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.

A share price model for Forest Laboratories between 2009 and 2011

Forest Laboratories (FRX), like Abercrombie & Fitch, also was one of the first companies with a stable and deterministic share price model estimated in September 2009 (back into November 2008).  This is a company from Healthcare subcategory of the S&P 500 list specialized in drugs manufacturing. We revisited this model in September and December 2010 and always found the same defining variables with almost the same time lags.

Our approach to deterministic share pricing (we have been tracking approximately 70 companies from S&P 500) is based on the decomposition of a share price into a weighed sum of two selected consumer price indices. For FRX, all models between 2009 and 2011 are defined by the (not seasonally adjusted) index of dairy and related products (DAIRY) and the price index of other household equipment and furnishing (OHEF), as reported by the US BLS. The former CPI component leads the share price by 3 month and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011.

In this post, we compare the 2009 and 2011 share price models for FRX. For the 2009 model we use the most recent defining CPIs, as available in April 2011, and the measured monthly closing prices through March 2011. This allows validating the initial model and demonstrating its reliability.  These models are as follows:

FRX(t) =  -0.53DAIRY(t-3) – 4.18OHEF(t-5)  - 13.41(t-1990) + 706.57 (September 2009)   

FRX(t) =  -0.61DAIRY(t-3) – 3.89OHEF(t-4)  - 11.65(t-1990) + 668.75 (March 2011)   

where t is calendar time. All coefficients are close with just minor variations related to the updated share prices. Therefore, the model is effectively the same between November 2008 and March 2011. In other words, we obtained a deterministic (leading by three months) model which was valid during 30(!) months.   Figure 2 illustrates the difference between the original and current models.  

The residual error is $4.40 for the period between June 2003 and March 2011. From the most recent model in Figure 2, we expect a fall to the level of $20 per share in 2011 Q2.

 

Figure 1. Evolution of the price of DAIRY and OHEF.

Figure 2. Observed FRX share prices and that predicted in 2009 and 2011. The early model has a larger time lag for the OHEF index which results in a slight underestimation of the share price in 2010 and 2011.  

Alcoa share price

Alcoa (AA) is a company from Materials subcategory of the S&P 500 list specialized in aluminum. According to our general approach to share price modeling we decompose the observed time history of the monthly closing AA stock price (adjusted for splits and dividends) into a weighted sum of two CPI components, time trend and free term.  Two defining CPI components are selected to minimize the model (RMS) error and may lead or lag behind the share.  

The AA model is defined by the (not seasonally adjusted) index of food away from home (SEFV) and the price index of rent of primary residence (RPR), as reported by the US BLS. The former CPI component leads the share price by 2 months and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011. It seems these indices have been evolving in sync since 2002 with the only step-like change in the SEFV in 2008.  The final empirical pricing model for AA is as follows:

AA(t) =  -6.71SEFV(t-2) + 3.34RPR(t-4)  + 19.23(t-1990) + 298.87

where AA(t)  is a share price in US dollars, t is calendar time. Figure 2 illustrates the observed and predicted models.  The residual error is $3.12 for the period between July 2003 and March 2011. One can expect the share price to hover at the level of $15 in the near future.  

Figure 1. Evolution of the price of SEVF and RPR.

Figure 2. Observed and predicted AA share prices.

Krugman's misinterpretation of long-term inflation

Paul Krugman has shown the evolution of headline CPI (level) since 2000 in order to demonstrate that the current trend manifests upcoming inflation. His conclusion is likely wrong due to couple mistakes in the presentation and interpretation.

1. He narrowed the period to ten years and thus implied that the headline CPI trend was the same before 2000 and will be extended into the 2010s. Both assumptions are not true.

Figure 1 definitely shows that the trend before 2000 was different from the current one. Between 1980 and 1998, the headline CPI grew at a lower rate than the core CPI and they diverged. In 2000, the indices started to converge and the CPI curve intercepted the core CPI one in 2009. Very likely that the future trend will repeat that observed between 1980 and 2000, not continue the trend observed in the 2000s.

