On the future rate of unemployment in the US

The current status and near future of inflation and unemployment in the U.S. has ignited fierce debates on the reasons behind both macroeconomic variables. There are quite a few academic economic models with the Phillips curve in the centre of many. Any academic knows that unemployment is likely among the principal driving force behind inflation. To be able for this mission the change in the rate of unemployment must be contemporaneous or lead the induced changes in the rate of inflation. This is a dogma despite observations contradict all such models.
Six years ago, we presented a model which links labour force to unemployment and inflation. In other words both variables are driven by the only force – the change in labour force. Year by year, this model has been providing accurate predictions in all biggest developed countries. Econometrically, the change in labour force is cointegrated with the rate of inflation and unemployment, as the Engle-Granger and Johansen tests have shown. Since both variables have the same root, we introduced a generalized model. This model links all three variables together. It also allows resolving some metrological and methodological problems and improving prediction. Unfortunately for the mainstream models, measurements show that unemployment lags behind inflation and labour force by 2.5 and 5 years respectively. In that sense, we called our model the anti-Phillips curve, i.e. the curve with reversed causality. The original model covered the whole period between 1963 and 2005 by one empirical relationship. It provided a much better prediction of inflation and unemployment than any other model (by a factor of 2 lower RMFSE at a two year horizon). Among other predictions, we foresaw the possibility of a deflationary period from 2012 with very low inflation after 2010. The original model is now enhanced by the introduction of structural breaks related to the major changes in monetary policy. Such structural breaks are manifested in the change of coefficients in the linear links between inflation, unemployment and labour force. The linearity is retained, however. For the U.S. we have obtained the following model:

ut = 1.2lt-5 + 0.21pt-2 +2.03; 1984>t≥1956
ut = 1.9lt-5 + 0.425pt-2 +1.53; 2008>t≥1984
ut = 3.4lt-5 + 0.84pt-2 + 2.00; t≥2008

where ut is the rate of unemployment at time t; lt-5 the relative change rate of labour force (= dlnLF/dt) five years before , t-5; pt-2 is the rate of (CPI) inflation two years before. There are two breaks in 1984 and 2008. Both are obtained by a free search minimizing the RMS model error between 1960 and 2010. One can guess that the change in monetary policy increases the sensitivity of unemployment to the change in labour force and inflation approximately by a factor of 2.

Figures 1 through 3 present the measured and predicted rate of unemployment and the model error. Considering the fact that the rate of unemployment is predicted at a two and a half year horizon the agreement is excellent. Of special importance is the current peak in unemployment which follows from the change in monetary policy in 2008.

Figure 1. Monthly observed and predicted rate of unemployment in the U.S. One can expect the rate to fall below 8% by the end of 2011 or in early 2012.

Figure 2. Annual observed and predicted rate of unemployment in the U.S. One can expect the rate to fall below 8% by the end of 2011 or in early 2012.

Figure 3. The annual model error. The model predicts at a two year horizon. We also present cumulative annual error between 1965 and 2010.

The Phillips curve in Germany

In the posts on the USA and the UK, we mentioned the anti-Phillips curve in which unemployment lags behind inflation by several years. This contradicts the paradigm of the modern economic theory. There are cases, however, which comply with the theory. The Phillips curve in Germany is a good example where unemployment leads inflation by one year.

Figure 1 displays the observed rate of unemployment, u, and that predicted from inflation, which is represented by the GDP deflator, DGDP, according to the following relationship:

u(t-1) = -1.30[0.1]DGDP(t) + 0.105[0.005]              (1)

where u leads by one year. Standard deviation of the residual error is (s=) 0.013 for the period between 1971 (start of DGDP time series) and 2010. Both coefficients in (1) are reliable, and thus, there exists a linear and lagged relation between unemployment and inflation in Germany.

Figure 1. Unemployment and DGDP (both reported by the OECD) in Germany between 1971 and 2010. The lower panel shows the cumulative curves for the annual readings in the upper panel.

Both coefficients in (1) are determined from the cumulative curves with a higher accuracy when provided by linear regression. Figure 2 depicts the Phillips curve in a standard way. The slope of -0.645 instead of the linear coefficient -1.30 in (1) is highly underestimated due to the uncertainty in both time series. At the same time, the determination coefficient R²=0.83 is a strong evidence in favour of the Phillips curve in Germany.

 The existence of a conventional Phillips curve in Germany raises a question about the consistency of monetary policy of the Bundesbank. Does the bank conduct a monetary policy, which balances inflation and unemployment? Affirmative answer is counter-intuitive as in the past twenty five years show the unwillingness of the bank to reduce unemployment in exchange for higher inflation.

Figure 2. The Phillips curve for Germany. The unemployment readings are shifted by one year ahead to synchronize with the GDP deflator estimates.

The Phillips curve and anti-Phillips curve in the U.K.

Looking at two pictures below, please decide which is closer to reality. I have found  a version of the Phillips curve for the U.K. in this paper - "What Drives Inflation in the Major OECD Economies?" by

Diego Moccero, Shingo Watanabe, Boris Cournède. To my mind, their presentation is misleading if compared to the anti-Phillips curve where unemployment lags behind inflation.

Their figure:

My figure: 

I do not understand what makes economists to have so strong prejudice against inflation leading unemployment when it is really  observed. Smells as a sect.

The anti-Phillips curve indicates that the rate of unemployment in the UK must drop below 7% by the end of 2013.

We introduced a model of unemployment in the USA and other developed countries six years ago. The rate of unemployment, u_t, and price inflation, CPI_t, are driven by the same force - the rate of change of labour force. Briefly, there exists a long-term equilibrium (linear and lagged) link between unemployment, inflation and labour force. As a consequence, the rate of inflation and unemployment are also linked by a linear and lagged relationship.  In the USA, unemployment lags behind both CPI and labour force by 3 and 5.5 years, respectively. This creates a situation contradicting any mainstream macroeconomic theory. Under the conventional framework, which is usually described by the Phillips curve, the change in unemployment must be contemporary or leading price inflation. As a joke, we proposed to call the actual link between inflation and unemployment in the USA the anti-Phillips curve. As always, the economics profession ignores observations and looks for the answer in the reservation limited by theoretical barbed wire.  Here we present the case of the United Kingdom. Monthly estimates of the rate of unemployment and CPI, both obtained from the OSCD, completely confirm the concept of the anti-Phillips curve. Unemployment in the UK lags behind inflation by 24 months.

In practice, we are looking for the best-fit linear and lagged equation in the following form:

u_t = aCPI_t-j  + b      (1) 

where a and b are empirical coefficients, and j is the time lag between these variables, which can be positive, zero, or negative. Figure 1 displays the best fit model with a=0.9, b=0.041 and j=24 months. Since the monthly estimates of CPI_t are very noisy we have smoothed the predicted curve with MA(24). Overall, the rate of unemployment repeats the shape of the scaled inflation curve two years later.  The coefficient of determination R²=0.89 for the period between 1981 and 2011, i.e. for 360 readings.

From Figure 1 one can conclude that there exists an anti-Phillips curve in the UK as it was revealed for the USA. Inflation does lead unemployment and the economic theory can not ignore this observation. A good validation of the model would be the fall in the rate of unemployment in the UK below 7% by the end of 2013. The observed curve should intercept the predicted one in the near future.

Figure 1. Observed and predicted rate of unemployment in the UK. Lower panel presents the cumulative values of the curves in the upper panel. This is the best control of the link.