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## The model

As originally defined by Kitov (2006a), inflation and unemployment are linear and potentially lagged functions of the change rate of labor force:

π(t) = A1dLF(t-t1)/LF(t-t1) + A2 (1)

UE(t) = B1dLF(t-t2)/LF(t-t2) + B2 (2)

where π(t) is the rate of price inflation at time t, as represented by some standard measure such as GDP deflator (DGDP) or CPI; UE(t) is the rate of unemployment at time t, which can be also represented by various measures; LF(t) is the level of labor force at time t; t1 and t2 are the time lags between the inflation, unemployment, and labor force, respectively; A1, B1, A2, and B2 are country specific coefficients, which have to be determined empirically in calibration procedure. These coefficients may vary through time for a given country, as induced by numerous revisions to the definitions and measurement methodologies of the studied variables, i.e. by variations in measurement units.

## Italy

Figure 1 displays two measures of unemployment and the change rate of labor force in Italy. First measure is introduced by national statistics and second is estimated according to the approach developed in the United States. All time series are available through the US Bureau of Labor Statistics. The difference between the curves is obvious. The unemployment curves cannot be so easily scaled, i.e. their cross-correlation is lower. Moreover, it seems that the national definition was replaced by the US one near 1993. This assumption is supported by the change rate of labor force having a large spike in the same year, the spike being a well-known sign of a large revision to definitions (OECD, 2008):

Series breaks: In October 1992, changes were introduced in the Household Labour Force Survey concerning the lower age limit of the active population (from 14 to 15 years old), the definition of unemployment, the population estimates, the estimation procedure and the imputation procedure. These changes resulted in a reduction in level estimates for employment and unemployment. In January 2004, major changes were introduced such as: the passage to a continuous survey, the implementation of CAPI/CATI instead of PAPI for interviews, better adherence to the international definition of employment, the change of the age limit in the definition of the unemployed (74 years old), and the data were revised back till the third quarter 1992.

Figure 1. Unemployment rate (left panel) and the rate of labor force change (right panel) in Italy according to national definition (NAC) and the definition adopted in the US.

In Figure 2, the observed unemployment is compared to that predicted from the change in labor force. Using only visual fit between the dynamic curves, we have estimated the coefficients in (2) for Italy: B1=3.0, B2=0.085, and t2=11 (!) years. Hence, an increase in labor force causes a proportional increase in unemployment with a factor of 3. The original time series dLF/LF is very noisy and thus is smoothed by a five-year moving average, MA(5). The right panel in Figure 2 displays a scatter plot - the measured UE vs. the predicted one, a linear regression line, and corresponding equation. The slope of the regression line is 0.96 (a slight underestimation of the slope results from the uncertainty in the independent variable) and R2=0.92. So, the predicted series explains 92% of the variability in the observed one.

Figure 2. Observed and predicted unemployment in Italy. The prediction horizon is 11 years. Due to large fluctuations associated with measurement errors in the labor force we are using centered MA(5) for the prediction, which reduces the horizon to 9 years. Goodness-of-fit (R2=) 0.92 for the period between 1973 and 2006, with RMSFE of 0.55%. The unemployment should start to increase in 2008.

As a rule, smoothing by MA(5) is an operation introducing a high bias in time series due to increasing autocorrelation. However, Italy is an exceptional economy with an eleven-year lag of unemployment behind the change in labor force. This lag is twice as large as in Germany and the largest among all studied countries. What kind of social and economic inertia should be involved in such a long delay of reaction? In any case, the smoothing with MA(5) is an adequate and accurate procedure for the prediction of unemployment at 9-year horizon in Italy with RMSFE of only 0.55% for the period between 1973 and 2006. This small RMSFE is associated with a wide range of change in the unemployment from 5.4% in 1974 to 12% in 1999. Together with the extremely large forecasting horizon, such uncertainty allows a decisive validation of our model in the next 9 years. One can expect that unemployment in Italy will be growing since 2008 and will reach ~11.4% [±0.6 %] near 2012. After 2012, unemployment in Italy will likely start to descend.

Kitov, I., (2006a). Inflation, unemployment, labor force change in the USA, Working Papers 28, ECINEQ, Society for the Study of Economic Inequality, http://www.ecineq.org/milano/WP/ECINEQ2006-28.pdf

OECD, (2008). Notes by Country, www.oecd.org/dataoecd/35/3/2771299.pdf

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