Employment in the United Kingdom

There is a trade-off between the change in unemployment and employment. Figure 1 compares the change in the rate of employment (the employment/population ratio), de, and the rate of unemployment, du, in the United Kingdom. As expected, the change in the rate of unemployment is more volatile. We have retrieved all data on unemployment and employment from the U.S. Bureau of Labor Statistics.

Figure 1. The (negative) change in the rate of employment compared to the change in the rate of unemployment in the UK.

 In our previous post we have estimated Okun’s law for the UK. It is instructive to estimate a model similar to Okun’s law for the employment/population ratio, e. For the UK, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

de_t = 0.41dlnG_t-1 – 1.11, t<1983

de_t = 0.41dlnG_t-1 – 0.81, t>1982     (1)  

where dlnG_t-1 is the change rate of real GDP per capita one year before, i.e. the predicted curve leads by one year. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1982 which is expressed by a significant shift in intercept without any change in slope.  The employment/population ratio varies around 58% between from ~54.3% in 1982 and ~61% in 1972. There is a dramatic deviation from the measured employment/population ratio after 2008.  This deviation is consistent with the difference for the same years in 2009. Figure 3 present results of linear regression with R²=0.89 for the period between 1972 and 2009.

Figure 2. The cumulative curves for the observed and predicted change in the employment/population ratio, de.

Figure 3. Linear regression of the measured and predicted curves in Figure 2.

Unemployment in Italy

In this blog, we have reported empirical relationships approximating Okun’s law for many developed countries: the USA, France, Spain, Canada, Australia, the UK and Germany. Instead of the original form of Okun’s law we have applied a LSQ technique to its integral version:

u(t) = u(t0) + bln[G/G0] + a(t-t0) (1)

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients.

For Italy, we have estimated a similar model with a possibility of a structural break somewhere between 1980 and 1990. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.13dlnG + 0.71, t<1990

du = -0.25dlnG + 0.00, t≥1990 (2)

This model suggests a significant increase in slope and a big fall in intercept around 1985.

Figure 1 depicts the observed and predicted curves of the unemployment rate, the latter is predicted by (1) with coefficients from (2). The agreement is not good, especially between 1985 and 2000. Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.84. Here we do not test both time series for stationarity but presume that the rate of unemployment has to be a stationary time series in the long run.

The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.82% for the period between 1971 and 2009. The average rate of unemployment for the same period is 9.0% with a standard deviation of the annual increment of 0.63%.

Previously, we reported on the model linking the rate of unemployment in Italy to the change in labor force. It was shown that the change in labor force leads by 11 years and allows a prediction of the rate of unemployment with an accuracy of 1.5% for approximately the same period. Figure 3 depicts this model.

Figure 1. The observed and predicted rate of unemployment in the Italy between 1971 and 2009.

Figure 2. The measured time series is regressed against the predicted one. R2=0.84 with both time series likely to be stationary.

Figure 3. The rate of unemployment in Italy predicted from the change in labor force.

Unemployment in Germany

We have estimated a version of Okun’s law for the USA, France, Spain, Canada, Australia and the UK. We have applied a LSQ technique to the integral version of Okun’s law:  

u(t) = u(t₀) + bln[G/G₀] + a(t-t₀)  (1)  

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients.  

For Germany, we have estimated a similar model with a structural break somewhere between 1980 and 1990.  The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.32dlnG + 1.19, t<1985

du = -0.43dlnG + 0.81, t≥1985   (2)  

This model suggests a significant increase in slope and a big fall in intercept around 1985.  

Figure 1 depicts the observed and predicted curves of the unemployment rate, the latter is predicted by (1) with coefficients from (2). The agreement is very good, except the years between 2007 and 2009. The deviation is extremely high and unexpected.  During the 2008/2009 recession, the rate of unemployment in Germany was decreasing what contradicts Okun’s law. Our model linking the rate of unemployment to the change in labor force has accurately predicted the observed fall in the unemployment rate.

Figure 2 shows that when the observed time series is regressed against the predicted one, R²=0.86.  Here we do not test both time series for stationarity but presume that the rate of unemployment has to be a stationary time series in the long run.

The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.57% for the period between 1971 and 2007 (2008 and 2009 excluded). The average rate of unemployment for the same period is 6.5% with a standard deviation of the annual increment of 0.83%.

Figure 1.  The observed and predicted rate of unemployment in the Germany between 1971 and 2009.

Figure 2. The measured time series is regressed against the predicted one. R²=0.86 with both time series likely to be stationary.

Unemployment in the UK

We have estimated a version of Okun’s law for the USA, France, Spain, Canada and Australia. We have applied a LSQ technique to the integral version of Okun’s law:  

u(t) = u(t₀) + bln[G/G₀] + a(t-t₀)  (1)  

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients.   

