Imagine we forecast real GDP growth for a nation to grow by 0.8 per cent in 2021 and 1.1 per cent in 2022. We also predict that the unemployment rate would fall from 11.7 per cent in 2021 to 11.4 per cent in 2022. Additionally, average annual growth in labour productivity has been running at just over 1 per cent per annum (GDP per hours worked). If average weekly hours worked remains constant over 2022, then the implication of our forecasts is that we think the labour force of this nation in 2022 will
Answer: shrink by 0.2 per cent.
The answer is Option (b) shrink by 0.2 per cent.
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.
There is some algebra we could use to show this but a simple story will suffice to get to the point we want.
Arthur Okun originally said that when the US real GDP fell by 3 percentage points in relation to its trend rate, the unemployment rate would rise by 1 percentage point. On the other hand, if real GDP grew by 3 percentage points, then the unemployment rate would fall by 1 percentage point.
The question then is what determines that outcome.
Clearly, real output is the product of how many workers are employed, the hours they work per period and how productive each worker hour is.
So if a worker produces 10 units of output per hour worked and works for 40 hours per week, he/she will produce 400 units of real output. Multiply that up to the economy level and we can calculate real GDP.
So when real GDP is rising it is likely the there will be growth in the labour force (number of people willing to work), hour worked per person, and/or labout productivity (output per hour worked).
In fact, Okun estimated that when real GDP rose by 3 percentage points relative to trend, there would be a 0.5 percentage point increase in labour force participation, 0.5 percentage point increase in hours worked per person, and a 1 per cent increase in labour productivity. The difference was the decline in the unemployment rate (or the rise in the employment rate).
This observation led economists (who derived the relationship using algebra) to come up with an approximate 'rule of thumb' for assessing how much the unemployment rate will change when real GDP changes.
The rule of thumb relates the growth in output to the labour-force and labour productivity growth rates.
The approximate rule of thumb is as follows: 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 labour 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, we know that the change in the unemployment rate is expected to be -0.3 percentage points.
We know that the difference between forecast real GDP growth (1.1 per cent) and labour productivity growth (1 per cent) is 0.1 percentage points. So if the labour force was constant then the unemployment rate would fall by 0.1 percentage points over the next year.
For the unemployment rate to fall by -0.3 percentage points then the actual real GDP growth rate must be 0.3 percentage points higher than the required real GDP growth (which is the sum of the labour productivity and labour force growth).
That means that the forecasted labour force must be shrinking by -0.2 percentage points over 2022 for the forecasts to be consistent.
So while the 1 per cent labour productivity growth is reducing the need for jobs and pushing up unemployent, the contraction in the labour force more than offsets that given the real GDP growth. As a consequence, the unemployment rate would fall.
The following blog posts may be of further interest to you: