RDP 2016-06: Jobs or Hours? Cyclical Labour Market Adjustment in Australia Appendix D: Decomposing the Change in Average Hours Worked
September 2016
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Average hours worked in period t can be expressed as the weighted average of the average hours worked by job movers (M), job stayers (S) and job finders (F):
where is overall average hours worked, is the combined weight of the individuals in category i ∈ (M,S,F) and is average hours worked by the individuals in category i.
The change in average hours worked between two quarters can then be written as:
which can be rearranged to obtain the contributions from the change in the weight of each category and the change in average hours worked within each category:
The first term on the right-hand side represents the contributions from changes in average hours worked within each category of employment and the second term represents the contributions from the change in the weight of each category (the between effect).
The main drawback of this decomposition is that is does not explicitly incorporate the effect due to changes in average hours worked by those leaving employment (job leavers). All else equal, if the average hours worked by job leavers increases, aggregate average hours worked should decrease.
In particular, the omission of job leavers could affect the within contribution for job stayers. To get an estimate of the potential impact of the increase in average hours worked by those leaving employment on average hours worked by job stayers, we constructed a counterfactual where a number of stayers were assumed to work additional hours equal to the change in average hours worked by leavers:
where is the counterfactual estimate of average hours by stayers, is the number of leavers at time t and is the number of stayers. This represents a case where those leaving employment came from a lower part of the distribution of actual hours worked. This counterfactual only had a marginal impact on the estimated within contribution from job stayers.
While indicative, this represents only one of several possible ways that the increase in average hours worked by leavers during the 2008–09 downturn could have affected the estimated contribution of job stayers to the decline in aggregate average hours worked. For example, the counterfactual does not incorporate the cumulative effect of the increase in average hours worked by leavers. Accounting for this could potentially further reduce the estimated within contribution for stayers.
There are two other caveats to the decomposition in Figure 9. First, we have treated our panel as if it was balanced (that is, that the workers in the matched sample do not change over time), when in fact it is unbalanced (the workers in the matched sample do change over time). As such, the decomposition assumes that changes in average hours worked within a category reflect the actual underlying behaviour of the individuals in that category. For example, changes in average hours worked by job stayers are assumed to reflect changes in the hours worked by individuals that stayed in the same job, rather than differences between successive cohorts of job stayers in the sample over time.^{[22]} However, although flows of workers into and out of the matched sample may have contributed to the estimated decline in average hours worked by job stayers, we do not believe this to be the case. Figure D1 shows the average hours worked for successive cohorts of job stayers over time. For each cohort, we have either two or three observations on each worker (with each representing a separate balanced panel). We plot cohorts with two observations in the left panel, and those with three observations in the right panel. By looking at individual cohorts (i.e. balanced panels) we can abstract from the effects of rotation into and out of the matched sample. We find that average hours worked fell for every cohort of job stayers during the 2008–09 downturn.^{[23]}
A second caveat is that the decomposition in Figure 9 is only for workers in the matched sample, rather than all workers surveyed in the LFS. The unmatched workers that we excluded from our analysis make up around 45 per cent of the overall LFS sample. This group experienced an even larger decline in average hours worked during the 2008–09 downturn than the matched sample of workers, which may reflect the fact that these two groups typically have different characteristics; for example, unmatched workers tend to be younger and less stably employed than those who are matched. If the decline in average hours worked within the unmatched sample was mainly due to labour market churn, then we may have overstated the role of labour hoarding by focusing on the matched sample.
Footnotes
We also formulated a decomposition that takes the unbalanced nature of the matched sample into account. However, the decomposition terms were hard, if not impossible, to give a meaningful interpretation to. [22]
The change in the average hours worked for a given category of employment (i.e. job stayers) will not necessarily be equal to the average change in the hours worked by employees in that category. These two measures should only be expected to coincide if we were dealing with a balanced panel. Measures of the average change in hours worked by job stayers suggests an even larger decline in the hours worked by job stayers during the downturn than suggested by Figure 9. [23]