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Backcasting

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... 30 5B 4 4 4B 16 16 3B 40 30 10 2B 25 20 5 1B Total 3A 2A 1A N 2607 1265 1237 105 Total 984 984 5B 53 53 4B 651 651 3B 351 281 70 2B 568 533 35 1B Total 3A 2A ... – PowerPoint PPT presentation

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Title: Backcasting


1
Backcasting
  • United Nations Statistics Division

2
Overview
  • Any change in classifications creates a break in
    time series, since they are suddenly based on
    differently formed categories
  • Backcasting is a process to describe data
    collected before the break in terms of the new
    classification

3
Overview
  • There is no single best method
  • Factors influencing a decision include
  • type of statistical series that requires
    backcasting (raw data, aggregates, indices,
    growth rates, ...)
  • statistical domain of the time series
  • availability of micro-data
  • availability of "dual coded" micro-data (i.e.
    businesses are classified according to both the
    old and the new classification)
  • length of the "dual coded" period
  • frequency of the existing time series
  • required level of detail of the backcast series
  • cost / resource considerations

4
Main methods
  • Micro-data approach (re-working of individual
    data)
  • Macro-data approach (proportional approach)
  • Hybrids thereof

5
Micro-data approach
  • Consists of assigning a new activity code ( new
    classification) to all units in every period in
    the past (as far back as backcasting is desired)
  • No other change is required
  • Statistics are then compiled by standard
    aggregation
  • Census vs. survey (weight adjustment issue)

6
Micro-data approach
  • Census
  • All in-scope unites are selected and therefore
    have a weight of one.
  • Each unit is therefore recoded and then the
    re-aggregation can take place.
  • Survey
  • The non-observed units in the population have
    influence on the outcome via sampling weights
  • Therefore all units under the population (both
    observed and non-observed) need to be coded
  • Re-aggregation of the sample units under the new
    classification can then occur.

7
Micro-data approach
  • Requires detailed information from past periods
    (for all units to be recoded)
  • More detailed than just the old code
  • If information is available, results are more
    reliable than those from macro-approaches

8
Micro-data approach
  • Issues
  • Resource intensive
  • Need solutions if unit information is not
    available for a period (not collected, not
    responded)
  • Nearest neighbor
  • Back calculation of the elementary unit is made
    in the same way as made for the closet unit.
  • Transition matrix approach
  • Using conversion coefficient at the elementary
    level

9
Macro-data approach
  • Also called proportional method
  • This method calculates a ratio (proportion,
    conversion coefficients) in a fixed dual coding
    period that is then applied to all previous
    periods
  • The ratios are calculated at the macro level
  • Could be based on number of units (counts) or
    size variables such as turnover or employment
  • Has a more approximate character

10
Macro-data approach
  • In simple form, applies growth rates of former
    time series to the revised level for the whole
    historical period
  • More sophisticated methods may use adjustments
    based on experts knowledge
  • Example mobile phones

11
Macro-data approach
  • Assumes that the same set of coefficients applies
    to all periods
  • This means it is assumed that the distribution of
    the variable of interest has not changed between
    the old and the new classification
  • Applied to aggregates does not consider
    micro-data
  • Relatively simple and cheap to implement

12
Macro-data approach Steps
  • 1 estimation of conversion coefficients
  • Done for dual-coding period
  • Longer/multiple periods help in overcoming
    infant problems of the new classification and
    allow for correction of data
  • Based on selection of specific variable
  • 2 calculation of aggregates using the
    conversion coefficients
  • Weighted linear combination
  • 3 linking the different segments
  • Old overlap new series
  • Breaks caused by mainly by change in field of
    observation
  • Simple factor or wedging
  • 4 final adjustment
  • Seasonal etc.

