Here we present quantitative evidences that
the effect of abenomics on CPI in Japan is invisibly weak, if any. Our
quantitative model, which we presented at the conference “Inflation
Developments after the Great Recession” hosted (December 2013) by the Deutsche Bundesbank and sponsored by the
EABCN, is available as a CEPR working paper “Inflation,
Unemployment, and Labor Force: The Phillips Curve and Long-term Projections for
Japan”. This model shows that the current
surge in consumer prices is an abenomics
achievement, but the result of labour force increase started in 2011, i.e.
before the start of the new monetary (and economic) policy introduced by Abe. Moreover,
when the effect of increasing labour force fades away in a few months deflation
in consumer prices will be back. It is worth noting that the GDP price deflator
is still in the negative zone and that the headline CPI is a highly biased (up)
measure of inflation not to be used by sane researchers.

At
first, we present our model in detail. In this blog, we have already mentioned
that Japan is the best illustration of our concept linking inflation/unemployment to the
change in labour force. In our previous posts on the GDP deflator in Japan, we showed two cumulative curves for observed
and predicted inflation since 1980. Here we revisit similar CPI curves also two
more readings and conclude that our concept is quantitatively excellent. The
underlying data have been borrowed from the OECD and Japan Statistics.

Using stata9 and allowing a structural
break, we sought for the best-fit (in RMS sense) 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 for
consumer price inflation (CPI):

*CPI(t) =*1.39

*dLF(t-t*

_{0}

*)/LF(t-t*

_{0}

*) +*0.0004

*(1)*

where the time lag

*t*_{0}=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 (a version of CUSUM technique) 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 CPI 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

*R*=0.99. The predicted and observed cumulative CPI curves are cointegrated and thus this estimate is consistent. For the annual estimates: R^{2}^{2}=0.73. With shrinking population, and thus, labour force, the level of CPI will be falling through 2050 and likely beyond.
Now, we return to the current rise in
the headline CPI and apply (1) to monthly readings of labour force and
inflation. Figure 2 shows the change rate in labour force. One can observe the positive
trend started in the middle of 2011 and will likely extend into the first
quarter of 2014. Figure 3 compares the predicted and observed rate of inflation
(year-on-year estimates for the monthly estimates) since 2010 and demonstrates
that the current rise in the headline CPI is likely a short deviation from the
long-term trend fully related to a small rise in the level of labour force, not
the abenomics tools. Because of the overall ageing and depopulation this
positive trend will not last long and the level of labour force will definitely
fall. This fall will induce price deflation, as Figure 1 predicts.

Figure 1. Measured CPI inflation and
that predicted from the change rate of labour force in Japan.

*Upper panel*: Annual curves smoothed with MA(3).*Lower panel*: Cumulative curves between 1981 and 2012. The extremely accurate agreement between the cumulative curves illustrates the predictive power of our model. The cumulative curves are I(1) processes and we thus it was instructive to test them for cointegration. This test was successful.
Figure 2. The rate of change in labour
force, dLF/LF, since 2010. Monthly readings are used and the year-on-year rate
is calculated.

Figure 3. Comparison of the measured
inflation rate (y-o-y) and that predicted from the change in labour force.

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