Time to validate economic models: data quality analysis for the relationship between unemployment and real GDP

 The driving forces behind the change in unemployment (rate) in developed economies represent a very important and actual problem for the modern economic theory. For example, there exists an opinion that the change in unemployment may manifest tangible structural changes in the labor market. The COVID-19 pandemic is a natural non-economic (exogenous forces) experiment to test and validate all economic theories of unemployment. One can expect major changes in the overall organization of all economies (developed, emerging, etc.) when significant parts of them are suppressed or just decimated due to non-economic reasons. In this blog, we addressed the problem of structural unemployment by modeling the rate of unemployment with Okun’s law, i.e. the relationship of unemployment and real GDP growth. 

The COVID-19 pandemic is a deciding/survival opportunity for any quantitative economic theory like Okun’s law. Obviously, all descriptive economic theories never take data seriously, and these religious sects have their own apologists and believers: “In the beginning was the Word”.  In a series of future posts, we are going to revisit and validate our previous results obtained for a specific version of Okun’s law developed in a series of papers. The last overview of our empirically estimated Okun-style models for selected developed countries (the United States, France, the United Kingdom, Australia, Canada, and Spain) was published in 2011. The quantitative results suggest the absence of structural unemployment in the studied developed countries. The persistence of high unemployment is completely related to a low rate of real economic growth. 

This overview used the data between 1950 and 2009 from two principal sources – the Total Economy Database of the Conference Board and the OECD. Currently, the data on real GDP per capita and unemployment are available for the years between 2010 and 2019. We use the same data sources (Maddison Project Database instead of the TED) and compare the selected time series with similar time series from the BEA and BLS. 

In our previous work, we had to introduce (virtual) structural breaks in Okun’s law in order to improve the agreement between the change in the unemployment rate and real GDP per capita. As we described in several posts in December 2020, such breaks likely manifest artificial changes in definitions of unemployment and real GDP rather than actual shifts in the economic behavior of the variables in Okun’s law. The crucial importance of data quality and consistency for quantitative analysis makes is mandatory to check all time series of unemployment, employment, labor force, and real GDP per capita for definitional breaks and also to compare similar time series from different sources. Any deviation between similar time series from different sources should be considered as an estimate of measurement accuracy and resolution.  

To begin with, we compare the CPI and GDP deflator (dGDP) in the USA since 1929. The deviation between these two price inflation estimates as discussed in details (post2011, post2020) and here we would like to highlight the change in coefficients needed to match the CPI and dGDP curves. Also, we include the Personal Consumer Expenditure (PCE) index in the discussion. The PCE is a major component of the Gross Domestic Product. Figure 1 presents all three indices in panel a), where the corresponding time series are normalized to their respective values in 1929, i.e. 1929 is the reference year. The (total price increase) CPI curve starts to deviate from the PCE and dGDP curves since the late 1970s.  The PCE and dGDP curves are very close in their cumulative representation. Panel b) in Figure 1, depicts the cumulative inflation, i.e. the sum of annual inflation rates, for the three indices. This representation is more sensitive to the differences in the indices and one can observe slight deviations between the PCE and dGDP, as well as the discrepancy between the PCE and dGDP in the late 1940s.

 a) 

b)

Figure 1. a) The price increase as described by the CPI, PCE, and GDP deflator in the USA since 1929. All curves are reduced to their respective levels in 1929. Data are borrowed from the BEA and BLS. The CPI price increase becomes higher than the PCE and GDP price growth since 1979. b): The cumulative inflation (i.e. the sum on annual inflation readings in percentage points) according to price indices: CPI, PCE, and GDP deflator. Deviations between the three curves are better seen in this representation.

 

Figure 2 depicts the differences between the annual inflation estimates and the cumulative inflation curves for all three pairs of the studied indices. Panel a) shows the CPI and dGDP differences. The difference between the cumulative inflation curves reveals the deviation between these two approaches to price inflation.  Before 1978, the difference between the CPI and dGDP curves was hovering in the range between -5 and +5. It looks like that the CPI was the basis of the GDP deflator. The period between 1981 and 2001 could be well approximated by a linear function. The years between 1978 and 1980 are like a spike or a correction distributed over 3 years. As we know, there was a comprehensive NIPA (national income and product accounts) revision around 1980 and the effect of this revision was distributed over years. It is not excluded that the comprehensive NIPA revisions may include new elements making the real GDP time series incompatible in time. 

