As mentioned in our previous post on Japan, it has no good prospective in the long run. This post was initially pubslished in November 2010. It is instructive to update it and demonstrate again that Japan has no stellar future in sense of the lowered rate of real growth, slightly elevated unemployment and very extended (decades) period of deflation.

**This is an excerpt from our monograph****“mec****ђanomics” or “Economics as Classical Mechanics”**Japan is a country with a modern statistical service. The Statistics Bureau (JSB, 2006) of the Ministry of Internal Affairs and Communications provides information on various economic and demographic variables. In this Section, we are specifically interested in real GDP per capita and the estimated and enumerated distributions of the Japanese population by distinct years of age. The OECD (2010) and the Conference Board (2010) provide additional population data and estimates of GDP per capita, as converted at various PPPs.

The peculiarity of real economic growth in Japan can be characterized by the difference in annual increment of real GDP per capita with the mean value of $494 between 1960 and 1991 and only of $168 between 1992 and 2003. Here we use real GDP published by the Conference Board (CB, 2006) as expressed in 1990 US dollars (i.e. converted at Geary Khamis PPPs). Excluding the smaller economies of Norway and Ireland, no other developed country has experienced a GDP per capita decline as significant as $326 (in mean value) between periods of strong growth and depression.

Obviously, there were periods of poor performance as well as prosperous years in many developed countries. But the duration and the amplitude of these phenomena in Japan need an explanation far beyond the current understanding provided by the mainstream economics. Kydland and Prescott (1982) developed a theory (RBC) explaining business cycle by exogenous shocks to productivity. Being a relatively useful tool for formal description of stochasticity during stationary periods, the RBC fails to predict the essential jump in the Japanese time series, if no extraordinary assumptions are used (Hayashi and Prescott, 2002). In addition, their approach does not suggest any solution for recovery from the current state.

There were several practical attempts to revitalize the Japanese economy based on various economic theories and assumptions. All failed as one can conclude from the figures of economic growth and inflation during the past thirty years. Almost all economic problems in Japan have been aggravating over time, mirrored by deflationary period that started in 1999 as well as frequent recessions. Only in 2005, some indications of potential recovery from deflation were discussed. Chapter 2 of this book will however shows that price deflation will likely extend into 2050. After the past twenty years of unsuccessful attempts to produce a model that would consistently explain the unprecedented and very special case of the Japanese economy, a new insight is necessary for the explanation of the poor economic performance.

Here, we apply the model presented in Section 1.1.1 to describe real economic growth as related to only one source - population. This growth is defined as a sum of two components: inertial growth and fluctuations. Inertia is associated with a constant annual increment in real GDP per capita. In the USA, the relative amplitude of fluctuations around the trend is equal to a half of the relative change in the number of nine-year-olds; this defining age may vary across developed countries.

The population-based economic concept is straightforward and parsimonious. It involves only one defining parameter and is accompanied by the advantage that any desirable accuracy is attainable provided precise enumeration of population is available. Before the true population is counted, any improvements in methodology and practice of this enumeration would result in more accurate predictions of economic growth.

For Japan, via using the trial and error approach for the estimation of coefficients in equation (1.1), we have originally revealed a stronger dependence on the change in population. Therefore, the relationship for the growth rate has to be re-written in a more general form:

dG(t)/G(t)dt = A/G(t) + BdNs(t)/Ns(t)dt (1.8)

where A and B are empirically determined coefficients, Ns(t) is the number of people of the defining age. For Japan, the defining age of eighteen years has been found.

Relationship (1.8) implies that the growth rate of GDP depends explicitly and entirely on the attained level of real GDP per capita and the population change. If to gather relevant terms on both sides of the equation, this relationship can be simplified in the following form:

d[G(t) - (At + C)]/G(t) = BdNs(t)/Ns(t) (1.9)

where C is the constant of integration, i.e. the initial condition of the initial value problem.

Relationship (1.9) demonstrates that the evolution of GDP depends only on the population change term with constants A, B, and C to be determined by calibration and initial conditions. It is worth noting that the number of people of defining age is an exogenous parameter because it does not depend on the history of GDP per capita. There is a menu of tools to control such demographic characteristics as birth rate, mortality rate, and net immigration in addition to the level of GDP per capita. Besides, many real forces influencing general demographic processes are out of control. However, there is correlation between birth rate and the speed of economic growth, which potentially introduces a slightly coherent interference.

We use two estimates of real GDP per capita provided by the OECD (2000 US$) and the Conference Board (1990 US$). These values are obtained as the overall real GDP divided by total population. As discussed in Section 1.1.2, GDP per capita should be related to working age population. So, both GDP series are corrected for the working age to total population ratio, which is displayed in Figure 1.17. The bump around 2000 is likely of artificial character and is associated with a sudden increase (after 2000 census) in the total population without any response in the working age population.

