Real GDP per capita in Japan

Couple months ago we presented the concept of constant annual increment in real GDP per capita, G(t), as observed in developed countries. The concept can be described by a simple model: in the long run, the GDP growth as a linear function of time:

G(t-t0)= G0+A(t-t0) (1)

where G0 is the initial level of GDP per capita at time t0 in a given country, A is the country dependent annual increment measured in PPP dollars. This is an empirical model and is based only on observations of real GDP in developed countries. This is in striking contrast to the mainstream macroeconomic models based on axioms; not empirically proved axioms.

Unlike in the Solow model and its successors, the rate of growth of real GDP per capita, dG/G, has a decelerating nonlinear trend. Differentiating with respect to time and dividing both sides of (1) by G(t), one obtains

dG/G = A/G (2)

This model gives excellent statistical results and explains the evolution of real GDP per capita in developed countries [1,2] since 1950. This year is considered as the year of relatively accurate measurements of GDP. We are using the data base provided by the Conference Board.

In the post related to labor productivity in Turkey, we introduced a model explaining the evolution of productivity as based on the deviation from constant annual increment of real GDP per capita. Therefore, model (1) provides an empirical framework for the productivity model and we need to illustrate the predictive power of (1).

Figure1 presents a very important case of Japan: annual increment in real GDP per capita is plotted against the level of real GDP per capita. (Equation (1) uses time implicitly.) It demonstrates the accuracy of our concepts. Since the increment is assumed to be constant, the mean value of the annual GDP increment should coincide (at least should be very close to) with its linear trend. The linear regression line for Japan is very close to the constant level. Actually, it slightly oscillates around the mean value over time, as the cases for 2007 (upper panel) and 2009 (lower panel) demonstrate. The hypothesis of the constant increment looks sound.

Figure 1. Annual increment of real GDP per capita (2007 and 2009 US$) vs. real GDP per capita in Japan for the period between 1950 and 2007 (upper panel) and between 1950 and 2009 (lower panel). Two sets are presented - the original (open circles) and that corrected for population (filled diamonds). Subsequent values of the latter set are connected by a solid line for illustration of the evolution in time. Bold lines represent the mean value of $605 (2007 US$) and $596 (2009 US$) for the population corrected sets. Two solid lines show linear regressions lines. Corresponding linear relationships are displayed, the lower relationship being associated with the original data set.

Both original linear regression line is practically parallel to the x-axis. The corrected line is characterized by a slightly negative trend. There were two periods of very quick growth between $12000 and $20000 and between $28000 and $33000. Both ended in periods of low (sometimes - negative) growth rates. This effect might be expected in any country which demonstrates very fast growth during an extended period of time. A good example is Ireland. A candidate is China, but its growth is supported by the army of unemployed with very low salaries. Therefore, China may grow mainly due to extensive factors and real GDP per capita do not grow so fast as the overall GDP.

Following the general rule of the constant increment, one may expect a slow recovery of the Japanese economy over decades. However, this recovery is unlikely because the Japanese population is on long-term decline [3].

References
1. Kitov, I., (2006). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/2738.html

2. Kitov, I., (2009). The Evolution of Real GDP Per Capita in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. IV(1(8)_ Summ), pp. 221-234.

3. Kitov, I., 2006. "The Japanese economy," MPRA Paper 2737, University Library of Munich, Germany

Does crude drive the price index of steel and iron?

This update includes the readings of the producer price indexes of crude oil and iron&steel for November 2010.

In September 2009, we reported that the price index of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months [1].  In order to present both indexes in a comparable form, the difference between a given index, iPPI, and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). The normalized differences represent the evolution of the rate of deviation from the PPI over years.  

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period since June 2010.  Simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2010

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates just short-term deviations from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an invaluable benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead.

Conclusion

Between 2006 and 2010, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one.  

