Thursday, January 28, 2016

Back to the 60's Phillips Curve ?

I have been postponing posting this post. Now it is a bit late as it is, I think, strictly inferior to Nick Bunker's post "Context may be everything when it comes to the Phillips curve" which you should probably just read. Both are mainly comments on Olivier Blanchard's Peterson Institute for International Economics policy brief (pdf) "The US Phillips Curve: Back to the 60s? " which itself is largely based on Blanchard Cerutti and Summers (2015) (which he cites).

Blanchard analyzed US unemployment and inflation with a model including time varying parameters and concluded two things. First it appears that inflation expectations are anchored. What this really means is that recent inflation has a small effect on current inflation (Blanchard and Blanchard et al don't attempt to directly measure expectations). Second, the slope of the Phillips curve has declined with large changes in unemployment followed by small changes in inflation. Blanchard stressed that the computer is convinced that the slope declined in the early 90s and that this is not a new great-recession pattern.

I will present some very simple graphs assuming expectations are completely anchored. That is, I will do what old Keynesians are often (incorrectly) accused of doing and ignore fluctuations in expected inflation entirely. The point, as noted by Bunker following Ekaterina V. Peneva and Jeremy B. Rudd, is that the change from the 60s to around now is a reduction of the pass through of labor costs to price inflation. Like Blanchard and BCS, they use a sophisticated time varying parameter model, but the point is simple -- in recent decades wage and price inflation have not moved together.

I think it is worth a blog post to check whether the relationship between unemployment and the increase of nominal labor costs (roughly wage inflation) has changed too. My impression is that it hasn't. I look at two series from FRED

HCOMPBS Business Sector: Compensation Per Hour, Index 2009=100, Quarterly, Seasonally Adjusted

and UNRATE "Civilian Unemployment Rate (UNRATE), Percent, Quarterly, Seasonally Adjusted" with 1950s econometrics, that is scatter plots. awinf is the % rate of increase of HCOMBS over 4 quarters (so the points on the scatter are not independent observations. I pool data from before 1973q1 and after 1985q1, that is back in the good old days and after the Volcker deflation. A 0 next to the dot means data from after 1985q1 and a 1 means data from before 1973q1.

The scatter is scattered. The old and new clouds of points overlap. I think there seems to be a reasonably stable and not shifting long run downward sloping Phillips curve. the main difference between the sub periods is that unemployment has often been very high post 1985.

Here is another scatter using only data from after 1953 so 1953-1972 and then 1985-2015.

For what it's worth, STATA isn't convinced that there has been a statistically significant change since 1973 even though it calculated standard errors ignoring the overlap of the intervals over which labor cost inflation was measured.

Now I look at annual GDP deflator iflation and labor cost inflation (always with overlapping intervals). The scatters look completely different pre 1973 and post 1985

before 1973, the two inflation rates were extremely highly correlated.

After 1985 the (still statistically signficant) correlation was much reduced

It sure seems to me that the change from one period of anchored expectations to another has a lot to do with price setting and not so much to do with wage setting. Given the gigantic changes in the US labor market (roughly the death of trade unions) this is very puzzling.

Monday, January 25, 2016

NAWRU VI Arbitrary Limits on Parameters

by Marco Fioramanti and Robert Waldmann

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.

Monday, January 11, 2016

NAIRU V Estimation

by Marco Fioramanti and Robert Waldmann

This is the second to last post on the European Commissions DG -Ec-Fin estimates of cyclical unemployment for the purposes of calculating output gaps. This estimate is called unemployment minus the NAWRU (non accelerating wage inflation rate of unemployment). We will call unemployment - NAWRU "cyclical unemployment" even though it is agreed that the NAWRU is partly cyclical.

For several countries (including Italy) it is calculated with a time series model based on an accelerationist Phillips curve in which the change in wage inflation depends on cyclical unemployment. The model is fairly complicated with 11 paramters (estimated for Italy with 50 annual data points and 3 years of atheoretic forecasts). It is briefly described here based on this working paper.

