NAWRU constructive (?) proposals

by
Robert Waldmann
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I have vigorously criticized the European Community DG EcFin approach to estimating the non accelerating wage inflation rate of unemployment (NAWRU). This is a step in their estimation of output gaps, which, in turn, are used to set allowed deficits for member countries under the Stability and Growth Pact. The calculations are critically important.
Marco Fioramanti and I think the DG EcFin approach (technically agreed with member governments) is not defensible.

I have two thoughts about how NAWRU should be estimated. One is a proposed modification of the current state space model. The other is more radical: it is to calculate NAWRU as a function of data without allowing unexplained variation at all.

1) a modest proposal

a) The problems with the currently agreed procudure based on a Kalman filter.
The current estimates of NAWRU depend critically on arbitrary restrictions on parameters. The restrictions are imposed ad hoc. Relaxing them leads to NAWRU estimates which are very different than the official estimates. The importance of the unmotivated restrictions is demonstrated by the fact that extremely similar estimates of trend unemployment are usually (for n of 28 countries ) obtained without any use of data on wage inflation simply as a trend-cycle decomposition of the univariate unemployment series given the restrictions on parameters. The arbitrary restrictions are different for different EU countries and are changed from year to year (without any motivation or explanation of the change). This means that estimated output gaps depend critically on arbitrary decisions made by people who should act as technicians.

The assertion that unemployment can be decomposed into a stationary and non-stationary components is not a testable hypothesis. Theory does not guide the specification of the non stationary component at all. There is no reason to expect that it is unaffected by fiscal policy and no justification for taking it as exogenous and given when setting fiscal policy.

It would be much better if there were simpler uniform limits on the time series models which can be clearly explained and motivated and which are not changed at will.
I think the key problem is that, for some reason, NAWRU is modelled as a second order random walk, so the drift term is itself a random walk. There is no motivation for this approach. It has no relationship with any existing model of unemployment — the original natural rate of unemployment hypothesis had no place for unexplained variations in the natural rate — only variations due to changes in labour market institutions were allowed. The second order random walk model is not taken seriously. It is used to decompose unemployment into NAWRU and cyclically adjusted unemployment, but it is not used to forecast future unemployment. A key principal of standard time series economics is that time series models are evaluated based on their ability to forecast accurately out of sample. Contradictory assumptions about the same time series for different purposes are not usually allowed.

Importantly the choice to model NAWRU as a second order random walk is not based on empirical evidence. For most (n of 28) countries, the estimated variance of the disturbance to the drift (the so called “slope variance” is zero if restrictions are not imposed on parameters. For (n of 28) countries a binding lower bound on this parameter estimate is imposed — in effect the parameter is set by hand arbitrarily. For another (m of 28) the parameter estimate is positive only because binding upper bounds are imposed on other variances.

It seems to me clear that this parameter should be set to zero, so NAWRU should be modelled as a first order random walk (as it currently is for Slovenia). There is no theoretical motivation for assuming stochastic drift. The data, if allowed, usually yield 0 as an estimate. The implications of varying drift are absurd . The model with varying drift is not used for out of sample forecasting. All arguments I have read which defend the current approach are vague and essentially appeal to the judgment of appointed experts.

I conclude that, if NAWRU is modelled as an indirectly observed state, it should be modelled as a first order random walk. I can’t think of any defence of the second order random walk model.

b) Problems with freely estimate parameters

I don’t know or care why the second order random walk specification was originally chosen. However, it is easy to see why first order random walk estimates are unappealing (so estimates where a slope disturbance is allowed but freely estimated and estimated to be zero are unappealing). Given the general increase in unemployment in most EU countries, a large positive drift is estimated. For many countries, freely estimated NAWRU is a deterministic trend (or nearly a deterministic trend). Given the theoretical model of NAWRU as function of labour market institutions this is implausible. I personally find it implausible. The natural reaction to this prior belief that dramatic positive drift is implausible is to restrict the drift parameter to zero. That is to model NAWRU as a first order random walk without drift. To do this is to say that we have no sense we can forecast of the sign of the change in NAWRU from AD 3000 to 3010.

