Economics as Classical Mechanics

1/6/21

The link between unemployment and real economic growth in the UK. Brits are able to retain data quality and integrity

In 2011, we published a paper modeling the link between the annual change in employment rate and the change rate in the real GDP per capita. This paper also included modeling of a similar link for unemployment. In 2011, we used data from various sources – the OECD, BEA, BLS, and the Total Economy Database of the Conference Board. Because of the data availability, the period under consideration varied between countries and the longest time series started between 1950 and 1960. For many developed economies, however, the start year was 1970. Since the studied period was limited to 2010, we promised to revisit all published models and validate the original versions. In the beginning of 2021, we have new estimates of the involved parameters between 2010 and 2019 and re-estimate the unemployment models. In this post, we revise the model for the United Kingdom.

As in hard sciences, the standard modeling procedure is to check data quality. As we learned before, the GDP deflator (dGDP), which is a principal component of the real GDP estimation procedure, is prone to artificial breaks induced by definitional revisions. Such breaks in the GDP time series look like the structural breaks related to inherent changes in economic performance. When taken as real, the definitional breaks ruin the statistical performance of the mainstream economic models.

The UK has likely the most developed school in hard and soft sciences. Data quality is the essence of experimental sciences in support to theoretical consideration. Economics is not an exception and the quality and compatibility of measurements is generally retained. In panel a) of Figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation rates) as defined by the CPI and dGDP between 1955 and 2018. Both variables are normalized to their respective values in 1955, and thus the curves start from 1.0. One can see that the curves are close, but deviate from the very beginning. In panel b), the rates of price inflation are shown as calculated using the CPI and dGDP indices. The only large deviation between the inflation curves was in 1994 and is likely artificial (corresponding documentation may describe the reasons behind the spike, but its nature is not important for this post). This spike is pretending to be described with a dummy variable, which we did not use in the previous models.

Panel c) in Figure 1, depicts the difference between the cumulative and change rate curves in panels a) and b). The cumulative curves demonstrate approximately linear deviation since the late 1970s. Taking into account the quasi-linear deviation between the cumulative curves, we propose the following piece-wise model for the best fit between the CPI and dGDP curves:

CPI = 0.926dGDP, 1970>t≥1960

CPI = 0.974dGDP, 2018≥t≥1971, except 1994

CPI = 0.974dGDP - 0.049, t=1994 (1)

Panel d) illustrates the match between the cumulative curves, which include a dummy variable of -0.049 in 1994. The spike is removed. The model residual is presented in panel e), where the standard deviation is 0.018 for the period between 1957 and 2018. The CPI and dGDP comparison indicates that there are potential breaks in the dGDP curve in the early1970s, the late 1980s, and likely between 2009 and 2012.

Figure 1. a) The evolution of the cumulative inflation (the sum of annual inflation rates) as defined by the CPI and dGDP between 1956 and 2018. Both variables are normalized to their respective values in 1956. b) Inflation rates for the CPI and dGDP. c) The difference between the CPI and dGDP curves in panels a) and b). d) The fit between the CPI and the dGDP corrected according to relationship (1). e) The residual error of model (1).

The break years obtained from the dGDP are used as start points for the search of the best fit in our version of Okun’s law for the UK. We are using the standard LSQR procedure to estimate a new set of coefficients for the period between 1963 and 2018. The data before 1963 are not used because the rate of inflation is very close to 1%, and is difficult to model. The preliminary analysis gives the following model:

du_p = -0.63dlnG + 1.75, 1987>t≥1963

du_p = -0.42dlnG + 0.64, 2010≥t≥1988

du_p = -0.39dlnG - 0.13, t≥2011 (2)

Figure 2 illustrates the model predictive power. In the upper panel, the measured rate of unemployment in the UK between 1963 and 2018 is compared with the rate predicted by model (2) with the real GDP per capita published by the Maddison Project Database. The rate of unemployment is borrowed from the OECD. In the middle panel, the model residual errors are presented with the standard deviation of 0.91% and the mean unemployment rate of 5.99%. The lower panel depicts the linear regression of the measured and predicted time series with Rsq.=0.91. Hence, the new set of coefficients provides and an excellent match between the measured and predicted values, i.e. the model linking the change in the unemployment rate and the change in real GDP per capita. The UK is able to retain the integrity of data in longer time periods. The overall sensitivity of unemployment to real GDP per capita seems to decrease with time. This decrease is likely artificial as if one implicitly jumps from Fahrenheit to Celsius degrees and gets cooler weather.

