Labour force participation in Sweden and the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel

We have published a number of models for the rate of participation in labour force, LFP. The intuition behind the model is very simple. The growth in real GDP influences the labour force supply through redistribution of personal incomes. Fluctuations in real GDP per capita relative to that defined by inertial economic growth, A₁/G, provide variations in the distribution of personal income relative to some inertial (or neutral) growth rate. The influence of the growth in real GDP on the LFP has to be complicated by the presence of exponential distribution of personal inputs to real GDP. If the effect of real growth is based on the excess of the total personal income above its potential (inertia) level, then higher levels of LFP are more sensitive to real growth. Really, more people can be included in or excluded from the redistribution because of their smaller personal incomes for paid jobs, which are replaced by some other (not measured) mechanisms of personal income earning. It is reasonable to assume that the sensitivity of LFP to the difference between actual and potential (inertial) growth rates, e(t)=dG/G–A/G, grows exponentially with increasing LFP. In addition, there might be a time delay between action and reaction and the LFP may lag behind the e(t). Now we are ready for a quantitative analysis with a tentative relationship: 

{B₁dLFP(t)/LFP(t) + C₁}exp{ a₁[LFP(t) - LFP(t₀)]/LFP(t₀) =

          = ∫{dG(t-T))/G(t-T) – A/G(t-T)}dt

Here we present the model of labour force participation in Sweden. Figure 1 shows that the LFP is very well predicted since 1975. This model is valid for all developed countries. No macroeconomic model can predict the observed changes in LFP using only one macroeconomic parameter. Since the presented model describes the case of Sweden I also mean the latter laureates of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel awarded “for their analysis of markets with search frictions” have failed to model the labour market and predict its evolution at the same level of accuracy and forecast horizon.

Why we need the sophisticated model not describing reality if there exists a simple model predicting as accurately as one can only dream?

                  

Figure 1. Observed and predicted LFP in Sweden: T=0.

Inflation in the UK - no sign of deflation any time soon

There exists a long-term equilibrium link between price inflation, CPI_t, unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt, as was demonstrated in this blog for many countries. The UK is one of the world biggest economies with a relatively good statistics started chiefly from 1973.  It is a major challenge to model inflation in the UK using our approach.

We have to separate two periods to fit observations: before and after 1985:

CPI_t = 1.0l_t  + u_t  - 0.046; t>1985

CPI_t = -1.0l_t -1.7 u_t + .025; t<1985              (1)

For both periods, inflation does not lag behind unemployment and l_t. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2011. All in all, the predictive power of the model is good and timely fits major peaks and troughs. The change from negative to positive linear coefficient in 1985 needs a special explanation. But such effects were observed in other developed countries as well.  A labour force projection could help to predict the future inflation. Since the inflow of new employees is still positive,  l_t >0, and the rate of unemployment does not foresees any dramatic decline in the long run one can be sure that inflation will be positive in the near future.

Figure 1. The rate of CPI inflation in the UK, predicted and measured.

Unemployment in Italy

We introduced a model of unemployment in Italy in 2008 with data available only for 2006. The rate of unemployment was near its bottom at the level of 6%. The model predicted a long-term growth in the rate unemployment to the level of 11% in 2013. In this post we revisit the model. The agreement between the measured and predicted unemployment estimates in Italy validates our concept which states that there exists a long-term equilibrium link between unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt. Italy is a unique economy to validate this link because the time lag of unemployment behind l_t  is eleven (!) years. 

The estimation method is trivial – we seek for the best overall fit between observed and predicted curves by trial-and-error method. All in all, the best-fit equation is as follows:

u_t = -5.0l_t-11  + 0.07        (1)

As mentioned above, the lead of l_t is eleven years. This defines the rate of unemployment many years ahead of the current change in labour force. Figure 1 presents two versions of unemployment as defined by the U.S. Bureau of Labor Statistics (BLS) and the OECD. We describe the estimates provided by the OECD (labour force estimates also obtained from the OECD) but have to emphasise that the divergence before 1994 makes it difficult to find a unique model for both agencies.

Figure 2 presents the observed unemployment curve and that predicted using the rate of labour force change 11 years ago and equation (1). Since the estimates of labour force in Italy are very noisy we have smoothed the annual predicted curve with MA(5). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1988. The period between 2006 and 2010 was predicted almost exactly. This is the best validation of the model – it has successfully described a major turn in the evolution of unemployment near its bottom. No other macroeconomic model is capable to describe such dramatic turns many years ahead. As four years ago, we expect the peak in the rate of unemployment in 2013-2014 at the level of 11%.

