A curve with a wider dead zone, and a higher slope (dots).
This flexibility will allow us to have any number of potential fits to the same data, with widely separated UR_LO values. This means that we have no idea when the economy will start to overheat.

Concluding Remarks

We need to look at operational differences between points of view in order to avoid being stuck in squabbling about terminology. However, the inability of NAIRU proponents to come up with a useful model makes it difficult to have a more concrete discussion.


* My attitude towards qualitative approaches to economics is somewhat complicated. Earlier in my career, I was not patient with qualitative approaches to economics -- I was an applied mathematician, and a quantitative analyst. After a couple of decades of looking at the wreckage of failed mathematical models, I now see the value of qualitative approaches. That said, qualitative economics has an unfortunate tendency to degrade into squabbling about terminology.

(c) Brian Romanchuk 2017


  1. The whole thing is still an aggregate. It completely ignores the issue that there can be a lack of labour in one part of the economy and a lack of competition in the same part of the economy in heavy demand, while at the same time other parts are falling apart (think any construction boom, mining boom, oil tar boom).

    Yet at other times you can have tightness met with increased production, innovation and elimination which allows the boom to progress neatly onto increased productivity.

    Hitting it all with a single policy sledgehammer is a very primitive control mechanism.

    1. No, I think ideas like the NAIRU are very much based on the concept of labour market segmentation.

      The idea that you can have upwards wage pressure whilst still having significant unemployment depends on there being different markets, some in excess demand and some in excess supply.

    2. The problem is Nick is that it happens all the time at all stages of the cycle.

      Anywhere where there is anything new you get wage pressure, because price pressure is how markets eliminate demand.

      Again the idea of segmentation is far, far too broad. So an aggregate 'NAIRU' across all of that makes no sense.

  2. I'd say the statement about unemployment does contain more useful information than the one about Santa Claus.

    Even if we don't understand exactly how and at what point low unemployment might trigger accelerating inflation, it is important to recognise that this can happen. It means that things need to be monitored and maybe action needs to be taken. It's not as easy as it would if we knew that 4% was the magic figure, but that doesn't mean that we ignore it.

    And to me it seems entirely plausible that you get accelerating inflation at some low level of unemployment. You cannot get unemployment all the way down to zero without having virtually every employer unable to fill positions, simply because the match is never that good.

    The problem I have with the NAIRU is that it suggests a simple interaction and I think the relationship between employment and inflation is actually a very complex one. Unfortunately, as you point out, this makes empirical estimation of that relationship very difficult. But, if I believe it is a complex relationship, I can't really pretend I think it's a simple relationship just for the sake of having something I can estimate.

    Lastly, in defence of those who do accept the NAIRU as a useful concept, I would say that I don't think this implies they are against measures like you suggest to reduce unemployment. Rather, I think the fact that they believe the option of reducing unemployment by demand management is limited by the inflation consequences means that they prefer such "supply-side" approaches (although not necessarily the ones you suggest).

    1. If countries going onto the naughty list is pro-cyclical (why not?), all we are left with is that inflation rises during the cycle. I could get the same information by looking at the time series for inflation and GDP.

      Once we are stuck with saying that inflation is complex, we are into post-Keynesian territory. (And NAIRU itself is dead, since it is an extremely simple rule, that is easily tested.) However, the mainstream has argued we can't publish that hand-waving qualitative stuff in journals, because that's "not scientific." My "Santa Claus Test" is my sarcastic variant of the mainstream critique of PK economics. I think the post-Keynesians are correct, but the situation is obviously unsatisfying if we want to do forecasting.

      A lot of "supply-side" reforms consist of training people for non-existent jobs. Indirect demand management (hydraulic Keynesianism) was too inflation-prone, which is why policy should focus directly on what it wants to achieve (create jobs). Direct job creation might not work in practice either, but that would likely reflect implementation failures.

      If the government-created jobs are at a low pay (almost by definition, below the lowest private sector wage), the people in those positions are the pool that the private sector dips in to when it wants to expand hiring. From a labour market analysis perspective, it looks similar, but it blows up NAIRU, as the measured unemployment rate should be near the level of frictional unemployment (0-2% by most estimates). Frictional unemployment might even rise during the cycle under such a scheme, as workers would be more confident of getting a private sector job.

  3. Brian,

    You completely fail to answer Wren-Lewis’s point (which is a good one and one I’ve made myself dozens of times over the years).

