Using Business Taxation Data as Auxiliary Variables and as Substitution Variables in the Australian Bureau of Statistics Frank Yu, Robert Clark and Gabriele B.
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Transcript Using Business Taxation Data as Auxiliary Variables and as Substitution Variables in the Australian Bureau of Statistics Frank Yu, Robert Clark and Gabriele B.
Using Business Taxation Data as
Auxiliary Variables and as
Substitution Variables in the
Australian Bureau of Statistics
Frank Yu, Robert Clark and Gabriele B. Durant
Outline of talk
Use of tax data in ABS
Using tax data as auxiliary variables
example: subannual surveys
Using tax data as variables of interest
missing taxation data
example: annual surveys
Dealing with missing tax data:
Missing at Random
Common Error Measurement model
Conclusion
Use of tax data
construct and maintain population frame
as auxiliary variables for estimation
substitute survey data to reduce provider burden
as source for imputing missing/invalid survey data
provide independent estimates for validation of
outputs
Data supplied by Australian
Taxation Office
Australian Business Register information
businesses identified by name, address
industry, payees
Business Activity Statement data - GST and PAYG data
available (90%) 6 months after reference quarter
turnover, wage and salaries, capital and non-capital expenses
Income Tax data
available (70 to 80%)18 months after reference quarter
detailed expenses and revenue and balance sheet
Use of tax data for frame creation
ABS Maintained Population
ABS MP
complex units
ATO maintained population
from Australian Busines Register
ATO MP
simple units: ABN = statistical unit
Use of tax data for frame
construction
construction: units from ABR
industry, sector
number of payees
multistate indicators
maintenance:
births and cancellation
tax roles : e.g. employing vs non-employing units
long term non-remitters excluded
stratification: single/multiple states, industry
Frame auxiliary variables (xi's)
derived size benchmarks:
from BAS, based on wage and salaries data
used as stratification variables
BAS turnover
BAS wages
need imputation (derived from average of quarterly
data)
lag reference quarter by 2 quarters
Survey data vs tax data
Sample
Survey
BAS data
BIT data
concept
accuracy
timeliness
detailed domain
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*
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richness of data
items
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*
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Use of tax data as auxiliary
variables
Survey
Variables of
interest
Auxiliary Variables
for estimation
Retail Trade
Sales
BAS turnover
Economic Activity
Survey
Annual Integrated
Collection
financial
BIT variables
variables
same as EAS BAS variables
tax data as auxiliary variables
s
xi
U\s
xi
yi
Generalised Regression Estimation
YGREG YHT ( X X HT ) B
where
YHT Yi / i
s
X HT X i / i
s
B ( X i ' X i / i ) 1 ( X i 'Yi / i )
s
s
Advantages and disadvantages
Advantages
provide efficiency
approximately unbiased
does not require X's to
be measuring the right
concepts
does not require X's to
be current
Disadvantages
does not model Y
directly e.g. zero units
influential points
efficiency in estimating
levels not equal to
efficiency for estimating
change
Issue: inactive/out of scope units
Solution: apply GREG to positive units only
efficiency for estimating level does not
necessarily translate to efficiency for
estimating change
Var (Y2,GREG Y1,GREG ) Var (Y2, HT Y1, HT )
iff res 1-
1- Y
1 rXY
where res is the lag 1autocorrelation of residuals,
Y is the lag 1 autocorrelatin of Y's, and
rXY is the correlation between Y and X's
Data Substitution Approach: Use
tax as the variable of interest
Assumes tax data are
better
respondents more
serious about getting it
right
more time to provide
information
audited accounts (for
BIT) for tax purposes
Detailed breakdown
Missing tax data
require matching to
frame
missingness is nonignorable
ƒ inactive units
ƒ late units have more
expenses
Examples: Economic Activity
Survey (annual) 1990s to 05/06
estimation of totals
for broad items for
microbusinesses
augmenting sample
for simple
businesses
estimation of
detailed items
tax data as substitution
variables
tax data to replace broad
level income and expenses
items
detailed items imputed by
pro-rating broad tax data
based on splits observd in
surveys
Examples: Annual Integrated
Collection (06/7 onwards)
AIC - core survey estimation of totals tax data as auxiliary variables
estimates
for survey variables for generalised regression
for small and large estimation
businesses
AIC complementary
estimates
AIC complementary
estimates
estimation of totals
for broad items for
microbusinesses
estimation of
detailed
state/industry
classes
tax data as substitution
variables
AIC complementary
estimation of
detailed economic
tax data as substitution variables,
disaggregated by model estimation
of pro-rating factors
tax data as substitution
variables
Notation
Y available
ri = 1
U
Y not available
ri = 0
Use MAR model on frame only
frame
variables
Xi
tax data of interest
Y available
ri = 1
model: Y= f(x) for ri = 1
U
Y not available
Xi
ri = 0
Use MAR model conditional on frame
variables only
U
Xi
Y available
ri = 1
model: Y= f(x) for ri = 1
MAR
Y not available
Xi
ri = 0
impute Y^ = f(x) for ri = 0
But for non-ignorable missingness
U
Xi
Y available
ri = 1
model: Y= f(x) for ri = 1
Y not available
Xi
ri = 0
impute Y^ = f(x) for ri = 0
Use a sample to inform about the nonreporters based
on their survey response.
