Why price inflation in developed countries is systematically underestimated

Following several posts in this blog, I've compiled a paper (link to a complete pdf version):

 Why price inflation in developed countries is systematically underestimated

Abstract
There is an extensive historical dataset on real GDP per capita prepared by Angus Maddison. This dataset covers the period since 1870 with continuous annual estimates in developed countries. All time series for individual economies have a clear structural break between 1940 and 1950. The behavior before 1940 and after 1950 can be accurately (R2 from 0.7 to 0.99) approximated by linear time trends. The corresponding slopes of regressions lines before and after the break differ by a factor of 4 (Switzerland) to 19 (Spain). We have extrapolated the early trends into the second interval and obtained much lower estimates of real GDP per capita in 2011: from 2.4 (Switzerland) to 5.0 (Japan) times smaller than the current levels. When the current linear trends are extrapolated into the past, they intercept the zero line between 1908 (Switzerland) and 1944 (Japan). There is likely an internal conflict between the estimating procedures before 1940 and after 1950. A reasonable explanation of the discrepancy is that the GDP deflator in developed countries has been highly underestimated since 1950. In the USA, the GDP deflator is underestimated by a factor of 1.4. This is exactly the ratio of the interest rate controlled by the Federal Reserve and the rate of inflation. Hence, the Federal Reserve actually retains its interest rate at the level of true price inflation when corrected for the bias in the GDP deflator.

Real GDP per capita since 1870

We've just finished and published a working paper. The reader may want to download it from the MPRA: Real GDP per capita since 1870

Abstract

The growth rate of real GDP per capita in the biggest OECD countries is represented as a sum of two components – a steadily decreasing trend and fluctuations related to the change in some specific age population. The long term trend in the growth rate is modelled by an inverse function of real GDP per capita with a constant numerator. This numerator is equivalent to a constant annual increment of real GDP per capita. For the most advanced economies, the GDP estimates between 1950 and 2007 have shown very weak and statistically insignificant linear trends (both positive and negative) in the annual increment. The fluctuations around relevant mean increments are characterized by practically normal distribution. For many countries, there exist historical estimates of real GDP since 1870. These estimates extend the time span of our analysis together with a few new estimates from 2008 to 2011.  There are severe structural breaks in the corresponding time series between 1940 and 1950, with the slope of linear regression increasing by a factor of 4.0 (Switzerland) to 22.1 (Spain). Therefore, the GDP estimates before 1940 and after 1950 have been analysed separately. All findings of the original study are validated by the newly available data. The most important is that all slopes (except that for Australia after 1950)  of the regression lines obtained for the annual increments of real GDP per capita are small and statistically insignificant, i.e. one cannot reject the null hypothesis of a zero slope and thus constant increment. Hence the growth in real GDP per capita is a linear one since 1870 with a break in slope between 1940 and 1950.  

Key words: GDP, model, economic growth, inertia, trend, OECD

Two more graphs on GDP in the USA

Two more graphs on real GDP in the USA. In the forth quarter of 2011, the level of real GDP was higher ($13,422 .4 billion) than that in the fourth quarter of 2007 ($13,326 billion) as Figure 1 shows. Figure 2 demonstrates that  the increasing population did not allow real GDP per capita t reach the level of 2007: $42,727 vs. $43,791. In seems to be the task for 2012 to 2014 if no recession will occur.  

Figure 1. Real GDP

Figure 2. Real GDP per capita

Real GDP and GDP deflator in 2011

Here are some quick notes on the new estimates of real GDP and GDP deflator for 2011.  Figurer 1 shows the rate of growth of real GDP, dlnGDP/dt, at annual and quarterly basis. In 2011, the rate is 0.017 1/y, i.e. 1.7% per year, despite the rate growth in the fourth quarter of 2.7% (SAAR). Previously, we predicted a small recession in 2012 and 2013. This prediction will be updated soon when the 2010 census results are published and incorporated into the so called postcensal population estimates.

Figure 2 shows the growth of total population for the purpose of per head calculations. Please notice a large step in population between 1999 and 2000 as associated with the error of closure, i.e. the difference between intercensal estimate for 2000 and the number enumerated in the 2000 census.  Figure 3 presents the rate of growth of real GDP per capita , dlnG/dt. In 2011, the rate of growth was 0.0098 1/y. This means that the total increase in population was of 0.7%.

