The link between real GDP growth and personal income distribution

Quantitatively, real economic growth has been studied since Kuznets’ works on accounting of national income and aggregate factor inputs. Hodrick and Prescott (1980) introduced a concept of two-component economic growth – an economic trend and a deviation or business cycle component. The trend component is responsible for the long-term growth and defines economic efficiency. In the long run, the fluctuating component of economic growth has to have (by definition) a zero mean value. In 2004, Prescott and Kydland received a Nobel Prize for the study of "the driving forces behind business cycle" (Bank of Sweden, 2004), what demonstrates the importance of the best understanding of the processes of real growth and the explanation of the two-component behavior.
Prescott and Kydland, together with many other researchers, have proposed and studied exogenous shocks as the force driving fluctuations of the growth rate of real GDP. During the last 25 years, their research has revealed numerous features (potential links) of principal variables involved in the description of the economic growth. There are many problems left in the theory of real economic growth. We propose a model with real GDP growth dependent only on the change in a specific age cohort and the attained level of real GDP per capita. According to our model, real GDP per capita has a trend defined by a constant growth increment (not constant rate) and observed fluctuations can be explained by the change in some population component. In developed countries, real GDP per capita has to grow along a straight line, (i.e. with a constant annual increment) if no large change in corresponding specific age population is observed. The growth rate of real GDP per capita has to be an inverse function of the attained level of real GDP per capita with a potentially constant numerator for developed economies.
Chapter 2 is devoted to the validation of this model using GDP per capita and population data for some selected developed countries. Our principal purpose is to demonstrate the possibility to decompose GDP per capita growth into the two components. A comprehensive study of the US personal income distribution and detailed modeling of some important characteristics of the distribution is carried out in Chapter 1. The principal finding is that people, as economic agents producing (equivalent - earning) money, are distributed according to a fixed and hierarchical structure resulting in a very rigid response of the PID to any external disturbances including inflation and real economic growth. There is a predefined distribution of relative income, i.e. the portion of total population obtaining a given portion of total (real or nominal) income. In addition, every available position in the distribution is occupied by individual agents. A person occupying a given place may propagate to a position with a different income, but the vacant place must be filled by somebody. For example, in might be occupied by the person who was shifted from his old position. Only such an exchange of income positions in the PID, or more complicated change of positions with circular substitutes, is possible. This mechanism provides a dynamic equilibrium and the observed stable personal income distribution. As shown in §1.7, the measured PIDs in the USA corrected for the observed nominal Gross Personal Income growth rate has been showing a very stable shape since 1947 – the start year of corresponding measurements. This stability is interpreted as the existence of an almost stable relative income distribution hierarchy in American society, which might be evolving very slowly over time according to the long-term changes in age structure. This income (or economic) structure also predefines the evolution of real economy. Only specific characteristics of the population age distribution in the US are important for the growth rate of real GDP beyond the economic trend, as defined by the attained level of real GDP per capita. Here I would like to stress that inflation has no impact on real economic growth since no component of the model depends on it. In Chapter 1, the growth rate of per capita real GDP in the USA was used as an external parameter in prediction of the observed evolution of the PID, its components and derivatives. The PID has been expressed as a simple and predetermined function of GDP per capita and the age structure of the working age population in the USA. Now we are trying to interpret this relationship in the reverse direction. The observed PID is considered as a result of each and every individual effort to earn money (equivalent - to produce goods and services) in the economically structured society as exists in the USA. Thus, these individual money productions (earnings) aggregated over the US working age population are the inherent driving force of the observed economic development. As before, the working age means the age eligible to receive income, i.e. 15 years of age and above. In addition, this population effectively includes all retired people. The principal assumption made in Chapter 1 and retained in the current study is that GDP denominated in money is the sum of all personal incomes of all people. This approach not only formulates the income side of GDP definition but extends the Walrasian equilibrium to all people above 14 years of age, with income (with predefined distribution) being the only measure of the produced goods and services whatever they are. This statement unambiguously defines the upper limit to the total real income (Gross Domestic Income) or real GDP which can be produced by a population with a given age structure and characterized by some attained level of real GDP per capita. As the age structure is estimated by the US Census Bureau or enumerated in decennial censuses and individual incomes in the society are predefined by a strict relationship between age and per capita GDP, the total potential income growth (and accordingly the growth of real GDP) has to be also predefined. By definition, a person produces exactly the same amount of money (in form of goods and services) as s/he receives as income. This provides a global balance of income (earnings) and production, but also a more strict and important local balance. Economic structure of a developed economic society confines its possible evolution as everybody has an income place (position in corresponding PID) and produces according to this place.This approach also implies that there is no economic means to disturb the economic structure of such a society. For example, it is impossible to reduce poverty or to limit individual incomes of rich people compared to the level predefined by corresponding economic (income) structure itself. According to the PID observations in the USA, all positions of poor and rich people in the structure are always occupied. This might be not the case in other developed or developing countries. The extent to which the positions are occupied can be potentially linked to the degree of economic performance. Performance in a somewhat disturbed income structure would be likely reduced compared to its potential level only defined by per capita GDP and age structure. Thus, only some non-economic means is available to reduce poverty. A society can provide higher living standards, as associated with better quality of goods and services, but not higher incomes if it does not want to lose economic competitiveness. When applied, any economic means (income redistribution in favor of poorer people) has to result in economic underperformance. Another possibility is that some mechanisms out of control of economic and political authorities will return the PID to its original shape with the same number of poor people. Therefore, people with low incomes should be ultimately interested in those social and political developments which are associated with accelerating improvements in living standards. Paragraph 2.2 and 2.3 presents the model for real economic development. The fluctuating component is analyzed using data on real economic growth and population in the USA, Japan, France, and the UK. The trend component is studied using an extended set of developed countries since the fluctuations are practically canceled out in most of the countries during the period of the last 50 years. In fact, it is shown that these fluctuations are normally distributed, i.e. are likely the manifestation of a large number of stochastic processes. I am not going to present here conventional theories of economic growth. Interested readers can easily find appropriate sources of information. Personally, I do not find them quantitatively convincing and reliable. The RBC model, for example, separates the growth into two parts. One part is inherently theoretical and links numerous measurable and immeasurable variables by a finite number of calibrated equations. Among these variables is the growth rate of real GDP. The unexplained difference between actually observed growth and that predicted by the theoretical part is announced as induced by stochastic exogenous shock. In other words, the unexplained difference is attributed to the effects beyond control (stochastic) and understanding (related to some unknown forces). It does not look like a fruitful direction for any quantitative modeling. In spite we also separate real economic growth into two components, the growth is completely defined. Therefore our model can be verified by statistical and econometrical tools and is open for validation using additional data sets.

