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3114.0 - Demography Working Paper 1998/2 - Quarterly Birth and Death Estimates, 1998  
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 09/03/1999   
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Demography Working Paper 98/2

QUARTERLY BIRTH AND DEATH ESTIMATES

Rhonda de Vos and John Paice
Demography Section
Australian Bureau of Statistics
PO Box 10
BELCONNEN ACT 2616

rhonda.devos@abs.gov.au
john.paice@abs.gov.au





Abstract

The estimated number of births and deaths are major components of ABS quarterly State and Territory population estimates. A small proportion of these events are not registered for months, or even years, after they have occurred. As a result, ABS quarterly estimates have slightly underestimated the true numbers of births and deaths.

This paper describes a method by which an inflation factor can be applied to births and deaths data to estimate the true number of such events occurring in a particular period.




This paper is a slightly revised version of one presented at the 1998 Australia-New Zealand Population Workshop, 18-20 November 1998.



Introduction

The accuracy of ABS quarterly population estimates depends in part on the accuracy of estimates of births and deaths which are based on registrations of births and deaths. The major difficulty in this area stems from the fact that while the vast majority of births and deaths are registered promptly, a small proportion of registrations are delayed for months or even years.

As indicated in the following tables, delays in registration are a greater problem for births than for deaths.


    Table 1.
        AVERAGE LAG (MONTHS) BETWEEN OCCURRENCE AND REGISTRATION OF BIRTHS, 1993 TO 1996

Year of registration
    State/Territory
1993
1994
1995
1996

    NSW
2.1
2.1
2.1
2.0
    Vic.
1.3
1.3
1.4
1.7
    Qld
1.8
1.8
1.8
1.8
    SA
1.4
1.4
1.4
1.5
    WA
1.7
1.7
1.7
1.7
    Tas.
1.3
1.3
1.4
1.4
    NT
1.7
1.7
2.0
1.8
    ACT
1.6
1.6
1.7
1.4
    Aust.
1.7
1.7
1.8
1.8



    Table 2.
        AVERAGE LAG (MONTHS) BETWEEN OCCURRENCE AND REGISTRATION OF DEATHS, 1993 TO 1996

Year of registration
    State/Territory
1993
1994
1995
1996

    NSW
1.1
1.0
1.1
1.1
    Vic.
1.1
1.0
1.1
1.1
    Qld
1.1
1.2
1.1
1.1
    SA
1.0
0.9
1.0
1.0
    WA
1.0
1.0
1.0
1.0
    Tas.
1.0
0.9
0.9
0.9
    NT
1.8
1.8
1.6
1.6
    ACT
1.0
1.0
1.0
1.0
    Aust.
1.1
1.0
1.1
1.1


Following an approach from the Queensland Government Statistician's Office, the ABS proposes to estimate the number of births and deaths occurring in a particular quarter for population estimates by applying an inflation factor to births and death registration data. Investigations outlined below appear to support introduction of this method for revised population estimates.

Preliminary, revised and final estimates

There are three stages in the production of birth and death estimates for population estimate purposes.

Preliminary estimates of births and deaths are produced 6 months after the reference date using period of registration data as a proxy for period of occurrence data. Preliminary estimates for a financial year are revised 15 months after the year using period of occurrence data. The revised estimates are then held constant until they are finalised after the next Census of Population and Housing using a later period of occurrence data. Prior to 1991, final period of registration data was used for both the revised and final estimates.

The major problems inherent in this process are that preliminary estimates are inconsistent with final estimates, revised estimates exclude births and deaths registered more than 15 months after the financial year and final estimates do not reflect births or deaths that have not been registered at the time finalisation occurs. Current ABS revised and final estimates slightly undercount the true numbers of births and deaths occurring in a particular period.

Registration lags

There are two types of registration delays, or lags, that we can measure for births and deaths in a given period. The first, referred to in this paper as historical lag, is the delay between births registered in the relevant period and their date of occurrence (ie it looks back into history such as in tables 1 and 2 ). Conversely, a future lag is the delay between births occurring in the target period and their (eventual) date of registration (ie it looks into the future).

The main principle behind ABS' proposed method for revising birth and death occurrence estimates is that the historical and future registration lags for a quarter are similar, although this can change if registration procedures change. In other words, the historical lag derived from registration data can be used to indicate the future lag for occurrence data.

Revised estimates: estimating occurrences not yet registered

To determine the revised estimate for a particular period, the occurrence data that will be subject to inflation needs to be determined. To enable publication by 15 months after the year involved, occurrence data available for up to 14 months after a financial year can be used. For example, ABS had data for births and deaths which occurred in the 1996-97 financial year and were registered up to and including March Quarter 1998 by August 1998 (14 months after 1996-97). This corresponds to 7 quarters (June Quarter 1996 to March Quarter 1998) in which births occurring in the 1996-97 financial year could have been registered. Thus, when inflating September Quarter 1996 data, occurrence data with a future registration lag of less than or equal to 7 quarters is available.

