Economics does not need a scientific revolution. Economics needs accurate
measurements according to high standards of natural sciences and meticulous
work on revealing empirical relationships between measured variables.Comment: 6 pages, 3 figure

Kitov, Ivan O.

English

arXiv

Economics does not need a scientific revolution. Economics needs accurate measurements according to high standards of natural sciences and meticulous work on revealing empirical relationships between measured variables

Kitov, Ivan

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveDoes economics need a scientificrevolution?Ivan KitovIDG RAS4. April 2009Online at http://mpra.ub.uni-muenchen.de/14476/MPRA Paper No. 14476, posted 4. April 2009 18:22 UTC  1Does economics need a scientific revolution? Ivan O. Kitov, IDG RAS  Abstract Economics does not need a scientific revolution. Economics needs accurate measurements according to high standards of natural sciences and meticulous work on revealing empirical relationships between measured variables.  Key Words: economics, science JEL classification: A1  The proclamation by J.-P.Bouchaud [1] of the necessity “to break away from classical economics and develop completely different tools” might please many researchers and definitely bought a strong ideological support among professionals in the hard sciences. Sharing the general mood of the proclamation it is worth to analyze it without any favor to the physical sciences and without prejudice to economics. There are several questions arising directly from the Jean-Philippe’s text and some real problems behind the text reflecting the inability of the broad scientific community to build a sound economic theory matching strict requirements developed in empirical and quantitative disciplines.  First question is related to a striking tone of the pamphlet. For a physicist, it is very uncommon to use a somewhat proclamatory language and slightly negligible attitude to opponents. The strength of physics has been always expressed in the overall fit between predictions and observations. This fit does not need trumpets – just scatter plots.  There is a flavor of total superiority in the wording about physics as the only source of all those useful things.  So, why this powerful science did not explain economic and financial crises yet?  Second question is a consequence of the failure to create a physics-like theory of economic evolution, as Bouchaud clearly evidences himself. Why should one make a blank shot? This attack from the side of natural sciences is easily suppressed by the first question and the dry residual is expressed by the cited economist: “These concepts are so strong that they supersede any empirical observations”.  This statement is 90 percent right because the opposite statement is not proved by available economic data.  And this statement will be 100% wrong only when some new economic concept fits economic data, as physics has been demonstrating since Sir Isaac Newton. Meanwhile, the blank shot undermines respect to physics as a science and makes any   2opposition to the current status of the mainstream economics void. The best weapon against alchemy is analytic chemistry, but not words about analytic chemistry.    Third question is related to the actions required from the target audience of the essay. It seems that the rhetoric better complies with specialist from the hard sciences.  What should those numerous researchers accomplish? The author gives a dangerous answer – “completely different tools”. Therefore, he admits that there exists no tool capable to resolve most urgent problems of theoretical and experimental economics. This is another evidence of the inconsistency of physics in the realm of economics. On the other hand, this answer implies the abolishment of the most powerful part of the hard sciences – measurements.  A minor theoretical but a big practical agenda is formulated in the end of the essay. The author proposes to change the mindset of the specialists in economics and finances by the introduction more natural sciences in curricula. It is difficult to disagree that the diversity in the mandatory subjects to read allows a wider view on short- and long-term problems in any discipline. However, dozens thousands of young physicists, mostly theoreticians, in quant funds failed to prevent the current crisis. Hence, the strength of solid knowledge and the diversity of physical education is not a remedy. One should first give an appropriate physical concept of economy and then include it in education.   The above polemics would be void if no convincing examples of physics-like behavior of economic variables are presented. In a sense, there is a bunch of words against another bunch, with economists condescendingly smiling. However, before demonstrating couple robust micro- and macroeconomic relationships, it is obligatory to formulate and discuss the fundamental problem of economics as a science, which is echoed in all three questions above. So, the real problem is data.     