Introduction

Economics is currently recognized by the broad scientific community, and economists themselves, as a soft science. Unlike objective quantitative methodology associated with hard sciences, economics provides at best some qualitative assessments, sometimes called "stylized facts", of its fundamental assumptions and findings. What one expects from a standard scientific theory is a description of known facts about some measured variables with a finite number of defining parameters and relationships. As a rule, the lower is the number - the better. Also the theory must give quantitative predictions both in time and in different ranges of defining parameters. In the case of economics - across countries.

For example, accurate prediction of lunar phases at very long time horizons was available thousands years ago. There was no theory describing gravitational interaction of masses, however, to describe and predict orbits. Now, using the theory of gravitation, one can explain long-term (as related to the planetary system) changes in the moon-earth-sun interaction and changes in lunar phases at a geological time horizon. Also, one can accurately predict orbit of any satellite in any planetary system knowing only distances and masses. There is a question at a Universe time scale with planetary orbits - what was before the Universe was born and what will be after it will dye or will undego some dramatic changes? This question is on the list of modern science.

There are several key points to characterize a theory as belonging to hard sciences. First, such a theory must use measurable parameters in order to establish quantitative relations between them. Second, the theory should describe a larger part or available measurements and give quantitative predictions. This allows testing and validation of the theory. In principle, one should be able to repeat known laboratory experiments or conduct new passive measurements in order to check both data and theoretical relationships. There is always a weak (or sometimes strong) discrepancy in various data sets and physical theories in the "naked"form are actually sets of scatter plots or statistical relationships. Thererfore, it is not usually required to have an exact description of the entire data set. Moreover, a good theory may be potentially used to distinguish between reliable and unreliable data sets. Third, the theory should define the boundaries of applicability. In other words, the theory should be falsifiable, i.e. the defining quantitative relationships of the theory do not describe real links between the involved parameters beyond some predefined range.

For example, the predictive power of Newtonian mechanics deteriorates with increasing speed of objects and the mechanics developed by Einstein replaces classic mechanics at relativistic velocities. When a theory can give an answer to any question, related or unrelated to the scope of the theory, it is always a wrong theory from scientific point of view.

This blog (being a mirror of a monograph) is aimed at presenting a quantitative theory of economics as expressed by strict quantitative relationships between several measured micro- and macroeconomic variables in such developed countries with market economy as the USA, Japan, the UK, France, Germany, Canada, Italy, Netherlands, Australia, Austria, and others. The set of measured variables includes population, real GDP per capita, inflation, unemployment, labor force participation rate, productivity, and personal income distribution. These macro-economic variables are shown to be functions of demographic parameters.

In our economic research, we follow the requirements for a hard science – quantitative description, quantitative predictions for validation, defining the time interval of validity or the range of defining parameters where the relationships work. On the other hand, we do not pay much attention to the details or "fine structure"of the driving mechanism underlying the observed relationships by limiting ourselves with a strong form of scientific reasoning, i.e. quantitative analysis. This means that we just mention some vague potential links and channels of influence but not provide any extended justification of the relationships expressed in words.