Figure 2. Upper panel: The measured rate of unemployment in the UK between 1963 and 2018 and the rate predicted by model (2) with the real GDP per capita published by the MPD. Middle panel: The model residual, stdev=0.91% Lower panel: Linear regression of the measured and predicted time series. Rsq = 0.91.

The link between unemployment and real economic growth in Spain

In our previous post, we revisited and validated the modified Okun’s law for Austria with new GDP and unemployment data for the years between 2010 and 2019. The revised model for Austria and other countries presented so far in this blog accurately describe the new data, i.e. the original model is validated. In order to reach the best fit between the measured and predicted unemployment rates, we introduce structural breaks related to the change in real GDP definition. To illustrate the breaks in the real GDP data (i.e. nominal GDP corrected for the price change) we compare price inflation estimates as defined by the GDP deflator and CPI. The latter is considered as a reference. It is also important that the goods and services in the CPI are also included in the GDP deflator, dGDP. In the past, the CPI and dGDP were almost equivalent and the deviation between them was forced by the introduction of such economic parameters as imputed rent in the 1970s. The experiments with the GDP deflator and nominal have been the essence of definitional activity ever since. The best is an enemy of good. Artificial breaks in the GDP and other economic variables make the work of researches very difficult.

In this post, we revise the model for Spain and begin with the CPI and GDP deflator difference, which is used to reveal potential definitional breaks in the dGDP estimates. Obviously, such breaks in the dGDP create breaks in the real GDP per capita estimates, and thus, in the statistical estimates associated with our model. One has to find potential breaks and allow the model to compensate for corresponding disturbances and to provide unbiased statistical estimates of the defining parameters. There is another strong instrument in econometrics – dummy variables, which can explain the steps in many economic variables like labor force and unemployment. We do not use dummy variables in the model and achieve the best fit only with the structural breaks, i.e. the change in the coefficients of linear regression in the years of definitional revisions to the GDP deflator and nominal GDP. In that sense, our model becomes piecewise in order to match the changes in definition. It is like changing the speed from 105 km/h to 55 mph crossing the Canada/USA border, with physical speed not changing.

In the upper panel of Figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1970 and 2018 (the OECD data). Both variables are normalized to their respective values in 1970. The dGDP curve is close to the CPI before 1995 and then a significant deviation is observed. There is a low amplitude deviation between 1980 and 1990. After 1996, the deviation increases in amplitude, and the dGDP is first above the CPI curve and then dives below the CPI line in 2012. In the middle panel, the rates of price inflation are shown for both indices. In the lower panel, we present the difference between the CPI and the dGDP cumulative inflation curves in the upper and middle panels. One can suggest the presence of breaks in 1979, 1985, 1995, 2007, and 2014. This is for the model to decide, however, when the breaks result in the bets LSQR fit.

Figure 1. Upper panel: The evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1970 and 2018. Both variables are normalized to their respective values in 1970. Middle panel: The dGDP and CPI inflation estimates. Lower panel: The difference between the curves in the upper and middle panels. One can observe the breaks in the difference between the cumulative curves. We suggest potential breaks in 1979, 1985, 1995, 2007, and 2014.

In a modified model for Spain, we are looking for breaks near the years presented in Figure 1 and obtain the following intervals and coefficients:

du_p = -0.40dlnG + 2.11, 1995>t≥1970

du_p = -0.95dlnG + 2.03, 1996≥t≥2013

du_p = -0.50dlnG - 2.10, t≥2014 (1)

where du_p – one-year change in the (OECD) the unemployment rate, G – real GDP per capita (2011 prices). The break years in Figure 2 are close to those estimated from the inflation curves in Figure 1, but not all potential breaks are used. The overall fit shown in the upper panel is excellent, as confirmed by the residual errors in the middle panel and the regression (Rsq=0.96) of the predicted and measured employment between 1973 and 2018. We retain in mind that the estimates of the unemployment rate are obtained in the surveys. The unemployment values are also corrected in the revisions to the unemployment definition.

Considering the fall in real GDP growth caused by the COVI-19 pandemic one could expect that the rate of unemployment in Spain may increase according to equation (1) and probably will stay at an elevated level. Coefficient -0.5 in (1) predicts that a 1% decrease in real GDP per capita is converted to a 0.5% increase in the rate of unemployment. For Spain with its extremely high historical unemployment rate, this is a big problem.

Figure 2. Upper panel: The measured rate of unemployment in Spain between 1970 and 2018, and the rate predicted by model (1) with the real GDP per capita published by the MPD and the unemployment rate reported by the OECD. Middle panel: The model residual: stdev=1.3%. Lower panel: Linear regression of the measured and predicted time series. Rsq. = 0.96.

