Labor productivity in Turkey, Spain, Belgium, Austria, Switzerland, and New Zealand has been analyzed and modeled. These counties extend the previously analyzed set of the US, UK, Japan, France, Italy, and Canada. Modelling is based on the link between the rate of labor participation and real GDP per capita. New results validate the link and allow predicting a drop in productivity by 2010 in almost all studied countries.productivity, labor force, real GDP, prediction, modelling

Kitov, Ivan

Kitov, Oleg

English

Research Papers in Economics

  1
Modelling and predicting labor force productivity 
Ivan O. Kitov, Oleg I. Kitov 
 
Abstract 
Labor productivity in Turkey, Spain, Belgium, Austria, Switzerland, and New Zealand has been analyzed and 
modeled. These counties extend the previously analyzed set of the US, UK, Japan, France, Italy, and Canada. 
Modelling is based on the link between the rate of labor participation and real GDP per capita. New results validate 
the link and allow predicting a drop in productivity by 2010 in almost all studied countries.  
 
JEL classification: J2, O4 
Key words: productivity, labor force, real GDP, prediction, modelling   2
Introduction 
We continue reporting results of the study devoted to the driving force behind labor productivity, 
P. In [1], we presented a nonlinear and lagged link between productivity and real GDP per 
capita, G, in the United States, Japan, the United Kingdom, France, Italy, and Canada. These 
countries are the largest developed economies in the world.  
We defined two components of the growth rate of G – a trend (also potential or neutral 
growth) and fluctuations. The trend component is proportional to the reciprocal value of the 
attained level of G, A/G, where A is an empirical country-dependent constant. The fluctuations 
are driven by the change in some specific age population. By subtracting A/G from dG/G one 
obtains the driving force of the change in productivity, as well as of the rate of labor force 
participation [2]. 
In developed countries, population estimates for the specific age are not available or too 
poor for quantitative analysis. However, for the modelling of the changes in productivity one can 
use estimates of real GDP per capita instead of the population estimates. This paper extends the 
set of studied countries and presents the link between P and G  in Turkey, Spain, Belgium, 
Austria, Switzerland, and New Zealand. Moreover, the lag of productivity behind the change in 
real GDP allows predicting the former at various time horizons.   
The remainder of the paper is organized as follows. Section 1 presents the model developed 
in [1,2] as a set of quantitative relationships between labor productivity, labor force participation 
rate, the growth rate of real GDP per capita. In Section 2, we continue testing these relationships 
against actual data and present some predictions of the future evolution of productivity in all six 
studied countries.  
 
1.  The model 
For the estimation of labor productivity one needs to know total output (GDP) and the level of 
employment,  E  (P=GDP/E), or total number of working hours, H ( P=GDP/H). In the first 
approximation and for the purposes of our modelling, we neglect the difference between the 
employment and the level of labor force because the number of unemployed is only a small 
portion of the labor force. There is no principal difficulty, however, in the subtraction of the 
unemployment, which is completely defined by the level of labor force with possible 
complication in some countries induced by time lags [3,4]. The number of working hours is an 
independent measure of the workforce. Employed people do not have the same amount of 
working hours. Therefore, the number of working hours may change without any change in the 
level of employment and vice versa. In this study, the estimates associated with H are not used.   3
Individual productivity varies in a wide range in developed economies. In order to obtain 
a hypothetical true value of average labor productivity one needs to sum up individual 
productivity of each and every employed person with corresponding working time. This 
definition allows a proper correction when one unit of labor is added or subtracted and 
distinguishes between two states with the same employment and hours worked but with different 
productivity. Hence, both standard definitions are slightly biased and represent approximations 
to the true productivity. Due to the absence of the true estimates of labor productivity and related 
uncertainty in the approximating definitions we do not put severe constraints on the precision in 
our modelling and seek only for a visual fit between observed and predicted estimates. 
In this study, we use the estimates of productivity and real GDP per capita reported by the 
Conference Board (http://www.conference-board.org/economics/database.cfm). Recently, we 
developed a model [2] describing the evolution of labor force participation rate, LFP, in 
developed countries as a function of a single defining variable – real GDP per capita. Natural 
fluctuations in real economic growth unambiguously lead to relevant changes in labor force 
participation rate as expressed by the following relationship: 
 
{B1dLFP(t)/LFP(t) + C1}exp{ α1[LFP(t) - LFP(t0)]/LFP(t0) = 
= ∫ {dG(t-T))/G(t-T) – A1/G(t-T)}dt       (1) 
 
where B1 and C1 are empirical (country-specific) calibration constants, α1 is empirical (also 
country-specific) exponent, t0 is the start year of modelling, T is the time lag, and dt=t2-t1, t1 and 
t2  are the start and the end time of the time period for the integration of g(t) = dG(t-T))/G(t-T) – 
A1/G(t-T) (one year in our model). Term A1/G(t-T), where A1 is an  empirical constant, represents 
the evolution of economic trend [4]. The exponential term defines the change in sensitivity to G 
due to the deviation of the LFP from its initial value LFP(t0). Relationship (1) fully determines 
the behavior of LFP when G is an exogenous variable. 
It follows from (1) that labor productivity can be represented as a function of LFP and G, 
P~G·Np/Np·LFP = G/LFP, where Np is the working age population. Hence, P is a function of G 
only. Therefore, the growth rate of labor productivity can be represented using several 
independent variables. Because the change in productivity is synchronized with that in G and 
labor force participation, first useful form mimics (1): 
  