13
Macro-data approach Hypothetical example
  • Basics of conversion matrices
  • Makes use of a simple, artificial example
  • Convert from A to B.
  • a 3
  • (codes 1A, 2A, 3A)
  • b 5
  • (codes 1B, 2B, 3B, 4B, 5B)
  • N (Count) 115

14
Dual-coded business register
15
Derive summary totals
N 1A 2A 3A Total
1B 5 20 25
2B 10 30 40
3B 16 16
4B 4 4
5B 30 30
Total 15 40 60 115
Emp 1A 2A 3A Total
1B 35 533 568
2B 70 281 351
3B 651 651
4B 53 53
5B 984 984
Total 105 1237 1265 2607
OR
16
Conversion matrix A to B counts
Conversion is via linear combination
Conversion coefficient from 1A to 1B
beta 1A 2A 3A
1B .33 .50
2B .67 .50
3B .40
4B .10
5B .50
Total 1 1 1
N 1A 2A 3A
1B 5 20
2B 10 30
3B 16
4B 4
5B 30
Total 15 40 60
17
Conversion is via linear combinations
  • and the aggregate totals are the same

18
Apply these proportions to each time point
19
Example ISIC Rev3 to Rev.4 Conversion at the
Section level
  • Denote turnover (y) of ISIC Rev.3 Section C, D
    E and out-of-scope unit (Z) by
  • Denote turnover (y) of ISIC Rev.4 Section B, C, D
    E and out-of-scope unit (Z) by

20
Conversion matrix
Conversion coefficient from Rev3 Section C to
Rev4 Section B
21
Turnover Summary table
  • The turnover value of activities that is
    classified in
  • Old classification Rev.3 Section C
  • New classification Rev.4 Section B

Rev .3 Rev .3 Rev .3 Rev .3
  C D E Z  Total
Rev.4 B 19,829,202 0 0 14,178 19,843,380
Rev.4 C 211,632 1,297,621,607 2,142 4,975,276 1,302,810,657
Rev.4 D 0 101,624 147,814,407 25,793,423 173,709,454
Rev.4 E 6,834 7,712,001 8,342,747 18,977,634 35,039,216
Rev.4 Z 101,654 44,961,905 783,298 3,152,252,617 3,198,099,474
   Total 20,149,322 1,350,397,137 156,942,594 3,202,013,128 4,729,502,181
22
Conversion matrix
  • Of the Rev.3 Section C activities,
  • 98.41 is reclassified to Rev.4 Section B
  • 1.05 is reclassified to Rev.4 Section C, and so
    on
  • Rev.4 Section C activities is a combination of
    1.05 Rev.3 Section C, 96.09 Rev.3 Section E,
    and 0.16 of Rev.3 activities that does not
    belong to the Rev.3 industrial sector

    Rev .3 Rev .3 Rev .3 Rev .3
    C D E Z
Rev.4 B 0.9841 0.0000 0.0000 0.0000
Rev.4 C 0.0105 0.9609 0.0000 0.0016
Rev.4 D 0.0000 0.0001 0.9418 0.0081
Rev.4 E 0.0003 0.0057 0.0532 0.0059
Rev.4 Z 0.0050 0.0333 0.0050 0.9845
   Total weight 1.0000 1.0000 1.0000 1.0000
23
Conversion via linear combination
  • Equations for converting total series from Rev.3
    to Rev.4 are

24
Comparison
  • Micro-data approach better retains structural
    evolution of the economy
  • Micro-data approach does not require choice of a
    special variable
  • Macro-data approach reflects evolution based on
    fixed ratio for a fixed variable
  • Seasonal patterns may be distorted
  • Macro-data approach is more cost-efficient
  • No consideration of micro-data necessary
  • Assumptions underlying the macro-data approach
    become invalid over longer periods
  • Benchmark years might help to measure the
    effect, if data is available

25
Other options
  • Combinations of both approaches are possible
  • Ratios for the macro-data approach could be
    calculated for shorter periods only
  • Micro-data approach could be used for specific
    years and the macro-data approach for
    interpolation between these years
  • E.g. based on availability of census data
  • Many factors can influence the choice (see
    beginning) but data availability is a key
    practical factor
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