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.

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.

On the absence of structural unemployment in Canada

We have estimated a version of Okun’s law for the USA, France and Spain. As beforfe, we have apply 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 Canada, 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 = -0.28dlnG + 1.16, t<1983
du = -0.28dlnG + 0.30, t>1982 (2)

This model suggests no shift in the slope and a bigger change in the intercept around 1983. 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=0.87. 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 0.68% for the period between 1971 and 2010. The average rate of unemployment for the same period is 8.2% with a standard deviation of the annual increment of 0.94%.

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

Figure 1. The observed and predicted rate of unemployment in the Canada between 1970 and 2010.

Figure 2. The measured time series is regressed against the predicted one. R2=0.87 with both time series likely to be stationary.

When the rate of unemployment will fall to 5%? Likely never

Update: A working paper is available with more technical details.

The intuition behind Okun’s law is very simple.  Everybody can feel that the rate unemployment is likely to rise when real economic growth is very low or negative. An economy needs fewer employees to produce the same or smaller real GDP because of permanent productivity growth. Thus, Okun’s law describes quantitatively the negative correlation between real economic growth and the change in unemployment rate.

We have rewritten Okun’s law using the growth rate of real GDP per capita instead of GDP. For the USA we have already obtained the following empirical relationship:     

dw = -0.406dlnG + 1.113, t<1979

dw = -0.465dlnG + 0.866, t>1978     (1) 

where dw is the predicted annual increment in the rate of unemployment, dlnG=dG/G is the relative change rate of real GDP per capita per one year. By definition, for a discrete form of Okun’s law one has: du_i=dw_i+e_i, where e_i is the model residual error at discrete time i. We have estimated all coefficients and the beak year in (1) by minimizing the cumulative sum of e_i squared.

In (1), the rate of real GDP growth has a threshold of (0.866/0.465=) 1.86% per year for the rate of unemployment to be constant. When dlnG is larger than 1.86% per year the rate of unemployment in the U.S. starts to decrease. Figure 1 displays the evolution of dlnG since 1979. On average, the rate of growth was 1.65% per year, i.e. slightly lower than the threshold and the rate of unemployment has been increasing since 1979.

Figure 1. dlnG as a function of time. Also shown is the threshold of 1.86% per year, the mean growth rate of 1.65% per year.            

When integrated between 1951 and t, equation (1) can be rewritten in the following form:

w_t = 3.3 – 0.406ln[G_t/G₁₉₅₁] + 1.113(t-1951)  + c₁  , t<1979
w_t = w₁₉₇₈ – 0.465ln[G_t/G₁₉₇₈] + 0.866(t-1978)  + c₂ ,  t>1978 (2)

where w_t is the predicted rate of unemployment. The intercept c₁=c₂≡0, as is clear for t=t₀.  Instead of using the continuous form (2), we calculate cumulative sums of the annual estimates of dlnG with appropriate initial conditions. By definition, the cumulative sum of the observdd du’s is the time series of the unemployment rate, u_t. Figure 2 depicts the measured and observed curves. 

The agreement is excellent and has been obtained by a formal statistical method. The integral form of the dynamic Okun’s law (2), i.e. w_t=f(lnG_t), is characterized by a standard error of 0.55% for the period between 1951 and 2010. The average rate of unemployment for the same period is 5.75% with the average annual increment of 1.1%.  All in all, this is a very accurate model of unemployment. And this fact is the most intriguing one.

Figure 2.  The observed and predicted rate of unemployment in the USA between 1951 and 2010. 

Our empirical model suggests a tangible shift in the slope and a significant change in the intercept around 1979. This is a very important finding. There are two terms in (2) which define the evolution of the unemployment rate: real economic growth, as expressed by the relative change in real GDP per capita, counteracts the positive linear time trend. Figure 3 depicts both components. The difference or the distance between a(t-t₀)  and –bln(G_t/G₀)-u₀ in Figure 3 is the rate of unemployment. 

The importance of the structural break in 1979 is obvious when we extend the trend a(t-t₀)  observed before 1979. The distance would be much larger with the old trend after 1979, i.e. the rate of unemployment would have been also higher than that actually measured. If to extend the current time trend and the dependence on G through 2050 one can project the rate of unemployment as Figure 3 also depicts. Without a new structural break, the rate of unemployment in 2050 will be near 25%. This is grim news. It might happen that the U.S. is currently struggling through a transition to a new relation in (2) which will keep the rate of unemployment below 10%. In any case, the growth rate of real GDP per capita has to be much higher than 2% per year in order to reduce the current rate of unemployment to the level of 5%.  Such a rate is not expected in the near future. 

