Three years ago we published a paper on inflation and unemployment in Canada, where we presented a model linking inflation and unemployment with the change in labor force. This earlier prediction was revisited in 2010 and demonstrated excellent predictive power of the original model. Today we add two more readings, for 2008 and 2009, to all time series and extend the prediction.

Skipping the part introducing data and presenting individual models linking inflation and unemployment to labor force separately, we revisit our generalized relationship. It gathers all individual ones. We find the best-fit coefficients for the generalized equation:

pi(t) = 3.8dLF(t-2)/LF(t-2) + 0.79UE(t-2) - 0.095 (1)

Figure 1 depicts the case associated with the data provided by the BLS. Both cumulative curves are very close. Moreover, these curves reveal three periods of different behaviour and prove that there was no change in the long-term equilibrium relation between these three studied variables.

The difference between the cumulative curves is very small compared to the net change between 1969 and 2004. Moreover, this difference decreases with time as Figure 2 shows. One can easily find that the coefficients obtained by linear regression of the CPI on the LF and UE do not provide such a closeness between cumulative curves as those coefficients, which are estimated by visual fit between the cumulative curves.

Figure 1. Comparison of cumulative curve for the measured CPI and that predicted using the BLS definition of labour force.

Figure 2. The difference between the cumulative curves in Figure 1.

Figure 3 demonstrates the advantages of the moving average technique applied to the annual measurements of labour force, unemployment, and CPI inflation in Canada. As discussed above, these measurements are characterized by random errors, which are weighted through years in accordance with benchmark measurements. It means that the average measurement error approaches zero for the increasing length of time series. Therefore, a five-year moving average, MA(5), should significantly suppress random errors and provide close cumulative curves, as one can observe in Figure 1.

Figure 3. Comparison of MA(5) curve for the measured CPI and that predicted according to relationship (1).

Considering the accuracy of the CPI prediction between 1971 and 2009, one can expect the rate of consumer price inflation in Canada to fall very close zero on average during the next 5 years. It is very likely that few years will bring negative inflation rates, i.e. formal deflation.

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