Growth rate of the GDP per capita revisited. 5. What is real GDP and real GDP per capita? Nobody knows!

We have presented dozens of real GDP per capita graphs using the Maddison Project Database in the previous posts. We fully trust the professionalism of the MPD team and their GDPpc estimates. They use raw data, however, which might be biased overall and specifically for our study. First of all, when we say "per capita" or "per head" what do we mean specifically - the total population, working-age population, or the population in the labor force? The main question is: Who is driving the real economy? When modeling real economic growth in mainstream economics, the GDP per capita is using the working-age population (not the values published in the MPD). There are several reasons for this approach. Two of them are: 1) children do not work and do not produce goods and services; 2) Children do not have income; at least their incomes are not determined in the annual Current Population Surveys and decennial censuses. 

The importance of the difference between the total and working-age population is illustrated in Figure 1 with the USA and Mexico as examples. Mexico had a larger portion of children between 1960 and 1980 and then the USA took the lead. It is not excluded that the growth in the portion of Hispanic and Latino Americans due to migration to the USA assisted the elevated birth rate. The correction for the difference between the total and working-age population is an interesting option to be exercised in any case. One could expect that the overall data consistency has to be improved. On the other hand, there are countries with official and non-official migration. The share of such people in the workforce may vary from country to country. For example, Qatar uses more than 2 million foreign workers.     

Figure 1. The evolution of the working-age and total population ratio in the USA and Mexico since 1960. 

The "per capita" definition is crucial for our study, but the real GDP definition is also important. One can be surprised that the real GDP cannot be measured as such. Instead, nominal GDP and GDP deflator are used to estimate the real GDP. The GDP deflator is a tricky variable, which includes direct measurements of a real price change and an estimate of the price change for new goods and services as well as the goods and services changing their own quality and capability (e.g. computers). Moreover, there are new items included in the nominal GDP estimates (e.g. imputed rent). All these aspects in the estimation of real (and nominal) GDP are well described and reported by national agencies (e.g., BEA). As a result, one can often see a striking comment that the GDP estimates are not compatible over time. 

As one can see, this is an extremely difficult problem to reconstruct the real GDP time series, and then harmonize them between various countries. We are not going to solve such a difficult problem and leave this work to the Maddison Project team. There is one important problem, however, which we are able to address in this study - the change in calculations of the CPI and GDP deflator (dGPD).  We have reported this problem in 2016. Figure 2 presents two curves in the USA - dGDP and CPI time series normalized to their values in 1929, i.e. these curves present the cumulative price growth since 1929. In many economic minds, the CPI and dGDP are almost equivalent. The data show a quite different picture - the curves start to diverge in 1979 (a new definition of GDP was introduced). Since the dGDP and CPI was the same before 1979 and then started to diverge due to the definition change one has to apply the same definition of inflation to the whole series. Otherwise, the real GDP in the USA is overestimated since 1979 since the dGDP is underestimated relative to the CPI used before 1979. For the GDPpc estimates in this study, the dramatic change in the definition of inflation might change the long term trends and the model of inertial growth. 

Figure 2. The CPI and dGDP cumulative inflation in the USA since 1929. Two curves start to diverge in 1979. 

The effect of the inflation change in the USA is illustrated in Figure 3. We have corrected the portion of the GDPpc after 1979 to the ratio of the dGDP and CPI. This effectively allows using the CPI time series as inflation in the real GDP estimates. One can also use the same dGDP definition before 1979, as shown in Figure 4,. This is a simple procedure since the ratio of CPI and dGDP is 1.2 since 1979. We take the same ratio and extend the corrected dGDP time series into the past.   

In Figure 2, one can see that the deviation from the linear regression line observed after 1979 completely disappear. In other words, the GDP per capita in the USA is biased in favor of better real economic growth, which is actually just a statistical trick. Unfortunately, this nasty trick is used by other developed countries. More work on the way to true GDP growth estimates is needed.

 

Figure 3. Real GDP per capita in the USA corrected for the difference between the CPI and dGDP in Figure 2.