Since we were limited to 2009 in our previous study in 2011, the segment between 2010 and 2019 is of the largest interest for the model validation. It is important to stress that there was a comprehensive NIPA revision in 2010. For Okun’s law, these revisions mean the change in the coefficients of linear regression between the GDP per capita and the rate of unemployment, i.e. virtual breaks in the dependence one can confuse with structural breaks in economic behavior. One can also pretend that the years between 2001 revision and 2010 revision to the GDP definition are characterized by a slightly lower slope of the different line than the years between 1982 and 2000. Potentially, there should be a break in 2001, but it might be too small to affect statistical estimates of our model. 

Panel b) in Figure 2 presents the same curves for the CPI-PCE pair. The PCE is close to the dGDP and the general features of the difference between cumulative inflation curves are similar to those in panel a). In panel c), the differences for the dGDP-PCE pair are presented. One can see that the dGDP and PCE indexes are slightly different. Interestingly, the level of variation in the differences between the CPI and PCE cumulative curves is higher before 1990 than after 1990. This observation is likely related to the improvement in the definition. 

a) 

b)

c)

Figure 2. a) The difference of the annual and cumulative inflation estimates for the CPI and  GDP deflator in the USA since 1929. b): The difference of the annual and cumulative inflation estimates for the CPI and the PCE in the USA since 1929.

 Figure 3 demonstrates that the PCE gives from 59% to 68% of the real GDP. Panel c) in Figure 3 is likely the most important for the success of the current study - it shows the change in various real GDP components in 2020. The quarter-to-quarter change rate in real GDP in the second quarter of 2020 was -36% and +30% in the third quarter.  The PCE dropped by 38.0% in the second quarter and increase by 36% in the third. 

According to our version of Okun’s law, the fall in real GDP per capita results in an increase in the rate of unemployment. The linear regression coefficient for the period before 2010 was -0.465 and the constant term was 0.9. When applied to the fall in the real GDP per capita these coefficients would give 21% unemployment rate in the second quarter. (Here we have to use the real GDPpc instead of real GDP.) The observed rate was 13.3%. The discrepancy is probably due to the break in the regression coefficients in 2010. To match the unemployment rate observed in the second quarter of 2020, the model needs the regression coefficient has to be ~0.25. The years between 2010 and 2019 have to be used to estimate the regression coefficient after the 2010 break. The recovery in the third quarter is also an important observation for the model validation. 

a) 

b)

c)

Figure 3. a) Components of the GDP. Personal Consumer Expenditures (PCE) varies between 59% and 68%. b) Contributions to Percent Change in Real Gross Domestic Product. c) The quarterly rate of change in real GDP components. 

In Figure 4, the GDP deflator is split into its major components and the total price change (panel a) and inflation rates (panel b) are presented. In panel c) we show the quarterly (y/y) estimates of the price inflation rates.  In 2020, only exports and imports demonstrate a negative inflation rate. The dGDP and PCE inflation rates are positive (0.6%). We are going to use the dGDP and PCE price inflation estimates in the extended model linking inflation, unemployment, and labor force. The accuracy of inflation estimates is crucial for this model.

a)

b) 

c)

Figure 4. a) The evolution of the GDP price deflator and its components since 1929. The GDP deflator is very close to the PCE, as the largest input to the GDP. b) Price inflation of the components in panel a). The largest inflation is related to Imports. c) Quarterly (y/y) inflation estimates for the GDP major components. Imports and exports demonstrate the largest fall in 2020. 

Finally, the real GDP per capita estimates may differ between the major providers of economic data. Figure 5 presents four different real GDP per capita curves for the USA: the Maddison Project Database, Bureau of Economic Analysis, and two curves from the OECD. Because of varying reference years and corresponding reference real GDPpc levels, the curves are similar is shape but have different levels. In the lower panel of Figure 5, the change rates (y/y) are presented and the difference between them is most prominent after 2010. The period between 2010 and 2020 is characterized by the highest uncertainty in GDP per capita. 

Figure 6 depicts the ratio of the MPD GDP per capita and three other time series, all 4 series are first normalized to their respective levels in 1970 and the ratios are calculated. As a result, all ratios start from 1 and one can see the discrepancy of the real GDP per capita estimates. For example, the MPD/BEA curve drops to 0.98 in 2015, and the other two ratios fall even deeper to 0.975. In standard statistical analysis, the results may differ, especially after 2010. Figure 7 illustrates the change in the real GDPpc estimates published by the same agency - OECD. One cannot exclude the possibility that the current estimates of any economic parameters are subject to revisions in the future, and these revisions may change statistical estimates for all economic relationships.  

Figure 5. Upper panel: Four real GDP per capita curves reported by different economic agencies. Lower panel: the reported change rates are slightly different between the agencies. 