    First, you attach much importance to the 4% figure quoted by WL. That 4% figure is irrelevant to his basic point. The UK government’s best guess as to where NAIRU lies might be 5% or 3%: I couldn’t care less what they think the figure is. And since you evidently don’t understand his basic point I’ll explain.

    NAIRU bashers claim there is no relationship between unemployment and inflation. WL’s response to that is eminently logical and reasonable and along the lines of “OK: in that case why not have a HUGE increase in demand? According to NAIRU bashers there is no particular reason to think that will raise inflation.”

    I want a clear simply answer to that. You don’t give one because you know perfectly well that THERE IS a relationship between unemployment and inflation: i.e. when unemployment falls too far (absent large scale JG schemes which in reality will probably never be implemented) you know perfectly well that inflation will rise.

    Obviously if there is some magic cure for unemployment that reduces it to zero, then the whole picture changes. But the reality is that no country in the world is contemplating a JG scheme that reduces unemployment to zero. And I very much doubt Trump will even set up a small scale scheme.

    So the reality is that there is a relationship between inflation and unemployment.

    Moreover, the people who originated the NAIRU idea and its close cousin, the natural rate of unemployment, were quite clearly envisaging CONVENTIONAL employment systems: they were not envisaging JG or anything similar. Thus those “originators” were correct in saying that given conventional employment systems or set ups, there is a relationship between inflation and unemployment.

    And they did not say, or at least they certainly should not have said that the relationship can be measured very accurately. They simply said that there is a relationship.

    1. Ralph,

      1) You wrote: "And they did not say, or at least they certainly should not have said that the relationship can be measured very accurately. They simply said that there is a relationship."

      The *definition* of NAIRU is that there is a easily-measured relationship between the unemployment rate and inflation. (Sure, there's other variables in the models, but they have been near-constant for a couple of decades.) That relationship does not exist, hence NAIRU does not exist.

      If you want to have your own private definition of NAIRU, feel free. But I am going to write about everyone else's definition of NAIRU, not yours.

      2) The short version of Professor Wren-Lewis' argument:
      a) Modelling inflation is complicated.
      b) Therefore, we need to accept NAIRU.

      This is logically equivalent to:
      a) Modelling a bonfire is complicated.
      b) Therefore, we need to accept the phlogiston theory of combustion.

      This type of logic might be good enough for Oxford, but it would get you shot down in flames in Cambridge.

      3) Professor Wren-Lewis' statement (that I quoted above) could easily be interpreted as: "We should not discuss schemes to lower the unemployment rate below 4%, as it is scientifically proven that this would cause ever-accelerating inflation." I do not really care about the Professor's political beliefs, but that interpretation is the standard post-1990 centre-left policy of complacency. Hillary Clinton is the standard bearer for liberal complacency, and you may note how she rode that to an easy victory over Donald Trump.

      4) The minimal level of peacetime unemployment is around 2%, which is usual estimated level of frictional unemployment. In the post-war era, some countries have achieved that level of unemployment, without accelerating inflation. Those data were available to the people who pushed the "natural rate of unemployment" and NAIRU for political reasons.

      5) The post-Keynesians developed qualitative theories of unemployment decades ago, and they did a good job developing them. Those qualitative theories were not accepted by mainstream economists as they were not mathematical and "scientific"; they insisted that only mathematical relationships -- like NAIRU -- should be published. This explains the rather heated reaction to NAIRU, and the resort to hand-waving by a mainstream economist.

  4. Ralph,

    you know perfectly well that inflation will rise ?

    So savings won't give the private sector time to adjust ? and you still have to debunk Warren's economic paper that shows quite clearly if you use the wage of the JG as the price anchor. Inflation actually falls after 2 years.

    Email Warren and ask him you speak to him a lot.

  5. Brian, Are you making graphs with Python? The graph atop this post might be improved by putting up the line for inflation which I assume is not at all correlated to moves of unemployment above or below the NAIRU for the period shown.

    Ralph - If there is one series of discrete data points for either inflation or unemployment, then we can interpolate to find a smooth curve for past data, and extrapolate to predict future inflation or unemployment. However the extrapolation is usually meaningless since the dynamic nature of the political economy may or may not change the parameters in the fitted curve in an unanticipated manner. The NAIRU is a type of fitted curve for two series of data in the past and it seems to lack any power to predict what level of reduced unemployment will trigger inflation in the future. So NAIRU is a false concept because it specified a number that is effectively meaningless as a measure of the future relationship between unemployment and inflation.

