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Feature Article - Issues With Seasonal Adjustment of Hours Worked
There are a number of additional adjustments made as part of the National Accounts to cater for remaining conceptual differences between the LFS and the National Accounts concepts of employment. For example, in the National Accounts measure of employment, defence force personnel are included and adjustments are made due to a change in the scope of the LFS in which unpaid family helpers working one to fourteen hours in the reference week were included in LFS employment estimates after 1986.
IMPROVING ESTIMATES OF HOLIDAYS
Seasonal adjustment is a process which estimates and removes systematic calendar related effects, , from the original series, , to give the seasonally adjusted estimates, .
As part of the seasonal adjustment process, known effects need to be estimated and removed prior to seasonal adjustment. These effects are called prior corrections. Intervention analysis is a technique used to identify the impact on a regular time series of certain known events. This technique is widely used in economic time series analysis. For example, Box and Tiao (1975), Tsay (1988), and Findley et al (1998) used this technique to identify outliers and calendar related effects for seasonal adjustment purposes. This process involves the design of an appropriate regressor to estimate a particular effect. For example,
where, are regression parameters estimated from the original estimates, is a regressor designed to assess for a specific effect, and describes the dynamics of the regular time series without the impact of particular events. Appropriate regressors can be designed to remove specific known impacts from the original estimates and improve the seasonally adjusted estimates. For example, effects such as public holidays, the starting date of the survey, use of supplementary surveys, and impacts of questionnaire redesign can be considered as measurement interventions to the "normal regular" hours worked time series, which should not contain effects due to the overlap of known holidays with the LFS reference period.
The aim of the holiday correction is to estimate and remove the holiday impacts prior to seasonal factor estimation. The resulting holiday corrected series will therefore be a series without known holiday impacts. This means that the seasonally adjusted holiday corrected series does not contain the impact induced from holidays as a part of calendar (seasonal) adjustment. The extent of the impact of a particular holiday will depend on how different persons are affected by that holiday. For example, there may be different reactions to specific holidays in different states, in metropolitan/ex-metropolitan areas and in different industries. For some holidays the effect may not be consistent from year to year due to factors such as the different dates of public holidays in different states.
A visual identification of the effect of holidays on hours worked is the seasonal x irregular chart (SI chart). SI charts are used to assess the seasonal x irregular components (SIs), used in the estimation of the seasonal factors, for a particular month or quarter. SIs are calculated by removing the trend estimate from the original series (for details see ABS, 2004). SI charts show the seasonal component as an unbroken line and the modified seasonal x irregular component as a set of filled points. The unmodified seasonal x irregular factors are included as the hollow points and are connected to the modified seasonal x irregular factors by a broken line. An example of the SI chart for hours worked in June is shown in Figure 1. The high values in 1982, 1983, 1988, 1993, 1994, 1999 and 2004 relate to months in which the Queen's Birthday public holiday did not overlap the Labour Force reference period. This shows a significant impact due to this public holiday on hours worked.
FIGURE 1: SEASONAL X IRREGULAR CHART FOR HOURS WORKED IN JUNE
WHAT HOLIDAYS HAVE A SIGNIFICANT IMPACT ON HOURS WORKED?
Previously, holiday correction factors were estimated based on a regression of the residuals after seasonal adjustment. This can result in biassed holiday correction factor estimates due to the effect of seasonal adjustment. The preferred approach is to estimate the holiday correction factors simultaneously as part of the seasonal adjustment process. This is the approach adopted in Regression-ARIMA intervention analysis.
To adjust for the impact of holidays on the hours worked estimates a range of appropriate regressors were developed and assessed individually. Each of the regressors was examined in detail and determined to adjust for a specific holiday affecting the hours worked series. Estimated correction factors were found to be statistically significant for the following holiday impacts: Easter, start date of the LFS in January, Queen's Birthday, Australia Day, and School holidays in particular months.
In practice, all holidays impacting the hours worked series cannot be considered individually. For example, if an employed person does not work any hours on the New Year's day public holiday they will not work any less hours on this day if it is also a school holiday. The regressors identified in Table 1 must be considered together to determine their combined significance. All regressors identified in Table 1 were still significant.
TABLE 1. SIGNIFICANT HOLIDAY REGRESSORS ON HOURS WORKED ESTIMATES
Quality measures can also be used to show that the use of the regressors improved the quality of the series. For example, the Average Absolute Percentage Change (AAPC) of the estimates under the two different approaches can be calculated. A large number for the AAPC will indicate a high level of volatility. Table 2 shows the AAPC values for the original, trend and irregular estimates. The larger the AAPC for the irregular, the more the irregular component is likely to dominate movements in the seasonally adjusted series, which implies greater revisions to the seasonally adjusted and trend series. Table 2 illustrates that the proposed holiday corrections applied to the monthly time series for hours worked results in considerably reduced volatility for the monthly estimates.