Formally, the sense of any scientific theory consists in obtaining objective (statistical) links between measured variables as described by mathematical equations. In the absence of axiomatic assumptions behind the theory, as adopted in mathematics, there is no way to reduce the observed links to a finite set of meaningful "words". The sence of any variable in a quantitative theory is in the possibility to measure its value only. One can define the term "mass", for example, only though measurements and only these measurements define the term mass as we know and use it both in routine life and science. There is no set of terms, which can explain and describe mass better than the entire set of corresponding measurements.

There are several principal concepts of the quantitative description of links between measured economic variables introduced similar to those adopted in mechanics. They describe the methods and procedures of empirical and theoretical analysis used in obtaining quantitative relationships, provide standard statistical assessment as adopted in physics and economics, and validate the concept by cross-country analysis. The limits of the applicability of the relationships are also defined to meet the principle of falsifiability. This blog (and the monograph) is focused on the resolving of three fundamental economic problems – sources for real economic growth, inflation and unemployment, and personal income distribution.

In our framework, real economic growth is related to only one demographic parameter and does not depend on any other parameter economic or non-economic. Inflation and unemployment are also entirely described by a single relation to the change rate of labor force level, which is completely defined by real economic growth and demographic fluctuations. Personal income distribution is also driven by age structure and real economic growth, the latter defining long-term changes in individual income trajectories.

Therefore, real economic growth in developed countries does not depend on monetary policy. This observation is in line with old hypothesis on the neutrality of money for real economies. This independence isnot correctly (actually just in opposite direction) interpreted by conventional economics, however. In fact, the independence implies that only monetary expression does matter and is the measured variable to study. In other words, there is no specific configuration of goods and services, which can cost more thangiven and measured one. Thus, all possible configurations of goods and services cost the same amount of money for given year. This effectively makes monetary description independent on physical and technological content - the observed set of goods and services is equivalent to any imaginary one, which might be realized in different conditions - political, social, climatic, etc., but not demographic.

The monograph describes real economic growth only in terms on the total final product cost. This effectively excludes from our study such exciting economic terms as marginal productivity, human capital, supply and demand shocks, productivity and technology shocks, education, and many others, which are related to technological and other kinds content of economy only. These terms are good for a conventional economic reasoning but absolutely irrelevant to the quantitative description adopted in the current study.

I have to confess. I do not like economic reasoning and conventional economic theory. There are several reasons for that. First, as an ordinary physicist, I always rely on measurements for any judgment. The absence of an experimental justification undoubtedly makes any theory just an assumption or educated guess. No of conventional economic models, which I am aware of, is empirically justified. Second, the evolution of any macroeconomic parameter is usually modeled with the same "success" using juxtaposed theoretical approaches and contradicting, if not random, sets of parameters. At a theoretical level, this observation is supported by the existence of numerous competitive models. At the level of practical applications, one can recall myriads of mutually excluding explanations of the same macroeconomic facts.

A simple example is the explanation of the influence of oil prices on real economic growth. In 2002, an increase in oil price above $20 per barrel was considered as a traction force for the global economy with an average deceleration of 0.5% to 1%. In 2006, the influence of the price decrease below $50 was also interpreted in the same way. My opinion on the influence is an opposite one. There is no one-to-one causal link between any part of developed economy and the whole economy. Any change in one part of the economy must be competely compensated by opposite change in some other part. In physics, such compensation is called a conservation law.

Third, top economists too often use words like mystery, mysterious, etc. This is more appropriate to religious activity than to science. To confirm this observation I would like to cite the 2004 Nobel Prize laureate E.C. Prescott, who wrote in "The Wall Street Journal" (December 11, 2006): One of the mysteries of the 1990s is how to explain the economic boom when the increase in capital investment – as measured by national accounts – grew at subdued pace. Harvard Professor G. Mankiw titled his essay "The inexorable and mysterious tradeoff between inflation and unemployment". In spite of clear metaphoric usage of these words, one can feel the flavor of the deep inconsistency between the practice of economic observations on one side and the accuracy of theoretical description and the power of economic predictions on the other side. This is a clear dissatisfaction. Imagine now that your personal and social prosperity is in the hands of a person who can only say that there is no economic variable, which has an well-understood behavior and can be controlled somehow. Moreover, they insist that nobody could, can, and will be able to present a consistent theoretical description of economic variables. So to say, economic problems are too complicated to allow ordinary hard sciences to resolve them.

Here I make an attempt.

Our model is presented in a review paper:

Comprehensive macro-model for the US economy

Abstract

We present a comprehensive macroeconomic model for the U.S. There exist strict long-term relations between real GDP, price inflation, labor force participation, productivity, and unemployment. The evolution of real GDP depends only on exogenous demographic forces. Other macro-variables follow up the real GDP. The links between the variables have been valid during the last several decades. All relations were (successfully) tested for cointegration. Statistical estimates are also presented. The relationships allow a reliable prediction of the macroeconomic state at very large (more than 9 years) time horizons