    One interesting idea I read in the literature is that inflation is a random walk over some periods. This would make it difficult to forecast inflation. If it is a random walk, and the central bank hits its inflation target of say 2% per year on average, then this would indeed be an interesting random walk since it would be deviating in a random fashion about the target 2% trend line!

    1. The chart above is generated in R. Only my recent SFC model charts are Python; I wanted a pure Python solution so that people coild easily replicate my work.

      Adding in the inflation chart would drag me in the direction of having to give the lengthy explanation of how NAIRU broke down in the 1990s. I covered that in "Interest Rate Cycles", and I do not want to have to cut and paste a huge block of text.

  6. Oops! Obviously if the NAIRU model is constructed from historical data wherein accelerating inflation co-occurs with reduced unemployment then an informal graph might show visual evidence of some such correlation.

    Still any specified value of NAIRU seems to be arbitrary because there is more than one type of model, there is wide discretion in finding the value of parameters, and the parameters are subject to change as time evolves.

  7. It seems to me the whole thing is backwards. Labor cost is restricted by the ability to sell a product at a price, but that's it. Say you have a shortage in fast food workers (as we do here). You may have some wage pressure to attract help, but there's a tremendous asymmetry in the market -- many, many more people are consuming fast food than are producing it and they're only willing to pay so much's fast food. And you can't juice the market with the little extra pay you give your workers -- there's just not enough money there. Furthermore, anybody doing hiring for fast food can see that it's not just their store that's short workers -- it's all stores up and down the street and raising wages can't work very long because you're simply fighting for a limited supply of help. Raising wages doesn't create new fast food workers unless you raise the wages to a point where you steal them from some other type of business altogether. It just doesn't make sense to do so and any smart businessperson can see that (though there are some not smart business people).

    Sure, there are exceptions to this, but they are unusual. You do see people fighting for specific skills by raising wages, but these are in markets that have very high profit margins and aren't really limited by labor costs (software or drug development come to mind), but this isn't generalizable. Most businesses either don't need such specific skills or have the same kind of asymmetry that exist in the fast food industry -- you're bound not by the labor shortage at the bottom (which is where shortages occur), but by the greater economy and the relative value that people place on products they purchase.

    1. "And you can't juice the market with the little extra pay you give your workers -- there's just not enough money there."

      Except you can - as minimum wage rises show. If you raise the minimum wage you raise demand which then pays for the wage rise. Henry Ford demonstrated that approach works.

      Interestingly what you have put forward - lots of fast food places short of workers but seemingly unable to put wages up - is in direct conflict with the 'wage/price spiral' ideas that a lot of Post Keynesians get hung up on.

      After all if wage price spirals always happened you'd just hire more workers and put up your price to cover it which would then be replicated by everybody around you.

      But as you say in fast food that isn't happening.

      So as usual with economics the real world is heavily conflicting with a whole load of suggested theories about how things work.

      And I suspect all those conflicts are to do with ignoring the aggregation functions - which have rather more to do with irrational beliefs than rational expectations.

    2. "Except you can - as minimum wage rises show. If you raise the minimum wage you raise demand which then pays for the wage rise. Henry Ford demonstrated that approach works."

      But there is no good evidence that raising the minimum wage causes general inflation.

      In the US the minimum wage has lagged inflation, so it's likely that wages hold steady while profits increase. Perhaps a minimum wage hike lowers profits, but I don't think there's evidence that it stokes inflation in any predictable way. I'd be interested in evidence to the contrary, but what I recall reading doesn't support this notion.

      Henry Ford? That's your example?

  8. "i.e. when unemployment falls too far (absent large scale JG schemes which in reality will probably never be implemented) you know perfectly well that inflation will rise."

    Why will it? Why won't businesses fail instead due to a lack of workers because the competion is too intense for them to confirm their price rises?

    Could it be because policy is protecting businesses and business owners by reducing the amount of competition in quite a lot of labour markets. If policy demanded a volume/productivity response and any price response was subject to intense competition scrutiny would there be inflation?

    There's a very strong argument that any inflation is entirely due to a lack of competition yet there is not NAIRC is there.

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