A NAWRU proposal

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Robert Waldmann
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A NAWRU proposal
Marco Fioramanti and I have strongly criticized the European Commission DG EcFin Output Gap working Group estimates of output gaps.
I have also written a lot here at angrybearblog

This topic is very important, because the output gaps are used to calculate cyclically corrected budget balances which are regulated by the Stability and Growth Pact. The calculations determine dictates for fiscal policy of Euro bloc member states.
Having criticized the current consensus approach, I have tried to make constructive suggestions. I discussed two alternative approaches here

I will now report progress on implementing one those proposals: to estimate NAWRU with a Kalman filter based on a Phillips curve model as the Output Gap Working Group currently does. However, assume that the NAWRU is a random walk without drift not a second order random walk (that is a random walk whose drift is itself a random walk).

I think that Marco Fioramanti and I already made a very strong case for at least that change in the filter. I briefly repeat the arguments after the jump.

Problems with the current official NAWRU series have been recognized by DG EcFin staff.
pdf warning Julia Lendvai, Matteo Salto and Anna Thum-Thysen (2015) discuss the possiblity of using the estimate of structural unemployment to calculate output gaps. They note that this implies quite different assessments of fiscal stances.

Recently (pdf warning) Atanas Hristov, Christophe Planas, Werner Roeger and Alessandro Rossi (2017) have proposed an approach to reconciling the estimation of NAWRU with the Kalman filter and the forecasts based on the assumption that NAWRU will converge to the most recent estimate of structural unemployment. Their approach is to include that assumption when calculating the conditional mean NAWRU for each period (the filtered NAWRU). This is mathematically equivalent to assuming that future NAWRU is actually measured and treating it as a datum. They call the newly calculated series “anchored NAWRU”

Notably, they do not use the assumption that future NAWRU will converge to the most recent estimate of structural unemployment when estimating the parameters of the model by maximum likelihood. This is important, because the assumption would reduce the likelihood of positive variance of changes in the drift. Importantly, the assumption that NAWRU will take some value in a given year (say 2026) does not imply the long term forecasts actually made by DG EcFin. The forecasts are based on the assumption that it will remain at that value, at least in expected value, from that year on. This means that, when forecasting, it is assumed that the NAWRU is either has a fixed mean or is a nonstationary process without drift. The model used to filter the data and calculate anchored NAWRU remains inconsistent with the model used to forecast.

Notably, the differences between unanchored and anchored NAWRU are small for most countries (Greece is an exception). Also they are tiny except for recent years. The huge (and mathematically impressive) effort to calculate anchored NAWRU doesn’t make very much difference. In particular, although the aim was to reduce the cyclicality of filtered NAWRU, the anchored NAWRU series remains extremely procylical.

These aspects of the filtered series are the results of the assumption that NAWRU is a second order random walk. As noted above, this assumption implies a gigantic variance of future NAWRU conditional on available data (and not conditional on assumptions about future NAWRU). This huge variance implies small corrections due to assumptions about future NAWRU. Basically, the model (including calculations of filtered NAWRU) says pretty much any NAWRU is about equally likely a few years in the future. This means that even if future NAWRU were actually observed, it would provide almost no information about current NAWRU. The same problem which makes it absurd to attempt to forecast based on the time series model used to calculate NAWRU also guarantees small changes from imposing the more reasonable assumptions used when forecasting (on one period and that period only).

However, Discussion Paper 069 suggests a solution to this problem. Hristov et al assume that the expected value of future NAWRU is a known constant. This implies that they assume that it is constant — that is that NAWRU either has a constant mean or is a non stationary process with zero drift. To remain as close as possible to the current methodology, it is tempting to assume that it is a random walk without drift. That happens to be the proposal I made about one month before Discussion Paper 069 was published.

The assumption that NAWRU is a random walk with drift implies radically different estimates than the assumption that it is a second order random walk (that is that the drift is itself a random walk). For most countries, the filtered series are much less cyclical. Sometimes, the estimated variance of the disturbance to NAWRU is zero, so the filtered series is a constant.
Discussion Paper 069 implies a natural approach to assessing the two models of NAWRU. It is assumed that the likelihood of the NAWRU series (treating filtered NAWRU as a series of estimates of a random parameter) is the product of the within sample likelihood and the likelihood that, in 8 years, NAWRU will be equal to the estimate of current structural unemployment. In practice this means that Hristov et al assume that it would be good for the NAWRU series to be close to the structural unemployment series.

I consider the cases of the 15 countries which were in the EU in 1997. For some reason, there doesn’t seem to be an anchor calculated for Ireland. This leaves 14 countries. Also for mysterious reasons, the most recent data set I can find is nairudata.xls dated February 9 2016. This file includes data and univariate forecasts for 2015, 2016 and 2017. The univariate forecasts are treated as data by the program.

For 12 of the 14 countries, my estimate of NAWRU in 2017 is closer to the anchor than the official estimate is. The exceptions are the UK (where the two estimates are very similar) and Germany (see Table 1).