It is a miracle that nor economists neither physicists (!) have focused on economic data as the only source and proof of economic concepts. The former have an excuse of the absence of any experience in handling model-producing data.  For centuries, data were an alien in the field of economics, as openly expressed by all (I mean literally all) statistical agencies responsible for economic measurements. When publishing data, they always warn users that the data (real GDP, inflation, labor force, unemployment, productivity, etc.) are not compatible over time due to revisions to definitions and procedures. As a consequence, no economist had any chance to work with quality data of appropriate length. No experience – no regret.  Prescott, the Nobel Prize winner in economics, wrote [2]:  … This raises the question of why inductive or empirical inference proved sterile in business cycle research. This sterility was not due to the incompetence of the researchers who pursued the inductive approach. The group who pursued this research program included a disproportionate number of the best minds in economics. The reason these inductive attempts failed, I think, is that the policy invariant laws governing the evolution of economic system is inconsistent with dynamic economic theory …     3It is more difficult to imagine the mental shift in numerous physicists who build theories based on wrong data. The habit to work with data of sufficient quality is so natural that they have never dug deep enough to recognize this basic mistake. There is no opportunity to build a reliable economic theory when data measured in different units are used together. The failure to develop empirically validated models of economic processes is an inevitable consequence of the absence of measurements matching standard requirements.  One must check data consistency before modelling, as we have done for several macroeconomic and demographic series. When checked and corrected, where possible, these data provide an invaluable source of information revealing numerous links between macroeconomic variables. Here only three examples are presented, from many. First is the model describing the evolution of personal income distribution (PID) over time and age, which is borrowed from geomechanics [3]. Left panel of Figure 1 depicts observed and predicted average income as a function of working experience in the United States for 1967 and 2001, the former is measured by the Census Bureau in the Annual Social and Economic Supplement of the Current Population Survey. Right panel of Figure 1 shows the evolution of Gini coefficient during the same period as measured and predicted by the model. This is the microeconomic level of description because the model accurately predicts the number of people with any given income or any given year after 1947 using only from real GDP per capita and age pyramid. It also predicts the observed evolution of income inequality. The model provides an adequate quantitative description of personal incomes and meets general requirements for physical models. It supports the idea that in economic terms society in the United States is a physical system.  010000200003000040000500000 10 20 30 40 50 60work experience, yearsmean income, $real - 1967 (original)real - 2001 (original)2001-predicted (x76)1967-predicted (x90)0.350.40.450.50.550.60.651960 1970 1980 1990 2000 2010calendar yearGIni coefficientallall w/income all - all Figure 1. Left Panel: Comparison of observed and predicted mean personal income dependence on work experience in 1967 and 2001. Averaging in 10-year intervals of work experience.  Right panel: Comparison of predicted (solid squares) and empirical (open triangle - all working age population; open circle – only people with income) Gini coefficient between 1967 and 2005.  Second example is from the field of macroeconomics and represents a part of a comprehensive macro-model for the US economy [4], which explains the evolution of macroeconomic variables only by the change in population, i.e. in the number of people in a given country.  Under this framework, the pair inflation/unemployment is driven by the change in the level of labor force. Figure 2 demonstrates the robustness of this link for inflation in the   4United States, with inflation lagged by 10 quarters behind the change in labor force. Annual readings of inflation in the left panel of Figure 2 are shifted back by 2.5 years in order to synchronize them with the change in labor force. Smoothing of the latter curve provides a much better fit between the curves at the level of R2>0.9 and still allows prediction a several quarters horizon.  