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arXiv2008

Modeling the evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005

The evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005 is analyzed and modeled. There are several versions of personal income distribution (PID) provided by the US Census Bureau (US CB) for this period with various levels of resolution. Effectively, these PIDs result in different Gini coefficients due to the differences between discrete and continuous representations. When all persons of 15 years of age and over are included in the PIDs, Gini coefficient drops from 0.64 in 1947 to 0.54 in 1990. This effect is observed due to a significant decrease in the portion of people without income. For the PIDs not including persons without income, Gini coefficient is varying around 0.51 between 1960 and 2005 with standard deviation of 0.004, i.e. is in fact constant. This Gini coefficient is practically independent on the portion of population included in the PIDs according to any revision of income definitions. The driving force of the model describing the evolution of individual incomes (microeconomic level) and their aggregate value (macroeconomic level) is the change in nominal GDP per capita. The model accurately predicts the evolution of Gini coefficient for the PIDs for people with income. The model gives practically unchanged (normalized) PIDs and Gini coefficient between 1947 and 2005. The empirical Gini curves converge to the predicted one when the number of people without income decreases. Asymptotically, the empirical curves should collapse to the theoretical one when all the working age population obtains an appropriate definition of income. Therefore the model Gini coefficient potentially better describes true behavior of inequality in the USA because the definitions of income used by the US Census Bureau apparently fail to describe true income distribution.

q-fin.GN↗
arXiv2008

Exact prediction of S&P 500 returns

A linear link between S&P 500 return and the change rate of the number of nine-year-olds in the USA has been found. The return is represented by a sum of monthly returns during previous twelve months. The change rate of the specific age population is represented by moving averages. The period between January 1990 and December 2003 is described by monthly population intercensal estimates as provided by the US Census Bureau. Four years before 1990 are described using the estimates of the number of 17 year-olds shifted 8 years back. The prediction of S&P 500 returns for the months after 2003, including those beyond 2007, are obtained using the number of 3 year-olds between 1990 and 2003 shifted by 6 years ahead and quarterly estimates of real GDP per capita. A prediction is available for the period beyond 2007. There are two sharp drops in the predicted returns - in 2007 and 2009, and one strong rally in 2008. Equivalently, S&P 500 index should drop in 2007 and 2009 to the level observed one year before. Potential link between S&P 500 returns and 9-year-old population is tested for cointegration. The Engle-Granger and Johansen tests demonstrate the presence of a long-term equilibrium (cointegrating) relation between these variables. This makes valid standard statistical estimates. Correlation between the predicted and observed indices, including RMS difference, linear regression, and VAR demonstrate good prediction accuracy at two-year horizon, when the prediction uses 7-year-olds instead of 9-year-olds. The RMS difference between the observed and predicted returns for the period between 1992 and 2003 is only 0.09 with standard deviation of the observed series for the same period of 0.12 and the naive (random walk) RMS deference of 0.18.

q-fin.ST↗
arXiv2008

Modelling the average income dependence on work experience

The average and median income dependence on work experience and time is analyzed and modeled for the USA. The original data set providing the mean and median income estimates in 10 year long intervals spans a long time period of almost 35 years ? from 1967 to 2003. A microeconomic model linking personal income, population age structure and GDP per capita is used to predict the mean income values in various age groups and their relative evolution in time. Also modeled is the value of work experience where the mean income growth ends and it starts to drop exponentially with increasing age. This work experience increases through time as the square root of the per capita GDP growth. Prediction for the following 20 years is given for each age group considering potential per capita growth rate of 1.6%. The USA mean income dependence on work experience for 1987 coincides with that for 2002 in the UK ? the years when per capita GDP were equal in the countries.

q-fin.GN↗
arXiv2008

Modelling real GDP per capita in the USA: cointegration test

A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per capita itself, with the nominator being constant through time. The second component is responsible for fluctuations around the economic trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the USA is tested for cointegration. For linearization of the problem, a predicted population time series is calculated using the original relationship. Both single year of age population time series, the measured and predicted one, are shown to be integrated of order 1. The Engel-Granger approach is applied to the difference of the measured and predicted time series and to the residuals or corresponding linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since a cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in the VAR representation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the USA from the economic trend, as defined by the constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.

q-fin.GN↗
arXiv2008

Real GDP per capita in developed countries

Growth rate of real GDP per capita is represented as a sum of two components -- a monotonically decreasing economic trend and fluctuations related to a specific age population change. The economic trend is modeled by an inverse function of real GDP per capita with a numerator potentially constant for the largest developed economies. Statistical analysis of 19 selected OECD countries for the period between 1950 and 2004 shows a very weak linear trend in the annual GDP per capita increment for the largest economies: the USA, Japan, France, Italy, and Spain. The UK, Australia, and Canada show a larger positive linear trend. The fluctuations around the trend values are characterized by a quasi-normal distribution with potentially Levy distribution for far tails. Developing countries demonstrate the increment values far below the mean increment for the most developed economies. This indicates an underperformance in spite of large relative growth rates.