Figure 4 shows the GDP deflator or price inflation associated with the economy as a whole. This is the most comprehensive measure of inflation as we discussed many times in this blog. For 2011, the GDP deflator is 2.1%. This is larger than we predicted but the last quarter signals about upcoming deflation, as we foresaw six years ago. Currently, the FRB also foresees very low inflation rates through 2014.

According to our concept of GDP growth,  real GDP per capita has a inertial component which is expressed in a constant annual increment, dG=const. Figure 5 updates the graph showing the evolution of real GDP per capita in the USA. One can observe a gradual return to the constant level of annual increment. This works as inertial movement in physics. However, one can expect some more years of dG less than average, dG<$490 (2011 US dollars).  It is worth noting, that there is no output gap when real GDP per cpaita is considered. The evolution of dG exactly follows it long term trend and the years after 2007 serve to return dG to the trend from its highs in the late 1990s.

We have to notice that the estimates of the nominal GDP and GDP deflator are subject to revision which may be as high as several per cent (+2.1% for 2001). However, the long term trends in all presented variables fit our concept and predictions. 

Figure 1. The growth rate of real GDP: annual and quarterly (annualized). MA(4) for the quarterly time series. For 2011, dlnGDP/dt=0.017  1/y.

Figure 2. The evolution of total resident population. Notice the jump between 1999 and 2000 – the closure error.

Figure 3. The growth rate of real GDP per capita. For 2011, the rate is (dlnG/dt=) 0.0098 1/y. 

Figure 4. Annual and quarterly (annualized) price deflator of GDP. In the last quarter of 2011 the GDP deflator dropped to 0.004 1/y. This is likely a turn to deflation.

Figure 5. The increment of real GDP per capita since 1950. As predicted, the trend returns to a zero slope. There is no output gap.

Real real GDP

We have already reported that real GDP in the United States is biased by the change in definition of the GDP deflator around 1978. (According to “Concepts and Methods of the U.S. NIPA” the growth rate of real GDP is the growth rate of nominal GDP reduced by the overall change in prices as expressed by the GDP deflator or the economy-wide price index.) Figure 1 shows that before 1978 the GDP deflator and CPI were similar and their difference is negligible since 1929. In 1978, a new definition of the GDP deflator was introduced and the curves coinciding before 1978 started to deviate. In 2010, the deviation was approximately 20%.

A reasonable assumption on the new definition of the GDP deflator is that it should also be applied to the time series before 1978. This would reduce the bias introduced in the time series around 1978. Figure 1 demonstrates (dashed line) that the growth rate of the CPI after 1978 is approximately 20% higher that the rate of the GDP deflator growth. Without loss of generality, one may assume that the GDP deflator had been growing at a rate approximately 20% lower than the CPI before 1978. In Figure 1, green line represents the GDP deflator before 1978. Since the growth rate of the GDP deflator was lower the over all change between 1929 and 2010 is also smaller than that of the CPI.   

The difference between the GDP deflator and CPI has an immediate consequence as related to real GDP. When applied to the real GDP estimates published by the Bureau of Economic Analysis,   the corrected GDP deflator provides a more accurate time series. One must use this corrected time series in economics and econometric research in order to avoid the apparent bias.

To begin with, we have updated our comparison of real GDP and real GDP per capita growth. This comparison has demonstrated that the fall in real GDP (recession) has actually returned the growth trajectory to the long-term trend and there is no output gap as estimated from real GDP time series. Figure 2 depicts two old and two new (corrected) curves. One can see that the new curves are above the old ones since the corrected GDP deflator is lower than the CPI and the updated real GDP estimates are higher than the original estimates. The corrected real GDP curve implies a much larger output gap that makes this hypothesis truly void. Essentially, the growth rate between 1930 and 1960 was so high that it can never be repeated.  As a result, the Solow model (constant returns to scale) behind the output gap is likely to be wrong.

Figure 1. Cumulative growth rate (the sum of annual inflation rates) of various definitions of inflation since 1929. 

Figure 2. Old and corrected (corr.) estimates of real GDP and real GDP per capita. The former estimates are below the new ones. 