 

Figure 4. The extension of the dGDP definition into the past. The dGDP is taken as CPI-20% before 1979.

О судействе в российском футболе

После введения новых правил в российском футболе наблюдается четыре разных трактовки. Практикующие судьи, видимо, не понимают ни духа, ни буквы новых правил и выносят решения, даже после просмотра ВАР, которые потом признаются неверными ЭСК. Противоречия между решениями судей и ЭСК указывает или на систематические ошибки в обучении судей правильной трактовке новых правил, или в отсутствии в ЭСК активного полевого опыта работы, который только и позволяет по-настоящему судить игру на высшем уровне. Третья трактовка связана с действующими игроками. Большинство из них не понимает тонкостей новых правил, что вызывает споры с судьями и нервные срывы от бессилья перед судебными ошибками, которые возникают даже после просмотра ВАР. Цена каждого неправильного решения, принятого с использованием ВАР, многократно выше, чем цена большего числа грубых ошибок в эпоху до ВАР.  раньше судьи могли следовать духу справедливости в футболе. Теперь использование ВАР делает это практически невозможным. Четвертая трактовка футбольных правил выражается в непонимании принимаемых всеми участниками футбольного процесса решений со стороны зрителей. Противоречия в понимании правил футбола между судьями и ЭСК вызывает сложную смесь чувств и эмоций у болельщиков. Случай с матчем "Спартак"-"Сочи", после которого большинство болельщиков "Спартака" поддержали желание владельца команды сняться с турнира было бы невозможно, если судьи не использовали бы ВАР. Ошибки судей это часть футбола и, если футбол быстрый и агрессивный, то трудно уловить в реальном времени некоторые нарушения. Все это понимали и принимали. Теперь ВАР поставил судей и болельщиков в практически одинаковые условия. И вдруг оказалось, что понимание футбола у зрителей и судей очень разной, а ЭСК находит совсем другую интерпретацию события. В целом, в российском футбольном судействе по новым правилам царит хаос. Конечно, "рука бога" в большом футболе теперь невозможна. Однако смотреть его становится все тяжелее, так как "боление" за футбол превращается в непрерывную попытку и пытку понять судейские решения и нерешения. Видимо, на пути к совершенно справедливой игре в футбол он станет отвратительным зрелищем.

Growth rate of the GDP per capita revisited. 5. Cross country comparison

 We have presented a large number of the real GDPpc country histories between 1960 and 2018 as reported in the Maddison Project Database. The range of initial conditions, GDPpc(1960), and the total growth, GDPpc(2018)/GDPpc(1960),  creates an impression of chaotic behavior and may compromise our understanding of actual growth processes in various countries. In this section, we present a general framework allowing consistent analysis of the MPD data and assessment of relative economic performance for a given country. The principal GDPpc inertial growth equation is the following:  

 g(t) = dlnG(t)/dt  = A/G(t)

Instead of integrating this equation between 1960 and 2018 and finding the total growth GDPpc(1960)/GDPpc(2018), we directly calculate this ratio. Figure 1 shows several theoretical curves of total GDPpc growth in 58 years, GDPpc(58)/GDPpc(0), for four different annual GDPpc increments, A. For example, the curve with A=$300 gives the total growth by a factor of 2, when the initial GDPpc(0)=$17200, and the total growth of 4 for GDPpc(0) =$5800. Because of the GDPpc level difference in 1960, the total growth, and thus the annual GDPpc growth, of rich countries is lower than in poor countries with the same annual GDPpc increment. A good example of the denominator effect of the growth rate is given in 2020. A 50% drop of real GDP followed by 50% growth in the next period does not return the economy to the initial level. Actually, simple calculations show that the new level is only 75% of the initial one because the 50% growth from the 50% level is 0.5+0.5/2 = 0.75. Hence, one should not pay attention to only the relative growth rate, but to compare the GDPpc level and the (average) annual increment.

 

Figure 1. Total growth as a function of initial GDPpc value, GDPpc(0), and the annual increment, A.

