We have been reporting on the
decline in the rate of unemployment in the US since
the beginning of 2012. We predicted an extended unemployment fall period
down to the level of 6.2% in the fourth quarter of 2013. This prediction was
made after we accurately forecasted (on March 1, 2012) the rate of unemployment
in the US to fall down to 7.8% by the end of 2012. Here we update our model and
present the evolution of the unemployment rate in the second quarter of 2013. Overall,
the measured rate has been following our prediction. We foresee the rate to fall
down to 6% [±0.4%] in the fourth quarter of 2013 or in the first
quarter of 2014.

In 2006, we developed
three individual empirical relationships between the rate of unemployment,

*u(t)*, price inflation,*p(t)*, and the change rate of labour force,*LF(t)*, in the United States. We also revealed a general relationship balancing all three variables. Since measurement (including definition) errors in all three variables are independent it may so happen that they cancel each other (destructive interference) and the general relationship might have better statistical properties than the individual ones. For the USA, the best fit model for annual estimates was a follows:*u(t) = p(t-*2.5

*) + 2.5dLF(t-5)/dtLF(t-5) + 0.0585 (1)*

where inflation (CPI) leads unemployment by 2.5
years (30 months) and the change in labor force leads by 5 years (60 months).
We have already posted
on the performance of this model several times.

For the model in this post, we
use monthly estimates of the headline CPI, u, and labor force, all reported by
the US Bureau of Labor Statistics. The time lags are the same as in (1) but
coefficients are different since we use month to month-a-year-ago rates of
growth. We have also allowed for changing inflation coefficient. The best fit
models for the period after 1978 are as follows:

*u(t) = 0.63p(t-2.5) + 2.0dLF(t-5)/dtLF(t-5) + 0.07; between 1978 and 2003*

*u(t) = 0.90p(t-2.5) + 4.0dLF(t-5)/dtLF(t-5) + 0.30; after 2003*

There is a structural break in
2003 which is needed to fit the predictions and observations in Figure 1. Due
to strong fluctuations in monthly estimates of labor force and CPI we smoothed
the predicted curve with MA(24).

The structural break in 2003 may
be associated with the change of sensitivity of the rate of unemployment to the
change of inflation and labor force. Alternatively, definitions of all three
(or two) variables were revised around 2003, which is the year when new
population controls were introduced by the BLS. The Census Bureau also reports
major revisions to the Current Population Survey, where the estimates of labor
force and unemployment are taken from. Therefore, the reason behind the change
in coefficients night be of artificial character - the change in measuring
units.

Figure 1 depicts the prediction
and the observed fall in the rate of unemployment. Figure 2 shows that the
observed and predicted time series are well correlated (R

^{2}=0.82). This is a good statistical support to the model.
Figure 3 depicts the predicted
rate of unemployment for the next 12 months. The model shows that the rate will
fall to 6.0 % by December 2013. For 113 observations since 2003, the modelling
error is 0.4% with the precision of unemployment rate measurement of 0.2%
(Census Bureau estimates in Technical Paper 66).
Hence, one may expect 6.0% [±0.4%]. After a 0.2% fall in July, we expect a
dramatic drop in the rate of unemployment in August/September 2013.

Figure 1. Observed and predicted
rate of unemployment in the USA as obtained in April 2013.

Figure 2. Observed

*vs*. predicted rate of unemployment between 1967 and March 2013. The coefficient of determination Rsq.=0.82.
Figure 3. The predicted rate of
unemployment. We expect the rate to fall down to 6.0% in December 2013.

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