Update 28.10.2011. Corrected table of real GDP per capita and real GDP in 2005 US $

 

2010 42270 13108145194

2009 41377 12722814211

2008 43242 13181625195

2007 43791 13225891467

2006 43399 12978410715

2005 42681 12643309646

2004 41792 12265967955

2003 40769 11857542216

2002 40108 11556298822

2001 39769 11347579296

2000 39750 11226180266

1999 38592 10779826176

1998 37238 10283422652

1997 36102 9854329716

1996 34977 9433786578

1995 34112 9093849856

1994 33671 8870793305

1993 32747 8523454654

1992 32255 8287019110

1991 31614 8015097420

1990 32112 8033812272

1989 31877 7885955399

1988 31069 7613800209

1987 30115 7313216945

1986 29443 7086429569

1985 28717 6849176802

1984 27823 6577190262

1983 26186 6136243938

1982 25282 5870935476

1981 26030 5987108240

1980 25640 5838894640

1979 26010 5855007060

1978 25503 5677707387

1977 24150 5320037949

1976 23103 5038386795

1975 21814 4711459533

1974 21689 4639185468

1973 21796 4619427179

1972 20696 4344618556

1971 19729 4097469291

1970 19161 3929633433

1969 19185 3889478681

1968 18673 3748418138

1967 17905 3558699243

1966 17580 3456136296

1965 16656 3237016460

1964 15817 3035727724

1963 15129 2864008171

1962 14684 2739924324

1961 14039 2579516585

1960 13910 2514340896

1959 13838 2451111168

1958 13078 2277479719

1957 13353 2287102029

1956 13298 2237003680

1955 13280 2194815712

1954 12594 2045223652

1953 12885 2055915430

1952 12487 1959856824

1951 12096 1866190324

1950 11400 1729138416

1949 10677 1592940944

1948 10795 1582831140

1947 10309 1485823522

1946 10482 1482021159

1945 11855 1658907921

1944 12093 1673619102

1943 11231 1535740268

1942 9643 1300405392

1941 8175 1090577563

1940 7044 930616096

1939 6542 857231031

1938 6120 795393311

1937 6356 819695449

1936 6072 778270922

1935 5389 686317930

1934 4963 627750020

1933 4535 570028178

1932 4683 585161480

1931 5488 681318834

1930 5933 730845272

1929 6562 799800744

Real GDP is NOT correct

This is an extension of the story on wrong metrology of macroeconomic measurements. Economics chiefly fails and produces a great amount of counterproductive work due to wrong measurements of basic macroeconomics variables. In our previous post we focused on real GDP in the US and here we extend the case by Australia, Canada, and the United Kingdom. As mentioned before, we have devoted enough efforts to reveal and recover many trivial cases in our book “mecħanomics. Economic as Classical Mechanics”. 

Real GDP (see Concepts and Methods of the U.S. NIPA for details) is the difference between nominal GDP and the GDP deflator (price index). The latter is not easy to calculate or even evaluate.  In this post, we found that it is so much a sophisticated problem that before 1978 there was no practical difference between the cumulative inflation values of the CPI and the GDP deflator in the US, as Figure 1 demonstrates. (The cumulative inflation, i.e. the cumulative sum of inflation rates, is different from price index when differently calibrated in the beginning.) Effectively, the curves in the Figure diverge from 1978. There is no direct statement about the reasons of the change in definitions in the aforementioned conceptual document, but we might guess that this is likely related to the introduction of a new methodology to evaluate the overall price inflation.  This difference has affected our analysis of Okun’s law and forced the introduction of a structural break in 1978 in the dependence between unemployment (and employment) rate and the rate of real economic growth. As we lately reported, this was an artificial break completely related to the change in real GDP definition in 1978.  

Thus, before 1978 the CPI was used to estimate of the overall price inflation. Since 1978, the GDP deflator has been used. The difference between these two variables can not be neglected: the cumulative change in inflation between 1978 and 2009 is 20 percentage points. This implies that when applied to the estimates before 1978, the concept of the dGDP would result in a bigger change in real GDP estimates. The overall real GDP increase since 1929 should be much larger in the current definition of the GDP deflator is applied.   

To validate this finding we have borrowed data from the OECD and calculated the CPI and dGDP cumulative inflation in Australia, Canada and the UK, as shown in Figure 2. There are clear breaks in different years: for Australia in 1983 (also 1983 was estimated from a structural break in Okun’s law); for Canada – 1980 (1982 was estimated from a structural break in Okun’s law); for the UK – 1979 (1982 was estimated from a structural break in Okun’s law). For the UK, the CPI and dGDP curves start to diverge in 1979 but the pace of deviation is very slow and the year of structural break in Okun’s law is hard to determine accurately.

