U.S. DEPARTMENT OF LABOR

Bureau of Labor Statistics

 

OFFICE OF PRICES AND

LIVING CONDITIONS

Interarea Price Comparisons for Heterogeneous

Goods and Several Levels of Commodity Aggregation

Mary F. Kokoski,

Brent R. Moulton, and

Kimberly D. Zieschang

Working Paper 291

September 1996

 

 This paper was presented at the Conference on Research in Income and Wealth: International and Interarea Comparisons

of Prices, Income, and Output, March 15-16, 1996. The opinions expressed in this paper are those of the authors, and do

not represent the policies of the Bureau of Labor Statistics or the views of other BLS staff members.
- ii -

Abstract. We derive a general form of Törnqvist multilateral (transitive)

place to place index numbers and a new variant of regression methodology

for imposing transitivity while minimally adjusting the initial system of

bilateral index comparisons. We show that when several levels of item

aggregation are to be published in a system of Törnqvist interarea parities,

the adjusted, transitive Törnqvist parities at each level of aggregation

preserve the aggregation rule in the unadjusted data. Finally, the method

incorporates characteristics-based, hedonic quality adjustment as an

integral feature. We apply the method to a subset of commodity price and

expenditure data for the 44 areas of the United States covered by the

Consumer Price Index. In closing, we also discuss an application of the

method that makes time series and geographical comparisons consistent

with one another, and note that it permits decentralization of calculation in

a way that may have distinct advantages for compiling international price

comparisons.
- iii -

I. INTRODUCTION ...............................................................................................................................1

II. ECONOMIC INDEX NUMBER CONCEPTS INCORPORATING INFORMATION ON THE

CHARACTERISTICS OF HETEROGENEOUS GOODS ...................................................................2

III. TöRNQVIST MULTILATERAL (TRANSITIVE) SYSTEMS OF BILATERAL INDEX

NUMBERS ..............................................................................................................................................9

IV. MULTILATERAL PRICE MEASUREMENT WITH SUBAGGREGATES OF ITEMS...........12

V. ESTIMATION OF THE REFERENCE VALUES FOR SHARES, PRICES, AND

DETERMINANTS OF QUALITY.......................................................................................................16

VI. AN EMPIRICAL EXAMPLE.........................................................................................................21

VII. CONCLUSION AND AN EXTENSION.......................................................................................24

VIII. APPENDIX I: PROOFS OF PROPOSITIONS...........................................................................28

IX. APPENDIX II: HEDONIC REGRESSION RESULTS FOR FRUITS AND VEGETABLES .....31

X. APPENDIX III: SAMPLE INDEX CALCULATION FOR FRUITS AND VEGETABLES .........50

XI. APPENDIX IV. FRUITS AND VEGETABLES CALCULATION FOR 44 CPI AREAS...........53

XII. REFERENCES ..............................................................................................................................53
I. Introduction

Judging from periodic contacts from data users to BLS staff, place to place

consumption cost comparisons for areas within the United States are very much in

demand. In this paper we consider the problem of incorporating ancillary information on

product characteristics to make place to place quality adjustments to interarea cost of

consumption indexes. Although not specifically designed for producing interarea

comparisons, the database from which the Consumer Price Index (CPI) is calculated is

nevertheless a rich source of geographical price information that we exploit in this study.

We adopt a Törnqvist measurement framework, and derive a very general form for

a transitive, multilateral system of parities within that framework. The Caves, Christensen,

and Diewert (CCD) (1982a) implementation of the Eltetö/Köves/Szculc (EKS)

methodology (described in English by Dreschler (1973)) for multilateral price

measurement uses a special case of this general multilateral form, which involves the

estimation of 2N -1 parameters when there are N items in the index aggregate. The

unknown parameters represent a reference set of value shares and prices against which the

shares and prices of all areas are compared. We show that, if Törnqvist aggregates are to

be formed from lower level aggregates on a single, i.e. commodity, aggregation tree, the

adjustment can be applied successively from the lowest to the highest levels of aggregation

to produce a set of reference prices that, while fixed across areas, have components

corresponding to each level of item aggregation.