My estimate of NAWRU for 2017 is also my forecast of NAWRU in 2025, because I assume that NAWRU is a random walk without drift. In contrast, the DG EcFin assumptions imply a non zero estimate of the drift in NAWRU as of 2017. This means that forecasts of NAWRU for 2025 can be quite extreme — for Germany the forecast is 2.1796 % and for Greece it is 29.0646 %. Again, my model performs better according to the criterion chosen by DG EcFin. For 11 of 14 countries my forecast of NAWRU in 2025 is closer to their anchor than their forecast is. The three exceptions are Belgium, Portugal, and Sweden for which the forecasts are very similar. (again see Table 1)

2017 nawru my nawru anchor NAWRU_2025

AT 6.1373 __ 5.6276 ___ 4.857178 ___ 7.7460
BE 6.2292M_ 6.8979 __ 8.230426 ___7.0711
DE 4.4600 __ 3.5965 __ 5.737078 ___ 2.1756
DK 6.0404 __ 5.7777 __ 4.607711 ___ 6.1252
EL 23.0171 __ 9.6774 _ 12.05144 ___ 29.0646
ES 19.8840 _ 15.2215 _ 15.44594 ___ 20.2009
FI 9.2566 ___ 8.5237 _ 7.556312 ___ 10.4474
FR 10.4753 _ 10.2194 _ 8.680219 ___ 11.0925
IT 11.0515 __ 9.1486 __ 9.717258 ___ 13.3583
LU 5.9337 __ 5.8268 __ 5.01865 ____ 7.2467
NL 6.5100 __ 4.2894 __ 4.524969 ___ 8.0404
PT 11.9014 ___ 7.4360 _ 9.148998 ___ 7.6632
SE 4.1951 __ 6.1472 ___ 5.73956 ____ 5.7181
UK 5.5120 __ 5.5018 __ 6.232115 ____ 4.6396

Table 1 suggests that those who think it is reasonable to anchor NAWRU estimates should consider it more sensible to model NAWRU as a random walk without drift than as a second order random walk. The same logic logic motivates the two choices, and forecasts of the 2025 NAWRU are similar.

There are other very marked differences between the currently official NAWRU estimates and alternative NAWRU estimates (that is estimates calculated assuming NAWRU is a random walk without drift). For most countries, the alternative NAWRU series does not track headline unemployment — alternative NAWRU is much less cyclical than official NAWRU. In fact, for many countries, the maximum likelihood estimate of the variance of the disturbance to alternative NAWRU is zero, so the filtered series is a constant.

It is reasonably clear that the output gap working group will never accept such an alternative estimate of NAWRU as a constant. I guess that, even if they accepted the random walk without drift assumption, they would impose a lower bound on the variance of the disturbance to the NAWRU. Also, for a few countries, the maximum likelihood estimate of the variance of the disturbance to cyclical unemployment is very low. I guess a lower bound would be imposed on this variance too. Even with these limits imposed a priori, the approach would still be very different from the current approach. The limits can be the same for all countries and never changed. I have estimated models assuming NAWRU is a random walk without drift, cyclical unemployment is an AR(2) and both have disturbances with variance at least 0.1.

Estimating the NAWRU assuming it is random walk without drift has striking advantages: the resulting series is not markedly procyclical, it does not reach implausibly high values for any countries, and the most recent value of the unanchored filtered series is close to the estimate of structural unemployment. It is very hard to think of arguments against modelling the NAWRU as a random walk without drift. It seems that it would be reasonable to model the NAWRU as a random walk without drift.

Brief summary of our arguments against the current NAWRU estimates

Briefly
1) the second order random walk model implies huge fluctuations of unemployment over time. If it were a good approximation, it is quite likely that unemployment would be less than zero and possible for it to be more than 100%. Given the assumptions, the fact that unemployment has always been positive in all European countries is a strange coincidence. If the model is used to forecast unemployment, for many member countries, it implies a high probability that unemployment will fall below zero in the next few decades. This is obvious, but it is also unacceptable in the time series literature in which it is absolutely standard practice to evaluate models by comparing out of sample forecasts to outcomes.
2) DG EcFin does not take the model seriously. They use a completely different model to forecast unemployment. They assume that it converges to their estimate of structural unemployment. This other estimate is calculated using the NAWRU estimates as if they were raw data and removing cyclical and idiosyncratic components. It is clear that DG EcFin staff consider their estimate of cyclical unemployment to be a better measure of the natural rate of unemployment. They use it to forecast, but the dictates to member states are, nonetheless, based on the NAWRU estimates. This means that cyclical corrections are based on the difference between headline unemployment and an artificial time series which has a strong cyclical component.
3) the assumed positive variance of the drift — the key strange and extreme aspect of the NAWRU time series model, is not based on empirical evidence. Maximum likelihood estimates of the parameters give an estimate of zero variance for most member countries. The positive estimated variances are due to arbitrary limits on the estimate parameters used to avoid “corner solutions”. That is the claim that NAWRU is a second order random walk is an assumption imposed a priori.
4) The arbitrary limits are absolutely unmotivated. They are very different for different member countries and are changed with each wave of forecasts as new data become available. They are absolutely critical to the estimates. In contrast, although the model is supposed to be based on a Phillips curve, data on wages are not critical to the estimates for most member countries. Similar estimates can be obtained for most member countries if data on wages is ignored entirely.
5) official NAWRU estimates are obviously pro-cyclical. It is recognized that this is problematic. Fabrice Orlandi demonstrated that they are significantly correlated with the ex post achieved real interest rate. This is a monetary policy intermediate targe. The original definition of the natural rate of unemployment (Friedman 1968) implies that it is not affected by monetary policy.
6) The purpose of cyclical adjustment is to evaluate the sustainability of the public debt determined by fiscal policy. A model which is not used for long term forecasts (because it implies absurd long term forecasts) can’t be used for this purpose which is necessarily focused on long term forecasts.