Setting the drift to zero is very different from relaxing arbitrary restrictions on estimated variances. It is a restriction no relaxation of a restriction. It implies a lower likelihood not a higher likelihood. It is based on theory, but the theory consists of simplifying assumptions made about trends by economists who want to focus on cycles. I think the drift in NAWRU should be set to zero, but I can see why others might be sincerely unconvinced.

The Phillips curve with NAWRU assumed to be a first order random walk without drift remains poorly identified. The problem is that data on wages (or real unit labour costs) provide no information about the variance of the disturbance to cyclical unemployment. If cyclical unemployment is multipled by 10 and the phillips curve parameters are divided by 10, then the forecasts of wage inflation aren’t changed at all. Wihtout restictions on parameters, the Phillips curve gives no information on the magnitude of the distubances to cyclical unemployment and the NAWRU. This explains the attraction of arbitrary restrictions on estimated variances. I personally think it is reasonable to impose (sometimes binding) lower bounds on the variance of the disturbance to cyclical unemployment and the NAWRU. I think it is very important, as a matter of fairness, to impose the same arbitrary limts on parameters estimated for different countries. I certainly think that the restictions should be chosen a priori and not changed ad hoc. To be specific I propose 0.1 %2 as a lower bound on both estimated variances.

c) preliminary conclusion

I think that the proposed model in which NAWRU is assumed to be a random walk without drift with variance the greater of the free estimate and 0.1 %2 and cylical unemployment a stationary AR(2) with a distubrance with variance the greater of the free estimate and would be a huge improvement on the existing approach. The model could be used for non absurd out of sample forecasts. The time series behavior of NAWRU in the model corresponds to the time series behavior of the natural rate of unemployment in the theoretical literature. The arbitrary restictions are simple, constant and the same for all EU countries. They can (and must) be clearly and prominently stated.

A more radical proposal after the jump

2) A more radical proposal.

Some might argue that the available annual data are not numerous enough to estimates state space models. Experience shows that existing models are poorly identified with ill behave likelihood functions with multiple local maxima. One possible conclusion is that, while it is certain that there is variation in the natural rate of unemployment due to unobserved changes in labour markets, it might be impossible to usefully estimate these fluctutuations with available data. A possible reaction is to impose (as a useful approximation) the assumption that all changes in the NAWRU are caused by observed changes in institutions. Again, I stress, this is a modelling assumption imposed in the hope that it is a useful approximation and not due to the illusion that it is literally exactly true.
This assumption leads to a radically different approach to estimation. The Kalman filter is no longer needed. The NAWRU can be estimated as follows.

a simple regression of the acceleration in wage inflation on unemployment, exogenous variables which affect wage inflation (the change in the change of price of petroleum etc) and exogenous variables which affect the NAWRU (the unemployment insurance replacement ratio, union density etc). Then the estimated NAWRU is obtained by multiplying the labour market instution variables by their parameters.

In effect, this is treating as a constant the the term which is modeled as a second order random walk in the current approach and as a first order random walk with zero drift in the modest proposal.
There is some basis for hope the DG EcFin would consider this radical change. In addition to the NAWRU they estimated another time series which they call “structural unemployment”. It is obtained by regressing their NAWRU series on labour market institution variables and calculating fitted values. For medium term forecasts, DG EcFin assumes that the NAWRU converges to structural unemployment. They offer no explanation for the choice to use the difference between headline unemployment and NAWRU when calculating ooutput gaps. They could use the difference between headline unemployment and structural unemployment. They note, in passing, that in the rest of the literature, the structural and natural are treated as synonyms.

In practice, the radical proposal is very close to the proposal to use the DG EcFin structural unemployment series not NAWRU when calculating output gaps.

I am not aware of any counter-argument against this proposal.