• Summary
• Downloads
• Explanatory Notes
• Related Information
• Past Releases

APPENDIX 2 CALCULATING HOURS WORKED

This appendix provides a brief overview of the method used to calculate hours actually worked. For a more detailed and technical description of the method please refer to Research Paper : Estimating Average Annual Hours Worked (cat. no. 1352.0.55.077).

STEP 1: AVERAGE HOURS WORKED FROM THE LFS

This is calculated as:

Average hours worked per employed person =

To estimate average annual hours worked information in respect of 14 reference periods is required. In addition to the 12 reference periods from each month of the target year, data for the reference periods from the December of the previous year and the January of the following year are needed. These two extra reference periods are used in the interpolation of the first and last weeks of the year. This process will be explained further in step 4. The following table presents the workings for the holiday corrected hours worked in 2004. The last reference period from December 2003 and the first reference period for 2005 constitute the additional reference periods.

Calculation of holiday corrected hours worked 2004
	Total hours worked	Total employed	Original	Corrected	Holiday correction applied
Period	'000	'000	average hours worked	average hours worked
1 Dec to 14 Dec	346 867	9 683	35.8	35.8	None
5 Jan to 18 Jan	272 607	9 458	28.8	29.7	2×Jan start date effect
2 Feb to 15 Feb	336 391	9 540	35.3	35.3	None
1 Mar to 14 Mar	331 090	9 627	34.4	34.4	None
5 Apr 18 Apr	275 413	9 622	28.6	34.0	Good Friday & Easter Monday
3 May to 16 May	333 951	9 641	34.6	34.6	None
31 May to 13 Jun	334 124	9 655	34.6	34.8	0.1×Queen’s Birthday
5 Jul to 18 Jul	316 670	9 670	32.8	33.7	0.7×July school holiday
2 Aug 15 Aug	332 643	9 578	34.7	34.7	None
30 Aug 12 Sep	338 612	9 803	34.5	34.6	0.01×September school holiday
27 Sep 10 Oct	323 489	9 799	33.0	33.9	0.3×October school holiday
1 Nov 14 Nov	338 216	9 787	34.6	34.6	None
29 Nov to 12 Dec	355 515	9 947	35.7	35.7	None
3 Jan to 16 Jan	252 699	9 765	25.9	29.4	New Year’s Day and 4×Jan start date effect

STEP 2: HOLIDAY CORRECTED REFERENCE WEEKS

The LFS relates to a two reference weeks each month. The information for the two reference weeks for each month is used to estimate hours actually worked for all 52 weeks of the year.

If a reference period contains a non-random event such as a public holiday, hours actually worked in that week will be very different to hours worked in neighbouring weeks. The effects of non-random events need to be temporarily removed to reduce their impact on the imputed hours worked estimates. Column 5 of the table above shows the average hours worked in each reference period of 2004 after the holiday corrections shown in column 6 have been applied.

STEP 3: ASSIGN REFERENCE PERIODS TO CALENDAR WEEKS

Although the LFS has a two week reference period, the two weeks are combined together to produce one representative reference period. One of the reasons for this is that the sample is not split evenly across the two enumeration weeks. In the first reference week of enumeration, around 50% of households in metropolitan areas and around 80% of households outside of metropolitan areas are interviewed.

As the sample composition of the two reference weeks are different the information on hours worked in the two reference weeks cannot be used separately. Since hours worked in the reference period were holiday corrected in step 2 and a higher proportion of people are enumerated in respect to the first reference week, it has been decided to allocate the information on average hours worked in the two week reference period to the first reference week. For 2004, these weeks refer to the weeks beginning on the Mondays in column 1 of the above table.

STEP 4: LINEAR INTERPOLATION

The fourth step is to estimate average hours worked in each week of the year. This is done by interpolating linearly between each holiday corrected reference week. In the linear interpolation it is necessary to take into account whether there are four or five weeks between consecutive first reference weeks. To estimate hours worked in the weeks at the beginning of January and the end of December of our target year holiday corrected reference weeks for the December of the previous year and the January of the following year are required.

Hours worked in the first and second weeks of each December it was found that hours worked tended to be higher in the second week of December than in the first. Since the holiday corrected reference weeks are very high in December and very low in January, linear interpolation will underestimate the number of hours worked in the unobserved weeks between the December and January reference weeks. To avoid this the average hours worked in the December holiday corrected reference week for both the first and second reference weeks are used. The next step is to interpolate linearly between the second reference week in December and the first reference week in January.