Workforce projections developed by the CBO or BLS allow forecasting at a horizon of several years – the U.S. should expect a deflationary period from 2012. This deflation is caused by low rate of labor force growth and thus is similar to that observed in Japan. A helpful consequence of the link is the possibility to replace the measurements of inflation by the measurement in labor force. Right panel of Figure 2 displays cumulative curves for those in the left panel. The difference between the predicted and observed cumulative curves is a stationary or an I(0) process [5], i.e. the difference cumulates to zero over time. Considering fundamentally different nature of these two variables, one might use relationship: π(t) = 4.5dLF(t-2.5)/LF(t-2.5) – 0.031 where π(t) is the CPI inflation  at time t, LF(t-2.5) is the level of labor force 10 quarters before, as an empirical law in economics. It is similar to the estimation of the distribution of density in the Earth from orbits of satellites.  -0.050.000.050.100.150.201960 1970 1980 1990 2000 2010calendar yearinflationCPI, OECD4.5*dLF(t-2)/LF(t-2) - 0.031-0.50.00.51.01.52.02.51960 1970 1980 1990 2000 2010calendar yearinflationCPI, OECD4.5*dLF(t-2)/LF(t-2) - 0.031 Figure 2. Observed and predicted (CPI) inflation in the United States. Left panel – annual rate curves. Right panel: cumulative curves. Finally, unemployment in Italy provides an extraordinary example of the time delay between the change in labor force and unemployment [5]. The lag is the largest determined so far, with 6 years in the USA.  Figure 3 depicts observed unemployment and that predicted from labor force according the following relationship: UE(t) = 3.0dLF(t-11)/LF(t-11) + 0.085 where UE(t) is the unemployment at time t, LF(t-11) is the level of labor force 11 years before. Because of large fluctuations in the change rate of labor force this time series is smoothed with a 5-year moving average, MA(5), which still allow an out-of-sample forecast at a 9-year horizon with RMS forecasting error (RMSFE) of 0.55%. This is an outstanding result, which also a   5decisive example for the validation of the model. Here we get our feet back on the ground of empirically driven sciences: data reveal a reliable (R2=0.92) relationship between two measured variables. The relationship predicts at a very long horizon with an uncertainty much lower than the expected change.   The horizon is lengthy but the reward is high – robust empirical bounds in economics.   All three examples, and dozens more not shown here for the sake of brevity, are completely data-driven. There was no theoretical assumption or a desire to develop a revolutionary tool behind the obtained relations. The model for personal incomes is the result of a random attempt to apply a concept specific for geomechanics to some measured value in economics, with as long time series as possible. The intuition behind the macro-model for developed economies is trivial – dirty trial-and-error with the simplest linear link, potentially lagged.  Therefore, there is no demand for revolution in economics. One desperately needs a significant increase in the quality of economic data, the data being measured according to sound definitions of macro-economic variables under study. As in physics, statistical inferences are only possible then the length and volume of quality data will reach the threshold, which is well established in the hard sciences. Hence, the way economics should walk along is to repeat the loop data-model-data, which has been productive for centuries in the natural sciences. On this path, actual revolution is not feasible, because there is nothing revolutionary in the repetition, with small deviations, of what other people have already done. One needs the meticulous everyday work and progressive correction of the attained knowledge, just as in physics. Then, real revolution is economic behavior of society and individuals is likely to come.       00.040.080.120.160.21960 1970 1980 1990 2000 2010 2020calendar yearUEUE(t), NACUE(t) = 3.0dLF(t-11)/LF(t-11) + 0.085  UE(t) = 3.0dLF(t-11)/LF(t-11) + 0.085 : MA(5) y = 0.9559x + 0.0047R2 = 0.92160.040.060.080.100.120.140.04 0.06 0.08 0.1 0.12 0.14UE, predicted: MA(5)UE, measured Figure 3. Observed and predicted unemployment in Italy. The prediction horizon is 11 years. Due to large fluctuations associated with measurement errors in the labor force the predicted series is smoothed with MA(5). Linear regression gives R2=0.92 for the period between 1973 and 2006, with RMSFE of 0.55%. The unemployment should start to increase in 2008. References [1] Boucahud, J.-P., (2008). Economics needs scientific revolution, Nature, v.455, 30 October 2008.    6[2] Prescott, E., (1998). Business cycle research: methods and problems, Federal Reserve Bank of Minneapolis, working paper 590. [3] Kitov, I., (2009). Mechanical model of personal income distribution, Working Papers 110, ECINEQ, Society for the Study of Economic Inequality, http://www.ecineq.org/milano/WP/ECINEQ2009-110.pdf [4] 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, vol. 3(4(6)_Wint), pp. 405-418.  [5] Kitov, I., Kitov, O., (2009). Unemployment and inflation in Western Europe: solution by the boundary element method, MPRA Paper 14341, University Library of Munich, Germany.  