References

1. Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. I(1(1)_ Summ), pp. 43-51

Labor productivity in Austria: further fall in 2010 and 2011

As in the previous post, Figure 1 is borrowed from our paper on productivity [1] (see Figure 4 in the paper). It presents the case of Austria. This is a less difficult example with the rate of productivity growth, dP/P, on a steady descent since the 1970s.  Between 1975 and 2005, the rate of productivity growth is oscillating around the level of 0.015y^-1. Notice the excellent prediction of the severe drop in the productivity after 1970.  This fall was induced by an increase in the growth rate of real GDP per capita relative to its inertial level, as Figure 2 depicts. The elevated rate of real growth induced a higher increase in the rate of participation, and thus, the drop in productivity.  It is worth stressing again that there was no shock to productivity or a structural break, as the mainstream economists would suggest. Our model presumes that labor productivity in Austria has been following the only driving force – real GDP per capita.

Figure 1. Observed and predicted (from real GDP pee capita) change rate of productivity in Austria.  The observed curve is represented by MA(5) of original version. Model parameters are as follows: A₂=$335, N(1959)=100000, B=-500000, C=0.243, T=3 year.

 Lets return to the deviation from the inertial growth, which is unambiguously determined by constant annual increment of real GDP per capita. Figure 2 shows that the rate of inertial growth is decreasing with the increasing level of GDP as a reciprocal function of GDP.  Coefficient A2 has to be determined empirically for each developed country. For Austria, the initial estimate was A₂=$335 (1990 U.S. dollars at GK PPPs as presented by the Conference Board). The current economic and financial crisis manifests itself in a severe drop in GDP, with dGDP/GDP=-0.045 y^-1 in 2009. 

A significant feature of the model is the presence of a delay between the change in real GDP and the reaction of P. This effect is similar to the delay of thunder relative to lightning. Any economic system needs some time to adjust to the exogenous change. In Austria, productivity lags by 3 years behind GDP, as caption of Figure 1 indicates. For details of the model see [2]. For the purpose of this blog, the three year lag means that the current drop in real GDP per capita will result in a hike in labor productivity three years later. Also, the currently observed decline in the rate of productivity growth is actually induced by several years of intensive real economic growth observed before 2009.

Figure 2. Comparison of the growth rate of real GDP per capita, dGDP/GDP, with the rate of inertial growth defined as A₂/GDP.

Finally, Figure 3 tests the model by adding two new data points to Figure 1. These new measurements are borrowed from the Conference Board database [3]. One can conclude that the model gave an excellent prediction for 2008 and 2009. The period of the productivity decline will continue in Austria for another couple years. Since 2012, the rate of productivity growth will show high positive values in response to the current drop in GDP and labor force particiaption. This will be a striking upturn which is always a challenge to any productivity model or concept. We will revisit the case of Austria for further validation of the model. In 2010 and 2011 the rate of labor productivity in Austria will be falling.

Figure 3. Same as in Figure 1 with two new points – 2008 and 2009. The original and MA(5) productivity series are shown. One can expect positive rate of productivity growth in 2012.

References

1. Kitov, I., Kitov, O., (2009). Modelling and predicting labor force productivity, MPRA Paper 15152, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15152/01/MPRA_paper_15152.pdf

2. Kitov, I., Kitov, O., (2008). The driving force of labor productivity, MPRA Paper 9069, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/9069.html

http://mpra.ub.uni-muenchen.de/9069/01/MPRA_paper_9069.pdf

3. Conference Board. (2010). Total Economy Database, January 2010. http://www.conference-board.org/data/economydatabase/

On further decline in labor productivity in Turkey

Figure 1 is borrowed from our paper on productivity [1]. It presents the case of Turkey. This is a difficult example with the rate of productivity growth oscillating since 1980. Since the measured time series is smoothed with MA(3), actual oscillation is even more prominent. Such a behavior is a nightmare for the mainstream models based on capital, labor and multifactor productivity. As a rule, the multifactor productivity has to resemble observations and severe “shocks” to productivity are introduced.  This is a lucky hour for an economist – millions of factors to explain these shocks. In reality, the number of explanations is steadily approaching the number of economists involved. At the end of the day, all mainstream models are able to explain only “stylised facts”. This is a euphemism of “failure”.

Our model uses only one variable – real GDP per capita. The intuition behind the model is almost banal.

