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A Comparison of Weighted Time
Dummy Hedonic and Time-Product
Dummy Indexes
Jan de Haan, Rens Hendriks and Michael Scholz
Background
• Aizcorbe, Corrado and Doms (2003)
– “When Do Matched-Model and Hedonic Techniques Yield Similar Price Measures?”
• Aizcorbe and Pho (2005)
– “Differences in Hedonic and Matched-Model Price Indexes: Do the Weights Matter?”
• Silver and Heravi (2005)
– “A Failure in the Measurement of Inflation: Results from a Hedonic and Matched Experiment Using Scanner Data”
• Krsinich (2016)
– “The FEWS Index: Fixed Effects with a Window Splice”
The TDH and TPD models
• The Time Dummy Hedonic model:
• The Time Product Dummy model:
tiik
K
kk
T
t
ti
tti zDp εβδδ +++= ∑∑
== 11
0ln
ti
N
iii
T
t
ti
tti DDp εγδα +++= ∑∑
−
==
1
11
ln
Weighted TDH and TPD Indexes
)ˆexp(0 ttP δ=
( )
−= ∑∏∏
=
∈
∈ tkk
K
kk
Si
si
Si
sti
tTDH zz
p
p
Pi
t
ti
0
10
0 ˆexp)(
)(
0
0 β
( )t
Si
si
Si
sti
tTPD
i
t
ti
p
p
P γγ ˆˆexp)(
)(0
0
0
0
0 −=∏∏
∈
∈
Decomposition in regression residuals (1)
• Weighted TDH and TPD sum to zero in each
period.
• The TDH and TPD indices can be written as:
1ˆˆ
0
0
0
0
=
=
∏ ∏∈ ∈Si Si
s
ti
ti
s
i
i
t
tii
p
p
p
p
∏ ∏∏∏∈ ∈∈∈
=
=
=
0
0
0
0
2
0
2
0000
ˆ
ˆ
ˆ
ˆ
Si Si
s
i
ti
s
i
ti
Si
s
i
ti
Si
s
i
tit
t
tii
t
tii
p
p
p
p
p
p
p
pP
Decomposition in regression residuals (2)
( ) •
−= 0
)(0
)(0
0
0
0
exp TDHDTPDDM
Dt
TDH
tTPD uu
s
s
P
P
( ) •
−• t
TPDNt
TDHNtM
tN uu
s
s)()(exp
( ) ( )[ ])(0)(
0)(
)(0)(
0)(exp t
TDHMTDHMtTPDMTPDM uuuu −−−•
Empirical Illustration (1)
Weighted TPD & TDH Indexes
40
50
60
70
80
90
100
110
120
130
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
TPD TDH
Empirical Illustration (2)
Weighted Average Residuals
-0,5
-0,4
-0,3
-0,2
-0,1
0
0,1
0,2
0,3
0,4
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Disapp. TPD Disapp. TDH New TPD New TDH
Empirical Illustration (3)
Aggregate Expenditure Shares
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Disapp. New Matched (0) Matched (t)
Empirical Illustration (4)
Decomposition of TPD-TDH Ratio
0,4
0,5
0,6
0,7
0,8
0,9
1
1,1
1,2
1,3
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Ratio Disapp. New Third term
Empirical Illustration (5)
TPD-TDH Indexes – Group Level
80
90
100
110
120
130
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
TPD TDH
Empirical Illustration (6)
Decomposition – Group Level
0,92
0,93
0,94
0,95
0,96
0,97
0,98
0,99
1
1,01
1,02
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Ratio Disapp. New Third term
Questions?
