A 130-year long argument against the Solow growth model

We have already presented strong quantitative arguments against the Solow growth model, which presumes that the rate of change in real GDP per capita must approach some constant level. In developed countries, the annual increments of real GDP per capita have been rather oscillating around constant level since 1955. We use the estimates of real GDP per capita published by the Conference Board’s total economy database.  Since the late 1990s this database has been developed and maintained in conjunction with the Groningen Growth and Development Centre (University of Groningen, The Netherlands). As of the summer of 2007 the database has been transferred from the University of Groningen to The Conference Board and is maintained there. The GGDC also provides historical estimates of real GDP developed by Angus Maddison.  It is instructive to use these historical estimates in order to reject the Solow model by empirical data.  

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=G_i(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, we present the estimates of annual increments of real GDP per capita in the USA since 1870. At first glance, these data support the Solow model, i.e. annual increments increase with time. However, we know that since 1955 the increment has been oscillating around constant level of $423 (2011 US dollars) and the accuracy of GDP measurements (actually obtained by reconstruction) before 1950 can hardly be characterized as a high one.  In Figure 2, we display the estimates of annual increment since 1955 as measured by the Bureau of Economic Analysis. There is no linear time trend in the curve and thus the Solow model does not work well.  

The period between 1940 and 1955 is characterized by extremely large oscillations. This period corresponds to the Second World War and the development of the concept of Gross Domestic Product (Simon Kuznets introduced this idea in 1934). Therefore, the war and the development of measurement procedure may introduce significant structural breaks in the time series and we remove the years between 1940 and 1955 from our consideration as a mixture of an artificial step in measurements (say, the transition from mph to km/h) and the effects of noneconomic factors in economic evolution.  Figure 3 shows the period between 1871 and 1940 (70 years). Not surprisingly, there is no linear time trend and the overall length of the period when the Solow model is not applicable is now ~130 years.  

All in all, the Solow model of economic growth (and all its branches and versions) contradicts hundred and fifty years of observations.   We are going to report the evolution of real GDP per capita in other developed countries.

Figure 1. The estimates of annual increment of real GDP per capita in the USA since 1970.

Figure 2.  Annual increments since 1955 as reported by the BEA. There is practically no linear trend.  

Figure 3. The annual increment between 1871 and 1940. The mean value is $65.

Crude and steel - an unbreakable pair

We have been reporting on the trade-off between the producer price index of crude oil (domestic production) and the PPI of iron&steel since 2009. It has been always a linear and lagged link between them. Our previous update included PPI data through July 2011. Here we present an annual wrap-up.

We reported that the PPI of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months in September 2009. In order to present both indices in a comparable form, the difference between a given index, iPPI (i.e. iron&steel and crude), and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). These normalized differences represent the evolution of the rate of deviation from the PPI over years.

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period through December 2011. Even a simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by approximately two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2011.

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates just short-term deviations from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an extra benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead.

Conclusion

The link between oil and iron seems to be unbreakable. Between 2006 and 2012, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one.

Putin and crisis – lie again

Another lie from Putin is that Russia was very successful during the last crisis and has recovered to the healthy pace of growth.  And we know the name of the hero who led us though these dark years. Unfortunately for Russia, it had hardest problems between the BRICS countries. Figure 1 shows that Russia was the only country in BRICS who had a dramatic fall in real GDP per capita – the best variable describing real economic growth independent on the change in population.

The years of Putin as the Prime Minister are characterized by a deep fall in economic growth and there is nothing to be proud of.  As shown in our previous post, the pace of economic growth between 2001 and 2008 was just an extension of the push given in 1998 and not by Putin.

 

Figure 1. The evolution of real GDP per capita in BRICS.

Why Putin lies about his input to economic growth in Russia?

One of the biggest lies from Putin is that he has pulled out the Russian economy from ruins and given it a big push.  It is not true because the evolution of real GDP per capita in Russia follows the same path since 1998, i.e. the push to the economy had been given by President Yeltsin.  Figure 1 presents the measured real GDP per capita in Russia since the start of transition in 1991. We have also plotted our prediction as based on a physical model of transition from socialism to capitalism.  

