European Pooled Panel Phillips Curve
This continues joint research with Marco Fioramanti. Our aim is to understand something about European natural rates of unemployment and whether the European Commissions estimated levels which they call NAWRU (for non accelerating wage inflation rate of unemployment) are useful approximations.
Here is a brief summary of work to date (prior to this note). Various subsets of us wrote at length here, here, here, here , and here.
In this note I look at a panel of the 15 countries which were in the European Union in 1997 (that is those for which long series of data are available) and ask if the Commission’s estimates of the NAWRU are useful if one wishes to forecast the acceleration of wage inflation. They don’t seem to be very useful at all.
First note strong evidence that the rate of wage inflation is mean reverting. This is a pooled regression with data from the Old EU 15 from 1960 through 2015. Indicator variables four countries are included. The excluded country is Germany. dw is the percent rate of wage inflation. ddw is the change of dw. The coefficient of ddw on lagged wage inflation is negative. Since wage inflation is not stationary, inference based on the conventional t-statistic is misleading, but it is very hard to defend excluding lagged wage inflation from regressions.
Number of obs = 810
F( 15, 794) = 3.19
R-squared = 0.0568
Root MSE = 2.829
ddw Coef. Std. Err. t P> t [95% Conf. Interval]
dw L1. -.1239047 .017967 -6.90 0.000 -.1591732 -.088636
cnt1 .1032103 .5446975 0.19 0.850 -.9660071 1.172428
cnt2 .248755 .5450047 0.46 0.648 -.8210653 1.318575
cnt4 .1835412 .5457425 0.34 0.737 -.8877275 1.25481
cnt5 .7989407 .5571101 1.43 0.152 -.2946421 1.892523
cnt6 .5611396 .5526087 1.02 0.310 -.5236072 1.645886
cnt7 .3922957 .5472476 0.72 0.474 -.6819274 1.466519
cnt8 .2057765 .5457027 0.38 0.706 -.865414 1.276967
cnt9 .532994 .5490764 0.97 0.332 -.5448189 1.610807
cnt10 .5235781 .5498832 0.95 0.341 -.5558184 1.602975
cnt11 .2336141 .5448333 0.43 0.668 -.8358697 1.303098
cnt12 .1339668 .5448109 0.25 0.806 -.9354731 1.203407
cnt13 .8125298 .5572127 1.46 0.145 -.2812543 1.906314
cnt14 .3167034 .5459765 0.58 0.562 -.7550245 1.388431
cnt15 .4156857 .5468436 0.76 0.447 -.6577444 1.489116
_cons .4467843 .3942688 1.13 0.257 -.3271479 1.220717
In all pooled regressions of the 15 countries which are reported below, country indicators are included, but the coefficients aren’t reported.
Table 2 shows a simple wage Phillips curve regression in which an equal slope for all countries is imposed. ur is the unemployment rate.
Number of obs = 797
R-squared = 0.1584
Adj R-squared = 0.1411
Root MSE = 2.6095
ddw Coef. Std. Err. t
dw L1. -.2207513 .0195562 -11.29
ur -.2801143 .0293183 -9.55
fn: the regression includes country indicator variables whose coefficients aren’t reported.
Table 3 adds EcoFin’s estimate of the non wage inflatin accelerting rate of unemployment (nawru). It provides almost exactly zero evidence that the estimated NAWRU is useful when forecasting the acceleration of the rate of wage inflation.
Number of obs = 755
F( 17, 737) = 7.60
R-squared = 0.1492
ddw Coef. Std. Err. t
dw L1. -.2085405 .0202414 -10.30
ur -.2952919 .0664916 -4.44
nawru .0355939 .0856379 0.42
fn: the regression includes country indicator variables whose coefficients aren’t reported.
Another way to present this is to regress the change of the rate of wage inflation on lagged wage inflation, the NAWRU and the difference between the unemployment rate and the NAWRU (ur_cyc_nawru). If the ewstimated nawru is the rate of unemployment corresponding to non accelerating wage inflation, its coefficient should be zero.
Number of obs = 755
R-squared = 0.1492
Root MSE = 2.5646
ddw Coef. Std. Err. t
dw L1. -.2085405 .0202414 -10.30
ur_cyc_nawru -.2952919 .0664916 -4.44
nawru -.259698 .0405304 -6.41
fn: the regression includes country indicator variables whose coefficients aren’t reported.
Results are fairly similar if lagged productivity growth in percent (lp00) and lagged personal consumption deflator inflation in percent (infpce) are included in the regression. When these variables are included, there is statistically signficant evidence that the EcoFin estimates of the NAWRU are of some use, but also very strong evidence that their estimate of cyclical unemployment is not correct.
Number of obs = 755
R-squared = 0.2540
Root MSE = 2.4048
ddw Coef. Std. Err. t
dw L1. -.5250445 .0371051 -14.15
ur_cyc_nawru -.4385307 .0639218 -6.86
nawru -.265385 .0405976 -6.54
lp00 L1. .2762333 .0447936 6.17
infpce L1. .3915155 .0397721 9.84
fn: the regression includes country indicator variables whose coefficients aren’t reported.
The estimated NAWRUs track actual unemployment. This is invevitable given the EcoFin estimation strategy. In particular estimated NAWRU has increased dramatically over time for the old EU 15.
Number of obs = 765
nawru | Coef. Std. Err. t
year | .1352558 .0051641 26.19
fn: the regression includes country indicator variables whose coefficients aren’t reported.
However, there is no evidence that the unemployment rate correspnding to stable wage inflation has increased. In fact, the coefficient of the change in wage inflation on the year suggests it has decreased.
Number of obs = 797
ddw Coef. Std. Err. t
dw L1. -.2773093 .0222217 -12.48
ur -.2073403 .0322012 -6.44
year -.0447071 .0087745 -5.10
fn: the regression includes country indicator variables whose coefficients aren’t reported.
This remains true when lagged labour productivity growth and lagged PCE deflator inflation are included in the regression.
ddw | Coef. Std. Err. t
dw L1. -.5871574 .0375628 -15.63
infpce L1. .3843769 .0383875 10.01
lp00 L1. .1731338 .0453206 3.82
ur -.2866504 .031613 -9.07
year -.042782 .0091336 -4.68
fn: the regression includes country indicator variables whose coefficients aren’t reported.
and even when current labout productivity growth is included
ddw | Coef. Std. Err. t
dw L1. -.5611617 .0365368 -15.36
infpce L1. .3656987 .0364453 10.03
lp00 .2025245 .044271 4.57
ur -.2889669 .0314802 -9.18
year -.0366196 .0094267 -3.88
fn: the regression includes country indicator variables whose coefficients aren’t reported.
Back when I was a consultant, I had a client that really, really liked the use of ARIMA models. It used to drive me up a tree because changing the AR, I, or MA terms could lead to wildly different results with the data available with no good reason to select among them. I think what was a bug to me was a feature to that particular client, and said client really didn’t understand the process at all. On the other hand, the folks monitoring the European Stability and Growth Plan do understand their model and how tweaking it can be used to push the results in desired directions. That makes the feature even more of a feature.
Too many numbers being used to support too much speculation. The very concept of a “natural” rate of unemployment seems very unnatural in and of itself.