The evolution of the rate of unemployment in Italy is completely defined 10 year ahead.  Since the linear coefficient in (1) is positive one needs to reduce the growth in labour force in order to reduce unemployment in the 2020s.

 

Figure 1. The rate of unemployment in Italy as measured by the BLS and OECD.

Figure 2. Observed and predicted rate of unemployment in Italy.

The reason of high unemployment in Spain

Here we model the rate of unemployment, u_t, in Spain using its dependence on the change in labor force, l_t=dLF/LFdt. This is another country joining the set of most developed economies with the same relationships between employment and labor force. For Spain, we used data provided by the OECD. Figure 1 depicts unemployment and the change rate of labor force between 1960 and 2010. In line with the OECD description of the breaks in the labor force series: 

Series breaks: In 2005, changes in the questionnaire and the implementation of CATI system in the field work affected the estimates. The 2005 questionnaire produced an additional increase of employment (132 000) and a decrease of unemployment (78 000). From 2001, the new unemployment definition established by the European Commission in 2000 has been introduced. From 1994, persons employed in the “Guardia Civil” are not included in the armed forces. As an indication, this category represented 59 600 people in 1994. In 1976, the lower age limit for inclusion in the Labour Force Survey was raised from 14 to 16, at the same time other modifications to the survey were introduced.

 there are two spikes in the dLF/LF series near 1976 and 2001 as related to step revisions to the level. The spike around 1988 has no explanation in terms of the revisions to labor force, but is of the same amplitude. One can not exclude the opportunity that this spike is related to the processes of joining the EU in 1986.              

As expected, the same functional form of dependence is valid for Spain. The estimation method is based on trial-and-error approach and seeks for the fit between annual curves.  The final model is as follows

u_t = -7.0l_t  + 0.31; t>1986

Figure 2 depicts observed and predicted curves. Before 1986, the curves diverge and another model is likely holds.   Because of high-amplitude oscillations in the original time series for the rate of labour force change, l_t,  we have to smooth it by MA(5). For the period after 1986, R²=0.82. Thus, the change in labor force has been driving the rate of unemployment in Spain. The negative coefficient implies that unemployment is Spain goes down when labor force starts to increase.

 Figure 1. Unemployment rate, u, and the rate of labor force change, l,  in Spain according to the definition introduced by the OECD.

Figure 2. Prediction of inflation by labor force. R²=0.82 for the period between 1986 and 2009.

Low inflation in Germany

There exists a long-term equilibrium link between price inflation, CPI_t, and the rate of change of labour force, l_t=dLF/LFdt, as was shown in this blog for many countries. Germany is a crucial economy to validate this link.  It had a major change in the latest history associated with the reunification. What was the effect of the merge? Here, we model the change in inflation dependence on labour force in 1989. Quantitatively, inflation became less sensitive to the change in labour force by a factor of 4: sensitivity has fallen from -2.2 to - 0.6.  

The estimation method is enhanced relative to our previous studies – the best overall fit is sought by the least squares method as applied to the cumulative curves. In addition to the formal LSQ minimization of the model error we have introduced a varying break year in the model. We allow such a break within 3 years around 1990. By definition, the break year has to provide the lowermost RMS residual. All in all, the best- fit equations for the period before and after 1990 are as follows:

CPI_t = -2.2l_t-6  + 0.046; t<1990

CPI_t = -0.6l_t-6 + 0.018; t>1990           (1)

For both periods, the lead of l_t is six years. This defines the rate of inflation six years ahead of the current change in labour force. Figure 1 presents the observed and predicted CPI curves, all variables were obtained from the OECD database in 2011. All in all, the predictive power of the model is good and timely fits major peaks and troughs. Because the big lag between the change in labour force and inflation one can foresee the change in prices many years ahead. In Germany, one should not expect high price inflation since the level of labour force has not been growing fast.

The coefficient in (1) obtained for the period after 1990 is not well constrained because the change in inflation is small and statistical estimates are not reliable. The future evolution of the overall CPI in Germany will help to resolve the model better. The previous model published in this blog, was obtained for the whole period and did not include the reunification. Corresponding coefficients were -1.71 and 0.041, which are close to those for the period before 1990.

Figure 1. The rate of CPI inflation in Germany, predicted and measured. The lower panel shows the cumulative curves.