Figure 6. The ratio of the MPD GDP per capita and three other time series.

Figure 7. The change in the real GDPpc estimates published by the OECD: OECD_ARCH – archived time series, OECD-2019 the most recent revision.

USA is losing the Malacca strait

On December 19, I published a post discussing the major global powers and the near-future competition between the USA and the implicit China-Russia alliance. I have mentioned the competition for the most important and very narrow straits and channels - Malacca, Panama, and Suez. On December 22, Guardian published an article on the more aggressive protection of the Malacca strait (called the South China Sea in the article) by the US Navy. Psychologically, it is obvious that aggressive behavior (e.g. barking) is a feature of weakness and fear. Stronger dogs bite first and then bark. It seems that the US is losing the strait of Malacca. 

Italy and France have to leave the EU because of negative effects on their real economic growth

 Brexit forces us to think about the future of the EU. We have presented a series of posts analyzing economic growth in selected countries using one invariant - constant annual increment in the real GDP per capita. This invariant defines the inertial part of real economic growth as observed in all large developed economies since the 1950s (no accurate data before).  Statistical analysis demonstrates that this invariant is actually a constant for a given country but varies between the countries. Therefore, it might be used to evaluate the relative performance of a given country.

Figure 1 compares several EU countries and splits the period from 1960 to 2018 into three sub-periods: 1960-1979, 1980-1999, and 2000-2018. Statistically, variations in the annual increment in the GDPpc between these periods are important for the estimates of the linear regression, i.e. the long-term behavior. For example, France and Italy demonstrate a significant decrease in the average increment from around $600 in the first period to $330 in France and $160 in Italy between 2000 and 2018. We have formulated this decay in terms of the gradual loss of economic competitiveness (efficiency) compared to Germany within the EU. This situation is likely fixed and neither Italy nor France is able to get back to the pre-EU level.  The case of the UK, which is also demonstrating lower performance than Germany and the Netherlands, gives a reasonable solution – to leave the EU and fight for the efficiency out of the EU bureaucratic framework which they actually do not control. Portugal and Spain should probably join such a move.  If the EU is a multi-speed union then Italy and Portugal are driving in first gear.

Figure 1 Real GDP per capita (2011 prices) in selected EU countries. Data are obtained from the Maddison Project Database.

Russia and China successfully fight for own piece of the global economic profit. This fight may come to a hot stage

 In our previous posts, we formulated and illustrated the idea that the countries with larger annual increment of the real GDP per capita, GDPpc, are also characterized by the CPI growing faster than the GDP deflator. The most striking examples of such dependence are the USA and Japan. In support of these observations, the most unsuccessful countries with low annual GDPpc increment are characterized by faster growth in the GDP deflator, e.g. Italy.

In this post, we analyze Russia and China within the same framework. Figure 1 compares both countries with Germany for the period between 1995 and 2018. The OECD provides dGDP data for this period and Russia started an independent economic history in 1991. In addition, the drop in real GDP between 1991 and 1998 in Russia was related to the transition from socialism to capitalism. The curves in Figure 1 demonstrate that all three countries were successful in real economic growth since 1995 and can be considered as having “strength” needed to participate in the division of global profit. Obviously, there are several countries fighting for the global/regional economic dominance and the highest benefits in non-equivalent exchange of goods and services, which is called robbery in normal life. Just a few countries have the potential to continue with (nuclear) armed brigandage. In the world of shrinking marginal profit, these countries will likely be the winners in the future Darwinian competition.  

Figure 1. Annual increment of the real GDP per capita in Germany, Russia, and China between 1995 and 2018. The average increments are presented. All three countries belong to the club of successful economies since 1995. 

There is an important signature of a successful economic player – CPI curve above the dGDP one. Figures 2 and 3 present these curves for China and Russia.  Within the limited period since 1993, China has a segment with the dGDP above the CPI curve, but since 2004 the situation is the opposite and the CPI is growing faster. For Russia, the CPI and dGDP were very close before 2004, and then the same pattern as in China and other successful economies is observed. 

Therefore, China and Russia are two countries that definitely joined the club of economies with large enough “strength” to participate in the process of division of global economic profit. The club extension is not welcome by the old club members and we currently observe the fight for dominance. Potentially, it may go to a hot war stage, and nowadays is the best time to check that “gunpowder is dry”. Marx said - “ …100 percent will make it ready to trample on all human laws; 300 percent, and there is not a crime at which it will scruple, nor a risk it will not run, even to the chance of its owner being hanged.”  

