## 7/9/11

### On the link between real growth and rate of unemployment again

My previous post was very exciting. Not every day one can find highly correlated economic time series.  The first move was to introduce a structural break into the link between the change in unemployment rate, du, and the change rate of GDP per capita, dlnG. In my previous post, I have found the following relationship:

dlnG = -2.4du+2.25
where dlnG  in the annual growth rate of real GDP per capita, du is the annual increment in the rate of unemployment, u. It also was shown that the sensitivity of the du to dlnG becomes lower after 2000, and the slope of -1.6 and the intercept of 2.1 better describe the link.   Actually, there is a structural break around 1984 and the new relationship is as follows
dlnG = -1.6du + 1.75, t>1984

Figure 1 depicts the predicted (with a structural break) dlnG and scaled du. Figure 2 presents regression results with Rsq.=0.84.  The agreement is more than exiting – it is breathtaking.
There is a more urgent question. Does it work for other developed countries? The answer is yes!
For France, I have estimated the following relation with a structural break in 1987
dlnG = -5.0du + 4.6, t<1987
dlnG = -1.5du + 1.4, t>1986
Figure 3 presents the observed dlnG curve and the scaled du, i.e. the change in GDP predicted from the change in the rate of unemployment.  The agreement is excellent, but both curves are volatile. I have smoothed them with MA(3).
For the UK, the following relation is obtained with a structural break in 1987:
dlnG = -1.5du + 2.5, t<1987
dlnG = -2.0du + 1.7, t>1986
Figure 4 presents the observed and predicted dlnG. The OECD reported the rate of unemployment only after 1972 for the UK.
Paul Krugman is right. One should not expect the rate of unemployment to fall before the rate of real GDP growth will exceed 2-3% per year in the US, UK and France.
Figure 1. Annual growth rate of real GDP per capita, dlnG, and the scaled rate of unemployment, du.
Figure 2. Scatter plot of the curves in Figure 2 and linear regression.

Figure 3. Same as in Figure 1 for France . The lower panel shows the curves smoothed with MA(3)
Figure 4. Same as in Figure 1 for the UK