The model attempts to fit 2 time series, unemployment and the change in the rate of increase of wages, and includes 4 disturbance terms. To be very brief, the expected acceleration of wage inflation is a linear function of cyclical unemployment and two lags of cyclical unemployment (the equation includes one of the disturbance terms). Cyclical unemployment is assumed to be an AR(2) (with the second of the disttubance terms) The NAWRU is assumed to be an I(2) second order random walk -- the drift of the NAWRU is itself assumed to be a random walk (so the disturbance to the drift and the disturbance to the level are the 3rd and 4th disturbance terms). The assumption that the drift is a random walk is crazy -- it always implies long term forecasts of unemployment less than zero or over 100%. The EC staff agree that this model can't be taken literally. They ignore it when making long term forecasts. However, the resulting estimates of cyclical unemployment are used to calculated output gaps.

Robert wrote "As one might guess, identification is a bit problematic. However, it is possible to convince a computer to estimate all the parameters." As we (mostly Marco) have attempted to do this for slightly modified models, we have discovered that it is very difficult to convince a computer to estimate all the parameters (DG -Ec Fin uses their own software). This (in addition to the usual procrastination) has caused a long delay between NAWRU IV and NAWRU V (this post).

The problem (at least for STATA addicts) is that STATA ends up at a corner attempting to set the variance of the disturbance to the drift of the NAWRU to zero. This means that estimated of the model as officially described using STATA's standard sspace command provides no empirical support for the theoretically unjustified assumption which has impossible long term implications. STATA (v. 11 to 14) refuses to report estimates after getting stuck in a corner (this is a feature not a bug).

Based on Robert's efforts to code a pseudo-annealing Kalman filter maximum likelihood estimator (which are not publishable even in a blog) we think the key issue is the imposition of an arbitrary maximum on the variance of the disturbance to cyclical unemployment. This will be the topic of NAWRU VI -- the final episode if and when the conclusion is based on the use of standard software.

But in this post, we want to discuss estimation of the model with the variance of that disturbance term set to zero -- that is -- estimation of a model in which the NAWRU is assumed to be a random walk with drift.

This model has less appalling implications for the long term. The NAWRU is not restricted to the range from 0% to 100% but it would be easy to impose this restriction (the standard approach would be to assume that the NAWRU is a martingale and the variance becomes small when the NAWRU is near the limits -- it is possible to assume that this state dependent variance is constant over the range experienced during the sample period so the model as written is valid). The fluctuations in the NAWRU remain exogenous and unexplained, but there is at least a literature on why the natural rate of unemployment might fluctuate.

This model has implications strikingly different from those of the EC DG- EcF Fin model. The The fitted NAWRU no longer tracks the business cycle. The variance of cyclical unemployment is much greater. The resulting fiscal dictates would have been very different if the EC had used our simpler model .

here un = NAWRU

ug = unemployment - NAWRU = "Cyclical Unemployment"

ddw = the acceleration of wage inflation

The estimate command is

(the constraints are identities such as unemployment = (unemployment-NAWRU) + NAWRU and the assumption that the NAWRU is not mean reverting)

matrix rjw=(1, 1, 1, 1, 1, 1.407003, -0.49923037, 0.1555339, 1, 1, -0.031958257, 0.048677339, -0.019232409, 0.032105009, 0.28977462, 0.000507234)

sspace (un L.un, state noconstant) ///

(mu, state noerror noconstant) ///

(ug1, state noerror noconstant) ///

(ug2 L.ug1, state noerror noconstant) ///

(ug L.ug1, state) ///

(u un ug, noerror noconstant) ///

(ddw ug ug1 ug2, noconstant) if year >=1965 & year<=2017, ///

iterate(100) from(rjw) constraints(1 2 3 4 5 6 7) ///

covstate(di) covobserved(di) difficult

Here are the estimates

For what it's worth, the likelihood is larger than that reported by the EC. We don't think too much attention should be paid to those two numbers -- the reported likelihood depends on technical assumptions used to initialized the Kalman filter when there are nonstationary variables. The null that the disturbance to the NAWRU has mean zero (so the NAWRU is a trend) is not rejected. There is little evidence that ug is related to the acceleration of wage inflation.