FIGURE 2: BOXPLOTS COMPARING VOLATILITY IN MONTHS PREVIOUS AND PROPOSED HOLIDAY CORRECTIONS
TABLE 2. AVERAGE ABSOLUTE PERCENTAGE CHANGE (AAPC) COMPARISON OF PREVIOUS AND PROPOSED HOLIDAY CORRECTED ESTIMATES
CONSTRUCTING A QUARTERLY HOURS WORKED SERIES
The monthly holiday corrected time series needs to be converted to a quarterly time series for use within the National Accounts. A range of methods are available.
The appropriateness of these methods is the subject of continued evaluation. The previously used method is a mid-month method. This method is consistent with market sector hours worked estimates which are only available for the middle month of each quarter from the LFS.
COMPARING THE PREVIOUS SEASONALLY ADJUSTED ESTIMATES WITH THE PROPOSED ESTIMATES
We now compare the proposed seasonally adjusted estimates based on the updated holiday corrections with the previous seasonally adjusted estimates. Both approaches use a mid-month method.
Figure 3 shows boxplots of the irregular component after seasonal adjustment under the two approaches. This shows that there is not much difference in the distribution of the irregular component between the proposed approach and the previous approach. That is, the approach of using the updated holiday corrections produces a quarterly seasonally adjusted hours worked series that has similar overall volatility, as measured by the AAPC of the irregular, to the previous approach in all quarters. This was expected, as most holidays do not affect the mid-month of the quarter and consequently the proposed and previous holiday corrected mid-month series are similar (The porposed holiday corrections had most impact in January, April, June and October which are not mid-months in the quarter). The volatility in March and December quarters has been reduced substantially using the proposed method although the previous method appears less volatile in the September quarter. There are fewer values identified as extreme under the proposed approach.
FIGURE 3: BOXPLOTS OF THE IRREGULAR COMPONENT COMPARING VOLATILITY BY QUARTER OF PREVIOUS AND PROPOSED SEASONAL ADJUSTMENT METHODOLOGIES
Figure 4 shows a comparison over the last five years of quarterly movements in the seasonally adjusted estimates. The seasonally adjusted movements for both approaches are very similar. For example, the percentage movements for both approaches are: 0.9% for September quarter 2004 and 0.7% for June quarter 2004, while they are 0.4% and 0.3% for March quarter 2004 for the previous and proposed approaches respectively. The seasonally adjusted estimates are revised as additional original estimates become available. The seasonally adjusted movement estimates may differ from those published in the National Accounts as they have been calculated without the impact of post-seasonal adjustment National Accounts additions such as the inclusion of defence force personnel. Figure 4 provides an indication of the impact of the previous and proposed holiday correction factors on quarterly seasonally adjusted hours worked estimates. The June quarter 2005 National Accounts publication will contain estimates of movements in seasonally adjusted hours worked, based on the proposed methodology for all periods up to June quarter 2005.
FIGURE 4: PERCENTAGE MOVEMENTS IN SEASONALLY ADJUSTED ESTIMATES FOR HOURS WORKED UNDER PREVIOUS AND PROPOSED APPROACHES
LEVELS OF HOURS WORKED AND PRODUCTIVITY
The proposed methodology is considered to provide an acceptable measure of movements in hours worked, but it does not provide an appropriate measure of levels of hours actually worked.
This is because;
As the proposed methodology does not provide an appropriate measure of the level of hours actually worked, the series will only be presented in the form of an index (as was the case with the previous series).
The proposed methodology can be used to construct estimates of movements in output per hour worked, which is a measure of labour productivity. These series are also presented in index form. However, it cannot be used to construct estimates of levels of output per hour worked; for example, to compare Australia with other countries. To do so requires an appropriate measure of the level of hours actually worked which includes the impact of holidays. As there are relatively less holidays in mid-months, this would have the impact of reducing estimates of hours worked.
The holiday correction factors have been improved for the seasonal adjustment of hours worked for use as an index within the National Accounts. A regression-ARIMA intervention analysis methodology (Findley et al, 1998) was applied to produce updated holiday correction factors which can be applied to and removed from the original hours worked estimates for the purpose of seasonal adjustment and constructing an index.
The approach of using the updated holiday corrections produces seasonally adjusted quarterly hours worked estimates that are similar, in terms of volatility and movements, to the previous production method. This is expected, as most holidays do not affect the mid-month of the quarter and consequently the mid-month seasonally adjusted estimates were not being significantly affected by previous inappropriate holiday correction factors.
This article has concentrated on the seasonal adjustment of hours worked for use as an index in the National Accounts. Further work is underway to consider alternative ways to construct quarterly time series estimates of hours worked that will provide appropriate measures of the level of hours actually worked, taking into account the real impact of the holiday pattens of employed Australians.
Further information about detailed holiday correction method can be obtained by contacting Nick von Sanden on 02 6252 7368 or fax 02 6252 8015, or email <email@example.com>.
ABS (2004), Time Series Analysis Frequently Asked Questions,
Findley, D.F. et al (1998) New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program, Journal of Business and Economic Statistics, Vol. 16, No. 2., 127-177.
Box, G.E. P. and Tiao, G.C. (1975) Intervention Analysis with application to economic and environmental problems. Journal of American Statistics Association, Vol 70, 70-79.
Tsay, R. S. (1988). Time series models specification in the presence of outliers. Journal of American Statistics Association, Vol 81, 132-141.
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