The years of Putin’s presidency are characterized by inertial economic growth, which is not different from the previous years. There is no chance that Putin could make any difference. On average, the rate of real economic growth in Russia was of 4.0% per year since 1998.  According to our model, the rate should be around 5% per year for the level of GDP per capita in 1998-2007. This means that the Russian economy has been lagging behind its potential output.

Figure 1. Observed and predicted evolution of real GDP per capita in Russia.

Why income inequality is very difficult to analyze?

There are several major agencies reporting various measures of personal income. The Census Bureau, CB, measures personal incomes in household surveys (CPS ASEC) at an annual rate. This measure is called Money Income, MI, and includes various types of personal income. The CB provides these estimates to the Bureau of Labor Statistics in form of distributions over age/race/sex. 

The Bureau of Economic Analysis also carries out annual estimates of gross personal income, GPI, as based on administrative records but does not provide any dependence on age/race/sex. In that sense the BEA reports only the cumulative number and does not allow inferring any evolution of personal income distribution in time. The most important similarities and differences of the CB and BEA measures are discussed in depth in this CB document.   

The IRS also measures and reports personal incomes filed for tax purposes. Since 1996, the IRS has been publishing detailed tables of personal incomes distribution is various income bins. This is similar to the CB reports but includes capital gains as income source.  

Unfortunately, multiple purposes and multiple agencies reporting personal incomes make it difficult to follow up actual evolution of income distribution and income inequality in the US. There is no unique way to merge all data in one consistent table and to estimate the distribution of income over age/race/sex and to calculate any quantitative measure of inequality like Gini coefficient or Thile index.  We illustrate the difficulties with two plots. Figure 1 shows the portion of personal income reported by three agencies in nominal GDP. The BEA reports around 85% of GDP as personal incomes but does not include capital gains. The CB and IRS both report only 55% to 62% of GDP as personal incomes with a very large difference in sources of income.

Figure 2 shows the portion of population with income as defined by the CB and IRS. There is a dramatic difference of 30% between these agencies. In other word, the IRS does not count as personal income what approximately 30% of the total population define as money income. This might be not a big difference in total income when all personal incomes are summarized over this 30 per cent of population.

One may conclude that the way these three major agencies consider and resolve the problem of personal income and income inequality is counterproductive and confusing for any quantitative analysis.  This also means that the speculations about income inequality are mostly qualitative and thus emotional.

Figure 1. Portion of personal income in GDP.

Figure 2. Portion of people with personal income in total population.  

The heroes of inflation

As reported yesterday, the consumer price indices of many goods and services in the USA have been falling or at least not growing since 1991. But the overall price inflation as described by the headline CPI (we use not seasonally adjusted indices) has been growing. What are the heroes of inflation? Two Figures below illustrate the situation

Tobacco and tobacco products are the absolute leader – 847 points in December 2011. This is not a surprise – this price is controlled by the government. The index of hospital and related services is at 641! It is interesting that the BLS includes communication and education in one top-level category. As shown yesterday, communication is a leader of deflation and some of education services have been chasing medical services is the inflation race. The index of tuition, other school fees, and child care has been rocketing.

Among transportation indices, some go down and some grow. The index of motor vehicle insurance has been growing and not is at ~400, with the index of new and used motor vehicles showing no growth since 1991. The index of fruits and vegetables also grows too fast relative to other components of the food index. Motor fuel apparently grows with oil price and the index of primary residence rent leads the housing index.

Information technology - the leader of deflation

Yesterday I missed the absolute hero of deflation in the US – the consumer price index of information technology, hardware and software (see Figure 1). It has been falling since 1991 and now levels at 9 points relative to 226 points of the headline CPI. This is a fascinating behavior of the most important modern goods and services. Computers and information is the core of real economic growth.

Figure 1. The evolution of the headline CPI and the index of information technology, hardware and software.