A year ago we published a paper “

**Does Banque de France control inflation and unemployment?”****We demonstrated that the French economy would likely sink into a longer period of deflation or very low inflation rate after 2013. This is an****excerpt**from the paper discussing how Banque de France could boost labour force growth and inflation by flooding the French economy with money. Instead of this simple measure there were several depressing years of contingency measures introduced by the ECB. Now the money issue is likely on the table and we repeat our analysis.
Here, we consider the rate of
inflation, unemployment, and the change in labour force altogether. For France,
the generalized relationship is obtained as a sum of (10) and (13), which
results, with some marginal tuning of all coefficients in order to reduce the
standard error of the model, in the following equation for the GDP deflator:

*π(t) =*2.69

*l(t-*5

*) - u(t-*5

*) +*0.108;

*1971*

*≤t≤*1995

*π(t) =*6.40

*l(t-*5

*) - u(t-*5

*) +*0.059;

*t≥*1996 (14)

For the OECD CPI:

*π(t) =*3.0

*l(t-*5

*) - u(t-*5

*) +*0.108;

*1971*

*≤t≤*1995

*π(t) =*5.0

*l(t-*5

*) - u(t-*5

*) +*0.067;

*t≥*1996 (15)

where we model inflation since it lags by 5 years behind the change in
labour force and unemployment. Formally, one can re-write both relationships
for

*u*(*t*). Notice that the change in the slopes and intercepts are much smaller than in individual relationships. The structural break is less prominent and thus its estimate is less reliable.
The annual and cumulative
curves for both cases are presented in Figure 12. Linear regression of the observed inflation
against that predicted according to (14) and (15) is characterized by
outstanding for annual curves statistical properties:

*R*=0.87 and RMSFE=0.015 y^{2}^{-1},^{ }and^{ }*R*=0.83 and RMSFE=0.017 y^{2}^{-1}, respectively. For the cumulative curves, both*R*are larger than 0.99 and RMSFE~0.025 y^{2}^{-1}, i.e. by 20% smaller than the naive ones (see Table 4). These estimates were obtained for the period between 1972 and 2012 with a five-year lag. These RMSFEs are the best obtained for France at a five year horizon so far. They explain the rate of price inflation to the extent beyond which measurement uncertainty should play the key role. Practically, there is no room for any further improvements in*R*given the accuracy of the current prediction.^{2}**Conclusion**

We have successfully modelled unemployment and inflation in France. Their
sensitivity to the change in labour force requires very accurate measurements
for any quantitative modelling to be reliable. Unfortunately, the OECD labour
force time series does not meet this requirement and poor statistical results
are obtained for annual readings. The best prediction is obtained with the
moving average technique applied to the change in labour force. For the period
between 1970 and 2012, linear regression analysis provides

*R*as high as 0.8 to 0.9 for the rate of unemployment and GDP deflator. The RMSFE for the best CPI model is 0.015 y^{2}^{-1}and 0.010 y^{-1}for the GDP deflator, both at a four year horizon. For the period after 1994, the best RMSFE=0.005 y^{-1}for both measures of inflation. In 1994, our models have structural breaks found by the OLS fit. For the VECM representation, the standard error for the GDP deflator is as low as 0.010 y^{-1}at a four year horizon and 0.005 y^{-1}for a two year horizon. The whole period and 0.004 y^{-1}for the period after 1994. All in all, we have obtained a very accurate description of unemployment and inflation in France during the past 40 years.
Having discussed the
technically solvable problems associated with the uncertainty in the labour
force measurements, we start tackling the problem associated with the
divergence of the observed and predicted curves starting around 1995. An understanding of this discrepancy is a
challenge for our concept. Potentially, these curves diverge due to the new monetary
policy introduced by the Banque de France. We may claim that the policy of
constrained money supply, if applied, could artificially disturb relationships (9),
(10), and (13). We had to introduce a structural break and to estimate new coefficients
after 1995 for unemployment and after 1994 for inflation, respectively. These
coefficients are less reliable because the relevant time series are short and
vary in narrow dynamic ranges, but they are definitely different from those before
the breaks. One could conclude that Banque de France has created some new links
between the unemployment, inflation, and labour force, shifting coefficients in
the original long term equilibrium relations.

Figure 12. Comparison of the observed and predicted inflation in France (DGDP and CPI) - annual and cumulative inflation since 1972. The predicted inflation is a
linear function of the labour force change and unemployment.

We think that the true money supply in excess of that related to real
GDP growth should be completely controlled by the demand related to the growing
labour force. This excessive money supply is accommodated in developed
economies through employment growth, which then causes price inflation. The
latter serves as a mechanism effectively returning the normalized personal
income distribution to its original shape (Kitov and Kitov, 2013).
The relative amount of money that the economy needs to accommodate through
increasing employment, as a reaction on independently growing labour force, is
constant through time but varies among developed countries. This amount has to
be supplied to the economy by central bank.

The ESCB limits money supply
to achieve price stability. For France, the growth in labour force was so
intensive after 1995 that it requires a much larger money supply for creation
of an appropriate number of new jobs. The 2% artificial constraint on
inflation, and thus on the money supply, disturbs relationships (10) and (13).
Due to lack of money in the French economy, the actual (and mainly exogenous)
growth in labour force was only partially accommodated by 2% inflation. The
lack of inflation resulted in increasing employment. In other words, instead of
2% unemployment, as one should expect according to the relationship before 1995,
France had 9% unemployment. Those people who entered the labour force in France
in excess of that allowed by the target inflation rate had no choice except to
join unemployment in order to compensate the natural 7% rate of inflation,
which was suppressed to 2%.

The lags and amplification
factors (sensitivities) found for unemployment and inflation in France are
quite different from those obtained for the USA and Austria (Kitov
and Kitov, 2010). The latter country is characterized by the absence of
time lags and low sensitivities. In the USA, inflation lags by two and
unemployment by five years behind the change in labour force, with
sensitivities much lower than those in France. Apparently, the variety of lags
is the source of problems for the Phillips curve concept.

The causal link between
inflation, unemployment, and labour force gives a unique opportunity to foresee
future at extra long time horizons. The accuracy of such long-term unemployment
and inflation forecasts is proportional to the accuracy of labour force
projections. For example, central banks can use labour force projections as a
proxy to “inflation expectation” in their NKPCs. Figures 8 and 12 imply that France
will be enjoying a period of low inflation rate in the near future. Monetary
policy of the ECB is also an important factor for these forecasts because of
its influence on the partition of the labour force growth between inflation and
unemployment. Moreover, this is the responsibility of the ECB and Banque de
France to decide on the partition.

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