Figure 1.18 presents two GDP series: the OECD’s one, which is equivalent to the JSB’s time series, and the one from the Conference Board. Both time series practically coincide except for the decade between 1980 and 1990, where the OECD estimates are slightly higher. In 2009, the growth rate of real GDP per capita was -5.3% per year. This is due to the overall fall in real GDP and also due to the decrease in the working age population.

Figure 1.17. The ratio of total and working age population in Japan.

Figure 1.18. Growth rate of real GDP per capita (corrected for working age population) as reported by the Conference Board and OECD. Notice the difference between 1980 and 1990. In 2009, the CB estimate is at the level of -5.3% per year. Solid line represents the trend as obtained from term A/G, where A=$600 (2000 US$).

Annual single-year-of-age population estimates are available from 1920 to 2009 (JSB, 2010). The accuracy of these estimates is apparently decaying back in the past. The population estimates between censuses are usually based on current information related to birth rate, age and sex dependent mortality, and net migration. In Japan, censuses are conducted every five years, i.e. twice as often as in the USA. The most recent census with the data available for analysis was conducted in October 2005. The intercensal estimates, relevant surveys, statistics and methodology are tested by the census data.

In practice, censuses are considered as a more reliable and accurate source of population related information than that associated with the intercensal estimates. In Japan, for example, it is obligatory to answer the census questions. It happens very often that the population estimated at the end of an intercensal period does not coincide with that enumerated in the later census. This effect is known as the “error of the closure” and sometimes reaches several per cent in such developed countries as the USA and the UK.

In order to match the enumerated figures, the estimated population is adjusted for the error of the closure. This correction is usually age dependent and may significantly differ even for neighbouring ages. Figure 1.19 illustrates the magnitude and timing of relevant corrections. The relative increment in the number of people of age i, [(Ni+1(t)-Ni(t-1)]/Ni(t-1), per one year is plotted for the number of 17- and 18-year-olds. One can easily find the census years in this Figure: sharp and high amplitude adjustments are very typical for statistical and census agencies over the world.

For the purposes of our study, strong disadvantage of these step corrections consists in the difference of their amplitudes as applied for adjacent years. For example, in 1995, the number of 18-year-olds was corrected by about 0.4% compared to the mean annual increment of 0.03% during the previous four years. At the same time, the correction applied to the number of 17-year-olds is very small. Thus, for 1994, it is apparent that the number of 18-year-olds is biased. In particular, the difference of 18-year-olds for 1995 is biased by 0.4%. The difference for 1996 is less biased because it involves two corrected values.

In 2000, the corrections in Figure 1.19 are opposite in sign, which indicates even larger measurement errors in the intercensal estimation procedure. In 1970, the corrections were as large as 2%. So, one has to be careful when using population estimates in economic analysis. Of course, the inherent uncertainty of population surveys and macroeconomic measurements cannot be avoided and, in quantitative analysis, one may only rely on larger population differences. Any discrepancy in amplitude between predicted and observed value, which is comparable to the inherent uncertainty in population, inflation or GDP measurements, might be neglected. Measurement errors may be uncorrelated over time and can be smoothed out with a zero residual by a long period filter or in cumulative representation.

Figure 1.19. Relative growth rate of a single year of age population per one year: [(Ni+1(t)-Ni(t-1)]/Ni(t-1).

The JSB’s population estimates are used for the prediction of the growth rate of real GDP per capita. According to (1.8), the relative change dN18/N18 defines all fluctuations in real economic growth around the inertial growth as determined by constant annual increment A. Figure 1.18 depicts the growth rate of measured GDP per capita, as obtained from the OECD and the Conference Board. Inertial growth, defined as a reciprocal function of GDP per capita with a constant increment A=$600 (2000 US dollars), is also shown in the Figure. The inertial component is not smooth because we use actual readings of GDP per capita. Currently, the inertial growth is above the average growth rate over the last 20 years. This is due to the negative input of the falling number of 18-year-olds.

Coefficients A and B in (1.8) have been determined in a calibration procedure aimed at matching the observed and predicted values of growth rate. By varying A and B one can reach the best visual resemblance between the curves. Figure 1.20 shows a model with A=$600 and B=2/3, as obtained with the OECD data available in 2010. All values of GDP per capita are expressed in 2000 US dollars. We found factor B to be somewhat larger than 0.5 for Japan. This finding might imply that the economic growth fluctuations in Japan are more sensitive to the change in the specific age population.