 In Figure 2, we merged the theoretical GDPpc growth curves for the 58-year period between 1960 and 2018 presented in Figure 1, and the estimates of the total GDPpc growth for the same period obtained from the MPD. Now the interpretation of economic performance is straightforward. In 1960, the USA had the largest GDPpc=$18057 (actually, the MPD gives $52299 in 1960 for Qatar, but we ignore this value) and the total GDPpc growth by a factor of 3.04. The latter value seems to be low compared to fast-growing economies like China and Malaysia (MYS).  However, China and Malaysia grow from a very low level and their GDPpc annual increment is around $300 when the USA has ~$600 per year increase. Therefore,  China and Malaysia grew at a slower rate when the USA, i.e. in the long run they never catch the GDPpc level in the USA. The annual increment in China and many other countries had a break to higher values in the 1990s, but they are still below $600 per year. 

Figure 2. Theoretical curves of the total GDPpc growth between 1960 and 2018, and the estimates for various countries. Country tags are borrowed from the MPD and correspond to international abbreviations.   

Many West European countries, Japan, Canada, and Australia are all close but below the A=$600 line. Their performance since 1960 was overall stationary with a few recession falls. Norway has lower total growth than Ireland, but taking into account the initial GDPpc, one can say that Norway had faster economic growth in terms of annual increment. The UK, France, and Italy were rather the relative losers among the most developed countries, likely because of the non-equivalent exchange with Germany (DEU) within the EU. New Zealand performed not well since 1960 despite a very high start level in 1960. Switzerland outperformed all developed economies except exotic cases of Ireland and Norway. At this point, it is important for the underperforming developed economies to understand that their lag behind the best performers will be increasing in the future. The causes of different growth rates observed within the EU might be internal and external. 

Latin American countries actually reside between A=$100 and A=$300. These are poor performers, except Puerto Rico, which is an obvious outlier. Chile is the closest to A=$300 line. Therefore, the only difference between Latin American countries shown in Figure 2 is the start GDPpc level.    

East European countries are close to A=$300 line, but the break in the 1990s demonstrates that their growth rate can be higher in the long run. Russia has all chances to move close to A=$600 line in the future judging by the GDPpc history since 2000. Despite the incredible growth period, China is still in the club of not excellent performers with good chances to move to A=$500 level, i.e. join the bunch of developed courtiers. India is just in the beginning of growth history and the linear growth in the annual GDPpc increment opens bright perspectives.

Growth rate of the GDP per capita revisited. 4. East European countries

In this section, we present 4 East European countries: Bulgaria, Hungary, Poland, and Romania. Their behavior and overall performance is similar to those demonstrated by Russia with a break in the GDPpc growth in the 1990s. Romania is likely an outlier with a total GDPpc increase by a factor of 12, which is an example of outstanding performance. It is likely that the start GDPpc value of $1605 is heavily underestimated considering that neighboring Bulgaria has $4642 at the same time. There are East European countries with data available from later dates. They are not included in this study.   

There are other regions not specifically covered in this study. In Africa, we selected only Morocco and South Africa for further analysis. Malaysia is an intensively growing economy and it is used in addition to China, Hong Kong, Singapore, and Taiwan. The main goal of this study is to demonstrate that the growth in GDP per capita is a linear and stationary process. When the stationary regime is violated, only the countries with exceptional conditions (most often oil and gas) can grow faster than the biggest economies in this world like the USA, Germany, and the UK. The non-stationary regime in other countries results in severe underperformance as observed in Africa, Latin America, and Asia. The highest responsibility of the state elites in such countries is to create conditions for stationary evolution and to avoid non-equivalent exchange with the most developed countries. Both tasks are connected since the biggest powers intentionally create non-stationary to push through the non-equivalent exchange. 

 

Figure 1. Bulgaria. The upper panel: the annual GDPpc increment between 1961 and 2018 with the average value for the studied period of $238 (2011 prices). The middle panel: the same annual increment as a function of GDPpc level. The lower panel: the relative growth rate of the GDPpc as a function of the GDPpc.