1/5/21

The rate of unemployment in Austria will increase

In our previous posts, we revisited and validated our version of Okun’s law for the USA, Canada, Germany, Australia, and France with new GDP and unemployment data the years between 2010 and 2019. In all five countries, the revised model accurately describes the new data, i.e. the original model is validated. In order to reach the best fit between the measured and predicted unemployment rates, we introduce structural breaks related to the change in real GDP definition. To illustrate the breaks in the real GDP data (i.e. nominal GDP corrected for the price change) we compare price inflation estimates as defined by the GDP deflator and CPI. The latter is considered as a reference. It is also important that the goods and services in the CPI are parts of the GDP deflator, dGDP. In the past, the CPI and dGDP were almost equivalent.

In this post, we apply the same approach to Austria and start with the CPI and GDP deflator difference, which is used to reveal definitional breaks in the dGDP estimates. Obviously, such breaks in the dGDP create breaks in the real GDP per capita estimates, and thus, in the statistical estimates associated with our model. One needs to find such breaks and allow the model to compensate for corresponding disturbances. In panel a) of Figure 1, we present the evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1970 and 2018 (the OECD data). Both variables are normalized to their respective values in 1970. The dGDP curve is close to the CPI before 1982 and then some low-amplitude deviations are observed. After 1995, the deviation increases in amplitude and the dGDP is below the CPI curve – an indicator of good economic performance similar to that observed in Germany since 1996. In panel b), the inflation rates are shown for both variables. In panel c), we present the difference between the CPI and the dGDP cumulative inflation curves in panels a) and b) and suggest the presence of breaks in 1982, 1996, and 2007. Panel d) of Figure 1 presents the original CPI curve and the corrected dGDP curve. The fit is good. As a result, our modified Okun’s law model is allowed to have breaks in 1982, 1996, and 2007.

Figure 1. a) The evolution of the cumulative inflation (the sum of annual inflation estimates) as defined by the CPI and dGDP between 1970 and 2018. Both variables are normalized to their respective values in 1961. b) The dGDP and CPI inflation estimates. d) The difference between the curves in panels a) and b). One can observe the breaks in the difference between cumulative curves. We propose the breaks in 1982, 1996 and, 2007. d) The fit between the CPI and the dGDP cumulative inflation curves after correction of the latter in 1982, 1996 and, 2007.

In our model, we are looking for breaks near the years and obtain the following intervals and coefficients:

du_p = -0.25dlnG + 0.60, 1982>t≥1970

du_p = -0.36dlnG + 0.97, 2006≥t≥1982

du_p = -0.40dlnG + 0.34, t≥2007 (1)

where du_p – one-year change in the (OECD) the unemployment rate, G – real GDP per capita (2011 prices). The break years in Figure 2 are the same as estimated from the inflation curves in Figure 1. The overall fit is shown in the upper panel in excellent, as confirmed by the residual errors in the middle panel and the regression (Rsq=0.92) of the predicted and measured employment between 1970 and 2018. We retain in mind that the estimates of the unemployment rate are obtained in the surveys. The unemployment values are also corrected in the revisions to the unemployment definition (e.g., Austria did not include in unemployment those who had no job before, i.e. graduates).

Considering the fall in real GDP growth caused by the COVI-19 pandemic one could expect that the rate of unemployment in Austria may increase according to equation (1) and probably will stay at an elevated level. Coefficient -0.4 in (1) predicts that 1% of the drop in real GDP per capita growth is converted in a 0.4% increase in the rate of unemployment.

Figure 2. Upper panel: The measured rate of unemployment in Austria between 1970 and 2018, and the rate predicted by model (1) with the real GDP per capita published by the MPD and the unemployment rate reported by the OECD. Middle panel: The model residual: stdev=0.37%. Lower panel: Linear regression of the measured and predicted time series. Rsq. = 0.92.

Total Economy Database estimates of real GDP per capita in Switzerland must be a joke

This is an extension of the previous post comparing the real GDP per capita (GDPpc) estimates obtained from various sources. We demonstrated that the GDPpc estimates for a given country for the same period from three major sources (the OECD, Total Economy Database, and Maddison Project Database) may give quite different total growth. In other words, the history of real economic development depends on the source, and the overall deviation is extremely large. One cannon consider this strong deviation as a stochastic bias. In this post, we extend the list by 6 countries: Australia, New Zealand, Italy, Spain, Switzerland, and Russia. Switzerland and Russia are likely the most striking examples of the difference between sources so far.