One can conclude that all structural breaks in the previously estimated models of the rate of unemployment (Okun’s law) and the employment/population ratio for the US, Australia, Canada and the United Kingdom were entirely artificial and forced by the change in real GDP definition in the years of these breaks. (The OECD does not provide sufficient data length for other modeled countries and we need to find other sources of information for France, Japan and Spain.) Hence, real GPD estimates are incompatible over the break years and thus wrong. One must not use them for modeling and statistical analysis.  

Real GDP is NOT correct!

Figure 1. Cumulative  rate (the sum of annual inflation rates, what is different from inflation index) of inflation in the United States since 1929, as described by the CPI and dGDP.

Figure 2. Same as in Figure 1 for Australia, Canada and the United Kingdom.

Disappointing Bernanke

Federal Reserve Chairman Ben Shalom Bernanke made several important statements in testimony to Congress's Joint Economic Committee that the Fed. In essence, they show the  impotence of economic theory and thus economic authorities basing their policies on wrong understanding. Several examples:
1. “.. Recent revisions of government economic data show the recession as having been even deeper, and the recovery weaker, than previously estimated; indeed, by the second quarter of this year--the latest quarter for which official estimates are available--aggregate output in the United States still had not returned to the level that it had attained before the crisis.”

Any economics, financial or monetary policy should include some expected level of uncertainty in real time measurements such as real GDP and inflation (the GDP deflator). If it is always a surprise, how can one build a reasonable response and policy? One should never characterize an economy with one number without uncertainty. It contradicts scientific methodology.

2. “Slow economic growth has in turn led to slow rates of increase in jobs and household incomes.”

This statement presumes that there can be a situation when slow growth may lead to higher rates of increase in jobs and incomes. Actually, all these processes are equivalent and no one leads to another. They coexist.

3. “ Consumer behavior has both reflected and contributed to the slow pace of recovery.”

This statement is beyond any understanding. Consumers are treated as a black box without any rules how “garbage in” is converted into “garbage out”. This is a typical economic statement which explains every deviation in real economic growth as consumer behavior expressed in demand/supply shocks. Nobody knows what drives these shocks and why the economy runs away from the balance. In a way, this explanation creates a malice loop without start and end.

4. “Other sectors of the economy are also contributing to the slower-than-expected rate of expansion. The housing sector has been a significant driver of recovery from most recessions in the United States since World War II. This time, however, a number of factors--including the overhang of distressed and foreclosed properties, tight credit conditions for builders and potential homebuyers, and the large number of "underwater" mortgages (on which homeowners owe more than their homes are worth)--have left the rate of new home construction at only about one-third of its average level in recent decades. “

This deserves a special attention. Here Ben unfolds reasons one layer down. The housing sector slumps due to a number of factors. These factors are obvious results of the overall economic slump. What raises again the question on the reasons of the economic slump itself, and this is not housing as one can judge.

5. “ Nonetheless, financial stresses persist.”

Thus, the current financial crisis is a process which does not depend on real economic growth and when it is over, the economy will rocket up. Does that mean that the financial crisis could be healed without economic growth, but as it is? I would expect that the financial crisis will end when real economic growth recovers. In my opinion, it will happen in 5 to 10 years.

6. “In view of the deterioration in the economic outlook over the summer and the subdued inflation picture over the medium run ...”

This is a mere declaration of the status quo. However, the inflation projection is right as we showed many years ago

Political Calculations on GDP in Q3

There is an interesting post by Ironman @ Political Calculations. The author predicts the possibility of recession in the third quarter of 2011. It is in line with our projections of real GDP per capita in the US for the next five years. This post also uses the term "inertia" which we consider  the key phenomenon in real economic growth.

Goldman Sachs on recession in Germany

Via Market Watch - Goldman Sachs foresees a period of recession in eurozone with Germany falling into negative growth in the forth quarter of 2011. In May 2011, we posted on recession in germany and showed that this period will be a lenghty one ( http://mechonomic.blogspot.com/2011/05/how-long-will-last-real-economic-growth.html) . Figure 1 reproduces  some details of our prediction  of real GDP per capita in Germany.

Figure 1. Observed and predicted rate of real GDP growth in Germany after the reunification.
Lower panel - The original curves are smoothed with MA(3).

V- vs L-shaped recovery: Is CBO’s economic projection wrong?