Validation of the New Zealand GDP model

Following the post on the German real GDP per capita, we revisit the 2008 model for New Zealand. It was also obtained by the trial-and-error method. Empirical constant A and the specific age, Ns, in the defining equation:

g(t) = dlnG(t)/dt  = A/G(t) + 0.5dlnN_s(t)/dt                                            (1)

have been varied in order to fit amplitude and major features of the observed curve. The best fit annual increment value is A=$220 (1990 US$, as published by the Conference Board).  The specific age population in New Zealand is 14 years. The age pyramid enumerated by the 2006 census was extrapolated in the past and in the future in order to estimate the number of 14-year-olds in (1).

Figure 1 presents the observed and predicted GDP growth rates for New Zealand as obtained in 2008. Both curves are characterized by high-amplitude oscillations likely associated with measurement errors. Therefore, in Figure 2 we present both annual curves smoothed with MA(5) and MA(3), respectively. The upper panel in Figure 2 reproduces the 2008 model and the lower one – the 2010 model (one should notice the difference between various vintages of GDP estimates published by the Conference Board). One can conclude that our prediction from 2008 was correct and real GDP per capita in New Zealand actually fell to zero. This is the best validation of our model for NZ and we will continue tracking the fit.

As before, one can expect that  there is no danger of a deep recession in New Zealand, but the rate of real economic growth will be very low (on average ~0.5% per year) in the years to come. 

Figure 1. Observed and predicted growth rate of real GDP per capita in New Zealand between 1980 and 2010.

Figure 2. The observed curve is smoothed with a 5-year moving average. The predicted rate is smoothed with MA(3). The upper panel displays the 2008 model and the lower panel – the 2010 model.  (We present two figures because the GDP estimates vary with data vintage.) One can observe an outstanding accuracy of GDP prediction for 2009 and 2010 (between the smoothed curves).

How long will last real economic growth in Germany

Germany has demonstrated an extraordinary increase in real GDP in 2010: +3.6 per cent.   In the first quarter of 2011, the level of real GDP was 5.2% above that in the first quarter of 2010. This jump is especially desirable after the tremendous fall in 2009: -4.5 per cent relative to 2008. After this strong fluctuation, the question is how strong in the growth trend for the German economy?  One can find a quantitative answer to this question and a long-term prediction of real GDP per capita in Germany up through 2020.

Several months ago we presented log an empirically correct model of real economic growth in Germany. Our concept describing the evolution of real Gross Domestic Product (per capita) is very simple and is based solely on the age structure in a given developed country. Since Germany does not carry out censuses as many countries do, the age pyramid is obtained from administrative record and partial censuses. It makes the final result less accurate and influences our prediction of real GDP in Germany.   

We have empirically and statistically proved that the growth rate, g(t), of real GDP per capita, G(t), is driven by the attained level of real GDP per capita and the change in a specific age population, N_s. According to our model, the asymptotic growth rate of real GDP in developed countries can be completely characterized by constant annual increment A = const. All fluctuations around this constant increment can be explained by the change in the number of people of the country-specific age:

g(t) = dlnG(t)/dt  = A/G(t) + 0.5dlnN_s(t)/dt                                            (1)

Equation (1) is the quantitative model that has been constructed empirically and tested statistically.

We published a preliminary model for Germany severalyears ago; before the 2008/2009 recession. The best fit constant increment is (A=) $260 (1990 US dollars, as published by the Conference Board) and the defining age is eighteen year. The age distribution from 2002 allows a prediction at an 18-year horizon. The original model displayed in the upper panel of Figure 1 suggested a slow-down in 2009 and likely a deeper recession in 2011, with a year of growth in 2010. On average, the beginning of 2010s was characterized by very poor performance of the German economy.

The lower panel in Figure 1 extends the observed curve through 2010. The predicted curve did not change. Overall, we predicted the fall in 2009 and the growth in 2010, with smaller amplitudes, however. This might be the result of severe smoothing of the age pyramid.  (Here, we would like to emphasise again that the prediction of the 2009 slowdown could be easily obtained in 2002, i.e. seven years before it happened!) Figure 2 presents a smoothed version of both curves in Figure 1. Three-year moving averages, MA(3), show a much better fit than the annual curves. Therefore, we do not change our forecast for 2011 and for the future decade. The German economy will not be growing fast. Immigration may induce only extensive growth in real GDP but not in GDP per capita.  

Figure 1. Observed and predicted rate of real GDP growth in Germany after the reunification. The predicted curve is obtained from relationship (1) with A=$260.

 Figure 2. The original curves in Figure 1 smoothed with MA(3).