Figure 1 presents the case of Australia with the GDPpc estimates spanning the period between 1959 and 2018. The MPD data provides the largest total growth of 3.62. This is likely due to the underestimation of the initial value in 1959 since the current GDPpc levels are close. The OECD and TED report very similar estimates. The lower panel in Figure 1 illustrates the fact that the difference between the OECD and TED is likely stochastic with a small negative trend. All three time series were close between 1960 and 1970, and then started to slightly deviate. The biggest break was observed in 1990 when the MPD started to demonstrate a much higher rate of growth. The Maddison Project Database (University of Groningen) likes Australia and the other two sources are less benevolent.

Figure 2 illustrates the case of New Zealand. The MPD and TED give the best result since 1970 – the real GDP per capita grew by a factor of 1.95. The OECD is less generous and gives the factor of 1.86. The difference between the sources is low and one can suggest that New Zealand is not an economic rival for any major economy, and thus, the estimates of real economic growth are not biased. One can trust these data.

Figures 3 and 4 present Italy and Spain (both European countries) with the MPD providing the highest total growth estimates since 1970. The second best source is the OECD for Italy and the TED for Spain.

The case of Switzerland must be a joke. The total increase in real GDP per capita reported by the MPD is 2.56, and the other two sources give approximately 1.6. The difference is related to the very low MPD estimate for 1970 - $23,459. It is not clear how the MPD estimates are so different if all economic agencies use the same original data and methodologies. In my view, such differences are not acceptable. One cannot assess the statistical performance of the real economic growth models using fully incompatible estimates of basic economic variables.

The positive side of the observed differences is that one can judge the implicit relationships between countries, i.e. who is who in this world. The closest US allies can be easily revealed as well as the friends of Germany or France.

Finally, Figure 6 presents Russia. The MPD and TED estimates between 1960 and 1990 are identical and then the MPD (Europe) reports faster real economic growth than the TED (USA). The difference between the TED and MPD has a linear dependence on the time between 1990 and 2010. No difference is observed since 2010.

Figure 1. Upper panel: The evolution of real GDP per capita estimates in Australia as borrowed from the Organization of Economic Cooperation and Development (OECD, Headquarters – Paris), Maddison Project Database (MPD – The Netherlands), and Total Economy Database (TED – USA, China, …). All time series are normalized to their respective values in 1959. Lower panel: Two pair-wise ratios revealing the relative differences in the three time series.

Figure 2. Same as in Figure 1 for New Zealand

Figure 3. Same as in Figure 1 for Italy

Figure 4. Same as in Figure 1 for Spain

Figure 5. Upper panel: GDPpc estimates from three sources. Middle panel: the curves in the upper panel are normalized to their respective levels in 1970. Lower panel: pair-wise ratios of the normalized curves.

Figure 6. Same as in Figure 1 for Russia

1/2/21

Economic data as a weapon in the economic war between developed countries. This is a shame

Economic data analysis is a hobby rather than a duty. My professional occupation is geophysics with an emphasis on the effects of nuclear explosions in three media – solid earth, underwater, and atmosphere. After the Comprehensive Nuclear-test-ban Treaty was signed, my interests and activity have been focused on monitoring nuclear explosions at a global level. The essence of monitoring is not to miss the event of interest (e.g. the DPRK tests) in the intensive flux of similar events (e.g. hundreds of earthquakes per day). Such a requirement creates professional deformation related to data quality and consistency. The CTBTO uses only authenticated and quality checked data obtained by the International Monitoring System. In routine data processing carried out by the International Data Centre for the State Parties of the CTBTO, it is not allowed to use unauthenticated national or international data. In economic data, I found an extremely strong argument against the use of data provided by developed countries in any independent activity (Technical Secretariat of the CTBTO is supposed to be an independent actor as well as other UN-related organizations in economic data published by several “independent” sources). In case the countries controlling these sources or any other country will provide data to the CTBTO or like organizations it should be denied. This data is highly likely biased in favor of the providers.

We have been studying statistical links between various economic parameters since 2003. In December 2020, the COVID-19 limitation to remote work was a good argument in favor of revisiting all studies conducted before 2013 and validation of the models by adding new data between 2010 and 2020. The most recent set of posts in this blog was associated with models similar to Okun’s law. The modification used in our approach is just conversion of the link between the rate of unemployment and real GDP per capita (as the measure of output gap) into a differential form. Then the integral change in the unemployment rate is predicted by the GDP per capita growth.

For this reason, the real GDP per capita data are needed as the major term of the differential equation. We have already reported on the definitional revisions (problems) to the GDP deflator which make our model piece-wise in accordance with these revisions. However, we have also found another problem – the real GDP per capita estimates provided by various sources (BEA, OECD, Total Economy Database, Maddison Project Database) are quite different. There was no reason to classify these differences in a conspiratorial sense and we used them without prejudice as fully interchangeable. There are some features, however, that made us think in non-economic vocabulary.