CBO has recently published a new economic projection covering the period between 2011 and 2021. It explicitly defines the rate of real economic growth (GDP) and inflation for several segments: forecasts for 2011 and 2012, and projections for 2013 -2016 and 2017-2021. Overall, after two years of slow growth in 2011 and 2012, CBO expects a dramatic increase to the rate of 3.6% per year between 2013 and 2016 with the next five years of slow economy with the rate of 2.4% per year on average. Inflation is low over the entire period: the rate of PCE inflation varies between 2.4% and 1.3% per year and that of CPI inflation will be in the range 1.3% to 2.8% per year. Considering these figures one can conclude that CBO expects a slow version of a V-shaped recovery in the 2010s.  There is no double dip.   

We have also projected the rate of inflation and real economic growth in this blog and academic papers. Our GDP (per capita) model is based on the change in demographic characteristics (the age pyramid). Another model describes price inflation as a function of the change rate of labor force. Skipping all mathematical details, we expect the rate of real economic growth (GDP per capita) to fall slightly below zero between 2012 and 2014 (recession) and hovering around 1%  per year after 2015. The rate of price inflation (the GDP deflator and CPI) in the 2010s has to be slightly negative on average with some years of formal deflation. All in all, we expect an L-shaped recovery, i.e. no actual recovery during the 2010s.

Recession? In 2012-2013!

Is a new recession coming? This is currently one of hot questions in economic blogosphere. We expect it in 2012 and 2013. Our prediction is based on a quantitative growth model.

The first post in this blog was devoted to real GDP growth and its relation to the change in a specific age population. We have presented a number of growth models for various developed counties and validated them by new data. The original model  for the U.S. links the change rate of real GDP per capita, dlnG/dt, to the change in the number of 9-year-olds, dlnN9/dt, and the reciprocal value of the attained level of GDP per capita, A/G:

dlnG/dt= A/G + 0.5dlnN9/dt (1)

where A is an empirically derived constant. One can rewrite (1) relative to N9 and obtain the following equation in a discrete form:

N9(t) = N9(t-1)[2.0( dlnG - A/G) + 1] (2)

where dt=1 year.

Figure 1 presents the result of the N9 modeling between 1960 and 2005. The agreement between the measured and predicted N9 is excellent and we have shown that these time series are cointegrated. Our model has passed all rigorous econometric tests and can be used for GDP forecasts when the quality of population estimates is good enough.

Figure 1. Measured number of 9-year-olds in the U.S. and that predicted from real GDP per capita.

After 2003, the U.S. Census Bureau has been publishing extremely smoothed and thus biased population estimates, which are not appropriate for the purposes of real GDP prediction. This unfortunate situation might be resolved only after the 2010 census. We do not have quantitative estimates of the 9-year-old population yet but can use the age pyramid presented in Figure 2, which we borrowed from the U.S. Census Bureau.

At first glance, the 2008-2009 recession was induces by a negative value of dlnN9/dt, as one can judge from the number of 12- and 11-year olds. These people were 9-year-olds three and two years ago. One should not forget that younger cohorts accumulate more and more people with time due to intensive immigration and thus the numbers of people above 12 years of age are all biased up relative to the younger generations.

 

The number of 10- and 9-year-olds is slightly higher than in two older cohorts, and thus, we observe a period of positive real economic growth in 2010 and in 2011(the growth rate of real GDP per capita is about 1% per year lower than that of the overall GDP). However, the fall in N8 and N7 (male) almost guarantees a new recession in 2012-2013. Hence, a new recession is around the corner. We will present a more accurate quantitative estimate when the 2010 census data are available.

Is the U.S. economy above or below the long term growth trend?

The 2008/2009 recession in the U.S. is perceived as a deep and painful fall in real GDP.  It is now a common place to show the current estimate of real GDP far below the long term growth trend. Many experts consider the point of complete recovery of the U.S. economy as the intercept with this trend somewhere in the future. This is a wrong assumption. One should exclude the extensive factor of total population growth from real GDP since the total population does not grow at the same rate as before. One confuses real economic growth with demographic fluctuations.  Here we present the history of economic growth in terms of real GDP per capita.

Previously in this blog, we found that real GDP per capita in developed countries grows as a linear function of time. Similarly to classical mechanics, we interpret this linear growth as “inertial” growth. When the population pyramid does not change over time one can write the following relationship for real GDP per capita, G(t):

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. Figure 1   shows that the annual increment A in the U.S. is practically constant between 1950 and 2010. (All data are borrowed from the Bureau of Economic Analysis.) This plot validates our empirical finding. Overall, 19 biggest developed countries demonstrate the same behavior between 1950 and 2010.