1. A developed economy is characterized by a constant speed of real economics growth, which we call “economic inertia” in line with mechanical sense of inertia. In other words, the economy would be growing with constant increment per year, i.e. at constant speed, if no change in the population age structure is observed. 
2. Any deviation from the inertial growth results in the change in labor force participation. Obviously, a higher speed of growth may attract more people into the labor.
3. The number of people who are able to join the labor force in response to a given growth above the inertial one is proportional to the relevant deviation.
4. The value added by any newcomer must depend on his/her overall professional capabilities. It is obvious that this characteristic (capability or productivity) is distributed (we claim that this distribution is exponential and personal income distribution is) over the working age population and people with efficiency between 50% and 51 % should bring more value added to the economy than those between 75% and 76%.  In other words, one per cent of “extra” (above the inertial level) economic growth may allow to join the labor, say, 1% of population, when this labor force grows from 50% to 51% , or 5% of population, when the labor grows from 70% to 75%.  These portion must give the same extra input into the real GDP.
5. The extra growth in real GDP has to be reflected in productivity, which is defined as a ratio of real GDP and the level of labor force. As suggested in point 4, the extra labor force depends on the current participation rate. Therefore, the growth in productivity depends on the current rate of participation in labor force for a given increase in real GDP.  As an example, the rate of participation in Italy and Canada is quite different and 1% extra growth in real GDP per capita results in absolutely different change in labor productivity.
6. Mathematical formulation of this simple consideration is given in [2].

Finally, Figure 1 (and the example of Canada ) demonstrate the predictive power of our simple and parsimonious model. 

Figure 1. Observed and predicted (from real GDP pee capita) change rate of productivity in Turkey.  The observed curve is represented by MA(3) of the original version. Model parameters are as follows: A₂=$105, N(1959)=1450000, B=-6000000, C=0.24, T=2 year.

Figure 2 tests the model by adding two new data points to Figure1. These new measurements are borrowed from the Conference Board database [3]. One can conclude that the model gave an excellent prediction for 2008 and 2009. The period of the productivity decline will continue in Turkey for another couple years, and then it will start to grow again. This turn is a challenge for any productivity model or concept. We will revisit the case of Turkey for further validation of the model. Meanwhile, we would not expect good news about labor productivity from Turkey.

Figure 2. Same as in Figure 1 with two new points – 2008 and 2009.

References

1. Kitov, I., Kitov, O., (2009). Modelling and predicting labor force productivity, MPRA Paper 15152, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15152/01/MPRA_paper_15152.pdf

2. Kitov, I., Kitov, O., (2008). The driving force of labor productivity, MPRA Paper 9069, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/9069.html

http://mpra.ub.uni-muenchen.de/9069/01/MPRA_paper_9069.pdf

3. Conference Board. (2010). Total Economy Database, January 2010. http://www.conference-board.org/data/economydatabase/

Cross-country comparison: labor force participation in Canada and Italy

One of the most important requirements to a sound macroeconomic model is the capability to explain the difference in evolution of modelled parameters across developed countries.  For example, a consistent model of the rate of participation in labour force, LFP, has to describe the striking difference observed in the long-term behaviour of LFP in Canada and Italy. Figures 1 and 2 depict the measured (open circless), as provided by the BLS: http://www.bls.gov/data/, and predicted LFP. The latter is obtained from the model linking LFP to real GDP per capita only [1]. The GDP estimates are taken from the Conference Board data base (at GK PPPs).

Our model shows an exceptional predictive power for both countries. This accurate prediction is obtained despite the measured LFP in Canada has been growing since 1960 and that in Italy has been on decline.  Moreover, even short-term deviations from the overall trend are well predicted in time and amplitude. In Figures 1 and 2 we added two new measurements made in 2008 and 2009 to the original curves published in [1]. 

One can conclude that the model does not contradict actual measurements in Sweden, Canada, and Italy.  We are going to extend the set of countries and the duration of relevant time series.

Figure 1. Measured and predicted LFP in Canada.                  

Figure 2. Measured and predicted LFP in Italy. 

References

1. Ivan O. KITOV, 2008. "The Driving Force of Labor Force Participation in Developed Countries," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(3(5)_Fall), pages 203-222.