We adapt earlier index number results from Zieschang (1985, 1988) and Fixler and

Zieschang (1992) to incorporate information on the characteristics of the products that are

systematically randomly sampled for the CPI using country-product dummy regression at

“entry level item” product detail. In this index number framework, coefficients from these

regressions are used in constructing quality adjustment factors for the place to place price

comparisons.

We show how the parameters of the transitive Törnqvist system can be estimated

with a particular regression model to impose transitivity with minimal adjustment of the
- 2 -

data. We believe the model represents, if not a completely new approach, a substantive

refinement of the regression-based multilateral adjustment that underlies the versions of

EKS expounded by, for example, Cuthbert and Cuthbert (1988) and Selvanathan and

Prasada Rao (1992).

Kokoski, Cardiff, and Moulton (KCM, 1994) estimate country-product dummy

regressions on microdata from the U.S. Consumer Price Index for the 13 month period

June 1988-July 1989. The models are fitted at the index item level to produce quality

adjusted price indexes for the lowest, item level of aggregation. The regression

methodology developed in this paper for imposing transitivity is demonstrated on data for

a small, three-aggregation-level example problem for fruits and vegetables from an extract

of 1993 data based on the KCM (1994) study, presaging the computation price of indexes

for successively higher commodity aggregates for the 44 major urban centers and regioncity size groups covered by the CPI.

We close by summarizing the methodological and empirical results, by describing

an application of the methodology enforcing consistency between the comparisons across

areas within a given time period and comparisons across time within a given area. Finally,

we point out a notable advantage of this framework for compiling international parities

over the narrow specification approach now used in the International Comparisons Project

(ICP). Provided a standard list of item characteristics and item groups is promulgated,

item strata can be broadened, increasing the likelihood of finding a useful specification

from country to country. Further, this advantage is not bought at the cost of operational

feasibility, since calculation can be decentralized, obviating the need for central, transnational access to closely-guarded national micro data.

II. Economic index number concepts incorporating

information on the characteristics of heterogeneous goods

Let pi

a be the price in area a, of which there are A areas in total, of commodity i.

Let qi

a be the corresponding quantity purchased and let xia be the vector of
- 3 -

characteristics of the ith item specification transacted in area a. Let eh

a represent the total

expenditures of consumer unit h in area a. We will use interchangeably the terms

“economic household” and “consumer unit” for the economic unit of analysis, following

BLS terminology. A consumer unit is a group of individuals whose consumption

decisions for significant components of expenditure are joint or shared. Let qh

a denote the

vector of goods consumed by household h in area a with vector of characteristics xh

a and

prices ph

a .

We suppose that each consumer unit in area a minimizes the cost of achieving a

given level of welfare at expenditure level e h

a so that the consumer unit cost of

consumption of a given quality of goods as determined by the vector x h

a would be

e Eux p pqF xq u h ( ) a

h

a

h

a

h

a

h

a

q h

a

h

a

h

a

h

a

h

a

h

a

h

= = q

′ ≥ 









 ( , , ) min : , .

where Fxq h ( ) a

h

a

h

a , is the utility function of consumer unit h and uh

a is the unit’s welfare

index.

We suppose further that the consumer unit in area a faces a hedonic locus of

market equilibrium prices across the quality spectrum given by p Hx h ( ) a a

h

a = , and that the

unit minimizes the cost of achieving welfare level uh

a over the characteristics of goods, so

that

∇ +∇ () () ′∇ = x h

a

h

a

h

a

h

a

x h

a

p h

a

h

a

h

a

h

a

h

a

h

a

h

Euxp p Euxp ,, ,, 0 a (1)

Since ∇ =∇ x h

a

x

a

h

a

h

p Ha and ∇ = p h ( ) a

h

a

h

a

h

a

h

a

h

aEuxp q , , , the latter by the Shephard/Hotelling

lemma, we have
- 4 -

∇ = −∇ ( ) ′

x h

a

h

a

h

a

h

a

x

a

h

a

h

a

h

Euxp Hq , , a (2)

If H a is semilog, as generally assumed in hedonic studies, so that

ln H x i

a

i

a

i

a

i

a = + ′ α β (3)

then the characteristics gradient expression can be rewritten

∇ =− ( ) ′

x h

a

h

a

h

a

h

a a

h

a

h

a

h

a E u x p we , , β (4)

where w

p q

p q

i h

a i h

a

i h

a

i h

a

i h

a

i

,

, ,

, ,

=

∑

w

w

w

h N a

h

a

N h

a

q

q

=





















=

1,

,

M ; number of commodities

β

β

β

a

a

N

a

x

x

N ′

=

′

′

























=

1

M ; number of product characteristics .

