## We Have Validated Our Model Allowing For An Accurate Prediction Of GDP Growth Using Unemployment Estimates

According to the gap version of Okun’s law, there exists a negative relation between the output gap, (*Y ^{p}-Y)/Y^{p}*, where

*Y*is potential output at full employment and

^{p}*Y*is actual output, and the deviation of the actual unemployment rate,

*u*, from its natural rate,

*u*. The overall GDP or output includes the change in population as an extensive component which is not necessarily dependent on other macroeconomic variables. Econometrically, it is mandatory to use macroeconomic variables of the same origin and dimension. Therefore, we use real GDP per capita,

^{n}*G,*and rewrite Okun’s law in the following form:

*du = a + bdlnG* (1)

where *du *is the change in the rate of unemployment per unit time (say, 1 year); *dlnG*=*dG/G* is the relative change rate in real GDP per capita, *a* and *b* are empirical coefficients. Okun’s law implies *b*<0.

The intuition behind Okun’s law is very simple. Everybody may feel that the rate of unemployment is likely to rise when real economic growth is very low or negative. An economy needs fewer employees to produce the same or smaller real GDP also because of labor productivity growth.

When integrated between *t _{0}* and

*t*, equation (1) can be rewritten in the following form:

*u _{t }= u_{0} + bln[G_{t}/G_{0}] + a(t-t_{0}) + c *(2)

where *u _{t} *is the rate of unemployment at time

*t.*The intercept

*c*≡0, as is clear for

*t=t*. Instead of using the continuous form (2), we calculate a cumulative sum of the annual estimates of

_{0}*dlnG*with appropriate

*initial conditions. By definition, the cumulative sum of the observed*

*du*’s is the time series of the unemployment rate,

*u*. Statistically, the use of levels, i.e.

_{t}*u*and

*G*, instead of their differentials are superior due to suppression of uncorrelated measurement errors.

We showed (Kitov, 2011) the necessity of structural breaks in (1). Therefore, we introduced floating structural breaks in (2), which years have to be determined by the best fit. Thus, relationship (2) should be split into N segments. The integral form of Okun’s law should be also split into N time segments:

*u _{t }= u_{0} + b_{1}ln[G_{t}/G_{0}] + a_{1}(t-t_{0}), t<t_{s1} *

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