The future lag of occurrence data available determines the length of the historical lag period used for successive calculations. To inflate September Quarter 1996 occurrences, historical lags of less than or equal to 7 quarters would be used.

Under ABS' proposed inflation method, occurrence data for a particular quarter type (September, December, March or June) are adjusted based on registration data for the latest quarter of the same type. In the case of September Quarter 1996 occurrences, a historical lag of 7 quarters is applied to registrations for September Quarter 1997.

The proportion, p, of all registrations for the quarter that occurred within the historical lag period is determined by:


The inflation factor, f, for the quarter can be calculated such that:


For example, the inflation factor for births occurring in September Quarter 1996 would be:



The estimate is calculated by applying the inflation factor to the count of births/deaths on file, such that:



Other inflation methods

Two other methods of generating inflation factors were also investigated by the ABS. The only difference between the three inflation methods is in the registration data used to generate historical lags.

The first alternative uses the historical registration lag of a particular quarter to determine the future registration lag for that same quarter. The inflation factor generated using this method for the September Quarter 1996 is therefore:



The second alternative method uses the most up-to-date data for both registrations and occurrences to estimate historical and future registration lags. To achieve this, it looks at lags over an extended period rather than lags for a particular quarter. The inflation factor generated using this method for the September Quarter 1996 is:



In concept, the proposed method has the advantage of use of more recent data than the first alternative and reflects seasonality better than the second alternative.

Results

Quarterly revised estimates of births and deaths from the June Quarter 1985 to the June Quarter 1996 were created using ABS' proposed inflation method and counts of occurrences. These estimates were then compared to the occurrence counts available for each quarter, updated for registrations up to March 1997. Annual results appear in Attachment 1. A positive difference between a revised estimate and the latest count on file means that more registrations for the period involved are expected. A negative difference means that more registrations for the period involved have been received than expected. Since there is less time for late registrations to take place, differences in recent years should be predominantly positive.

The results indicate only minor differences existing between actual occurrences of births and deaths (latest count on file) and revised estimates, particularly for early years. Comparison with current method results for preliminary, revised and final estimates in 1991-92 are shown in Table 3.


    Table 3.
        COMPARISON OF CURRENT METHOD AND PROPOSED METHOD OF ESTIMATING BIRTH AND DEATH OCCURRENCES, 1991-92

Current method
Revised estimate
- proposed method
Count on file(a)
Preliminary estimate
Revised estimate
Final
estimate

    Births
255.6
256.8
259.2
259.7
259.0
    Deaths
120.7
120.8
120.8
121.0
121.0

          (a) Includes registrations up to March 1997.

Estimates for the alternative methods were also produced and show similar results. For births there is negligible difference between the methods in the period 1985-86 to 1990-91. After 1991 the second alternative method appears to provide better results, but this reflects a probable conservative estimate by not fully taking into account occurrence that have yet to be registered. For deaths, the proposed method provides a mid-range estimate.

Conclusions

The proposed method would provide a better revised estimate of the true number of births and deaths than is available from registration data alone. Subject to further investigation, ABS also proposes to apply an inflation factor to preliminary and final estimates. For preliminary estimates this is likely to involve alternative method 1, while the method proposed for revised estimates is likely to be suitable for final estimates.



Attachment 1. Revised estimates of birth and death occurrences by State or Territory of usual residence


Births
Deaths
Count on file(a)
Revised estimate

Diff
Count on file(a)
Revised estimate

Diff

1985-86NSW
83967
84106
139
42620
42632
12
VIC
60368
60438
70
31077
31001
-76
QLD
40266
40218
-48
18434
18435
1
SA
19619
19755
136
10404
10403
-1
WA
23363
23337
-26
9026
9023
-3
TAS
7000
6991
-9
3638
3637
-1
NT
3335
3347
12
695
649
-46
ACT
4108
4110
2
1005
1005
0
AUST
242026
242302
276
116899
116785
-114
    Sum of absolute differences
442
140
1986-87NSW
84830
84830
121
42685
42685
0
VIC
61266
61266
166
30500
30537
37
QLD
40042
40042
-70
18214
18217
3
SA
19414
19414
85
10522
10523
1
WA
24082
24082
-37
9091
9109
18
TAS
7008
7008
-8
3478
3478
0
NT
3328
3328
8
719
696
23
ACT
4108
4108
8
1010
1008
-2
AUST
244078
244350
272
116219
116252
33
    Sum of absolute differences
503
84
1987-88NSW
85070
85118
48
43769
43762
-7
VIC
62392
62443
51
31347
31374
27
QLD
39995
39920
-75
19097
19096
-1
SA
19194
19238
44
10788
10794
6
WA
24260
24269
9
9074
9074
0
TAS
6726
6720
-6
3648
3651
3
NT
3342
3345
3
723
786
63
ACT
4235
4242
7
1013
1015
2
AUST
245214
245294
80
119459
119551
92
    Sum of absolute differences
243
109
1988-89NSW
86458
86357
-101
43575
43576
1
VIC
83130
63250
120
31097
31093
-4
QLD
41858
41744
-114
19201
19195
-6
SA
19429
19503
74
10846
10846
0
WA
25003
24957
-46
9434
9430
-4
TAS
6877
6870
-7
3637
3637
0
NT
3381
3391
10
721
731
10
ACT
4259
4266
7
989
988
-1
AUST
250395
250338
-57
119500
119496
-4
    Sum of absolute differences
479
26
1989-90NSW
88793
88629
-164
45237
45217
-20
VIC
65454
65631
177
32038
32090
52
QLD
44074
43968
-106
20287
20264
-23
SA
19606
19855
249
11284
11284
0
WA
25569
25491
-78
9569
9558
-11
TAS
6967
6966
-1
3662
3651
-11
NT
3500
3506
6
757
762
5
ACT
4474
4472
-2
1053
1055
2
AUST
258437
258519
82
123887
123880
-7
    Sum of absolute differences
783
124
          (a) Includes registrations up to March 1997