q-fin.GN↗
arXiv2008

Inflation as a function of labor force change rate: cointegration test for the USA

A linear and lagged relationship between inflation and labor force change rate, p(t)= A1dLF(t-t1)/LF(t-t1)+A2 was found for developed economies. For the USA, A1=4.0, A2=-0.03075, and t1=2 years. It provides a RMS forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best among other inflation forecasting models). This relationship is tested for cointegration. Both variables are integrated of order one according to the presence of a unit root in the series and its absence in their first differences. Two methods of cointegration testing are applied: the Engle-Granger one based on the unit root test of the residuals including a variety of specification tests and the Johansen cointegration rank test based on the VAR representation. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds. According to the Granger causality test, the labor force change is proved to be a weakly exogenous variable - a natural result considering the time lead and the existence of a cointegrating relation. VAR and VECM representations do not provide any significant improvement in RMSFE. There are numerous applications of the equation: from purely theoretical - a robust fundamental relation between macroeconomic and population variables, to a practical one - an accurate out-of-sample inflation forecasting at a two-year horizon and a long-term prediction based on labor force projections. The predictive power of the relationship is inversely proportional to the uncertainty of labor force estimates. Therefore, future inflation research programs should start from a significant improvement in the accuracy of labor force estimations.

q-fin.GN↗
arXiv2008

Relationship between inflation, unemployment and labor force change rate in France: cointegration test

A linear and lagged relationship between inflation, unemployment and labor force change rate, p(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+ A2, where A0, A1, and A2 are empirical country-specific coefficients, was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a RMS forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between 1971 and 2004. The relationship is tested for cointegration. All three variables involved in the relationship are proved to be integrated of order one. Two methods of cointegration testing are used. First is the Engle-Granger approach based on the unit root test in the residuals of linear regression, which also includes a number of specification tests. Second method is the Johansen cointegration rank test based on a VAR representation, which is also proved to be an adequate one via a set of appropriate tests. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds together with statistical estimates of goodness-of-fit and RMSFE. Relationships between inflation and labor force and between unemployment and labor force are tested separately in appropriate time intervals, where the Banque de France monetary policy introduced in 1995 does not disturb the long-term links. All the individual relationships are cointegrated in corresponding intervals. The VAR and vector error correction (VEC) models are estimated and provide just a marginal improvement in RMSFE at the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on the results obtained in the regression study.

q-fin.GN↗
arXiv2008

Modelling the transition from a socialist to capitalist economic system

The transition of several East and Central European countries and the countries of the Former Soviet Union from the socialist economic system to the capitalist one is studied. A recently developed microeconomic model for the personal income distribution and its evolution and a simple functional relationship between the rate of the per capita GDP growth and the attained level of the per capita GDP are used to describe the transition process. The developed transition model contains only three defining parameters and describes the process of real GDP per capita evolution during the last 15 years. It is found that the transition process finished in the Central European countries several years ago and their economic evolution is defined by pure capitalist rules. In the long run, this means that the future of these countries has to follow the same path, i.e. dependence on the per capita GDP growth rate of the per capita GDP itself, as the developed countries have had in the past. If the best GDP evolution scenario occurs for the studied countries, they will be able to maintain the absolute lag in per capita GDP relative to most developed countries including the USA. But they will never catch the advanced countries if they follow the same rules of development. In Russia and some countries of the Former Soviet Union the transition process is still far from complete.

q-fin.GN↗
arXiv2008

The driving force of labor productivity

Labor productivity in developed countries is analyzed and modeled. Modeling is based on our previous finding that the rate of labor force participation is a unique function of GDP per capita. Therefore, labor productivity is fully determined by the rate of economic growth, and thus, is a secondary economic variable. Initially, we assess a model for the U.S. and then test it using data for Japan, France, the UK, Italy, and Canada. Results obtained for these countries validate those for the U.S. The evolution of labor force productivity is predictable at least at an 11-year horizon

q-fin.GN↗
arXiv2008

GDP growth rate and population

Real GDP growth rate in developed countries is found to be a sum of two terms. The first term is the reciprocal value of the duration of the period of mean income growth with work experience, Tcr. The current value of Tcr in the USA is 40 years. The second term is inherently related to population and defined by the relative change in the number of people with a specific age (9 years in the USA), (1/2)*dN9(t) /N9(t), where N9(t) is the number of 9-year-olds at time t. The Tcr grows as the square root of real GDP per capita. Hence, evolution of real GDP is defined by only one parameter - the number of people of the specific age. Predictions for the USA, the UK, and France are presented and discussed. A similar relationship is derived for real GDP per capita. Annual increment of GDP per capita is also a combination of economic trend term and the same specific age population term. The economic trend term during last 55 years is equal to $400 (2002 US dollars) divided by the attained level of real GDP per capita. Thus, the economic trend term has an asymptotic value of zero. Inversion of the measured GDP values is used to recover the corresponding change of the specific age population between 1955 and 2003. The population recovery method based on GDP potentially is of a higher accuracy than routine censuses.