Labor force participation in Sweden

The labor productivity model discussed in the previous post is based on the concept linking labor force participation rate, LFP, to real GDP per capita [1]. This is a primary model, which explains the dynamics and the long-term behavior of labor force level in developed countries. As before, the LFP model is extremely parsimonious and uses only one (!) defining parameter to explain all variations in the observed behaviou of labor force in developed countries. As a consequence, one needs no other macro- or micro-economic variable to explain the portion of labor in total population.  

In this post, we do not formally introduce the quantitative model since it is available in the paper and monograph. Our purpose is to extend the previous data set by two years (2008 and 2009) since new observations are now available. This is in line with our validation strategy – to test all models with new data.

Figure 3.13 is borrowed from our monograph and illustrates the predictive power of the model for Sweden. The agreement between the original LFP estimates (open circles) and those predicted by the model is excellent in timing and amplitude. Considering the fact that only one defining variable is used the prediction suggests the presence of long-term on-to-one link between LFP and real GDP. (More examples in the paper and monograph.)

Figure 1 extends the original data set by two estimates (real GDP per capita reported by the Conference Board). The agreement is also excellent.  This observation evidences in favor of our model.

We will continue reporting the accuracy of LFP predictions for Sweden and other developed countries.

Figure 3.13. Observed and predicted growth rate of LFP in Sweden: N(1959)=100000, A₂=$310 (1990 U.S. dollars), B=2.2∙10⁶, C=-0.0465, T=0. Lower panel depicts the original LFP, changing in the range from 67% in 1990 to 62.5 % in 1998, and the predicted LFP.

Figure 1. Same as in Figure 3.13, but extended with data in 2008 and 2009. The original LFP series is  reported by the BLS.

References

1. Ivan O. KITOV, 2008. "The Driving Force of Labor Force Participation in Developed Countries," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(3(5)_Fall), pages 203-222.

Labor productivity in Canada

Two years ago we published two papers [1,2] which introduced a new macroeconomic model explaining the evolution of labor productivity in developed countries. The model is absolutely parsimonious and uses only one measured macroeconomic variable as the driving force of the productivity growth – real GDP per capita. Figure 3.22 is borrowed from our monograph “mechanomics. Economics as Classical Mechanics” and illustrates the predictive power of the model as applied to Canada. (Due to extremely high volatility of productivity measurements, the measured data set is represented by its 5-year moving average, MA(5)).  All coefficients in the model for Canada were obtained empirically, as explained in the monograph.

Considering the simplicity of the model and the accuracy of data on real GDP and productivity, the prediction of the time history in Canada is excellent. (We would be grateful if the reader could provide us with a reference to a model which gives better predictions.) It is also important that the prediction covers the whole period since 1960 with one deterministic link without any structural breaks. The latter is the inevitable and crucial element of any explanation of productivity in developed countries. Moreover, all mainstream macroeconomic models (e.g. DGSE) are using the notion of shocks to productivity as a central phenomenon explaining all bigger deviations in the rate of real economic growth. This implies that productivity must define real GDP. This assumption contradicts observations, as our model demonstrates – the change in labor force productivity lags by two (!) years behind the defining change in real GDP. Therefore, productivity is not a proactive macroeconomic variable.

Figure 3.22. Observed and predicted productivity in Canada: N(1959)=270000, A₂=$300, B=-3200000, C=0.108; R²=0.8.

Since the data set was limited by 2007, one can test the predictive power of the model using new data and extend the forecasting horizon. As before, we use the data set published by the Conference Board [3].  Figure 1 shows that our prediction for 2008 and 2009 was accurate. In the near future, one can expect a significant growth in labor productivity in Canada.

For further validation of the model, we are going to revisit our predictions for other developed countries.

Figure 1. Same as in Figure 3.22 extended by measurements in 2008 and 2009.

References

1. Kitov, I., Kitov, O., (2008). The driving force of labor productivity, MPRA Paper 9069, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/9069.html

http://mpra.ub.uni-muenchen.de/9069/01/MPRA_paper_9069.pdf

2. Kitov, I., Kitov, O., (2009). Modelling and predicting labor force productivity, MPRA Paper 15152, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15152/01/MPRA_paper_15152.pdf

3. Conference Board. (2010). Total Economy Database, January 2010. http://www.conference-board.org/data/economydatabase/