Does economics need a scientific revolution?

Ivan Kitov

Crossref

SSRN Electronic Journal

Does Economics Need a Scientific Revolution?

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Does economics need a scientific
revolution?
Ivan Kitov
IDG RAS
4. April 2009
Online at http://mpra.ub.uni-muenchen.de/14476/
MPRA Paper No. 14476, posted 4. April 2009 18:22 UTC
  1
Does economics need a scientific revolution? 
Ivan O. Kitov, IDG RAS 
 
Abstract 
Economics does not need a scientific revolution. Economics needs accurate measurements according to 
high standards of natural sciences and meticulous work on revealing empirical relationships between 
measured variables.  
Key Words: economics, science 
JEL classification: A1 
 
The proclamation by J.-P.Bouchaud [1] of the necessity “to break away from classical 
economics and develop completely different tools” might please many researchers and definitely 
bought a strong ideological support among professionals in the hard sciences. Sharing the 
general mood of the proclamation it is worth to analyze it without any favor to the physical 
sciences and without prejudice to economics. There are several questions arising directly from 
the Jean-Philippe’s text and some real problems behind the text reflecting the inability of the 
broad scientific community to build a sound economic theory matching strict requirements 
developed in empirical and quantitative disciplines.  
First question is related to a striking tone of the pamphlet. For a physicist, it is very 
uncommon to use a somewhat proclamatory language and slightly negligible attitude to 
opponents. The strength of physics has been always expressed in the overall fit between 
predictions and observations. This fit does not need trumpets – just scatter plots.  There is a 
flavor of total superiority in the wording about physics as the only source of all those useful 
things.  
So, why this powerful science did not explain economic and financial crises yet?  
Second question is a consequence of the failure to create a physics-like theory of 
economic evolution, as Bouchaud clearly evidences himself. Why should one make a blank shot? 
This attack from the side of natural sciences is easily suppressed by the first question and the dry 
residual is expressed by the cited economist: “These concepts are so strong that they supersede 
any empirical observations”.  This statement is 90 percent right because the opposite statement is 
not proved by available economic data.  And this statement will be 100% wrong only when some 
new economic concept fits economic data, as physics has been demonstrating since Sir Isaac 
Newton. Meanwhile, the blank shot undermines respect to physics as a science and makes any 
  2
opposition to the current status of the mainstream economics void. The best weapon against 
alchemy is analytic chemistry, but not words about analytic chemistry.    
Third question is related to the actions required from the target audience of the essay. It 
seems that the rhetoric better complies with specialist from the hard sciences.  What should those 
numerous researchers accomplish? The author gives a dangerous answer – “completely different 
tools”. Therefore, he admits that there exists no tool capable to resolve most urgent problems of 
theoretical and experimental economics. This is another evidence of the inconsistency of physics 
in the realm of economics. On the other hand, this answer implies the abolishment of the most 
powerful part of the hard sciences – measurements.  
A minor theoretical but a big practical agenda is formulated in the end of the essay. The 
author proposes to change the mindset of the specialists in economics and finances by the 
introduction more natural sciences in curricula. It is difficult to disagree that the diversity in the 
mandatory subjects to read allows a wider view on short- and long-term problems in any 
discipline. However, dozens thousands of young physicists, mostly theoreticians, in quant funds 
failed to prevent the current crisis. Hence, the strength of solid knowledge and the diversity of 
physical education is not a remedy. One should first give an appropriate physical concept of 
economy and then include it in education.   
The above polemics would be void if no convincing examples of physics-like behavior of 
economic variables are presented. In a sense, there is a bunch of words against another bunch, 
with economists condescendingly smiling. However, before demonstrating couple robust micro- 
and macroeconomic relationships, it is obligatory to formulate and discuss the fundamental 
problem of economics as a science, which is echoed in all three questions above. So, the real 
problem is data.     
It is a miracle that nor economists neither physicists (!) have focused on economic data as 
the only source and proof of economic concepts. The former have an excuse of the absence of 
any experience in handling model-producing data.  For centuries, data were an alien in the field 
of economics, as openly expressed by all (I mean literally all) statistical agencies responsible for 
economic measurements. When publishing data, they always warn users that the data (real GDP, 
inflation, labor force, unemployment, productivity, etc.) are not compatible over time due to 
revisions to definitions and procedures. As a consequence, no economist had any chance to work 
with quality data of appropriate length. No experience – no regret.  Prescott, the Nobel Prize 
winner in economics, wrote [2]:  
… This raises the question of why inductive or empirical inference proved sterile in business cycle 
research. This sterility was not due to the incompetence of the researchers who pursued the 
inductive approach. The group who pursued this research program included a disproportionate 
number of the best minds in economics. The reason these inductive attempts failed, I think, is that 
the policy invariant laws governing the evolution of economic system is inconsistent with dynamic 
economic theory …   
  3
It is more difficult to imagine the mental shift in numerous physicists who build theories 
based on wrong data. The habit to work with data of sufficient quality is so natural that they have 
never dug deep enough to recognize this basic mistake. There is no opportunity to build a 
reliable economic theory when data measured in different units are used together. The failure to 
develop empirically validated models of economic processes is an inevitable consequence of the 
absence of measurements matching standard requirements.  
One must check data consistency before modelling, as we have done for several 
macroeconomic and demographic series. When checked and corrected, where possible, these 
data provide an invaluable source of information revealing numerous links between 
macroeconomic variables. Here only three examples are presented, from many. First is the model 
describing the evolution of personal income distribution (PID) over time and age, which is 
borrowed from geomechanics [3]. Left panel of Figure 1 depicts observed and predicted average 
income as a function of working experience in the United States for 1967 and 2001, the former is 
measured by the Census Bureau in the Annual Social and Economic Supplement of the Current 
Population Survey. Right panel of Figure 1 shows the evolution of Gini coefficient during the 
same period as measured and predicted by the model. This is the microeconomic level of 
description because the model accurately predicts the number of people with any given income 
or any given year after 1947 using only from real GDP per capita and age pyramid. It also 
predicts the observed evolution of income inequality. The model provides an adequate 
quantitative description of personal incomes and meets general requirements for physical 
models. It supports the idea that in economic terms society in the United States is a physical 
system.  
0
10000
20000
30000
40000
50000
0 10 20 30 40 50 60
work experience, years
m
ea
n 
in
co
m
e,
 $
real - 1967 (original)
real - 2001 (original)
2001-predicted (x76)
1967-predicted (x90)
0.35
0.4
0.45
0.5
0.55
0.6
0.65
1960 1970 1980 1990 2000 2010
calendar year
G
In
i c
oe
ffi
ci
en
t
all
all w/income 
all - all
 