 

Figure 2. Same as in Figure 1 for Hungary.

 

Figure 3. Same as in Figure 1 for Poland.

 

Figure 4. Same as in Figure 1 for Romania.

Growth rate of the GDP per capita revisited. 4. BRICS

 BRICS (Brasilia, Russia, India, China, and South Africa) was organized in 2006 by four economies from the top 10. South Africa joined in 2009. The idea behind the club was mutual assistance to provide the fastest economic growth.  In this post, we look into the real GDP per capita as the principal indicator of economic growth. In our previous post,  we presented Brasilia in the context of Latin America and reported mostly inertial (constant increment of $183 per year)  since 1960. No dramatic fall or surge over the studied period was observed, except for the drop of $1953 in 2016. Participation in BRICS did not give Brasilia any significant economic push with the average annual increment of $210 since 2006 which is compatible with the long-term mean increment $183.  

In this section, we present the other 4 BRICS members. In Figure 1, the evolution of the annual GDPpc increment is presented as a function of time (the upper panel) and GDPpc (middle panel). The annual GDPpc increment between 1960 and 2018 is $330 (2011 prices). This value is lower than in developed countries (New Zealand has $349 for the same period). The period after 1999 was the most successful in Russian history since 1960 and the average annual growth was $806 between 1999 and 2018 and $648 between 2006 and 2018. This level is the same as observed in developed countries. The fall in 2015 and 2016 was just a short term and the Russian economy returned to a healthy growth rate (the lower panel of Figure 1). Two periods in Russian history since 1960 are related to the change in political and economic concept in 1991. This change, despite the deep fall in the mid-1990s, seems to be positive in the long run and we expect that the future development will follow the inertial growth scenario with constant annual increment in the range from $500 to $700. This is possible in cooperation with other BRICS countries also experiencing extremely fast growth in the annual increment of GDPpc since the 1990s. 

Figure 2 presents the case of India. This is a poor country with a long history of non-equivalent exchange with developed countries (e.g. the UK). On average, the GDP per capita has been increasing by $97 per year since 1960. Since 2000, the annual increment increased to $357 per year, however, in the longest stretch of intensive economic growth. We also expect Indian to reach a stationary growth regime with annual GDPpc growth above $500. This will move this country to the second position in the real GDP level in 10 to 15 years. 

The first position in the list of the biggest economies (real GDP PPP) belongs to China. The evolution of real GDPpc since 1960 presented in Figure 3. The average increment is $208 per year. The years after 2000, were extremely successful for the Chinese economy with an average increment of $498 since 2006, and $454 since 2000. These values are already in the club of developed countries and we will not be surprised to find the Chinese economy in the list of best performers among the biggest developed countries. It is worth noting here, that the relative growth rate is the ratio of the increment and the GDPpc level. The latter is much lower for China and the rate of growth has to be much higher than in developed countries with the same GDPpc increment. 

Figure 4 presents South Africa. This is the smallest BRICS economy, but it also reveals fast growth since the mid-1990s. The average increment since 1960 is $126 and $255 since 2006. There is a period of underperformance since 2014, which stopped the linear growth segment observed since 2000.  

The BRICS countries are all different in many ways – from language to history. They decided to cooperate with the BRICS club because of different reasons except one – promote the fastest economic growth using all possible methods of cooperation not affecting their own interest (i.e. they avoid the non-equivalent exchange). It is hard to say which part of the observed economic growth belongs to this cooperation, but the club is still working. We will follow the news about BRICS cooperation and the rate of economic growth.

 

Figure 1. Russia. The upper panel: the annual GDPpc increment between 1961 and 2018 with the average value for the studied period of $330 (2011 prices). The middle panel: the same annual increment as a function of GDPpc level. The lower panel: the relative growth rate of the GDPpc as a function of the GDPpc.  

Figure 2. Same as in Figure 1 for India.

 

Figure 3. Same as in Figure 1 for China. 

Figure 4. Same as in Figure 1 for South Africa.