Attachment 1. Revised estimates of birth and death occurrences by State or Territory of usual residence (continued)
Births
Deaths
Count on file(a)
Revised estimate

Diff
Count on file(a)
Revised estimate
Diff

1990-91NSW
89349
89479
130
42818
42817
-1
VIC
65920
66369
449
30937
30990
53
QLD
44960
44840
-120
19208
19206
-2
SA
19542
19633
91
11084
11099
15
WA
25330
25363
33
9475
9482
7
TAS
7063
7057
-6
3718
3732
14
NT
3619
3614
-5
1000
1008
8
ACT
4601
4615
14
1151
1152
1
AUST
260384
260970
586
119391
119484
93
    Sum of absolute differences
848
101
1991-92NSW
89023
89209
186
43579
43602
23
VIC
64822
65018
196
31304
31299
-5
QLD
45533
45510
-23
19749
19758
9
SA
19653
19789
136
11060
11059
-1
WA
24874
25017
143
9610
9603
-7
TAS
6918
6905
-13
3694
3691
-3
NT
3698
3704
6
924
923
-1
ACT
4512
4516
4
1069
1069
0
AUST
259034
259668
634
120989
121004
15
    Sum of absolute differences
707
49
1992-93NSW
89064
90336
1272
43060
43078
18
VIC
64961
65174
213
31284
31278
-6
QLD
46204
46253
49
20232
20267
35
SA
19814
19904
90
11351
11348
-3
WA
24735
24972
237
9937
9938
1
TAS
6813
6848
35
3676
3679
3
NT
3593
3596
3
738
742
4
ACT
4492
4502
10
1060
1059
-1
OT
25
24
-1
4
1
3
AUST
259701
261610
1909
121342
121389
47
    Sum of absolute differences
1910
74
1993-94NSW
87649
88817
1168
43597
43611
14
VIC
64198
64144
-54
31627
31638
11
QLD
46822
46902
80
20716
20719
3
SA
19375
19479
104
11375
11375
0
WA
24971
25159
188
10491
10500
9
TAS
6869
6886
17
3754
3760
6
NT
3660
3661
2
781
776
-5
ACT
4439
4449
10
1150
1152
2
OT
34
36
2
5
5
0
AUST
258017
259533
1516
123496
123536
40
    Sum of absolute differences
1516
50
          (a) Includes registrations up to March 1997.




Attachment 1. Revised estimates of birth and death occurrences by State or Territory of usual residence (continued)
Births
Deaths
Count on file(a)
Revised estimate
Diff
Count on file(a)
Revised estimate
Diff

1994-95NSW
87177
88792
1615
44776
44789
13
VIC
63614
63853
239
32272
32322
50
QLD
47405
47408
3
21455
21478
23
SA
19469
19542
73
11522
11527
5
WA
25080
25248
168
10310
10311
1
TAS
6811
6854
43
3836
3839
3
NT
3706
3726
20
829
835
6
ACT
4471
4481
10
1223
1223
0
OT
54
53
-1
11
9
-2
AUST
257787
259957
2170
126234
126332
98
    Sum of absolute differences
2172
112
1995-96NSW
84414
86236
182
44464
44530
66
VIC
61292
61733
441
32827
32846
19
QLD
46391
46994
603
21265
21287
22
SA
18833
19111
278
11339
11343
4
WA
24557
24901
344
10661
10679
18
TAS
6373
6455
82
3856
3857
1
NT
3592
3628
36
767
771
4
ACT
4274
4288
14
1213
1213
0
OT
41
42
1
8
8
0
AUST
249767
253388
3621
126400
126534
134
    Sum of absolute differences
3621
134
          (a) Includes registrations up to March 1997.



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