A month ago, we discussed the rate of unemployment in the US and published our forecast for 2013. Two months ago, we predicted an extended unemployment fall period down to the level of 6.2% in the third quarter of 2013. This prediction was made after we accurately forecasted (on March 1, 2012) the rate of unemployment in the US to fall to 7.8% by the end of 2012. For the first time in 2012, the BLS announced 7.8% in September and the rate for November is 7.7%. One may expect a lower figure in December 2012. Here we update our model and estimate that the rate of unemployment in the fourth quarter of 2013 may fall below 6%.

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 as 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.

On March 1, 2012 the monthly model predicted a drop from 8.3% in February to 7.8% by the end of 2012. Figure 1 depicts the original prediction (upper panel) and the observed fall in the rate of unemployment (lower panel). 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 5.8% by November 2013 and even lower in the fourth quarter of 2013. For 107 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 5.8% [±0.4%].

Figure 1. Observed and predicted rate of unemployment in the USA as obtained in April and November 2012.

Figure 2. Observed *vs*. predicted rate of unemployment between 1967 and 2012. The coefficient of determination Rsq=0.82.

Figures 3. The predicted rate of unemployment. We expect the rate to fall down to 5.8% in November 2013.

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