The sources of economic data are highly biased in favor of the sponsoring countries.

In this post, we just present examples of the biased estimates. The reference years in economic time series are related to real GDP change to later dates with the major/comprehensive revisions. One cannot directly compare the real GDP per capita estimates from two sources when the reference years are different. Therefore, we normalize all time series to the same year, usually to the start year of the shortest time series. Obviously, the relative change in the real GDP per capita has to be the same, when all time series are normalized to the same year and we can consider any difference as related to definitions used in the corresponding estimation procedure. Economics is a developing science in both theoretical and experimental (measurement) parts and we understand the necessity of different approaches as an important methodological aspect of the overall progress. However, the differences between the normalized time series reveal high bias in the estimation of real GDP growth specifically in the countries sponsoring these estimates. It is unacceptable in any science and this is a shame. We start with the USA.

The upper panel in Figure 1 displays the evolution of real GDP per capita estimates borrowed from four sources: the Bureau of Economic Analysis (BEA - USA), Organization of Economic Cooperation and Development (OECD, Headquarters – Paris), Maddison Project Database (MPD – Netherlands), and Total Economy Database (TED – USA, China, …). In the past, the MPD was also controlled by the Conference Board publishing the TED. Currently, MPD and TED are two different databases. As described in the previous paragraph, all time series are normalized to their respective values in 1970 (OECD’s start point). One can see that the TED gives the highest growth in the GDP per capita since 1970. The MPD provides the lowest estimates. In the lower panel, several pair-wise ratios are presented in order to illustrate the relative differences in the four time series. It is worth noting that the BEA and OECD provide the same estimates except for the most recent period, which is subject to further revisions, however. The BEA provides data only for the USA and is not used in further comparison.

Figure 1. Upper panel: The evolution of real GDP per capita estimates borrowed from the Bureau of Economic Analysis (BEA - USA), Organization of Economic Cooperation and Development (OECD, Headquarters – Paris), Maddison Project Database (MPD – The Netherlands), and Total Economy Database (TED – USA, China, …). All time series are normalized to their respective values in 1970 (OECD start point). Lower panel: Several pair-wise ratios revealing the relative differences in the four time series.

Figure 2 is similar to Figure 1 and illustrates the case of Germany. The best result to Germany is given by the MPD – the total growth in the real GDP per capita since 1970 is 2.67. The OECD is less generous and gives the factor of 2.41. The TED gives the worst estimate – 2.09. The US-based source with tight connections to China does not see Germany as a country with healthy economic growth. The MPD is a part of University of Groningen and Figure 3 presents the Netherlands. Again, the MPD gives the highest growth and the TED is not nice to the Netherlands. The connection between the TED and MPD is expressed in straight lines in the lower panel displaying the ratios.

Figure 2. Same as in Figure 1 for Germany

Figure 3. Same as in Figure 1 for the Netherlands

The OECD headquarters resides in Paris, France. Figure 4 displays the real GDP per capita estimates and their ratios. It proves the assumption that the OECD is in favor of France in terms of the rate of economic growth since 1950. The OECD estimate is a factor of 4.93 between 1950 and 2018, which is much higher than 4.66 from the MPD and 4.69 from the TED. The OECD curve is above the other two sources from the very beginning.

Figure 4. Same as in Figure 1 for France

Finally, we report potential bias in the real GDP per capita estimates for the UK. Figure 5 shows that the largest growth is estimated by the Office of national statistics (ONS). The ONS is a national source and its bias is not unexpected. The OECD gives almost the same estimates as the ONS. The TED is in favor of modest economic growth in the UK, and the MPD is the least generous.

Summarizing the observations in Figures 1 through 5, one can conclude that the data origin (sponsor or country) defines the method of real GDP estimation (i.e. definition of nominal GDP and GDP deflator) most appropriate for the sponsor/country real economic growth to be the largest. Such an approach definitely introduces a serious bias in the estimates of various economic variables used for quantitative analysis. The latter becomes vulnerable to non-economic forces and likely suffers larger problems with statistical estimates in the mainstream economic models. We do not know the decisions and reasons behind this bias, but one cannot deny the fact that this bias is always in favor of the source controlling the country. The advantage of the formally higher economic growth is likely related to the attractiveness of a country for investors and the likes. In that sense, the biased estimates of real economic growth is a weapon in the fight for international finances. And this fight seems to be nasty and without rules. This is called civilization – all means are good.

We add Japan, China, Austria, and Canada (Figure 6 through 9) to the main set. One can judge who is who in this world: easily find who the US allies are, and who has better relations with Germany.