Notation: Use Y to represent tax variables and Y* for
survey variables (a surrogate of Y)
U
Xi
Y available
ri = 1
Y* available
s
Y not available
Xi
ri = 0
Y* available
Imputing tax data from survey data
U
Xi
Y available
model: Y= f(Y*, xi)
ri = 1
Y* available
s
Y not available
Xi
ri = 0
Y* available
Imputing tax data from survey data
U
Xi
Y available
model: Y= f(Y*,
f(Y*) xi)
ri = 1
Y* available
s
Y not available
Xi
Y* available
ri = 0
impute Ŷ
Imputing tax data from survey data
U
Xi
Y available
model: Y= f(Y*, x)
ri = 1
Y* available
s
Y not available
Xi
Y* available
ri = 0
impute Ŷ=f(Y*, x)
Models for Y
Missing at Random: Y independent of r given x and Y*
r Y
x ,Y *
Common measurement error: Given Y, distribution of Y*
Is independent of r
r Y *
x ,Y
Use MAR model: missing at random r Y
x ,Y
given X and Y*
*
U
Xi
Y available
model: Y= f(Y*, x) for ri = 1
ri = 1
Y* available
MAR
s
Y not available
Xi
ri = 0
Y* available
impute Ŷ for ri = 0
Imputation using MAR model
1.
2.
3.
Using data on Y and Y* observed from the units in
the sample where where both survey and tax data are
reported, model Y as a function of Y*.
Use this model to impute Yi* for tax non reporters in
the sample (assuming Y* is known for them).
For units not in the sample, if their tax data is
missing, impute using the distribution
f (Yi | ri 0, xi ) f (Yi | ri 0, xi , Yi * ) f (Y *i | ri 0, xi )dYi *
f (Yi | ri 1, xi , Yi* ) f (Y *i | ri 0, xi )dYi *
r Y *
Use CME model
x ,Y
U
Xi
Y available
ri = 1
model: Y*= f(Y, x) for ri = 1
invert to get Ŷ= g(Y*)
CME
Y* available
s
Y not available
Xi
ri = 0
Y* available
impute Ŷ = h(X) for
ri = 0
for i in U\s
Imputation using CME model
r Y *
x ,Y
f (Yi | Yi , xi , ri 0) f ((Yi | Yi , xi , ri 1).
*
*
A typical model can be:
Y Yi i where E ( i | Yi .ri ) 0,
*
i
This model motivates an unbiased impute:Yi (Y )
*
i
We also want to model Yi in terms of X i when
Y* and Y are both not observed (i.e. for i s and ri 0)
E (Yi | xi .ri 0) 0i xi giving an impute 0i xi
1
i
Modelling survey data (Y*) and tax data
(Y) - invert this to predict Y from Y*
Model: survey data Y* (EAS 05/06) as a
function of frame variable X (tax_turn_0405)
for tax nonrespondents (i.e. r =0)
Empirical Best Linear Unbiased
Predictor (EBLUP) of Yi
BLUP impute:
EBLUP impute
CME imputation process
use units in sample where tax and survey variables are
observed and model the survey variable (Y*) as a function
of tax and frame data. (Y, X)
Under CME this model applies to r = 0 too.
use units in the sample where survey data are observed (i in
s) but tax data are not (ri = 0) to model the survey variable
(Y*)as function of frame data (x).
combine to give an impute for (Y) for tax nonrespondents (r
= 0):
Combine to get EBLUP
Further work
domain estimation for CME/MAR
variance estimation
discriminating between CME and MAR based on
data
Conclusion
GREG is useful for estimation of survey data but
efficiency gain is limited.
There is increasing interest in using tax data
directly on its own to produce economic statistics.
Non-ignorable missingness becomes a key issue
with tax data.
Survey data could be useful to help impute the tax
data