It is time to compare the trends in real GDP and GDP per capita. Figure 2 depicts the evolution of both variables between 1950 and 2010 and also presents the relevant trends. The real GDP curve has an exponential shape as related to the growth in total population. One can easily observe the current deviation from the exponential trend and blame poor economic conditions after 2007.

The real GDP per capita evolves along a straight line. There is no significant deviation from the linear trend in the past 4 years. Moreover, during these years the observed curve returned to the long-term trend.  In this sense, the current downward correction is a natural consequence of the fundamental law of inertial economic growth. One should not confuse economy with demography.  The latter is responsible for 200 per growth in real GDP from 1950 to 2010, i.e. the total population has increased by a factor of 2 since 1950.

Figure 1. Annual increment of real GDP per capita in the U.S. between 1950 and 2010.

Figure 2. The evolution of real GDP and real GDP per capita between 1950 and 2010.

Real economic growth. The importance of being … small

Here, we compare real economic growth based on real GDP per capita, G. In developed countries, annual increment of GDP per capita is constant over time with all fluctuations caused by the change in the age pyramid. The average value of the annual increment of GDP per capita varies between countries, however. Among large economies, the USA grows with the highest annual increment.  In that sense, it is the most efficient economy.

Lately, we presented several posts showing the difference between real GDP per capita in the USA, Gusa,  and select countries, Gi:

dG = Gusa-Gi

When the difference dG has a positive trend, the gap with the USA increase with time. When dG has a negative trend, this country grows faster than the USA. There are not many economies outperforming the U.S. since 1990. Six developed countries deserve special consideration: Ireland, Norway, Luxembourg, Hong Kong, Singapore, and Trinidad and Tobago which joined recently.  Figure 1 demonstrates that these six economies all have negative trend in the dG time series. Ireland, the biggest among them, has been experiencing problems since 2006.

Hence, one can conclude that small countries have higher probability to grow fast. To be small is not enough, however!  

Figure 1. The differences between real GDP per capita in the USA and six select countries

Mark Thoma on the trend in real economic growth

Mark Thoma has published a long post on the evolution of real economy in the U.S. The question is -When will real GDP intercept its long-term trend? Or will it intercept at all? Mark also cited some related posts by Mankiw, Krugman, DeLong and own papers.

Before any discussion of real growth models one must replace real GDP with real GDP per capita in order to exclude the exponential working age population growth. This is a major source of confusion also missed by Mark. Then, one should compare other developed countries in order to reveal common features. Also, one has to test predictive power of all models.

My recent post on the growth model was based on observations in developed countries and showed that the growth rate of real GDP per capita has a trend decaying proportionally to the reciprocal value of the real GDP per capita. All fluctuations in the growth rate in developed countries, including the USA, return to this trend, at least since 1950 (no reliable data before).

Thus, the US economy will likely return to the decaying trend, not to the linear trend in the growth rate as borrowed from the Lucas lecture.

When discussing models one has to validate them by data. Otherwise this discussion is worthless.

New Zealand. Sad economic forecasts

Here we introduce a new model of unemployment in New Zealand.  It extends the set of models linking the rate of unemployment and the change in labour force.  The agreement between the measured and predicted unemployment estimates in New Zealand validates our concept which states that there exists a long-term equilibrium (causal) linear and lagged link between unemployment, u_t, and the rate of change of labour force, l_t=dLF/LFdt. For this purpose, we use data borrowed from the OECD.

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

u_t = -2.0l_t-3  + 0.09         (1)

Therefore, the lead of l_t is three years. The intercept of 0.09 implies the rate of unemployment at the level of 9% when the labour force does not change. Hence, New Zealand needs increasing labour force in order to reduce unemployment.   

Figure 1 presents the observed unemployment curve and that predicted using the rate of labour force change 3 years before and equation (1). Since the estimates of labour force in New Zealand are very noisy we have smoothed both annual curves with MA(3). All in all, the predictive power of the model is excellent and timely fits major peaks and troughs after 1984.

Relationship (1) allows a relatively accurate prediction of the rate of unemployment at a three-year horizon. Figure 1 demonstrates that unemployment will likely grow to the level of 7% in 2012 from the current level of 6.5%.  Hence, the drop in the rate of real economic growth will be accompanied by an elevated unemployment.

Figure 1. Observed and predicted rate of unemployment in New Zealand. The lower panel shows the cumulative curves for the annual curves in the upper panel.

