The GDP deflator in Japan

We have already mentioned that Japan is the best illustration of our concept linking inflation/unemployment to the change in labour force. In the previouspost on inflation in Japan, we modelled the overall CPI. Here we illustrate the long term equilibrium relation between the GDP deflator, DGDP, and labour force. All data were obtained from the OECD.

By trial-and-error, we seek for the best-fit coefficients in the linear and lagged link between inflation and labour force. Because of the structural (measurement related?) break in the 1980s, we have chosen the period after 1981 for linear regression, which is common for almost all economic studies related to Japan. By varying the lag and coefficients we have found the following relationship:

DGDP(t)= 1.9dLF(t-t₀)/LF(t-t₀) – 0.0084        (1)

where the time lag t₀=0 years; Figure 1 depicts this best-fit case. There is no time lag between the inflation series and the labour force change series in Japan. Free term in (1), defining the level of price inflation in the absence of labour force change, is close to zero but negative.

A more precise and reliable representation of the observed and predicted inflation consists in the comparison of cumulative curves shown in the lower panel of Figure 1. We always stress that the cumulative values of price inflation and the change in labour force are the levels of price and labour force, respectively. Therefore, the summation of the annual reading gives the original estimates of price and workforce, which when are converted into rates.

Another advantage of the cumulative curves is that all short-term oscillations and uncorrelated noise in data as induced by inaccurate measurements and the inevitable bias in all definitions are effectively smoothed out. Any actual deviation between these 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).

For Japan, the DGDP cumulative curves are characterized by very complex and unusual for economics shapes. There was a period of intensive inflation growth and a long deflationary period. The labour force change, defining the predicted inflation curve, follows all the turns in the measured cumulative inflation with the coefficient of determination R²=0.96. (Again, these are actually measured curves.) With shrinking population, and thus, labour force, the GDP deflator will be falling through 2050 and likely beyond.

Figure 1. Measured GDP deflator and that predicted from the change rate of labour force. Upper panel:  Annual curves smoothed with MA(3). Lower panel: Cumulative curves between 1981 and 2010. A good agreement between the cumulative curves illustrates the predictive power of our model.