Krugman on low inflation

Krugman is a great supporter of the opinion that the rate of price inflation in  the U.S. will be low in the near  future. In this post he asks fundamental questions related to the real driving force behind inflation:

First, do you see any sign that workers are about to (or are even able to) demand higher wages to compensate for the higher prices of gas and food?

Second, do you any sign that employers are getting ready to make more generous wage offers?

Third, have you heard anything about companies feeling that they have room to raise prices by substantially more than the rise in their raw material costs?

The mainstream economics fails to derive any quantitative model of inflation explaining the  conditions of big changes. This is real reason for the current discussion on the future of inflation in the U.S. Experts do not understand when workers, employers and companies are ready to raise wages and prices. We answered this quastion 6 years ago. It will take another decade  to convince specialists and general public.
Why economists do not trust accurate quantitative prediction?  The answer is obvious - economics  is not a science; and economics profession is  kind a sect.

The history of GDP growth: between Luxembourg and Cyprus

One of interesting consequences of the finding discussed in the previous post is that the gap in GDP per capita between developed countries should be constant or a linear function of time. The former case is possible only when two mean annual increments are equal. When two countries are characterized by different mean annual increments, the gap between their GDP per capita will be growing linearly.

Using the Conference Board Total Economic Database we have estimated the evolution of real GDP per capita in European countries relative to that in the US. In other words, we have calculated differences between countries and the US:

Gus(t)-Gi(t)

, where i runs between Austria and the UK.  GDP is measured in 2010 US dollars at EKS PPPs.

Figure 1 depicts all obtained differences. Luxemburg and Ireland have been growing faster than the US since 1989.  The fastest growing country is Luxembourg according to the Conference Board. Several countries show poor results. Amongst them are Cyprus, Portugal, Italy and Switzerland. Other countries have been slightly lagging behind the US after 1989, except Norway.  Nevertheless, almost all differences are very close to linear functions of time.

The gap in real GDP per capita between these countries and the US is likely forever.

Figure 1. Differences between the US GDP per capita and those in European countries.

1000 arguments against the Solow growth model

In the Solow growth model, the rate of change in real GDP per capita must approach some constant level. This is a result of the following assumption: labor and knowledge grow at constant rates and the rate of capital growth is proportional to the level of output and the rate of capital depreciation. All assumptions are taken without empirical justification. However, actual data on real GDP tell a different story.  

Under the empirical framework we presented in this blog, real GDP per capita in developed countries grows as a linear function of time, we call it inertial growth, when population pyramid does not change much in the long run:

G(t)=At+C                (1)

Relationship (1) defines the linear trajectory of the GDP per capita, where C=G_i(t₀)=G(t₀) and t₀ is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. The relative rate of growth along the inertial linear growth trend, g(t), is the reciprocal function of G:

g(t)= A/G(t)         (2)

Relationship (2) implies that the rate of GDP growth will be asymptotically approaching zero, but the annual increment A will always be constant. This is different from the Solow model where the rate of growth is a positive (nonzero) value. Moreover, the absolute rate of GDP growth is constant and is equal to A [$/y]. This constant annual increment thus defines the constant “speed” of economic growth in a one-to-one analogy with Newton’s first law. Hence, one can consider the property of constant speed of real economic growth as “inertia of economic growth” or simply “inertia”.  In Figure 1, we present annual increments of real GDP per capita (borrowed from the Conference Board Total Economic database) in the biggest developed economies as a function of real GDP per capita in sense of equation (1). These plots validate our empirical finding and reject the Solow model. Overall, there were 19 countries analyzed in the study and no one has any distinct positive trend over the past 60 years, i.e. between 1950 and 2010.

In Figure 1, the original GDP time series are extended by those corrected for the ratio of total and working age population (the latter must be used in GDP per capita calculations). For both time series linear regression lines and equations are shown with corresponding slopes. For the biggest countries these slopes are very close to zero but can be positive or negative. A zero slope corresponds to constant annual increment.

So, we have 1000 years validating the hypothesis of a constant (but country dependent) annual increment.

  

Figure 1. Dependence of annual GDP increment on GDP (both real per capita) for select developed countries. Original GDP data are extended by those corrected for the ratio of total and working age population (the latter must be used in GDP per capita calculations). For both time series linear regression lines and equations are shown with corresponding slopes. For the biggest countries these slopes are very close to zero but can be positive or negative. A zero slope corresponds to constant annual increment.

Back to the future: Ireland versus Japan

In the previous post we mentioned the time history of the Japanese GDP per capita as a template of the future evolution in Ireland. In the 1980s, Japan was very similar to Ireland in between 1995 and 2005.  It demonstrated an outstanding real economic growth, which seemed to last forever. This growth ended in 1991, however, with the past twenty years of mediocre growth.  Ireland suffers the same decease and its fabulous growth ended in 2007. This break was foreseen in 2004 [1]. Figure 1 compares Japan and Ireland in sense of annual increment of real GDP per capita, G. We plot dG (annual) against G because of our empirical finding that dG must converge to constant:

dG=B or G(t)=G(t0) + Bt, where  B is constant and t is the elapsed time.