q-fin.GN↗
arXiv2011

An Apology for Money

This review is about the convenience, the benefits, as well as the destructive capacities of money. It deals with various aspects of money creation, with its value, and its appropriation. All sorts of money tend to get corrupted by eventually creating too much of them. In the long run, this renders money worthless and deprives people holding it. This misuse of money creation is inevitable and should come as no surprise. Abusive money creation comes in various forms. In the present fiat money system "suspended in free thought" and sustained merely by our belief in and our conditioning to it, money is conveniently created out of "thin air" by excessive government spending and speculative credit creation. Alas, any too tight money supply could ruin an economy by inviting all sorts of unfriendly takeovers, including wars or competition. Therefore the ambivalence of money as benefactor and destroyer should be accepted as destiny.

q-fin.GN↗
arXiv2008

Market bubbles and crashes

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of the hypotheses offered to explain the market crashes that often follow asset price bubbles. Starting from historical accounts and syntheses of past bubbles and crashes, we put the problem in perspective with respect to the development of the efficient market hypothesis. We then present the models based on heterogeneous agents and the limits to arbitrage that prevent rational agents from bursting bubbles before they inflate. Then, we explore another set of explanations of why rational traders would be led to actually profit from and surf on bubbles, by anticipating the behavior of noise traders or by realizing the difficulties in synchronizing their actions. We then end by discussing a complex system approach of social imitation leading to collective market regimes like herding and the phenomenon of bifurcation (or phase transition) that rationalize what crash can occur in unstable market regimes. The key insight is that diagnosing bubbles may be feasible when taking into account the positive feedback mechanisms that give rise to transient "super-exponential" price growth, the bubbles.

q-fin.RM↗
arXiv2009

On the Financial Crisis 2008 from a Physicist's viewpoint: A Spin-Glass Interpretation

In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist's viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keynesian "deficit spending" methods, tax reductions, and finally the method "ruin and recreate" known from optimization theory. Also the de Almeida-Thouless instability line of spin-glass theory is given a financial interpretation.

cond-mat.dis-nn↗
arXiv2008

Steady coexistence of the subjects of the market representing the private and state capital

The sustainability conditions for the market participants with a different ownership model were also determined. It was revealed, that the nonlinear form of the equations describing the market behavior with the prevailing private capital, predetermines the development of such a market according to the subharmonic cascade scenario. The latter is presumably the reason of the periodically arising economic crises.

q-fin.GN↗
arXiv2008

Economic law of increase of Kolmogorov complexity. Transition from financial crisis 2008 to the zero-order phase transition (social explosion)

In Maslov (2003), a two level model of the occurrence of financial pyramid (bubbles) has been considered. We also considered the mathematical analogy of this model to Bose condensation. In the present paper, we explain why Ponzi schemes and bubbles result in a crisis in real economics. In Maslov (2005), the law of increase of entropy in financial systems, and consequently increase of Kolmogorov complexity, is formulated. If this law is broken, the financial system makes a phase transition to a different state. In Maslov (2005) the author considered a two level model of the zeroth-order phase transition which was interpreted in Maslov (2006) as an analog of social catastrophe. In the present paper we also examine this model.

q-fin.GN↗
arXiv2011

Optimal dividend distribution under Markov-regime switching

We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a deterministic function of the current state of the chain. In this setting the objective of the company is to maximize the expected cumulative discounted dividend payments until the moment of bankruptcy, which is taken to be the first time that the cash reserves (the cumulative net revenues minus cumulative dividend payments) are zero. We show that, if the drift is positive in each state, it is optimal to adopt a barrier strategy at certain positive regime-dependent levels, and provide an explicit characterization of the value function as the fixed point of a contraction. In the case that the drift is small and negative in one state, the optimal strategy takes a different form, which we explicitly identify if there are two regimes. We also provide a numerical illustration of the sensitivities of the optimal barriers and the influence of regime-switching.

q-fin.GN↗
arXiv2009

Superstatistics of Labour Productivity in Manufacturing and Nonmanufacturing Sectors

Labour productivity distribution (dispersion) is studied both theoretically and empirically. Superstatistics is presented as a natural theoretical framework for productivity. The demand index $κ$ is proposed within this framework as a new business index. Japanese productivity data covering small-to-medium to large firms from 1996 to 2006 is analyzed and the power-law for both firms and workers is established. The demand index $κ$ is evaluated in the manufacturing sector. A new discovery is reported for the nonmanufacturing (service) sector, which calls for expansion of the superstatistics framework to negative temperature range.

q-fin.GN↗