A Comparison of Weighted Time Dummy Hedonic and Time-Product Dummy - - PowerPoint PPT Presentation

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:

t i ik K k k T t t i t t i

z D p ε β δ δ + + + =

∑ ∑

= = 1 1

ln

t i N i i i T t t i t t i

D D p ε γ δ α + + + =

∑ ∑

− = = 1 1 1

ln

Weighted TDH and TPD Indexes

) ˆ exp(

t t

P δ =

( )

     − =

∑ ∏ ∏

= ∈ ∈ t k k K k k S i s i S i s t i t TDH

z z p p P

i t t i

1

ˆ exp ) ( ) ( β

( )

t S i s i S i s t i t TPD

i t t i

p p P γ γ ˆ ˆ exp ) ( ) ( − = ∏

∏

∈ ∈

Decomposition in regression residuals (1)

• Weighted TDH and TPD sum to zero in each

period.

• The TDH and TPD indices can be written as:

1 ˆ ˆ =         =        

∏ ∏

∈ ∈ S i S i s t i t i s i i

t t i i

p p p p

∏ ∏ ∏ ∏

∈ ∈ ∈ ∈

                =         =         =

2 2

ˆ ˆ ˆ ˆ

S i S i s i t i s i t i S i s i t i S i s i t i t

t t i i t t i i

p p p p p p p p P

Decomposition in regression residuals (2)

( ) •

      − =

) ( ) (

exp

TDH D TPD D M D t TDH t TPD

u u s s P P

( ) •

      −

• t

TPD N t TDH N t M t N

u u s s

) ( ) (

exp

( ) ( ) [ ]

) ( ) ( ) ( ) ( ) ( ) (

exp

t TDH M TDH M t TPD M TPD M

u u u u − − −

Empirical Illustration (1) Weighted TPD & TDH Indexes

40 50 60 70 80 90 100 110 120 130 1 3 5 7 9 1113151719212325272931333537394143454749 TPD TDH

Empirical Illustration (2) Weighted Average Residuals

• 0,5
• 0,4
• 0,3
• 0,2
• 0,1

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

0,1 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 1113151719212325272931333537394143454749 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?