Figure 1. Left Panel: Comparison of observed and predicted mean personal income dependence on work 
experience in 1967 and 2001. Averaging in 10-year intervals of work experience.  Right panel: 
Comparison of predicted (solid squares) and empirical (open triangle - all working age population; open 
circle – only people with income) Gini coefficient between 1967 and 2005.  
Second example is from the field of macroeconomics and represents a part of a 
comprehensive macro-model for the US economy [4], which explains the evolution of 
macroeconomic variables only by the change in population, i.e. in the number of people in a 
given country.  Under this framework, the pair inflation/unemployment is driven by the change 
in the level of labor force. Figure 2 demonstrates the robustness of this link for inflation in the 
  4
United States, with inflation lagged by 10 quarters behind the change in labor force. Annual 
readings of inflation in the left panel of Figure 2 are shifted back by 2.5 years in order to 
synchronize them with the change in labor force. Smoothing of the latter curve provides a much 
better fit between the curves at the level of R2>0.9 and still allows prediction a several quarters 
horizon.  Workforce projections developed by the CBO or BLS allow forecasting at a horizon of 
several years – the U.S. should expect a deflationary period from 2012. This deflation is caused 
by low rate of labor force growth and thus is similar to that observed in Japan. A helpful 
consequence of the link is the possibility to replace the measurements of inflation by the 
measurement in labor force. Right panel of Figure 2 displays cumulative curves for those in the 
left panel. The difference between the predicted and observed cumulative curves is a stationary 
or an I(0) process [5], i.e. the difference cumulates to zero over time. Considering fundamentally 
different nature of these two variables, one might use relationship: 
π(t) = 4.5dLF(t-2.5)/LF(t-2.5) – 0.031 
where π(t) is the CPI inflation  at time t, LF(t-2.5) is the level of labor force 10 quarters before, 
as an empirical law in economics. It is similar to the estimation of the distribution of density in 
the Earth from orbits of satellites.  
-0.05
0.00
0.05
0.10
0.15
0.20
1960 1970 1980 1990 2000 2010
calendar year
in
fla
tio
n
CPI, OECD
4.5*dLF(t-2)/LF(t-2) - 0.031
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1960 1970 1980 1990 2000 2010
calendar year
in
fla
tio
n
CPI, OECD
4.5*dLF(t-2)/LF(t-2) - 0.031
 