For Japan, the principal feature to be modelled is the sharp fall in growth rate that started in 1991. This is a critical point for any theoretical description of the Japanese economic evolution. Our model links this drop to the dramatic change in the number of 18-year-olds. Figure 1.21 displays the evolution of population for several adjacent ages. The specific age of 18 years has been chosen because this age is characterized by a fast decay starting in 1991. When extrapolated from N10, as shown in Figure 1.21, N18(t) (=N10(t-8)) approaches the level of 1,200,000 in 2010 and does not fall further in the 2010s.

Figure 1.20. Modelling the observed evolution of growth rate of GDP per capita using relationship (1.7). The most important feature is the fall in the growth rate in 1991.

There is a discretization problem associated with timing of the GDP and the population readings. By definition, GDP per capita values are given for the last day of corresponding years. The population estimates are published for the first day of October. So, formally these variables are separated by one quarter. Then the number of 17-year-olds should be used if to judge by the start of decrease demonstrated in Figure 1.21. One has to bear in mind, however, that for N18 the mid-term point is April 1. This date divides N18 in approximately equal portions. Thus, we consider the estimate of N18 (April 1, 1991) as the closest to the end of 1990 and use this age population as the defining one. We have to shift the predicted curve by a quarter back (from April 1, 1991 to January 1, 1991) in order to synchronize these curves. The procedure has brought an excellent match in the most important period between 1990 and 1993. One can also use N17 with a one year shift or any other younger age with relevant time shift.

Figure 1.21. The evolution of single-year-of-age populations. Shown is the number of 10-, 17-, 18- and 19-year-olds. The number of 18-year-olds starts to decrease in 1991.

Figure 1.22 forecasts real economic growth for the next ten years. We use two projections of N18: the one extrapolated from the estimated number of 8-year-olds in 2009 and that from the 2005 (census) age pyramid. Supposedly, both projections are relatively good approximations for the future demographic development in Japan.

Figure 1.22. Modelling the observed and future evolution of growth rate of GDP per capita. The prediction till 2020 is given from the number of 8-year-olds (N8) and the 2005 population age distribution extrapolated into the number of 18-year-olds. Both approximations give close predictions.

The difference between the measured and predicted dG/G in Figures 1.20 and 1.22 is less than 1% between 1985 and 2003. In the second half of the 2000s, the actual growth rate is higher than the predicted one. Still the difference is within the tolerance range as related to the measurement errors. So, it is instructive to use (1.8) and predict N18 from GDP.

Figure 1.23 depicts the predicted time series and two enumerated ones: the estimated N18 and that projected from the 2005 age pyramid. Both actual curves coincide in 2005 and the adjacent years, but the projected curve is below the enumerated one in the past. This is opposite to the effect observed in the United States (see Figures 1.12 through 1.14). Obviously, the difference consists in the rate of the overall population growth. In Japan, the population shrinks and the US population grows. However, the predicted curve fits the number of 18-year-olds between 1975 and 2005. The deviation between 2005 and 2010 is likely to be compensated by the 5.3% fall in 2009.

The best fit model in Figure 1.23 is characterized by A=$550 (2000 US$), but B=1/2 that is different from the previously estimated value of 2/3. This discrepancy is associated with the poor resolution of the dG/G prediction. Essentially, we have fit only the drop in 1991 and neglected the long-term behaviour. The prediction of N18 uses the level of GDP per capita instead of its first difference. As a result, the short-term fluctuations in the dG/G curve are cancelled out and the predicted N18 curve fits observations much better. It is interesting that the deep and sharp trough in N18 observed in 1984 is expressed by a wider but shallower depression between 1983 and 1989. This is the effect to be investigated in detail. Otherwise, our model shows a reasonable level of accuracy for data between 1970 and 2009. If the number of 18-year-olds will follow up the predicted curve in Figure 1.21, one may expect the rate of growth between 1% and 2% per year in the 2010s. Essentially, the growth will follow up the inertial component, A/G, since the defining age population will be constant.

Figure 1.23. Enumerated and predicted number of 18-year-olds.

There is almost no migration and the Japanese population structure is very stable with a well-predictable death rate. Hence, it is possible to predict the GDP growth rate with a high reliability. Having the forecast and knowing the principal mechanism driving real economic growth one can propose a new migration strategy, however, in order to speed up the economy. Any means to accelerate the birth rate will give results only in 18 years. It is obviously too long a wait for such means to be incorporated in the current socio-economic policy. On the other hand, the Japanese have paid fifteen years of low performance for the ignorance of the importance of demographic processes. Reoccurrence of such a depressive economic period should ideally be avoided in the future.

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