There is a trade-off between the change in unemployment and employment. Figure 1 compares the change in the rate of employment (the employment/population ratio),

Figure 1. The (negative) change in the rate of employment compared to the change in the rate of unemployment in the UK.

In our previous post we have estimated Okun’s law for the UK. It is instructive to estimate a model similar to Okun’s law for the employment/population ratio,

*de*, and the rate of unemployment,*du,*in the United Kingdom. As expected, the change in the rate of unemployment is more volatile. We have retrieved all data on unemployment and employment from the U.S. Bureau of Labor Statistics.*e*. For the UK, the best-fit model has been obtained by the least-squares (applied to the cumulative sums):

*de*0.41

_{t}=*dlnG*1983

_{t-1}– 1.11, t<*de*0.41

_{t}=*dlnG*1982 (1)

_{t-1}– 0.81, t>where

*dlnG*is the change rate of real GDP per capita one year before, i.e. the predicted curve leads by one year. Figure 2 shows the cumulative curves for the time series in (1). There is a structural break near 1982 which is expressed by a significant shift in intercept without any change in slope. The employment/population ratio varies around 58% between from ~54.3% in 1982 and ~61% in 1972. There is a dramatic deviation from the measured employment/population ratio after 2008. This deviation is consistent with the difference for the same years in 2009. Figure 3 present results of linear regression with R_{t-1}^{2}=0.89 for the period between 1972 and 2009.Figure 2. The cumulative curves for the observed and predicted change in the employment/population ratio,

Figure 3. Linear regression of the measured and predicted curves in Figure 2. *de*.
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