Figure 2. Observed and predicted (CPI) inflation in the United States. Left panel – annual rate curves. 
Right panel: cumulative curves. 
Finally, unemployment in Italy provides an extraordinary example of the time delay 
between the change in labor force and unemployment [5]. The lag is the largest determined so 
far, with 6 years in the USA.  Figure 3 depicts observed unemployment and that predicted from 
labor force according the following relationship: 
UE(t) = 3.0dLF(t-11)/LF(t-11) + 0.085 
where UE(t) is the unemployment at time t, LF(t-11) is the level of labor force 11 years before. 
Because of large fluctuations in the change rate of labor force this time series is smoothed with a 
5-year moving average, MA(5), which still allow an out-of-sample forecast at a 9-year horizon 
with RMS forecasting error (RMSFE) of 0.55%. This is an outstanding result, which also a 
  5
decisive example for the validation of the model. Here we get our feet back on the ground of 
empirically driven sciences: data reveal a reliable (R2=0.92) relationship between two measured 
variables. The relationship predicts at a very long horizon with an uncertainty much lower than 
the expected change.   The horizon is lengthy but the reward is high – robust empirical bounds in 
economics.  
 All three examples, and dozens more not shown here for the sake of brevity, are 
completely data-driven. There was no theoretical assumption or a desire to develop a 
revolutionary tool behind the obtained relations. The model for personal incomes is the result of 
a random attempt to apply a concept specific for geomechanics to some measured value in 
economics, with as long time series as possible. The intuition behind the macro-model for 
developed economies is trivial – dirty trial-and-error with the simplest linear link, potentially 
lagged.  
Therefore, there is no demand for revolution in economics. One desperately needs a 
significant increase in the quality of economic data, the data being measured according to sound 
definitions of macro-economic variables under study. As in physics, statistical inferences are 
only possible then the length and volume of quality data will reach the threshold, which is well 
established in the hard sciences. Hence, the way economics should walk along is to repeat the 
loop data-model-data, which has been productive for centuries in the natural sciences. On this 
path, actual revolution is not feasible, because there is nothing revolutionary in the repetition, 
with small deviations, of what other people have already done. One needs the meticulous 
everyday work and progressive correction of the attained knowledge, just as in physics. Then, 
real revolution is economic behavior of society and individuals is likely to come.       
0
0.04
0.08
0.12
0.16
0.2
1960 1970 1980 1990 2000 2010 2020
calendar year
U
E
UE(t), NAC
UE(t) = 3.0dLF(t-11)/LF(t-11) + 0.085  
UE(t) = 3.0dLF(t-11)/LF(t-11) + 0.085 : MA(5)
 
y = 0.9559x + 0.0047
R2 = 0.9216
0.04
0.06
0.08
0.10
0.12
0.14
0.04 0.06 0.08 0.1 0.12 0.14
UE, predicted: MA(5)
U
E
, m
ea
su
re
d
 
Figure 3. Observed and predicted unemployment in Italy. The prediction horizon is 11 years. Due to large 
fluctuations associated with measurement errors in the labor force the predicted series is smoothed with 
MA(5). Linear regression gives R2=0.92 for the period between 1973 and 2006, with RMSFE of 0.55%. 
The unemployment should start to increase in 2008. 
References 
[1] Boucahud, J.-P., (2008). Economics needs scientific revolution, Nature, v.455, 30 October 2008.  
  6
[2] Prescott, E., (1998). Business cycle research: methods and problems, Federal Reserve Bank of Minneapolis, 
working paper 590. 
[3] Kitov, I., (2009). Mechanical model of personal income distribution, Working Papers 110, ECINEQ, Society for 
the Study of Economic Inequality, http://www.ecineq.org/milano/WP/ECINEQ2009-110.pdf 
[4] 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, vol. 3(4(6)_Wint), pp. 405-418.  
[5] Kitov, I., Kitov, O., (2009). Unemployment and inflation in Western Europe: solution by the boundary element 
method, MPRA Paper 14341, University Library of Munich, Germany.  


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