Employment in Japan

We continue modeling the evolution of the employment rate in developed countries with Japan. In this study we use the trade-off between the change in unemployment and employment and Okun’s law. Figure 1 compares the change in the rate of employment (the employment/population ratio), de, and the rate of unemployment, du, in Japan. The change in the rate of unemployment is as volatile as that of unemployment and they differ drastically compared to the synchronized evolution of these variables in the U.S. That’s why we have failed to obtain a reasonable Okun’s law for Japan. As before, all data sets on unemployment and employment have been retrieved from the U.S. Bureau of Labor Statistics. The estimates of real GDP per capita have been retrieved from the database provided by the Conference Board.

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

In this blog, we have already presented several empirical relationships predicting the employment/population ratio from the growth rate of real GDP per capita. This was a natural extension of Okun’s law for unemployment.

Here we estimate an employment/GDP model for Japan similar to Okun’s law. For Japan, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

det = 0.02dlnGt – 0.53, t<1978

det = 0.14dlnGt – 0.42, t>1977 (1)

 

where dlnGt is the change rate of real GDP per capita at time t. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1978 which is expressed by a dramatic shift in slope and a slight break in intercept. The employment/population ratio varies between from 64%% in 1970 and 56% in 2010. The agreement is excellent. Figure 3 present results of a linear regression with R2=0.95 for the period between 1971 and 2010. We consider both variables as stationary ones over the long run despite the obviously negative trend since 1970.

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.

Employment in Australia

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 Australia. As expected, the change in the rate of unemployment is more volatile. All data sets on unemployment and employment have been retrieved from the U.S. Bureau of Labor Statistics.

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

In this blog, we have already presented several empirical relationships predicting the employment/population ratio from the growth rate of real GDP per capita. This was a natural extension of Okun’s law for unemployment.

Here we estimate an employment/GDP model for Australia similar to Okun’s law. For Australia, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

det = 0.50dlnGt – 0.92, t<1983

det = 0.41dlnGt – 1.08, t>1982 (1)

where dlnGt is the change rate of real GDP per capita at time t. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1994 which is expressed by significant shifts in slope and intercept. The employment/population ratio varies between from 55%% in 1983 and 64% in 2008. The agreement is very good. Figure 3 present results of a linear regression with R2=0.84 for the period between 1971 and 2010.

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.

Employment in France

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 France. As expected, the change in the rate of unemployment is more volatile except the shift in the employment rate near 1982. This is a completely artificial break from 53.2% in 1981 to 55.3% in 1982, and we do not need to model it. All data sets on unemployment and employment have been retrieved from the U.S. Bureau of Labor Statistics.

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

In this blog, we have already presented several empirical relationships predicting the employment/population ratio from the growth rate of real GDP per capita. This was a natural extension of Okun’s law for unemployment.

Here we estimate an employment/GDP model for France similar to Okun’s law. For France, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

de = 0.155dlnG– 0.65, t<1994

de= 0.25dlnG – 0.30, t>1993 (1)

where dlnG is the change rate of real GDP per capita at time t. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1994 which is expressed by significant shifts in slope and intercept. The employment/population ratio varies between from ~56%% in 1970 and 50.4% in 1992. The agreement is very good. Figure 3 present results of a linear regression with R2=0.91 for the period between 1971 and 2010.

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.

Employment in Canada

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 Canada. 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 Canada.  

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

de_t = 0.40dlnG_t – 0.70, t<1984

de_t = 0.56dlnG_t – 0.76, t>1983    (1)  

where dlnG_t is the change rate of real GDP per capita at time t. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1984 which is expressed by a significant shift in slope and a minor change in intercept.  The employment/population ratio varies between from ~54.5% in 1971 and ~64.1% (!) in 2008. The agreement is very good. Figure 3 present results of a linear regression with R²=0.84 for the period between 1971 and 2010.

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.

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.