This is the final post on European Commission decomposition of unemployment into cyclical unemployment and the NAWRU (non accelerating wage inflation rate of unemployment). This calculation is important because cyclical unemployment is used to calculate the output gap and cyclically corrected budget deficits, which are used to calculated allowed spending under the stability and growth pact.

In an earlier post we have noted that the assumption that cyclical unemployment affects the acceleration of inflation rather than the level is problematic. It has become controversial (again) with many macroeconomists convinced that inflation expectations have become anchored so cyclical unemployment is related to the level not the acceleration of inflation (pdf warning).

It seems to us that the effort to extract a time series of cyclical unemployment which is correlated with the acceleration of wage inflation has lead to at least two very strange modelling choices. First, as noted here, the EC assumes that the NAWRU is a twice integrated random walk, that is that the drift of the NAWRU is itself a random walk. This means that the NAWRU sometimes trends up and sometimes trends down. The long term implications of this assumption are nonsensical, and, in fact, the EC doesn't take it seriously. In fact, EC long term forecasts are based on the assumption that the NAWRU is mean reverting.

Second, the EC imposes arbitrary limits on the parameters of their time series model. In particular, and crucially, they impose an upper limit on the variance of disturbances to cyclical unemployment (another pdf warning). This limit has two important effects.

First, it reduces the variance of cyclical unemployment. Second it increases the correlation between the estimated time series of cyclical unemployment and the acceleration of wage inflation. The second point is a bit technical for a blog, but it can be explained (we hope).

The series of cyclical unemployment is estimated in order to fit two observed series: total unemployment (equal to cyclical unemployment + the NAWRU) and the acceleration of wage inflation. Importantly, there are no free parameters in the identity: unemployment = cyclical unemployment + NAWRU. In contrast there are free parameters in the wage acceleration equation -- the slope parameters of the Phillips curve. This means that if, for example, cyclical unemployment is divided by 10, the estimated NAWRU must change and so must disturbances in the NAWRU time series. In contrast, there is no necessary reduction of the fit of the wage acceleration equation -- the Phillips curve slope parameters can be multiplied by 10 giving the exact same forecasts for wage acceleration.

Extreme restrictions on the variance of cyclical unemployment would make cyclical unemployment a negligeable component of total unemployment, while it could still be just as associated with wage acceleration as before. This means that as the allowed variance of cyclical unemployment goes to zero the estimated values of cyclical unemployment will go to those most correlated with wage acceleration.

Importantly this argument has nothing to do with any assumption about the true behavior of wages. Even if the time series of the acceleration of wage inflation were replaced with random numbers, it would be possible to force the computer to chose a time series of cyclical unemployment which is significantly correlated with those random numbers by imposing a low enough variance of the disturbances to cyclical unemployment.

It seems at least possible that the low variance of estimates of cyclical unemployment (and the resulting cyclical rigidity of required austerity) are the by product of an effort to force the data to fit an accelerationist Phillips curve.

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