In Figure 1, the growth in the Japanese GDP per capita between $25000 and $32000 (2010 US dollars) is a template for the Irish growth between $25000 and $45,000. Therefore, we expect the future of real GDP per capita in Ireland to be unpleasant – it has to return to the average value (which is currently  $736) close to the Japanese one ($587).

Figure 1. Comparison of the Japanese and Irish GDP per capita between 1950 and 2010.

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.

Why the level of unemployment does not matter for real economic growth II

In the previous post we demonstrated that the level of unemployment could hardly influence real economic growth because the portion of people out of labor force changes in a much wider range (by  a factor of 5) and still does not affect the real growth. Here we present a quantitative model explaining the long-term change in the labor force participation rate, LFP, which, obviously, defines the portion of people not in labor force. In this blog, we presented similar models for Canada and Italy but without appropriate math.

We first try to model dLFP/LFP as a nonlinear function of real GDP per capita, G, and tested a simple relationship:

dLFP(t)/LFP(t) =  D₁[dG(t-T)/G(t-T) - A₂/G(t-T)] +D₂                                       (1)

where D₁ and D₂ are empirical constants, and A₂ is also an empirical. The time interval is dt=1 year, and thus, omitted in the equation. The intuition behind this model is that it is real economic that drives the change in LFP. The evolution of LFP depends on the difference between the observed rate of growth and the potential rate of growth defined by a reciprocal function of G, A₂/G.  

Figure 1 depicts the measured LFP and that predicted from real GDP per capita using equations (2) and (3). Both variables are borrowed from the Total Economy Database provided by the Conference Board. All in all, the model describes the evolution of LFP in the US since 1964 with an extremely high accuracy. In the mainstream economics, there is no other model of LFP predicting its evolution with a compatible accuracy. Moreover, the predicted curve leads by 2 years (T=2) that allows forecasting at a 2 year horizon. (See our post in January 2011 on the short term LFP prediction.)  

Al in all, the rate of participation in  labor force depends only on the evolution of real GDP per capita two years ago. Therefore, the level and rate of unemployment, as a part of labor force, plays no role in real economic growth. At least empirical facts say so.

Figure 1. Measured and predicted LFP in the US, where A₂= $360 (1990 US dollars) is empirical constant. T=2 years.

Why the level of unemployment matters nothing for real economic growth

Unemployment is a painful economic phenomenon which drives many social and political processes. For example, the Federal Reserve System has a dual mandate aimed at balancing of inflation and unemployment.  (In macroeconomic, there is no empirically derived link between these variables, however.) By definition, unemployment is treated as a crucial parameter which theoretically responsible for the level of real economic performance. When unemployment is high, real economic growth is considered as a suppressed one, and thus, below its potential value with some “natural” rate of unemployment.  In reality, economic recessions are usually accompanied by tangible increase in the rate of unemployment.  Economic logic is often faulty and says “in sync means interlinked”.   This is not the case for the relation between unemployment and real growth. Fluctuations in real growth are caused by external forces and result in the change of unemployment. This does not mean that one can decrease unemployment and thus drive economic growth.

The reason of the independence of real economic growth on unemployment is simple. The portion of unemployed, in the total working age population, UE/POP, is too small compared to the portion of people out of labor force, NLF/POP. Figure 1 displays both ratios. The portion of unemployed fluctuates near 4%  (mean value 3.8%) of the total population with amplitude of 2%. Currently, the portion of unemployed is around 6%. At the same time, the portion of people out of labor force has dropped from 42% in 1983 to 33% in 1999. Effectively, the economy included 10% more population in 2000 than in 1963. This is a much bigger change than the observed variation in the portion of unemployed. All unemployed in 2000 would be out of labor force in 1963, i.e. irrelevant to real economic growth according to the mainstream macroeconomic paradigm.

Figure 1. Comparison of the portion of unemployed, UE/POP, and the portion of people out of labor force, NLF/POP, in the total working age population, POP.

Now, it is instructive to evaluate the influence of the increasing portion of employed people, E/POP, on the rate of real economic growth. Figure 2 compares E/POP (reduced by 0.55) and the rate of GDP per capita growth, dGDP/GDP, where the overall real GDP is divided by the working age population, POP. One can see that the rate of growth has a negative trend since 1960. During this period the E/POP has increased from 55% to 63% and then dropped to59%.  From Figure 2, it is possible to conclude that the increasing proportion of employed population suppresses the rate of economic growth.

Figure 2. The portion of employed in the working age population, E/POP, compared to the rate of GDP per capita growth, dGDP/GDP.

Finally, we can answer the question why the level of unemployment means nothing for real economic growth. The fluctuations in UE are too small and their effect is opposite to the growth in the level of employment, which reduces the rate of real economic growth. In this regard, an increasing rate of unemployment is a positive phenomenon in the long run.