Cumulative inflation in Japan: 1982-2009

As promised in one of the previous posts, we present here a more detailed analysis of price inflation in Japan. The case of Japan is the best illustration of our inflation vs. labor force concept. Here we carry out an estimation of the empirical relationship between the change rate of labour force, dLF(t)/LF(t), inflation, pi(t).

Data on labour force and inflation were obtained from various sources. The Statistics Bureau of the Ministry of Internal Affairs and Communications provides information on various economic and demographic variables. The U.S. Bureau of Labour Statistics provides two sets of data: one obtained according to the national definition (NAC) and another obtained according to the U.S. definition of corresponding variable.

There are several measures for inflation. Most popular definitions for the overall price change are GDP deflator and Consumer Price Index. In many countries, the CPI definition was extended recently by imputed rent. Thus, various inflation time series might be studied, but only two of them are used. Figure 1 shows two inflation estimates: the OECD GDP deflator and the CPI provided by the Japanese Statistical Bureau. The difference between these curves is minor but very illustrative. The GDP deflator curve is consistently below CPI inflation since 1990.

Figure 1. CPI and GDP deflator in Japan.

As for many economic parameters, labour force estimates are also agency dependent due to various definitions and different population adjustments. Figure 2 compares the change rate of labour force provided by the OECD, Eurostat, according to national and U.S. definition. Despite strong similarity, discrepancies reaching 0.1 (or 10% of the total labour force) are observed. Such a difference is an important indicator of the difficulties in defining labour force. Further investigations are necessary to elaborate a consistent understanding of the term “labour force”. The model linking labour force change and inflation is likely a good candidate for quantitative consolidation of various definitions and approaches.

Figure 2. Comparison of four versions of the change rate of labour force in Japan: Eurostat, OECD, national accounts (NAC) and US definition.

First, we test the existence of a link between inflation and labour force. Because of the structural (measurement related?) break in the 1980s, we have chosen the period after 1982 for linear regression. By varying the lag between the labour force and inflation one can obtain the best-fit coefficients for the prediction of CPI inflation, pi(t), according to the following relationship:

pi(t) = 1.31dLF(t-t0)/LF(t-t0) + 0.0007 (1)

where the time lag t0=0 years; standard errors for both coefficients are shown in brackets. Figure 3 depicts this best-fit case. There is no time lag between the inflation series and the labor force change series in Japan. Free term in (1), defining the level of price inflation in the absence of labour force change, is practically undistinguishable from zero.

A more precise and reliable method to compare observed and predicted inflation consists in the comparison of cumulative curves. Short-term oscillations and uncorrelated noise in data as induced by inaccurate measurements and the inevitable bias in all definitions should be smoothed out in cumulative curves. Any actual deviation between two cumulative curves persists in time if measured values are not matched by the defining relationship. The predicted cumulative values are very sensitive to free term in (1). Therefore, in the upper panel of Figure 3 we use the slope obtained by the matching of cumulative curves shown in the lower panel of Figure 3:

pi(t) = 1.43dLF(t)/LF(t) + 0.000 (1′)

For Japan, the cumulative curves are characterized by complex shapes. There are periods of intensive inflation growth and a deflationary period. The labour force change, defining the predicted inflation curve, follows all the turns in the measured cumulative inflation. One can conclude that relationship (1) is valid and the labour force change is the driving force of inflation.

For obvious reasons, it is difficult to precisely estimate the change in labour force level during one year. However, there are some benchmark years when all previous estimates are revised in order to match a better measured level of labour force. So, one can expect an increasing relative precision of the change in labour force with increasing time baseline; the net change during 10 years should be measured with lower relative uncertainty than during one year.

Figure 3. Measured inflation (CPI) and that predicted from the change rate of labour force. Upper panel: Annual curves. Lower panel: Cumulative curves between 1982 and 2009. A good agreement between the cumulative curves illustrates the predictive power of our model.

Using relationships (1′), it is possible to quantitatively predict the evolution of inflation and unemployment through 2050 using various labour force projections. The National Institute of Population and Social Security Research provide quantitative projections of the total population, which can be used to obtain future estimates of the labour force. We consider the case of constant labour force participation rate fixed to 0.521, as measured in 2000. For this scenario, Figure 4 demonstrates that the level of labour force in Japan will decrease from 67,000,000 in 2010 to 57,000,000 in 2050.

Figure 4. Projection of the labour force evolution between 2005 and 2050.

Figure 5 displays the prediction of inflation until 2050. According to this prediction, 2009 was the last year of positive inflation (CPI) as Japan enters a prolonged deflationary period. The rate of depopulation will be accelerating after 2020. This will result in the increasing deflation approaching 1% per year on average. According to (1′), the overall population decline of 10 per cent will reduce the overall price level (CPI or GDP deflator) in Japan by approximately 15% by 2050. However, this forecast is based on an assumption about constant rate of labour force participation, which may also change over the next 40 years. Ageing population usually has lower participation rate.

Figure 5. CPI inflation rate in Japan through 2050.

One can conclude that the change rate of labour force is definitely the determining process behind inflation in Japan.

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