Therefore, the core CPI will be growing at a higher rate again and the headline CPI will sink below the core CPI level. Then the CPI inflation rate will be smaller than that defined by the core CPI. 

Figure 1.  Upper panel: The headline and core CPI levels between 1980 and 2011. Lower panel: the difference between the core and headline CPI demonstrates linear trends. One may expect the next trend to be positive and the headline inflation rate will be lower that the core inflation rate.  Krugman's assumption on the long-term trend in the headline CPI was not correct.

2. The core inflation rate has been on decline since 2007, as Figure 2 shows. Despite very high volatility, the headline CPI always returned to the core CPI level. Our inflation model [1] shows that the current trend in the core CPI will be retained in the next decade below the zero line. Hence, the overall inflation rate will be also negative. An extended deflationary period will be observed.

Figure 2. The rate of price inflation as defined by the headline and core CPI.

1. Kitov, I. (2006). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

FOMC on inflation

Several days ago we presented a graph (see Figure 1) with headline and core (CPI) inflation which showed a downward trend in the core price inflation. Yesterday the Federal Open Market Committee (FOMC) issued a press release also addressing inflation among other topics. Specifically, the FOMC said:

…. Inflation has picked up in recent months, but longer-term inflation expectations have remained stable and measures of underlying inflation are still subdued…

The Committee will … continues to anticipate that economic conditions, …, subdued inflation trends, and stable inflation expectations, are likely to warrant exceptionally low levels for the federal funds rate for an extended period.

Hence, the FOMC is currently expecting that the surge in oil price will calm down and the CPI will fall back below the core CPI in the next few quarters. In Economic Projection, the expected central tendency of price inflation (PCE) in 2012 is between 1.2 and 2.0 per cent per year with the range 1.0 and 2.8 % per year. 

We still expect that the core CPI inflation will fall below the zero line in 2012 and the headline CPI will rebound from its current higher level below the core CPI manifesting a deflationary period in the US [1].

Figure 1. The rate of price inflation as defined by the headline and core CPI.

Kitov, I. (2006). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

Abercrombie & Fitch between 2009 and 2011

Abercrombie and Fitch (ANF) was one of the first companies with a stable and deterministic share price model estimated in September 2009.  This is a company from Services subcategory of the S&P 500 list specialized in apparel stores. We have revisited this model several times since 2009 and always found the same defining variables. The model is based on the decomposition of a share price into a sum of two selected consumer price indices. All models are defined by the (not seasonally adjusted) index of pets, pet products and services (PETS) and the price index of transportation services (TS), as reported by the US BLS. The former CPI component leads the share price by 1 month and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011.

In this post, we compare the 2009 and 2011 share price models for ANF. For the 2009 model we use the most recent defining CPIs as available in April 2011 and the measured monthly closing prices through March 2011. This allows validating the initial model and demonstrating its reliability.  These models are  as follows:

ANF(t) =  -4.56PETS(t-1) – 2.96TS(t-4)  + 47.09(t-1990) + 544.90 (September 2009)   (1)

ANF(t) =  -4.74PETS(t-1) – 2.45TS(t-4)  + 44.47(t-1990) + 494.79 (March 2011)   (2)

where t is calendar time. All coefficients are very close with just minor variations related to the updated share prices. Therefore, the model is effectively the same between January 2009 and March 2011. In other word, we obtained a deterministic (leading by one month) model which was valid during 27(!) months.   Figure 2 illustrates the difference between the original and current models.  

The residual error is $5.88 for the period between June 2003 and March 2011. One can expect a fall in the share price. Otherwise, the model will fail in the near future after 2 successful years.  

 

Figure 1. Evolution of the price of PETS and TS.

Figure 2. Observed ANF share prices and that predicted in 2009 and 2011.