Figure 2. CPI and dGDP price growth in China since 1993 (OECD data available)

Figure 3. CPI and dGDP price growth in Russia since 1995 (OECD data available)

 

“ No division can be effected otherwise than in “proportion to strength”, and strength changes with the course of economic development”: Germany

 In this post, we present significant breaks in the linear dependence between the CPI and dGDP (i.e. between two measured time series) in Germany as related to new definitions of inflation. The case of Germany, however, has a very specific meaning – this country is the economic leader of the European Union. In the Annex below, we present an independent opinion on the behavior of economic leaders, including Germany, formulated 105 years ago.

Figure 1 presents 4 panels illustrating the process of the definitional break findings as applied to Germany. Panel a) depicts two inflation curves – for CPI and GDP deflator. One can see that the CPI curve is slightly above the dGDP curve from the mid-1990s. Panel b) presents similar curves, but for cumulative inflation as the running sum of inflation readings. The slightly higher CPI inflation is now producing a significant deviation of the cumulative curves. Pane c) shows the difference between the curves and panel a) and panel b). The difference between the two cumulative curves reveals a break followed by deviation as a linear function of time. Using the slope of the difference, one can calculate the coefficient of the linear correction (1.5) needed to fit the CPI and dGDP curves. Panel d) shows the original CPI curve and the corrected dGDP curve, i.e. the dGDP curve multiplied by a factor of 1.5 since 1997. There is still some deviation between the curves after 2013. It might be a manifestation of a new break. We are going to follow the new deviation and will report on it in the future. The presence of definitional breaks is similar to those observed in different countries. However, timing and circumstances related to the ECB creation win the headquarters in Frankfurt make the case of Germany suspicious. We wrote about the potential benefits of German leadership in previous posts. Here, we are going to support the case.

Figure 2 depicts curves of the real GDP per capita growth in several European countries between 1960 and 1996.  In order to provide a consistent view of the total growth, we normalize all curves to their respective (GDPpc) levels in 1960. Two champions are Spain (ESP) and Portugal (PRT), and this is natural because of the low GDPpc level in 1960 in both countries.  Germany (red line) is close to the bottom together with the Kingdom of the Netherlands (NLD) and the United Kingdom. Figure 3 displays similar curves but for the period between 1997 and 2018. Since 1997, Germany (DEU) is by far the leader of the race. Cumulative GDPpc growth is 1.51 compared to the second place occupied by NLD - 1.42. It is important that the agreement of the ECB was signed in 1997. Instructively, Italy and France are much close to the bottom of the list. The UK is in the middle. As we mentioned in previous posts, the higher is the real GDPpc growth rate the lower is dGDP relative to CPI. Germany, Netherlands, France, and Italy are the best examples.

In Figure 4, I am trying to understand the influence of EU subventions on East European countries. The overall real GDP growth since 1997 is spectacular in Poland, Hungary, and Bulgaria. Their corresponding curves are much above Germany and The Netherlands. One might suggest that the EU financial and other assistance has a positive impact on real economic growth in these countries. However, Serbia demonstrates almost the same growth rate since 1997. It might be an indication that the EU help is not so much effective.

 a)

b)

 c)

d)

Figure 1. See text for details

 

 

Figure 2. Evolution of GDP per capita normalized to 1960 in selected EU countries between 1960 and 1996.

Figure 3. Evolution of GDP per capita normalized to 1997 in selected EU countries between 1996 and 2018.

 

Figure 4. Evolution of GDP per capita normalized to 1997 in selected EU countries between 1996 and 2018.

 Annex

“A United States of Europe under capitalism is tantamount to an agreement on the partition of colonies. Under capitalism, however, no other basis and no other principle of division are possible except force. A multi-millionaire cannot share the “national income” of a capitalist country with anyone otherwise than “in proportion to the capital invested” (with a bonus thrown in, so that the biggest capital may receive more than its share). Capitalism is private ownership of the means of production, and anarchy in production. To advocate a “just” division of income on such a basis is sheer Proudhonism, stupid philistinism. No division can be effected otherwise than in “proportion to strength”, and strength changes with the course of economic development. Following 1871, the rate of Germany’s accession of strength was three or four times as rapid as that of Britain and France, and of Japan about ten times as rapid as Russia’s. There is and there can be no other way of testing the real might of a capitalist state than by war. War does not contradict the fundamentals of private property —on the contrary, it is a direct and inevitable outcome of those fundamentals. Under capitalism the smooth economic growth of individual enterprises or individual states is impossible. Under capitalism, there are no other means of restoring the periodically disturbed equilibrium than crises in industry and wars in politics.” Lenin V.I., 1915, “On the Slogan for a United States of Europe”.