STEP 5: RE-ESTIMATE HOLIDAY CORRECTIONS FOR OBSERVED NON-RANDOM EVENTS

Steps 5, 6 and 7 involve the estimation and inclusion of the effects of non-random events on the average hours worked in each week of the year.

In step 5 the effects of observed non-random events such as Easter, the June Queen’s Birthday holiday and some school holidays are estimated. As the LFS has a two week reference period, the effect of an event that only occurs in one of the two reference weeks (for example the June Queen’s Birthday holiday is only observed in the second reference week) will underestimate the effect of the event on the actual week. In addition, events that occur in the first reference week will appear to have a larger effect than events which are observed in the second reference week simply because more people are enumerated in the first week.

To reflect differences in the enumeration of people between the first and second enumeration weeks, weights have been applied depending on whether an event is observed in the first or second week respectively. If an event usually occurs in the first reference week of the LFS, when around 65% of people are enumerated, a weight of 1/0.65 (1.54) is applied. If an event usually occurs in the second reference week of the LFS, when around 35% of people are enumerated, a weight of 1/0.35 (2.86) is applied.

The effect of observed school holidays on a standard week requires a different type of estimation. The holiday correction parameter estimates are obtained by assuming that all states experience school holidays at the same time for the entire two week reference period.

For each week of the year the proportion of the employed population affected by school holidays needs to be estimated. The school holiday effect is then weighted by the proportion of employed people living in states with school holidays. If school holidays do not extend for the entire week, the school holiday effects are also weighted to reflect this. For each weekday affected by the school holidays a weight of 0.2% is applied to the school holiday effect.

STEP 6: ESTIMATE HOLIDAY CORRECTIONS FOR UNOBSERVED NON-RANDOM EVENTS

In step 6 the effect on average weekly hours worked of unobserved non-random events such as Australia Day, Anzac Day, the Christmas period and unobserved school holidays are estimated. The first stage in estimating the effects of unobserved holidays is to utilise the information available on the effects of observed holidays. Research Paper : Estimating Average Annual Hours Worked (cat. no. 1352.0.55.077) outlines the decision rules used to assign school holiday effects to each week of the year.

Public holiday effects

The LFS collects information in each month during a two week enumeration period, usually beginning on the Monday which falls between the 6th and 12th of the month. The survey collects information on work patterns in the week preceding the interview. This means that the two reference weeks of the monthly LFS provides information on work patterns in the early part of each month.

Because of the timing of the reference weeks, a number of national public holidays are never observed in the LFS (For example, Australia Day, or Christmas Day and Boxing Day are never observed). Each of these public holidays are held on a particular date and may fall on any day of the week between Monday and Sunday. The effect of the holiday will be different on each day of the week.

In contrast, it was found that every national public holiday observed in the LFS falls on a particular day, rather than a particular date. For example, Good Friday is always held on a Friday and the June Queen's Birthday holiday is always held on a Monday. The only fixed date holiday observed is the official New Year's Day holiday when it falls on a Monday(Footnote: Note: This is the official holiday for New years day, which could be the 1st, 2nd or 3rd depending on whether the 1st Jan is a Monday, Sunday or Saturday respectively.). If New Year's Day falls on any other day of the week, the timing of the January LFS reference period will not cover the holiday.

The effect of observed public holidays is used to estimate the effect of unobserved public holidays, however, there is no information on the effect of a public holiday which falls on a Tuesday, Wednesday, Thursday, Saturday or on a Sunday. This presents a difficulty in estimating the effects of unobserved public holidays. The method used to estimate unobserved public holidays, and in particular Christmas period holidays are discussed in Research Paper : Estimating Average Annual Hours Worked (cat. no. 1352.0.55.077).

STEP 7: ADJUSTING FOR NON-RANDOM EVENTS

Once the magnitude of each non-random event has been estimated in steps 5 and 6, step 7 is a relatively simple matter of adjusting the average number of hours worked in a week to take into account the effect of each non-random event.

STEP 8: ESTIMATING PARTIAL WEEKS

Not all years begin on a Monday, or end on a Sunday. Because of this we need to estimate the proportion of hours worked on each day of the week. While the LFS does not contain this information, the survey does collect information on whether a person worked in their main job on each day of the week. From this we can estimate the proportion of employed people who work on a Monday, Tuesday, and on all other days of the week. The following graph shows the proportion of all employed people who actually worked on each day of the week based on the LFS.

All employed people in their main job, Proportion who worked by day of the week

With this assumption, we can use the information shown above to weight partial weeks.