How long will last real economic growth in Germany

Germany has demonstrated an extraordinary increase in real GDP in 2010: +3.6 per cent.   In the first quarter of 2011, the level of real GDP was 5.2% above that in the first quarter of 2010. This jump is especially desirable after the tremendous fall in 2009: -4.5 per cent relative to 2008. After this strong fluctuation, the question is how strong in the growth trend for the German economy?  One can find a quantitative answer to this question and a long-term prediction of real GDP per capita in Germany up through 2020.

Several months ago we presented log an empirically correct model of real economic growth in Germany. Our concept describing the evolution of real Gross Domestic Product (per capita) is very simple and is based solely on the age structure in a given developed country. Since Germany does not carry out censuses as many countries do, the age pyramid is obtained from administrative record and partial censuses. It makes the final result less accurate and influences our prediction of real GDP in Germany.   

We have empirically and statistically proved that the growth rate, g(t), of real GDP per capita, G(t), is driven by the attained level of real GDP per capita and the change in a specific age population, N_s. According to our model, the asymptotic growth rate of real GDP in developed countries can be completely characterized by constant annual increment A = const. All fluctuations around this constant increment can be explained by the change in the number of people of the country-specific age:

g(t) = dlnG(t)/dt  = A/G(t) + 0.5dlnN_s(t)/dt                                            (1)

Equation (1) is the quantitative model that has been constructed empirically and tested statistically.

We published a preliminary model for Germany severalyears ago; before the 2008/2009 recession. The best fit constant increment is (A=) $260 (1990 US dollars, as published by the Conference Board) and the defining age is eighteen year. The age distribution from 2002 allows a prediction at an 18-year horizon. The original model displayed in the upper panel of Figure 1 suggested a slow-down in 2009 and likely a deeper recession in 2011, with a year of growth in 2010. On average, the beginning of 2010s was characterized by very poor performance of the German economy.

The lower panel in Figure 1 extends the observed curve through 2010. The predicted curve did not change. Overall, we predicted the fall in 2009 and the growth in 2010, with smaller amplitudes, however. This might be the result of severe smoothing of the age pyramid.  (Here, we would like to emphasise again that the prediction of the 2009 slowdown could be easily obtained in 2002, i.e. seven years before it happened!) Figure 2 presents a smoothed version of both curves in Figure 1. Three-year moving averages, MA(3), show a much better fit than the annual curves. Therefore, we do not change our forecast for 2011 and for the future decade. The German economy will not be growing fast. Immigration may induce only extensive growth in real GDP but not in GDP per capita.  

Figure 1. Observed and predicted rate of real GDP growth in Germany after the reunification. The predicted curve is obtained from relationship (1) with A=$260.

 Figure 2. The original curves in Figure 1 smoothed with MA(3).  

BRICS vs BRIC

South Africa is suggested as a new member of the BRIC with the extension of the abbreviation to BRICS. We have a working model to estimate the SA’s economic performance relative to other BRICS countries. As in the previous post, we calculate the difference between real GDP per capita in the USA and that in South Africa. Figure 1 shows all differences (1990 US dollars at Geary-Khamis PPPs, as published by the Conference Board). Four of the five were already analysed. What can we say about the new member? Honestly, its performance is far from standard, when the difference does not change over time. South Africa underperforms as India and Brazil did during the past 20 years. These BRIC members are really big (in top ten worldwide) what makes their membership justified by the size of economy. It is not valid for SA.

Figure 1. The differences between real GDP per capita in the USA and the BRICS countries

Who is the best performer in the BRIC?

We have a very simple and empirically correct concept of real economic growth based on the finding that annual increment of real GDP per capita is constant in the long run. All developed countries obey this empirical law, at least between 1950 and 2010.

Developing and emerging countries demonstrate various level of performance relative to developed countries. In the previous post we presented Brazil and Russia. These are two representatives of the BRIC. In this post we compare all four countries. Figure 1 depicts the differences between real GDP per capita in the USA and the BRIC countries. A positive slope indicates a poorer when expected performance – the line must be parallel to the x-axis for equivalent performance.

From Figure 1, one can easily decide that India and Brazil were under par (between 1990 and 2010) relative to the standard performance of the USA. China has been growing faster than expected in the 2010s and significantly reduced the gap. Russia had a period of very poor performance in the 1990s as associated with the transition to capitalist economic system. Since 1999, its performance was on a par with China. Obviously, a higher rate of growth in China was related to a lower level of GDP per capita.

