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Federal Planning BureauEconomic analyses and forecasts
Federal Planning Bureau Economic analyses and forecasts On weights in dynamic-
ageing microsimulation models
Some work in progress
Gijs Dekkers1 and Richard Cumpston2
1. Federal Planning Bureau and Katholieke Universiteit Leuven
2. Australian National University
Paper presented at the Ministero dell'Economia e delle Finanze, Rome, February 15th, 2011
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
This work is confidential and under embargo until June 8th, 2011
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Overview of this presentation
What is the problem?
A simple solution (which does not really work)
A proposed method of using weights in dynamic-ageing MSM’s
Weights and alignment
Some empirical results on Australian data
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Overview of this presentation
What is the problem?
A simple solution (which does not really work)
A proposed method of using weights in dynamic-ageing MSM’s
Weights and alignment
Some empirical results on Australian data
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Why weights?
Datasets are often used to assess trends of aggregated units. So, they need to contain unbiased and credible sample estimators on population parameters. This need for representativeness is however hampered by bias caused by differential cross-sectional selection
probabilities non-response
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Overview of this presentation
What is the problem?
A simple solution (which does not really work)
A proposed method of using weights in dynamic-ageing MSM’s
Weights and alignment
Some empirical results on Australian data
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
An obvious solution: transform the probability weights in frequency weights and expand the dataset...
#(x=1|p) : number of cases of x=1 in population (p). #(x=1|s): the same number in the sample (s). #p and #s :total number of cases in the population and sample.
The probability weight
ssx
ppx
PW
#)|1(##
)|1(#
or
p
s
sx
pxPW
#
#
)|1(#
)|1(#.
Hence
p
sFWPW
#
# or
1
#
#
p
sPWFW .
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
1010.0 PWsampleFW
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Drawback: - Expanding is inefficient, because it ultimately
means simulating the entire population.
- Use standardized weights, but:- Can one expand using standardized weights?- I have my doubts on the way in which
standardized weights are derived.
- Sampling to round the weights introduces sampling variance, which may be more important than the rounding error (this certainly is the case with standardized weights).
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Overview of this presentation
What is the problem?
A simple solution (which does not really work)
A proposed method of using weights in dynamic-ageing MSM’s
Weights and alignment
Some empirical results on Australian data
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
An alternative strategy: using weights as a simulation variable in the model
The method presented in this paper involves the partial expansion or “splitting up” of individual weighted households in case of moves of individuals in between households of different weights.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
An example:
suppose two households X and Y. Both households consist of two individuals, denoted X1, X2, Y1 and Y2.
Suppose that individuals X2 and Y2 fall in love and form a new household, say, Z. What frequency weight should this household get?
Case a: the frequencies of households are equal
Case b: the frequencies of households are unequal:F(1)=2 and F(2)=3
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
When the frequency weights of the two ‘donating’ households differ, the household with the highest frequency is expanded to two households. And then the merge is done with equal frequency weights.
‘Donating’ household 1 (F1)=3
household 2 (F2)=2
‘Donating’ household 1 (F1)=1
‘Donating’ household 1 (F1)=2
MER
GE
household 1 (F1)=1
Merged household 3 (F3)=2
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
General form: X[x1..xnx; fx] and Y[y1..yny; fy]: donating households X and Y consists of nx and ny individuals (nx, ny≥1) and have frequency weights fx and fy (fx, fy≥1, fx≠fy). Individuals x1 and y1 from the donating households form a new household Z with an unknown frequency weight fz. The solution is to break up X and Y to subsets with equal weights fz=min(fx, fy), and then create Z with weight fz. The resulting situation is
1) Household Z[x1, y1; min(fx,fy)] is the new created household. 2) Household X[x2..xnx; min(fx,fy)] is the donating household X without individual x1. 3) Household Y[y2..ynx; min(fx,fy)] is the donating household Y without individual y1. 4) Household X[x1..xnx; fx-min(fx,fy)] is the remaining donating household X with individual x1. 5) Household Y[y1..ynx; fy-min(fx,fy)] is the remaining donating household Y with individual y1.
Note that either cases 4 or 5 are empty.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Overview of this presentation
What is the problem?
A simple solution (which does not really work)
A proposed method of using weights in dynamic-ageing MSM’s
Weights and alignment
Some empirical results on Australian data
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Weights and alignment:
1.
2. Rank according to risk
3. Select the first # individuals, #=S x auxiliary proportion
)exp(1
)exp()(logit 1-
ii
iiiii X
XXr
The maximum possible proportional error is max(fi-1:i=1..S)/NP, but the expected proportional error equals ൫ฮ0.5 𝑓ҧฮ൯/𝑁𝑃, which is considerably smaller.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Weights and alignment: some solutions
Strategy 1: split up the last household
Strategy 2: select a household for alignment so that there is no mismatch
Strategy 3: iteratively reduce mismatch - the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Overview of this presentation
What is the problem?
A simple solution (which does not really work)
A proposed method of using weights in dynamic-ageing MSM’s
Weights and alignment
Some empirical results on Australian data
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Unweighted unit records:
2001 Australian Household Sample Survey (HSF), Unweighted sample size of about 175,000.
Weighted unit records: Australian 2000-01 Survey of Income and Housing Costs (SIHC), These
files covered 16,824 persons, grouped into 6,786 households.
Household weights in the SIHC sample were intended to replicate the Australian population of about 19.4m. To give an unweighted sample size of about 175,000, the weights were multiplied by 0.00937 and rounded to the nearest integer.
household microsimulation model (Cumpston 2009).
Using the aforementioned datasets HSF and SHIC as the starting point, the Cumpston model was ran in its original and weighted form for the years 2001-2050.
Alignment was done using random selection, using strategy 3.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Table 1 Results of 50-year projections using Australian data Data Weighted Event Run time Persons Persons Persons Persons
source data alignment seconds 2001 2001 2051 2051
Weighted Unweighted Weighted Unweighted
HSF No No 43.0 175044 225694
HSF No Yes 55.4 175044 237317
SHIC Yes No 30.4 16824 219948 222422
SHIC Yes Yes 42.0 16824 234678 237530
SHIC No No 41.6 175108 229292
SHIC No Yes 54.5 175108 237381
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Figure 1 Weighted and unweighted person projections
0
50,000
100,000
150,000
200,000
250,000
2001 2011 2021 2031 2041 2051
Projected persons
Weighted persons
Unweighted persons
Weighted persons (no moves)
The total efficiency gain depends on the average initial size of the weight, and the speed of the convergence process.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions So far, there are no efficient ways in which dynamic MSM’s can
include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions So far, there are no efficient ways in which dynamic MSM’s can
include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions
So far, there are no efficient ways in which dynamic MSM’s can include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions
So far, there are no efficient ways in which dynamic MSM’s can include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions
So far, there are no efficient ways in which dynamic MSM’s can include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions
So far, there are no efficient ways in which dynamic MSM’s can include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Conclusions So far, there are no efficient ways in which dynamic MSM’s can
include weights.
This method uses weights as ‘just another’ variable in the model.
It prevents losses in efficiency involved in expanding the starting dataset.
This paper proposes three methods for alignment of weighted data
It applies an iterative procedure where the ‘overshooting’ individual in each iteration is taken out of the pool before starting the next iteration.
Efficiency gains may be quite considerable, though limited to the first few decades.
Federal Planning BureauEconomic analyses and forecasts
On weights in dynamic-ageing microsimulation models
Thank you