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# Ivan Kitov's  Instablog

Ivan Kitov
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I am a Doctor of Physics and Mathematics, Lead Researcher at the Institute for the Geospheres' Dynamics, Russian Academy of Sciences. Founding member of the Society for the Study of Economic Inequality Published three monographs in economics and finances: Deterministic mechanics of pricing... More
My company:
Stock Market Science
My blog:
Economics as Classical Mechanics
My book:
Deterministic mechanics of pricing
• ##### Another 1000 Arguments Against The Solow Growth Model
In May 2011, we presented 1000 arguments against the Solow growth model, which states that the rate of change in real GDP per capita must approach some constant level. Here we present new arguments against the Solow model as based on the historical GDP data developed by Angus Maddison at the Groningen Growth and Development Centre. In two previous posts we presented the cases of USA and Austria. We showed that the annual increment of GDP per capita is constant from 1871 to 2010 with an artificial structural break between 1940 and 1950. In other words, the slope of linear trend in real GDP per capita and thus the mean annual increment jumped by a factor of 10 between 1940 and 1950. Here we summarize numerous observations for the developed counties presented in the May's post and validate our model.

Under our empirical framework [1,2,3], real GDP per capita in developed countries grows as a linear function of time, we call it inertial growth, when population pyramid does not change much in the long run:

G(t) = At + C (1)

Relationship (1) defines the linear trajectory of the GDP per capita, where C=Gi(t0)=G(t0) and t0 is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. The relative rate of growth along the inertial linear growth trend, g(t), is the reciprocal function of G:

g(t) = A/G(t)(2)

Relationship (2) implies that the rate of GDP growth will be asymptotically approaching zero, but the annual increment A will always be constant. This is different from the Solow model where the rate of growth is a positive (nonzero) value. Moreover, the absolute rate of GDP growth is constant and is equal to A [\$/y]. This constant annual increment thus defines the constant "speed" of economic growth in a one-to-one analogy with Newton's first law. Hence, one can consider the property of constant speed of real economic growth as "inertia of economic growth" or simply "inertia".

In Figure 1 (borrowed from the post in May 2011), we present annual increments of real GDP per capita (borrowed from the Conference Board Total Economic database, TEDI) in the biggest developed economies as a function of real GDP per capita in sense of equation (1). These plots validate our empirical finding and reject the Solow model. Overall, there were 19 countries analyzed in the study and no one has any distinct positive trend over the past 60 years, i.e. between 1950 and 2010. So, we had 1000 years supporting the hypothesis of a constant (but country dependent) annual increment.

Figure 2 extends all time series back to 1871 by using the Maddison's historical estimates of real GDP and population in developed courtiers. All estimates are in 1990 International Geary-Khamis dollars which allow a cross-country comparison. These dollars are different from 2010 EKS dollars in Figure 1. Thus the mean values may not coincide between these Figures. We have also plotted the estimates of real GDP per capita from the Total Economic Database (TEDI) now available through 2011. Essentially, this is the same data set as in the historical database and all curves after 1950 have to coincide, but Japan and Spain show significant discrepancy during the most recent period. For Japan, the TEDI and historical curve started to deviate in 1993.

Overall the time series before 1940 and after 1950 are both well approximated by linear time trends with slopes suddenly increasing by approximately a factor of 10. Not considering the reasons for this break in the tie series we just conclude that the annual increment is constant before 1940 and after 1950, as stated by our model of real GDP growth. This validates our model and rejects the possibility for the Solow model to be right.

There are important implications of the constant annual increment for economic policy in developed countries. Economists and economic authorities (like FRB and CBO) are waiting for a significant increase in the rate of real economic growth to close so called output gap, i.e. the difference between the measured level of real GDP and that expected form exponential extrapolation of the trend observed before 2007. In reality, there is not output gap, as Figure 1 and 2 demonstrate. Only Italy and Japan are far below the linear trend in real GDP per capita and Australia is above the expected level. France is also slightly below its long term linear trend. These countries might expect a recovery to the trend in the long run, depending on the evolution of their age pyramids.

The US and UK have been returning to the trend during the recent crisis and should not wait for any elevated rate of real economic growth. The expectation of a growth rate of 3.5% per year (in terms of GDP per capita) which has been explicitly articulated by the FRB and CBO in their economic outlooks is a naïve extrapolation of exponential growth related to the exponential population growth.

Figure 1. Dependence of annual GDP increment on GDP (both real per capita) for select developed countries. Original GDP data are extended by those corrected for the ratio of total and working age population (the latter must be used in GDP per capita calculations). For both time series linear regression lines and equations are shown with corresponding slopes. For the biggest countries these slopes are very close to zero but can be positive or negative. A zero slope corresponds to constant annual increment.

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Figure 2. The evolution of real GDP per capita in developed countries between 1871 and 2011.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

Tags: economy
Feb 13 11:43 AM | Link | Comment!
• ##### Growing Rate Of Unemployment In Italy
A new estimate of unemployment rate in 2011 is now available for Italy. In December 2011, it almost touched 9.0%. Here we validate our model of unemployment as a function of the change in labour force.

We introduced the model of unemployment in Italy in 2008 with data available only for 2006. The rate of unemployment was near its bottom at the level of 6%. The model predicted a long-term growth in the rate unemployment to the level of 11% in 2013-2014.