Figure 1. The differences between real GDP per capita in the USA and the BRIC countries

Ireland and Solow's exogenous growth model

Three months ago we revisited the evolution of real GDP per capita in Ireland. This was an example of a country which demonstrated an extremely high annual increment of GDP per capita growth between 1990 and 2005. This observation undermined our concept of constant increment in GDP per capita in developed countries which expresses the idea of inertia in economic growth (see our post on theory of economic growth).  In this post, we present an updated version of the previous post on Ireland with new estimates of GDP per capita as published by the Conference Board in 2011. The newly published set includes readings for 2010 and also revises the previous estimates, sometimes severely. It allows seeing the case of Ireland in some new light and strongly supports our concept. As we supposed 5 years ago, Ireland GDP was highly overestimated and has fallen quickly to fit the concept of constant annual increment or inertial growth.  

Originally, the concept of constant annual increment in real GDP per capita, G, as observed in all developed countries, was introduced 5 years ago in a working paper [1] and then published in the Journal of Applied Economic Sciences [2]. We found that in the long run the trajectory of GDP growth is a linear function of time:

G(t-t₀)= G₀+B(t-t₀)

where G₀ is the initial level of GDP per capita at time t₀ in a given country, B is the country dependent increment measured in dollars. Therefore, the rate of growth of real GDP per capita, dlnG/dt, has a decelerating trend:

dlnG/dt = B/G

This assumption gives excellent statistical results and explains the evolution of real GDP per capita in the biggest developed countries. There were two exceptions – Ireland and Norway. (The latter economy is likely driven by oil demand.) Before 1990, Japan also demonstrated a larger positive deviation from the constant trend but then quickly returned to it during the 1990s and 2000s. We foresaw the same effect for Ireland.

So, five years ago, I wrote 

An opposite example of an excellent recovery gives Ireland with corresponding results displayed in Figure 11. A slow start was quickly compensated and the last twenty years of an extremely fast growth resulted in the leading position in the world economy with the mean increment $678. There are some doubts, however, that future will be so successful. Such a long and quick growth always ends up in a depression. This was observed in Japan and is related to the long-term decrease in the number of the specific age population [Kitov, 2005a]. Ireland has managed to increase birth rate for a very long period and has an age structure similar to that observed in Japan 20 years ago. The population distribution is currently peaked near 20 years with the defining age of 18 years. The years to come will demonstrate only decrease in the defining age population.

Fig. 11. Same as in Figure 4 for Ireland. The mean value is $678. The growth of the real GDP per capita is outstanding during the last twenty years. There is a downward tendency during the last four years, however.

In Figure 11 borrowed from the paper, one can observed an extremely high deviation of constant increment. Nevertheless, we put the progress of the Irish economy under doubt. The reason was its similarity to the Japanese case and the underlying model of real GDP growth, which includes population of a country specific age. In January 2011, we presented a new version of the curves in the above Figure (see Figure 1 below) with data up through 2009 which were available in January 2011. The slope of the trend was +0.0272 instead of +0.0608 in 2004, i.e. fell by a factor of 2. This slope is much close to the zero value.

Figure 1. Same as in Fig. 11  above with data between 1950 and 2009. The increment of real GDP per capita vs. real GDP per capita in Ireland. All data are borrowed from the Conference Board data base (http://www.conference-board.org/economics/database.cfm).

The revised GDP per capita data and one new reading present a quite different picture in Figure 2. The positive excursion between $30000 and $50000 in the curve does not look so dangerous for our concept and the slope now is only +0.0155, i.e. by a factor of 3 lower than in 2004. Hence, the Irish GDP per capita is not an exclusion form the general rule that real GDP per capita does grow with a constant increment in the long run, as other developed countries.

This observation makes Solow's model of economic growth empirically inconsistent, and thus, void.  

 

Figure 2. Same as in Figure 1 for the 2011 version of the Conference Board Total Economic Database

The near future of the Irish GDP per capita is under question as well: it will likely decrease or increase just marginally in 2011 and in the next several years. We will keep reporting on the case.   Ireland provides a higher volatility in the GDP growth, which is driven by unusual population pyramids with a strong peak at one age. (Same shape is observed in Japan, but the peak age is 25 years larger.) 

References

[1] Kitov, I., (2006). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/2738.html

[2] Kitov, I., (2009). The Evolution of Real GDP Per Capita in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. IV(1(8)_ Summ), pp. 221-234.