NAWRU II . There is no such thing as a NAWRU

This is the first of five posts I promised to write in this post.

NAWRU stands for the Non Accelerating Wage inflation Rate of unemployment. It is a concept used by the European Commission when deciding how much to allow Treasuries adhering to the Stability and Growth Pact to spend. The commission considers cyclical adjustments based on, among other things, unemployment minus the NAWRU. The Commission gives mere elected officials some slack if unemployment is above the NAWRU as estimated by Commission staff.

Unemployment is never far above the estimated NAWRU. The estimated NAWRU has dramatically increased in countries whose unemployment rates have increased. Estimates for Spain vary from 21% to 25%.

I think it is clear that there is something very wrong with the estimates. I think the approach has five fatal defects and should not be accepted as an area for further exploration let alone a basis for dictates to member countries. The first fatal defect of estimates of the NAWRU is that the hypothesis that there is such a thing has been rejected by the data. The concept survives only by changing the 1968 natural rate hypothesis into a natural rate model which is used without any assertion that it has testable implications which have not been rejected by the data.

The NAWRU is a meaningful concept only if the acceleration of wage inflation is a function of the unemployment rate. This might or might not be true. The logic was that wage settlements are made aiming for a real wage, so expected price inflation is incorporated one for one into wage inflation. It is assumed that all recognize that the nominal wage doesn’t matter, so there is no particular problem with cutting nominal wages when expected price inflation is negative. The opinions on this question of everyone who has ever had any role in negotiating wages were considered irrelevant. The argument went on that people won’t make forecasting mistakes with the same sign forever, so the coefficients of expected inflation on lagged inflation must add to one. Oh yes, it was assumed that expected inflation was a linear function of lagged inflation, because, uh, that makes the math easier. It was decided to cut out the middle periods and make the coefficient on once-lagged inflation one. Finally, somehow, lagged wage inflation took the place of lagged price inflation (I can’t even imagine a bad argument for this step, but the Commission took it).

The concept requires both that only the difference between nominal wage growth and expected inflation matter. This means that there is no downward nominal rigidity, that is there there is nothing special about nominal wage increases of zero nor any difference between wage inflation near zero and far from zero.

It also requires that expectations can not be anchored. Expectations which are sometimes anchored and sometimes not anchored are not a linear function of past outcomes. They are absolutely a feature of expectations elicited in experiments. When presented with random walks, people usually forecast mean reversion. However a series of increases in a row causes them to forecast further increases (Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor sentiment,  Journal of Financial Economics 49, 307–343). This is a robust result.

If there is downward nominal rigidity or expectations can be anchored, then there may be no well defined NAWRU. This doesn’t mean that it is impossible to calculate a number and call it the NAWRU. Rather it implies that there is a range of unemployment rates such that wage inflation does not accelerate. If that is the case, cyclical fluctuations of unemployment within that range will be incorrectly identified as fluctuations in the NAWRU. I think it is clear that, for Italy, this range stretches at least from 8% to 13%, since wage inflation has remained roughly constant as unemployment rose from 8% to over 13%. Wage inflation didn’t increase back when Italian unemployment was 8% nor did it decrease after unemployment rose to over 13%.

The simple fact is that, in the 21st century, there is almost exactly precisely zero correlation between the Italian unemployment rate and the change in Italian wage inflation. To calculate a NAWRU year after year with such data requires heroic data processing.

Here is a Phillips scatter of unemployment and wages for Italy



Data from FRED. There is one observation per month from February 1980 through February 2015. Winf is the percent increase in LCWRIN01ITM661S the “Hourly Wage Rate: Industry for Italy©: Seasonally adjusted” over the preceding year (so the series for Winf consists of overlapping 12 month intervals). Unem is LRHUTTTTITM156S”Harmonized Unemployment: Total: All Persons for Italy©:Seasonally Adjusted” from January 1983 on but is ITAURHARMMDSMEI “Harmonized Unemployment Rate: All Persons for Italy© : Seasonally Adjusted” for 1980-1982. I have no idea why one series is available only after January 1983 or why the other is available only before August 2012 or how they differ (in the period when both are available, they are very similar but not identical).

I think it is obvious that the graph doesn’t look as a Phillips curve should. Since January 2000, the unemployment rate has varied from 5.8% to 13.2 % yet wage inflation has varied only from 1.1% to 4.8%. 21st century changes in Italian wage inflation are dwarfed by the huge declines in the 1980s. According to the accelerationist Phillips curve, Italian wage inflation should have remained in double digits in the 80s and 90s or declined to well below zero by now.

It is possible to pick an arbitrary series of numbers and call them the highly variable NAWRU, that is, it is impossible to prove that no NAWRU exists (as it is impossible to prove a negative) but there is clearly no more evidence that Italy has a NAWRU than that it is haunted by ghosts.

Here is the graph for the 21st century



There is, perhaps, some hint of higher wage inflation at lower unemployment rates, but no clear acceleration. Nothing much seems to have happened to wage inflation as unemployment rose from around 8% to 13.2%.

The NAWRU refers to the acceleration of wage inflation. I consider the difference between wage inflation in one month and 12 months earlier (so it is an annual difference of an annual difference and the data refer to overlapping 24 month intervals)


This is an extremely impressively horizontal scatter. There is no sign of any association of unemployment and accelerating wage inflation at all. Here is a regression (with uncorrected standard errors)

. gen awinf = winf-winf[_n-12]

. reg awinf unem if month>2000

Number of obs = 181
F( 1, 179) = 0.00
Prob > F = 1.0000
R-squared = 0.0000
Adj R-squared = -0.0056

awinf | Coef. Std. Err. t
unem | 3.30e-07 .0396278 0.00
_cons | .0270689 .3569347 0.08

So “almost exactly precisely zero correlation ” means a correlation coefficient of 0.00 something and a regression coefficient of 0.00000033 . The T-statistic is not correct, the standard errors should be corrected for the 24 periods of overlap. But I don’t think that a T-statistic which is biased away from zero and equal to 0.00 really needs to be corrected. The almost exactly complete absence of any evidence of any effect of unemployment on the acceleration of wage inflation is extraordinary. It is extremely unlikely that two independent series would happen to have such low correlation.

This is the first regression I estimated with Italian data. Using the full sample I get a (statistically insignificantly) upward sloping accelerationist Phillips curve.

. reg awinf unem

awinf | Coef. Std. Err. t
unem | .0373827 .076396 0.49
_cons | -.8178216 .7054678 -1.16

I just now think that, maybe I should lead wage inflation acceleration (or lag unemployment)

awinf2 = winf[_n+12]-winf

. reg awinf2 unem if month>2000

awinf2 | Coef. Std. Err. t
unem | .0211333 .0482586 0.44
_cons | -.1483054 .4191373 -0.35

That doesn’t make much difference does it ?

There is no hint in the Italian data that there is such a thing as a NAWRU. Those with firm faith can still believe in the NAWRU, but their faith receives no assistance at all from the data.

update: typos corrected thanks to Reason and Marco Fioramanti. An explanation was revised aiming for comprehensibility following advice from Marco Fioramanti.