## 5/24/11

### 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, ut, and price inflation, CPIt, 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:
ut = aCPIt-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 CPIt 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.