Eight years ago we developed an empirical model describing inflation in developed countries and published a forecast for the USA at a ten year horizon in 2006 (Kitov, 2006ab) as a linear and lagged function of labour force. For the USA the model is as follows:

DGDP(t) = 4.0dLF(t-2)/LF(t-2) – 0.03 (1)

where DGDP is the GDP deflator at time t, and LF is the level of labour force two years before, t-2. In equation (1), the slope of linear relationship is 4.0 and intercept is -0.03. With labour force constant (dLF=0), the overall price inflation in the USA would remain negative at the level of -3% per year. For inflation to be sustainable at the level of 2% (the fed’s unannounced target) the growth in labour force of 1.25% per year is required.

Eventually, the link between price inflation and labour force was successfully tested for cointegration (Kitov, Kitov, Dolinskaya, 2007) and validated using 1-D boundary elements methods (Kitov, Kitov, 2010). This links holds for other developed countries as well (Kitov, Kitov, 2010).

Figure 1 illustrates the linear and lagged relationship between inflation (GDP deflator) and the change rate of labour force in the USA for the period between 1960 and 2006. The estimates of the change rate of labour force are shifted by two years ahead in order to synchronize the predicted peaks of inflation with those actually observed in 1975 and 1984. Due to the uncertainty in the labour force (and inflation) measurements the most reliable readings correspond to the changes of the largest magnitude, as described by the BLS. Every sound model of price inflation must explain these peaks.

Figure 1. Measured inflation (GDP deflator) and that predicted from the dLF/LF (shifted 2 years ahead). An agreement is observed throughout the whole period with some short fluctuations in labour force potentially induced by the population corrections implemented by the Census Bureau in the census years.

Figure 2 presents two smoothed inflation curves – the measured and the predicted one. The smoothing was attained by a 7-year moving average, MA(7), with a one-year step. The predicted curve is shifted by 2.5 years (we used two time scales with a half-a-year shift) ahead in order to fit the inflation peak near 1978. The original (not shifted) predicted curve is also shown in order to illustrate that it is actually leading by 2.5 years.

Figure 2. MA(7) of the predicted and measured inflation. The prediction is made according to the relationship (1). The predicted curve is shifted by 2.5 years ahead.

Figure 3 displays the observed and predicted cumulative inflation curves starting from 1965. The predicted cumulative curve is obtained by a progressive summation of values from 1963 and is also shifted ahead by 2 years. There is an almost complete agreement between the cumulative curves for the whole period. The only small deviation occurred around 1993 and corresponds to a sharp drop of the rate of labour force growth as induced by the baseline working age population correction.

The predicted cumulative curve is very sensitive to free term in (1). Even the initial difference of 0.0001 results in a tangible deviation from the measured curve after 50 years. Therefore, the value of free term in (1) can be estimated with a good accuracy. With cumulative curves, one can obtain the most accurate coefficients solely on the basis of visual fit. Also, since these two cumulative curves have R2>0.999 and actually represent indexes one can replace the secular growth in the overall price as the cumulated growth in labour force two years before. In a sense, these curves are similar to conservation laws or integral equations in physics (Kitov, Kitov, 2010).

Figure 3. Comparison of the cumulative values of the observed and predicted inflation presented in Figure 1. The predicted curve starts from 1963 and is shifted by 2 years ahead. An agreement is observed with a notable change from convexity before 1980 to concavity one after 1980.

Relationship (1) can be used for a prediction at a larger time horizons using labour force projections made by various institutions. For example, the projections made by CBO (2004) and BLS (2005) undoubtedly indicate a decrease in the participation rate and a decaying growth rate of the working age population. According to these projections, staring from 2010, the annual increase in labour force will be less than 1,200,000 – the value separating inflation and deflation. Hence, the year of 2012 is likely to mark the beginning of the deflationary era in the USA (which hopefully is the global disaster the Mayans talked about) because of the two-year lag between the labour force change and inflation. Figure 4 details the prediction based on the CBO’s projection of the labour force. After peaked at 3.2% in 2007, the rate of price inflation has been at a gradual decrease, which will lead to the first red figure in 2012.

Hence, we are waiting an extended deflationary period in the USA since 2012.

Figure 4. Predicted inflation rate for the period between 2006 and 2016 according to the CBO’s (2004) labour force projection. A deflationary period starts in 2012.

**Conclusion**

Considering the accuracy of labor force projections and inflation estimates we have the prediction closest to the actual rate inflation observed since 2006. Our horizon was ten years. The FRB is not able to change the future rate.

**References**

Bureau of Labor Statistics. (2005a). Labor force projections to 2014: retiring boomers. Monthly Labor Review, November 2005.

Congressional Budget Office. (2004). CBO’s Projections of the labor force. September 2004.

Kitov, I. (2006a). Inflation, unemployment, labor force change in the USA, Working Papers 28, ECINEQ, Society for the Study of Economic Inequality,http://ideas.repec.org/p/inq/inqwps/ecineq2006-28.html

Kitov, I. (2006b). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

Kitov, I., Kitov, O., Dolinskaya, S. (2007). Inflation as a function of labor force change rate: cointegration test for the USA, MPRA Paper 2734, University Library of Munich, Germany

Kitov, I., Kitov, O. (2010). Dynamics of Unemployment and Inflation in Western Europe: Solution by the 1-D Boundary Elements Method, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. V(2(12)_Summer), pp. 94-113.

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