dP(t)/P(t) = {B2dLFP(t)/LFP(t) + C2}·exp{ α1[LFP(t) - LFP(t0)]/LFP(t0)}   (1′) 
   4
where B2 and C2 are empirical calibration constants. Inherently, the participation rate is not the 
driving force of productivity, but (1′) demonstrates an important feature of the link between P 
and LFP – the same change in the participation rate may result in different changes in the 
productivity depending on the level of the LFP. 
In order to obtain a simple functional dependence between P and G one can use two 
alternative forms of (1), as proposed in [1]:  
 
{B3dLFP(t)/LFP(t) + C3} exp{α2[LFP(t) - LFP(t0)]/LFP(t0)} = Ns(t-T) 
      
dP(t)/P(t)  = B4Ns(t-T)+ C4     (2) 
 
where Ns is the number of S-year-olds, i.e. in the specific age population, B3,…, C4 are empirical 
constant different from B2, C2, and α2=α1. In this representation, we  use our finding that the 
evolution of real GDP per capita is driven by the change rate of the number of S-year-olds. 
Relationship (2) links dP/P and Ns directly. 
The following relationship defines dP/P as a nonlinear function of G only: 
 
N(t2) = N(t1)·{ 2[dG(t2-T)/G(t2-T) - A2/G(t2-T)] + 1}     (3) 
 
dP(t2)/P(t2) = N(t2- T ) / B   +   C       (4) 
 
where N(t) is the (formally defined) specific age population, as obtained using A2 instead of A1; B 
and  C  are empirical constants. Relationship (3) defines the evolution of some specific age 
population, which is different from actual one. 
  
1.  Productivity prediction 
In this Section, we use relationships (3) and (4) for the prediction of labor productivity in 
Turkey, Spain, Belgium, Austria, Switzerland, and New Zealand. These countries extend the 
previous set of the largest developed economies in the world. 
  Figure 1 presents the growth rate of productivity in Turkey - observed and predicted one. 
The observed values are presented by open circles and the predicted ones with solid diamonds. 
Because of strong fluctuations in original time series the observed curve is smoothed with a 3-
year moving average, MA(3). Real GDP per capita is obtained from the Conference Board data 
base [2008] in 1990 GK dollars. Productivity estimates ($ per working person per year) are also   5
taken from the same database. The predicted rate is obtained using (3) and (4) from real GDP per 
capita.  
The observed rate has been varying from (dP/P=) 0.07 y
-1 to -0.02 y
-1 in 1980 and near 
2000. Real economic growth has been oscillating around its very low potential rate defined by 
A2=$105. Both productivity curves in Figure 1 are well synchronized with all major peaks 
matched. Linear regression analysis gives R
2=0.51 for the period between 1966 and 2006. All in 
all, the predicted curve is in excellent agreement with the observed one and this observation 
confirms our previous results reported in [1].  
An outstanding and expected feature of the predicted curve is that the change in real GDP 
leads the growth in productivity by 2 years. In Figure 1, the predicted curve is shifted by 2 years 
back (T=2 year) in order to synchronize it with the measured one. This lead allows prediction of 
the future evolution of productivity in Turkey at a two-year horizon. After 2005, the productivity 
has been suffering a dramatic fall that will continue into 2010. Such a dynamic change during a 
short period will be used to validate relationships (3) and (4) with the above parameters.  
  
-5.0E-02
0.0E+00
5.0E-02
1.0E-01
1960 1970 1980 1990 2000 2010 2020
calendar year
d
P
/
P
predicted
measured dP/P, MA(3)
 
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 depicts observed and predicted productivity for Spain. These curves are similar 
to those for France [1] and are also in an excellent agreement: R
2=0.9. Such high correlation is 
likely a biased result because both series are non-stationary. The change in productivity in Spain 
varies from 0.1 y
-1 in the 1960s to -0.01 y
-1 in the 2000s. Hence, real economic growth has been 
far below its potential rate (A2=$175) since 1960s. The current rate of productivity growth is 
negative and one should not expect any break in the declining trend. Surprisingly, there is no 
time lag of the productivity behind the change in real GDP, T=0.    6
-5.0E-02
0.0E+00
5.0E-02
1.0E-01
1.5E-01
1960 1970 1980 1990 2000 2010
calendar year
d
P
/
P
 
predicted
measured dP/P, MA(5)
 
Figure 2. Observed and predicted (from real GDP pee capita) change rate of productivity in Spain.  The 
observed curve is represented by MA(5) of original version. Model parameters are as follows: A2=$175, 
N(1959)=1050000, B=-3000000, C=0.13, T=0 year.  
  The case of Belgium may be considered as a standard one. Figure 3 displays measured 
and predicted rate of productivity growth. The curves are very close with R
2=0.78 for the period 
between 1967 and 2007. For Belgium, the range of productivity change is smaller than in many 
developed countries: from 0.05 y
-1 in the 1970s to 0.01 y
-1 in the 2000s. The current rate of 
productivity growth is also close to 0.01 y
-1. However, Belgium is characterized by a 5-year lag 
of the productivity. This value is not abnormal but is close to the largest lags. The rate of neutral 
(or potential) growth is not the highest one as defined by A2=$280.  
 
