Krugman on the effect of quantitative easing in Japan

Paul Krugman shows in this post that the original quantitative easing (QE) in Japan did not help at all. Money supply did not react to an artificial increase in the monetary base. This observation raises a question on the effectiveness of a similar monetary policy in the U.S.

We have a simple explanation of the observed insensitivity of price inflation on QE:  inflation depends on the change in labor force, LF, not on monetary policy. The following models for the GDP deflator, DGDP, and CPI inflation, CPI, were obtained and presented in our previous posts:

DGDP(t) = 1.9d(lnLF(t))/dt – 0.0084      

CPI(t) = 1.3d(lnLF(t))/dt + 0.0004

Two figures below illustarte these models. There is no room for the BOJ to influence deflation after 1995.  

How long will last the crisis in Greece?

In our previous posts, we discussed the evolution of real GDP per capita in selected developed countries. One of striking examples of dramatic changes is Ireland, where we predicted a deep fall many years ago. This prediction was based on the empirically justified concept of constant annual increase in real GDP per capita, G, in developed countries. We found that in the long run the trajectory of G 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 (chained) dollars. Because of the constancy of the annual increment of real GDP per capita (in the long run) in developed countries we call this type of real economic growth the inertial growth. It is an analog of mechanical notion of inertia.

It should be noticed that the rate of growth, dlnG/dt, has to decelerate with time:

dlnG/dt = B/G

Empirically, the introduction of a constant increment gives excellent statistical results and explains the evolution of real GDP per capita in the biggest developed countries. For Greece, we first calculated coefficients A and B in 2003 using data from the Conference Board (http://www.conference-board.org/economics/database.cfm). Figure 1 depicts two curves dG/dt vs G. The original curve is based on the published data. The corrected curve takes into account the ratio between total and working age population. Technically, one should not calculate per capita values using total population since only working age population produces all goods and services. In 2002, the slope of the annual increment (also show in the Figure) was large and positive. It was lower than that for Ireland or Norway but larger than in the biggest European countries. Since we predicted a deep fall in Ireland, we also could expect a smaller drop in the increment for Greece. It was not our primary interest, however.

Fig. 1. Annual increment of real GDP per capita in Greece as obtained from the Conference Board database. The mean value for the period between 1951 and 2002 is shown for the population corrected time series.

 The current economic and financial crisis in Greece has attracted enormous attention. The reasons behind the crisis were actively discussed and we propose a simple explanation as based on the inertial economic growth.  Figure 2 demonstrates that the constancy of annual increment is a fundamental feature of real GDP growth. Several years of extraordinary fast growth in Greece observed in the 2000s must be finished in order to return the trend of the increment curve back to the mean value. The slope in Figure 2 is much smaller than that in Figure 1. Thus, one can expect that the annual increment of real GDP per capita in Greece may return to the level of $520 any time soon. The fall between 2008 and 2010 has played its stabilizing role and the Greek economy is almost ready to continue its healthy growth.

Figure 2. The increment of real GDP per capita vs. real GDP per capita in Greece between 1951 and 2010.

On the slow growth of working age population

There is a discussion on the Seeking Alpha of my post on the last Employment Situation Summary issued by the BLS several days ago. Lee Adler asked about the evolution of working age population, WAP, in the U.S. during the past 50 years. This question has arisen because I had shown only the last ten years in the post. These were the years of a steady decrease in the annual increment of the working age population, which is defined as the number of people of 16 years of age and over.  Lee is right; the annual increment has two peaks - in the 1970s and between 1998 and 2003 as Figure 1 shows.  During the 1980s and 1990s, the increment was at the level of 2,200,000 per year, and in the 2000s it fell from 3,000,000 and more per year to ~2,000,000 per year in 2008 and 2009. One should not trust the peaks in 2000 and 2003. These are caused by one-sided revisions of the total population after the 2000 census. The numbers were corrected after 2000 and 2003 but not before what created severe steps in the WAP.

Figure 2 depicts the evolution of the change rate of the WAP, dWAP/WAPdt or dlnWAP/dt. This is to show that in relative terms (the rate of unemployment and employment-population ratio are defined in relative terms) the current growth of the WAP is not fast from the historical point of view. The 2008 through 2010 values are the smallest since the early 1950s when the aftermaths of the Great Depression and WWII were the most painful. Thus, the current decrease in the growth rate of working age population is one of the reasons behind the slow employment recovery.

Figure 1. Annual increment of the working age population (black line) and its 5-year moving average (red line).

Figure 2. The rate of growth of the working age population (black line) and its 5-year moving average (red line).

What's happened to the economy?

There is an old joke. One economist asks another economist:

- Do you understand what's happened to the economy?
-O'k.  I'll explain you.
- I can explain myself, but do you understand? 

Before one starts explaining the current state of economy it is always good to think a bit about understanding.
In my view, if one can not predict quantitatively what will happen in the near future (a sort of understanding) s/he should not start explaining.  

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.

Forecasting S&P 500 returns. Quarterly update

Three months ago we revisited our prediction of the S&P 500 return including the estimate of real GDP for the fourth quarter of 2010. Here, we update our model and include the GDP estimate for the first quarter of 2011 and the monthly closing prices through May 2011. As discussed in our working paper on S&P 500, there exists a trade-off between the growth rate of real GDP, G(t),  and the S&P 500 returns, R(t). The predicted returns, R_p(t), can be obtained from the following relationship: 

R_p(t) = 0.0064dlnG(t) - 0.03   (1) 

where G(t) is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA. 

Figure 2 displays the observed S&P 500 returns and those obtained using real GDP. As before, the observed returns are MA(12) of the monthly returns. The period after 2003 is relatively well predicted. Therefore, it is reasonable to assume that G(t) can be used for modeling of the S&P 500 index and returns. Reciprocally, current S&P 500 may be used for the estimation of real GDP. The predicted return is lower than that observed in April and May 2011. We can assume that the level of S&P 500 should be corrected downwards or the preliminary estimate of GDP should be revised up.

Figure 1. Observed S&P 500 return and that predicted from real GDP. For a given quarter, all monthly values of the growth rate relative to the previous quarter are equal.  

The rate of unemployment in the U.S. may fall to 6% by the end of 2011

As in the previouspost, we refer to our model which links the rate of participation in laborforce, LFP, to the change in real GDP per capita. For short time intervals, one replaced labor force with employment, E, and GDP per capita with GDP. Now we use the rate of unemployment, UE, instead of the employment-population ratio, E/P. Unlike the E/P, unemployment negatively depends on real economic growth, i.e. should fall when dGDP/GDP is large. Thus, we scale the UE in the following way: dGDP/GDPdt = 1.1(8.0-UE), where coefficients 1.1 and 8.0 were estimated empirically.   Figure 1 shows the evolution of dGDP/GDPdt and UE) in the U.S. after 1990. The latter variable is shifted 12 months back in order to fit the peaks and troughs in the dGPG/GDP between 1990 and 2010.

 The overall agreement between the curves is excellent and allows forecasting the UE since the dGDP/GDPdt curve leads by 12 months. Then, the current UE (9.1%) value corresponds to May 2010 in the DGDP/GDP curve. Therefore, the rate of unemployment should fall to the level of 5% to 6% by the end of 2011.

Figure 1. The annual change rate of real GDP, dGDP/GDP, and the scaled rate of unemployment, UE.