The agreement between the measured and predicted unemployment estimates in Italy validates our concept which states that there exists a long-term equilibrium link between unemployment, ut, and the rate of change of labour force, lt=dLF/LFdt. Italy is a unique economy to validate this link because the time lag of unemployment behind lt is eleven (!) years.

The estimation method is standard - we seek for the best overall fit between observed and predicted curves by the LSQR method. All in all, the best-fit equation is as follows:

ut = 5.0lt-11 + 0.07 (1)

As mentioned above, the lead of lt is eleven years. This defines the rate of unemployment many years ahead of the current change in labour force. Figure 1 presents two versions of unemployment as defined by the U.S. Bureau of Labor Statistics (BLS) and the OECD. We describe the estimates provided by the OECD (labour force estimates also obtained from the OECD) but have to emphasise that the divergence before 1994 makes it difficult to find a unique model for both agencies.

Figure 2 presents the observed unemployment curve and that predicted using the rate of labour force change 11 years ago and equation (1). Since the estimates of labour force in Italy are very noisy we have smoothed the annual predicted curve with MA(5). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1988. The period between 2006 and 2011 was predicted almost exactly. This is the best validation of the model - it has successfully described a major turn in the evolution of unemployment near its bottom. No other macroeconomic model is capable to describe such dramatic turns many years ahead. As four years ago, we expect the peak in the rate of unemployment in 2013-2014 at the level of 11%.

The evolution of the rate of unemployment in Italy is completely defined ten year ahead. Since the linear coefficient in (1) is positive one needs to reduce the growth in labour force (see Figure 3) in order to reduce unemployment in the 2020s. For the 2010s everything is predefined already and the rate of unemployment will be high, i.e. above 9%.

For Italy, the increasing rate of unemployment reflects deceleration in real economic growth. It might be not the best time to expect any large returns from the Italian stock market.

Figure 1. The rate of unemployment in Italy as measured by the BLS and OECD.

Figure 2. Observed and predicted rate of unemployment in Italy.

Figure 3. The rate of growth in labour

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

Tags: economy
Feb 07 4:12 PM | Link | Comment!
• ##### Personal Income Distribution In The US
We are going to revisit our model for personal income distribution, PID. It was first formalized in 2003 and used income distributions through 2001. We had to convert all reports published by the Census Bureau in pdf format between 1947 and 1993 into excel tables. It took a month of hand work together with proof reading. These reports are not converted into digital format yet.

In 2006, we used new data (through 2005) and re-estimated the model. In 2010, we published a book on personal income distribution using data through 2008. It is a good time to refresh the model and evaluate its performance since 2001 with ten more years of data. All major results will be presented in this blog.

We start with presenting original data. The distribution of personal incomes since 1994 is characterized by a higher resolution - income bins are only \$2500 wide. Our model assumes that the overall income distribution depends on the age pyramid and the level of real GDP per capita. However, the evolution of PID is slow and at a twenty year horizon one actually sees a frozen PID. The frozen PID results in an almost constant Gini ratio over time, which is actually reported by the Census Bureau.

We illustrate PID in a few figures below. Figure1 presents all PID published since 1994 between \$0 and \$100,000 as they are. We have included all people without income into the bin between \$0 and \$2500. One can observe that the number of people in higher income bins increases with time as well as the number of people with incomes above \$100,000 shown in Figure 2. The portion of people with incomes above \$100,000 has been increasing by 0.3% per year since 1994. Figure 3 shows the number of people with income above \$100,000 as a function of work experience. The fastest growth is observed for the groups between 30 and 40 years of work experience, i.e. between 45 and 55 years of age.

Figure 4 depicts the population density functions, PDFs, for the years between 1994 and 2010. First, the estimates presented in Figure 1 were normalized to the total population for a given year. Then we reduced the income scale for individual years, i.e. from 1995 to 2010, by the total growth of real GDP. This allows normalizing the curves to the total income, i.e. we reduce all scales to that of 1994. Finally, we normalize the portions of populations in given bins to their widths for individual years and obtain the population density functions. Figure 4 proves that the distribution of personal incomes has not been changing over time in relative terms, i.e. a given portion of population always has a given portion of total income. From the PIDs one can always build the relevant Lorenz curves and estimate Gini ratios. For higher incomes, the distribution has to be described by the Pareto distribution. Figure 5 shows that the PDFs at higher incomes do follow a common power law with an exponent of -3.9.

Our first assessment of the income data obtained after 2001 is that they do follow up the previously obtained relationships. We expect that our model for personal income distribution should perform well.

Figure 1. Personal income distributions from 1994 to 2010.

Figure 2. Portion of people with income above \$100,000. The portion increases by 0.3% per year.

Figure 3. The number of people with income above \$100,000 as a function of work experience. The fastest growth is observed for the groups between 30 and 40 years of work experience, i.e. between 45 and 55 years of age.

Figure 4. Population density function, i.e. the number of people in a given bin normalized to the total number of people and the width of income bin, as a function of income reduced by the overall GDP growth.

Figure 5. The Pareto distribution at higher incomes.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

Tags: demographics
Feb 06 10:34 AM | Link | Comment!

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