For the United Kingdom, we have estimated a similar model with a structural break somewhere between 1980 and 1990.  The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows: 

du = -0.63dlnG + 1.75, t<1988

du = -0.39dlnG + 0.63, t>1987    (2)  

This model suggests a significant drop in slope and a big change in the intercept around 1988. (All coefficients are close to those for Australia.)  

Figure 1 depicts the observed and predicted curves of the unemployment rate, the latter is predicted by (1) with coefficients from (2). The agreement is very good.  Figure 2 shows that when the observed time series is regressed against the predicted one, R²=0.90.  Here we do not test both time series for stationarity but presume that the rate of unemployment has to be a stationary time series in the long run. 

The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.85% for the period between 1971 and 2010. The average rate of unemployment for the same period is 6.9% with a standard deviation of the annual increment of 1.07%.  

One can suggest that the rate of unemployment has been driven by real economic growth and there is no room for structural unemployment. The will be no decease in the rate of unemployment if the growth rate of real GDP per growth does not exceed (0.63/0.39=) 1.63% per year.  

Figure 1.  The observed and predicted rate of unemployment in the UK between 1971 and 2010. 

Figure 2. The measured time series is regressed against the predicted one. R²=0.90 with both time series likely to be stationary.

On the absence of structural unemployment in Australia

We have estimated a version of Okun’s law for the USA, France, Spain and Canada. We have applied a LSQ technique to the integral version of Okun’s law:

u(t) = u(t0) + bln[G/G0] + a(t-t0) (1)

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical coefficients.

For Australia, we have estimated a similar model with a structural break somewhere between 1980 and 2000. The best-fit (dynamic) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.69dlnG + 1.50, t<1995

du = -0.45dlnG + 0.75, t>1994 (2)

This model suggests a significant drop in slope and a big change in the intercept around 1994. Figure 1 depicts the observed and predicted curves of the unemployment rate. The agreement is very good. Figure 2 shows that when the observed time series is regressed against the predicted one, R2=0.84. Here we do not test both time series for stationarity but presume that the rate of unemployment has to be a stationary time series in the long run.

The integral form of the dynamic Okun’s law (1) is characterized by a standard error of 0.78% for the period between 1975 and 2010. The average rate of unemployment for the same period is 6.9% with a standard deviation of the annual increment of 1.9%.

One can suggest that the rate of unemployment has been driven by real economic growth and there is no room for structural unemployment.

Figure 1. The observed and predicted rate of unemployment in Australia between 1975 and 2010.

Figure 2. The measured time series is regressed against the predicted one. R2=0.84 with both time series likely to be stationary.

President Medvedev as the incumbent

The presidential elections in Russia in 2012 are a hot topic for Russian mass media and blogosphere. There are some doubts that president Medvedev will join the race ignoring his advantages as the incumbent. So to say, the race will be an open seat one.  

I have some doubts that this is possible in Russia, however. Not to go for a new term is almost equivalent to admitting that the first term was unsuccessful and challenges all decisions during the term. President Medvedev is an active participant of the legislation process and has drafted many laws. Their quality and legitimacy will be scrutinized.  

There is not only domestic activity but also many international agreements and negotiations. If president Medvedev resigns all of them, especially current negotiations, will be reconsidered with an inevitable loss in position.

This is not to say that president Medvedev has to win the race. This is to say that he cannot allow nonparticipation. 

Gasoline price in 2011

On December 21, 2010 we revisited the evolution of the price index of motor fuel (a component of the transportation consumer price index). It is time to test our predictions and make new projections.

 Here we follow our concept of deterministic and sustainable trends in the differences of consumer price indices. The model implies that the difference between the headline (or core) CPI and a given individual price index, iCPI,  can be described by a linear time function over time intervals of several years:

CPI(t) – iCPI(t) = A + Bt (1)

 where A and B are empirically estimated coefficients, and t is the elapsed time. Therefore, the “distance” between the CPI and the studied index is a linear function of time, with a positive or negative slope B. Free term A compensates the difference related to the start levels for a given year.

 On December 21, 2010 we presented Figure 1 and suggested that the difference reached some new trend and would follow it in the future. However, the evolution since January 2011 has been following another trajectory which resembles the fluctuation in 2008. We have already mentioned in this blog that the volatility in commodity prices has been extraordinary since 2005. This might be associated with speculative capital and/or quant funds. In any case, the swing in 2011 has come to its peak, as we expected a month ago, and not is returning to the trend. We expect the price index of motor fuel to grow at a lower rate than the headline CPI in order the difference to reach the trend by the end of 2011. In physical terms, the motor fuel price will likely be falling together with crude oil.

Figure 1. The difference between the headline CPI and the index for motor fuel. Solid diamonds represent the prediction given in March 2009 through December 2009. The total increase in the difference is +60 units of index or +35%: from 173 in March to 233 in December 2010. Dashed line represents the new trend, which is a mirror reflection to that between 2001 and 2008 shown by solid black line. In 2010, the difference has been fluctuating around the trend and thus should return to the trend in the beginning of 2011.

Figure 2. Same as in Figure 1with data through June 2011.