0.0E+00
2.0E-02
4.0E-02
6.0E-02
1960 1970 1980 1990 2000 2010
calendar year
d
P
/
P
predicted
measured dP/P,MA(5)
 
Figure 3. Observed and predicted (from real GDP pee capita) change rate of productivity in Belgium.  
The observed curve is represented by MA(5) of original version. Model parameters are as follows: 
A2=$280, N(1959)=150000, B=-1900000, C=0.13, T=5 year. 
The evolution of productivity in Austria is presented in Figure 4. Currently, labor 
productivity in the Austrian economy evolves at a very low rate near 0.01 y
-1. This is not a new 
situation – after 1975 the rate has been hovering between 0.01 y
-1 and 0.02 y
-1. An outstanding 
feature is the rate of potential growth defined by A2=$335, almost the largest among developed 
countries.  This rate is three times higher than in Turkey and twice as big as in Spain, when 
referred to the same level of real GDP per capita. This demonstrates a remarkable efficiency of 
the Austrian economy.     7
As in many developed countries, productivity in Austria lags behind the change in real 
GDP by 3 years. This lag allows predicting a sudden drop in the growth rate of productivity to 
negative figures in 2010.  Considering high correlation (R
2=0.8) between the observed and 
predicted curves since 1963 the drop in the growth rate is practically inevitable. At the same 
time, the predicted drop will serve as a validation of the model.    
-2.0E-02
0.0E+00
2.0E-02
4.0E-02
6.0E-02
8.0E-02
1960 1970 1980 1990 2000 2010 2020
calendar year
d
P
/
P
predicted
measured dP/P, MA(5)
 
Figure 4. 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. 
Switzerland and New Zealand are presented in Figures 5 and 6. They are similar in terms 
of time lag: T=4 years in both countries, and the rate of neutral growth defined by A2=$175 and 
A2=$170, respectively.  In both countries, relatively accurate prediction from G is possible only 
after ~1975. The discrepancy before 1970 is not well explained and might be linked to revisions 
to employment and real economic growth definitions, and/or measurement errors. In both 
countries, the rate of productivity growth will approach the zero line by 2010.  
 
-2.0E-02
0.0E+00
2.0E-02
4.0E-02
1960 1970 1980 1990 2000 2010 2020
calendar year
d
P
/
P
predicted
measured dP/P, MA(5)
 
Figure 5. Observed and predicted (from real GDP pee capita) change rate of productivity in Switzerland.  
The observed curve is represented by MA(5) of original version. Model parameters are as follows: 
A2=$175, N(1959)=200000, B=-4500000, C=0.076, C=0.243, T=4 year. 
   8
-2.0E-02
0.0E+00
2.0E-02
4.0E-02
1960 1970 1980 1990 2000 2010
calendar year
d
P
/
P
predicted
measured dP/P, MA(5)
 
Figure 6. Observed and predicted (from real GDP pee capita) change rate of productivity in New Zealand.  
The observed curve is represented by MA(5) of original version. Model parameters are as follows: 
A2=$170, N(1959)=40000, B=-550000, C=0.076, C=0.243, T=4 year. 
  
Conclusion 
We have successfully modelled labor productivity in Turkey, Spain, Belgium, Austria, 
Switzerland, and New Zealand. These six countries extend the previously modelled set 
consisting of the largest economies.  Therefore, our concept is valid: labor productivity is a 
secondary macroeconomic variable because it is completely defined by the growth in real GDP 
per capita relative to its neutral rate, A2/G. Since real economic growth depends only on the 
evolution of specific age population, one has to care about demographic processes in order to 
control labor productivity and stable economic growth. 
 
References 
[1] Kitov, I., Kitov, O., (2008). The driving force of labor productivity, MPRA Paper 9069, University Library of 
Munich, Germany, http://mpra.ub.uni-muenchen.de/9069/01/MPRA_paper_9069.pdf 
[2] Kitov, I., Kitov, O., (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. 2(3(5)_Fall), pp. 203-222. 
[3] Kitov, I., Kitov, O., Dolinskaya, S., (2008). Comprehensive Macro–Model For The US Economy, Journal of 
Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting 
Craiova, ol. 3(4(6)_Wint), pp. 405-418.  
[4] Kitov, I., Kitov, O., Dolinskaya, S., (2007). Modelling real GDP per capita in the USA: cointegration test, 
MPRA Paper 2739, University Library of Munich, Germany, http://mpra.ub.uni-
muenchen.de/2739/01/MPRA_paper_2739.pdf  

Modelling and predicting labor force productivity

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