European Commission fiscal dictates are based on outdated economic theory, strange econometrics and arbitrary ad hoc restrictions on parameter estimates. It is not easy to discuss the technique behind that which presents itself as technocracy with a straight face. The 'cracy part is genuinely powerful, so this matters.

This will be the first of a long long series of posts. It is written to blogging editorial standards, which means I think everything is true, but it's not as if I were submitting this to a peer reviewed Journal. I will try to present an outline.

A. Allowed deficits under the Stability and Growth Pact as revised in 2005 depend on estimated output gaps -- the restrictions on deficits refer to the "structural balance" (SB) which is the cyclically adjusted deficit minus one off expenditures and revenues. These posts will focus on the cyclical adjustment. ~~The allowed deficit is 3% plus 0.5 times potential output minus actual output (the output gap).~~ update: (correction due to Marco Fioramanti) Allowed spending depends on a "medium term objective" (MTO) which in turn is defined in terms of the SB end update. This means that estimation of potential output are very important as they is step required to apply an international treaty.

B. The European Commission (from now on EC) estimates of potential output are based on a production function and require estimates of the capital stock, total factor productivity and potential employment. This series of posts will consider only the estimates of potential employment. Potential employment is equal to the labour force times the natural employment rate. The natural employment rate is 100% minus the non wage inflation accelerating rate of unemployment (NAWRU). Estimates of the NAWRU are needed to construct estimates of potential output.

C. Another way of putting it is that the estimate output gap is a function of cyclical unemployment which equals actual unemployment minus the NAWRU. This means that estimates of the NAWRU are very important.

D. This means we (in the Eurozone) have a problem. The stability and growth pact requires estimation of the NAWRU which means that it dictates that there is a NAWRU and that, if unemployment is above the NAWRU the rate of increase of nominal wages declines. If the accelerationist Phillips curve does not correspond to reality, the Stability and Growth Pact is like the possibly mythical local ordinance which declared that Pi is equal to 3.0.

E This means that reassurances (to Paul Krugman) that policy makers and staff have moved on to use of Phillips curves with anchored expectations are uh not accurate.

F. There are many many problems with EC estimates of the NAWRU. This is obvious, because estimates of the NAWRU track actual unemployment and are absurdly high -- the EC estimate of the Spanish NAWRU for 2014 is greater than 20% (pdf warning) . I will write a post on each of the problems which I have noticed.

1. The theory which implies there is a NAWRU is rejected by the data. The acronym NAWRU implies that there is one and only one unemployment rate consistent with non accelerating inflation. European data from the past 7 years show huge fluctuations in unemployment and extremely stable inflation. There is no falsifiable hypothesis including a NAWRU which has not been falsified. The reaction has been to assume that the NAWRU fluctuates for unexplained reasons so the NAWRU story has no implications for the association between unemployment and inflation.

2. The changes in the NAWRU must be exogenous. It is not just that they are exogenous to the model (not explained) they must be unaffected by policy. This is an assumption. It is assumed that fiscal policy has no effect on the future NAWRU. In other words it is assumed that there is no hysteresis. This assumption is required for calculations of the effects of spending and revenues on the long term debt to GDP ratio (as stressed by DeLong and Summers pdf warning). The vitally important assumption is not tested.

3. The NAWRU is assumed to be an I(2) process -- not only does the level shift exogenously but so does the trend. This means that the first difference of the first difference of the NAWRU is stationary. This assumption implies that long term forecasts of the NAWRU, say 100 years from now, are always either greater than 100% or less than 0%. Clearly this is crazy. The original argument for an accelerationist Phillips curve is very explicitly an argument about the long run. There is a fundamental contradiction between the concept of a NAWRU and a time series model of the NAWRU whose long term implications are ignored.

4. The NAWRU is estimated by EC using two time series -- the acceleration of wage inflation and the unemployment rate. A model (explained for example in Fioramanti Padrini and Pollastri 2015 (warning same pdf to which I linked above). This model has 4 series of disturbance terms used to fit 2 time series. As one might guess, identification is a bit problematic. However, it is possible to convince a computer to estimate all the parameters.

5. In a last arbitrary ad hoc step, EC imposes limits on three of the parameters of their model. Crucially one of these is the variance of disturbances to cyclical unemployment. This last intervention is not motivated by theory or evidence. It has a very large effect on estimates of cyclical unemployment and allowed deficits.

I think it is clear that point 5 is very interesting. Even the reader who has been patient enough to read this far, might not be patient enough to read posts 1 through 4. I think 2, 3 and 4 will be skipable, but I don't guarantee that the future post 5 will be comprehensible without reading 1-4 (or even after reading 1-4).

update: the post has been corrected based on comments by Marco Fioramanti.

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