Question #1043

The IMF recently downgraded their real GDP growth estimates. Taking the example of the Spain, it is now projected to contract in real terms by around 1.6 per cent in 2013 rather than 1.7 per cent as previously forecast. Real GDP per employed person is estimated to fall by about 0.9 per cent over the same period and the labour force is contracting slightly by about 0.1 per cent per annum. If average weekly hours worked will remain more or less constant in 2013, these projections would suggest that the unemployment rate will rise in 2013 by

Answer #5446

Answer: 0.6 per cent

Explanation

The answer is Option (b) 0.6 per cent (although in reality the IMF are predicting the unemployment rate will rise from 25 to 27 per cent over 2013 - our example is stylised for pedagogic purposes).

The facts were:

The late Arthur Okun is famous (among other things) for estimating the relationship that links the percentage deviation in real GDP growth from potential to the percentage change in the unemployment rate - the so-called Okun's Law.

The algebra underlying this law can be manipulated to estimate the evolution of the unemployment rate based on real output forecasts.

From Okun, we can relate the major output and labour-force aggregates to form expectations about changes in the aggregate unemployment rate based on output growth rates. A series of accounting identities underpins Okun's Law and helps us, in part, to understand why unemployment rates have risen.

Take the following output accounting statement:

(1) Y = LP*(1-UR)LH

where Y is real GDP, LP is labour productivity in persons (that is, real output per unit of labour), H is the average number of hours worked per period, UR is the aggregate unemployment rate, and L is the labour-force. So (1-UR) is the employment rate, by definition.

Equation (1) just tells us the obvious - that total output produced in a period is equal to total labour input [(1-UR)LH] times the amount of output each unit of labour input produces (LP).

Using some simple calculus you can convert Equation (1) into an approximate dynamic equation expressing percentage growth rates, which in turn, provides a simple benchmark to estimate, for given labour-force and labour productivity growth rates, the increase in output required to achieve a desired unemployment rate.

Accordingly, with small letters indicating percentage growth rates and assuming that the average number of hours worked per period is more or less constant, we get:

(2) y = lp + (1 - ur) + lf

Re-arranging Equation (2) to express it in a way that allows us to achieve our aim (re-arranging just means taking and adding things to both sides of the equation):

(3) ur = 1 + lp + lf - y

Equation (3) provides the approximate rule of thumb - if the unemployment rate is to remain constant, the rate of real output growth must equal the rate of growth in the labour-force plus the growth rate in labour productivity.

It is an approximate relationship because cyclical movements in labour productivity (changes in hoarding) and the labour-force participation rates can modify the relationships in the short-run. But it provides reasonable estimates of what happens when real output changes.

The sum of labour force and productivity growth rates is referred to as the required real GDP growth rate - required to keep the unemployment rate constant.

Remember that labour productivity growth (real GDP per person employed) reduces the need for labour for a given real GDP growth rate while labour force growth adds workers that have to be accommodated for by the real GDP growth (for a given productivity growth rate).

So in the example, the required real GDP growth rate is perversely (because we are talking about a contraction) -1 per cent, which equals the sum of the productivity growth (-0.9 per cent) and labour force growth (-0.1 per cent).

The projected real GDP growth is thus lower than the rate required to keep the unemployment rate from rising by 0.6 per cent.

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