Transcript Rais

Statistics Canada’s Survey Methodology
for the New Services Producer Price Index
Surveys
By: Saad Rais, Statistics Canada
Zdenek Patak, Statistics Canada
Statistique
Canada
Statistics
Canada
1
Outline of Presentation





Introduction
Sampling Design
Estimation
Outlier Detection
Conclusion
2
Introduction
What is a Price Index?

Proportionate change in the price of goods
or services over time
What is its purpose?


Deflator
Indicator
3
Introduction
Users:



Government departments
Private companies
Economists, analysts, researchers etc.
Examples:

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
Consumer Price Index
Import and Export Price Index
Producer Price Index
4
Introduction
Price Indices in Canada




Price indices were mostly limited to the
goods sector
2003 - Service industry accounted for 75%
of employment and 68% of the GDP in
Canada
Five year plan to produce a set of Services
Producer Price Indices (SPPI)
Focus on a survey methodology that is
based on sound statistical principles
5
Sampling Design
Two Stage Design:


Sampling of businesses
Sampling of items within each business
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Sampling Scheme
Common method: Judgmental sampling



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Straightforward sampling and estimation
Absence of a complete reliable frame
Limited resources
Statistical quality measures cannot be
calculated
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Sampling Scheme
Cut-off sampling

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Yields a sample with the optimal coverage of
some size measure variable – revenue in our
surveys
Susceptible to biased estimates
No sample rotation
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Sampling Scheme
Stratified Simple Random Sampling
Without Replacement (Stratified
SRSWOR)
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Common Sampling scheme for business
surveys
A probability sample
Abundance of literature
Size stratification
Each unit has equal probability of selection
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Sampling Scheme
Probability Proportional-to-Size (PPS)
Sampling
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Probability sampling
High revenue coverage in sample
Requires appropriate size measure
Not robust to errors in measure of size
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Sampling Scheme
Sequential Poisson Sampling
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All the desirable properties of Poisson
Sampling
Additional benefit: fixed sample size
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Sampling Design
First-Stage Frame

Statistics Canada’s Business Register
Primary Sampling Unit

Varied from survey to survey, ranging from
establishment, company, enterprise
Primary Stratification
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By industry line
Sometimes by province
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Sampling Design
Stratum Allocation
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x – optimal allocation, where x = unit
revenue (Särndal, et al., (1992))
Adjustment for over-allocation (Cochran
(1977))
Adjustment for under-allocation
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Sampling Design
Sample Size

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Based on availability of resources and expert
knowledge and experience
No previous or related data available to
anticipate response rate or target a CV to
estimate a sample size
Improvements to sample size will be made
after obtaining sufficient data
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Sampling Design
Size Stratification
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TN units: the smallest revenue-generating
units that contribute to 5% of the applicable
primary stratum.
TA units: Any units for which  i  1
TS units: Units for which  i  1
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Sampling Design
Second Stage Sampling: Selection of Items

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PPS sampling scheme
 Requires a list of items for each business
unit
 Resource intensive, high response burden
Therefore a judgmental sample is selected
 Concerns:
 No variance estimation
 Sampling bias could result from not
pricing representative items
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Estimation
Estimation in 2 stages:
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Elemental Indices
Aggregate Indices
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Estimation
Elemental Index: Jevons Index
(t / 0)
J
P
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
 p p
t
i

b 1/ n
i
 
  p
t
i
p

b 1/ n
i

 p

(t / b ) 1/ n
i
Exhibits desirable economic and axiomatic
properties
Closer to Fisher’s index
Cannot use zero or negative prices
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Estimation
Target Aggregate Index: Laspeyres Index
N
I L(t / 0 ) 
 Pi Q
i 1
N
t
0
i
N

i 1
 Pi Q
0
i 1
 ri0 Pi (t / 0 )
0
i
N
 ri0
where ri0  Pi 0Qi0  revenue
i 1
Ratio Estimator:
n
IˆL(t / 0 ) 
 ri0 Pi (t / 0 ) /  i
i 1
n
 ri0 /  i
Yˆ

Xˆ
i 1
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Estimation
Cancellation of economic weights and
sampling weights:
n
 ri Pi
0
(t / 0)
i 1
n
/i
 ri /  i
i 1
0
n

 ri Pi
0
(t / 0)
i 1
n
 ri0
i 1
n
nri0
 Pi (t / 0)
R  i 1
0
n
nri
1
i 1
R
However, in the presence of non-responding
units, cancellation of weights does not
occur.
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Estimation
Variance Estimation:
Approximated using the Taylor linearization method:
 
v IˆL(t / 0)
 ij   i j ei(t / 0) e (jt / 0)
yi(t / 0)  IˆL(t / 0) xi
(t / 0)
 
where ei 
i j s
 ij
i  j
Xˆ
In Poisson sampling, since  ij   i j when i  j , the
formula reduces to:

v IˆL(t / 0)

 ei(t / 0) 
  (1   i ) 

i s
 i 
2
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Outlier Detection
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α-trimming
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Interquartile range
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Proportion α is removed from tails
Requires prior knowledge to be efficient
Handles up to 25% aberrant observations
Construct robust z-score to identify outliers
MAD (Median Absolute Deviation)
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Handles up to 50% aberrant observations
Construct robust z-score to identify outliers
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Conclusion
Current and future projects

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Research on the efficiency of PPS sampling
versus SRSWOR sampling
Outlier detection methods
Imputation methods
Bootstrap variance estimation
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Conclusion
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Services industry is an integral component of
our economy
We are currently in the pilot/developmental
stage of index production
With the collection of data, efficiencies in the
sample size, and further research will help
improve our methodology
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Thank You
Pour de plus amples informations ou pour obtenir une
copie en français du document veuillez contacter:
For more information, or to obtain a French copy of the
presentation, please contact:
Saad Rais
E-Mail: [email protected]
Statistique
Canada
Statistics
Canada
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