As an alternative, we have tried a logarithmic time trend instead of the linear one. The logarithmic trend easily follows from our model of economic growth which has an inertial component inversely proportional to the attained level of real GDP per capita:

dlnG/dt = 0.5dlnN₉/dt + C/G (3)

where dlnN₉/dt is the change rate of the number of 9-year-olds and C is an empirically estimated constant. The term C/G represents the inertial rate or growth, i.e. the rate of growth corresponding to no changes in the age pyramid.  Figure 4 demonstrates the observed evolution of G since 1950 and gives two projections: a linear one with an annual increment C=$591.5 and an exponential growth following the trend before 2010.  The deviation between these projections is fast and the next few years should distinguish between them. Figure 5 provides some examples of developed countries with linear trend in real GDP per capita. 

We have introduced a similar trend term in the original Okun’s law and obtained:

dw/dt  = A/G_t + bdlnG/dt  (4)

By integrating (4) one obtains

w_t = u₀ + bln[G_t/G₀] + A∫dt/G_t  (5)

In the long run, the evolution of G_t is linear over time. Observations show that the change in the specific age population over the period of 50 and more years is negligibly small, ∫dlnN₉/dt ~ 0. Then dlnG/Gdt=C/G and G_t=G₀+C(t-t₀). Therefore, both terms in (5) have a logarithmic trend in time and w_t may vary around u₀. For equation (2), these trends are different (linear and logarithmic) and w_t must grow with time if there are no structural breaks. Figure 3 illustrates this divergence and the necessity of structural breaks. 

We have checked the predictive power of (5) relative to (2) and found no improvement. On the contrary, (5) does not allow to describe the whole period between 1951 and 2010 with one constant A.  Figure 6 depicts a model with A=28000 and b=-0.45. The model is very accurate between 1970 and 1990, overestimates the rate before 1970, and underestimates the observed rate after 2000. 

Figure 3. The evolution of two components in (2) defining the unemployment rate. 

Figure 4. The evolution of G over time with a projected linear trajectory for C=$591.5 and an exponential trajectory G=G₀exp(0.0209t), where the exponent corresponds to that obtained for the period between 1950 and 2010.

Figure 5. Some examples of linear evolution of real GDP per capita in developed countries.

Figure 6. The observed rate of unemployment and that predicted by (5) with A=28000 and b=-0.45. 

There is a fundamental concern about the excellent performance of Okun’s law in the U.S. The rate of unemployment is measured as a portion of labor force with the fluctuating rate of participation.   This means that the sensitivity of unemployment to real economic growth, expressed by Okun’s law, does not depend on the rate of employment itself.  Figure 7 compares the change in the rate of employment (the employment/population ratio), e, and the rate of unemployment. These two variables have been evolving in sync. Before 1980, the change in the rate of unemployment is relatively higher. After 1980, their amplitudes are very close. 

Figure 7. The (negative) change in the rate of employment compared to the change in the rate of unemployment. 

We have estimated a model similar to Okun’s law for the employment/population ratio, e:

de = 0.277dlnG – 0.457, t<1983

de = 0.496dlnG – 0.87, t>1982     (6) 

Figure 8 compares the observed and predicted change in the employment/population ratio. Figure 9 shows the cumulative curves for the time series in Figure 8 and explains the structural break near 1982.  The employment/population ratio grew from ~57% in 1982 and ~63% in 1989. This break also explains a similar break in the unemployment rate near 1980. The change in slope in (2) and (6) is rather similar: both the rate of employment and unemployment is more sensitive to the rate of change in GDP. 

This is the effect we have already reported and modeled for the rate of participation in labor force, l_t. To account for the effect of varying rate we introduced a factor, f_t, exponentially depending on the difference between some reference rate, l₀, and current rate, l_t: f_t=f₀exp[g(l_t-l₀)], where f₀  and g are empirical constants. The intuition behind the model is simple. The employment/population ratio and thus labor force increases with real GDP. When the rate of labor force participation undergoes a, say, 1% increase almost all new employees enter the workforce at the level of marginal personal income. Observations show that personal incomes are distributed exponentially in the low income range, i.e. the number of people with a given income decreases exponentially with increasing income. Accordingly, the input of the newcomers into the increasing GDP decreases exponentially with increasing labor force.  Thus, the sensitivity of employment/population ratio to real GDP increases with the ratio.   

This factor should be applied to Okun’s law as well. We will address this topic in the next post on employment. 

Figure 8. The observed and predicted change in the employment/population ratio, de.

Figure 9. The cumulative curves for the observed and predicted change in the employment/population ratio, de.