The US Federal Reserve this week put out its updated projections which provide "central tendency" estimates of real GDP growth between 3.5 and 4.3 per cent in 2013. Their lowest estimate for 2013 was 3 per cent per annum. Assuming the current labour productivity growth continues (around 2 per cent per annum) and the labour force growth resumes more normal rates (around 1.4 per cent per annum) by 2013 and the average working week is constant in hours, then one consequence of the difference between the lower bound of the central tendency projections and their lowest estimate will be that the unemployment rate will fall more slowly in 2013 if the the latter projection is true.
Answer: False
The answer is False.
The facts were:
We need a method of relating the projections of real GDP growth into labour market outcomes. 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 3.4 per cent per annum.
If the lowest bound of the central tendency estimates (3.5 per cent in 2013) are correct then the national unemployment rate (under our assumptions) would decline by a miserly 0.1 points in 2013.
If the lowest real GDP growth estimate overall (3 per cent in 2013) is correct then the rate of real GDP growth is below the required rate to keep the unemployment rate constant and the unemployment rate would rise by 0.4 per cent in 2013.
The rising unemployment rate would reflect the fact that real output growth was not strong enough to both absorb the new entrants into the labour market and offset the employment losses arising from labour productivity growth.
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