Turning now to aggregate expenditure over consumer units in an area, Diewert

(1987) has considered this problem as a weighted average of individual household index

numbers comparing the prices in two areas in the “democratic weighting” case. In this

paper we follow his characterization of the “plutocratic” expenditure weighted case with

some modifications for the heterogeneity of goods within and between areas. The area

aggregate expenditure function is
- 5 -

Eux p Euxp ( )( ) aaa a

h

a

h

a

h

a

h

a

h

r r r

,, ,, = ∑

where the → over an argument indicates the concatenation of vectors across households.

We then consider the expenditure function in terms of log transformed price arguments as

Qux p Eux p Eux p Qux p ( )( ) ( ) ( ) aaa a aaa a

h

a

h

a

h

a

h

a

h

h

a

h

a

h

a

h

a

h

r r r r r r , ,ln , , , , , ,ln == = ∑ ∑ .

We “plutocratically” aggregate across households in area a such that the

expenditure weighted average for characteristics and log-prices represent the indicators

determining area demand behavior, where area item demand is the sum of the economic

household item demands for the area.1

 We do not require strong aggregation conditions,

but effectively hold the distribution of product characteristics and prices fixed across

economic households within area a as in

~ , ,ln , , ln Qux p Qu x p ln

a aa a aa a

x

a a

p

 r r a



 



 = ⊗+ ⊗ + 



 

 ι νι ν  (5)

where

ν ι

ν ι

ι

x

aa a

p

a a a

x x

p p

= −⊗

= −⊗

=

⊗

r

r ln ln ln

a vector of ones of dimension equal to the number of households

= Kronecker product

 

1

 Actually, the results to follow do not depend on the particular form of area aggregation

for product characteristics and prices. Although this discussion is couched in terms of an

arithmetic area mean for characteristics and a geometric mean for prices, others will also

work.
- 6 -

give the deviations of the area means from the individual household values for commodity

characteristics and prices paid.

Diewert (1976) and Caves, Christensen, and Diewert (1982b) have shown, using

the derivatives of the expenditure function with respect to log prices expressed in terms of

observable expenditure shares, that the Törnqvist index number is exact for the Translog

flexible functional form. The translog aggregator function differentially approximates any

price aggregator function (i.e., cost of utility, input cost, revenue function) to the second

order at a point, and it is exact for the Törnqvist index number even when some of the

parameters (those on the first-order terms) of the underlying aggregator function are

different in the two periods or localities compared. We take the derivative of the area

expenditure function with respect to intera-area average household characteristics and

price arguments to obtain

( ) ( )

( )

∂

∂

∂

∂

∂

∂ β β

x

Eux p

x

Qux p

x

Q u x p Q ws w

iz

a

aaa a

iz

a

aaa a

izh

a h

a

h

a

h

a

h

a a

h

iz

a

ih

a

h

a

h

iz

a

i

a

ln ~ , ,exp(ln ) ln ~ , ,ln

, ,ln / ~ `

r r = =

= =− =− ∑ ∑

 

 

(6)

( )

∂

∂

∂

∂

∂

∂

ln

ln ~ , ,exp(ln )

ln

ln ~ , ,ln

ln , ,ln / ~

p

Eu x p

p

Qu x p

p

Q u x p Q ws w

i

a

a a a

i

a

a a a

ih

a h

a

h

a

h

a

h

a a

h

ih

a

h

q

h

i

a

r r 



 



 = 



 





 = ∑ ∑= =

(7)

where

w

p q

p q

p q

e

ih

a ih

a

ih

a

ih

a

ih

a

i

ih

a

ih

a

h

= = a

∑

s

e

e

h

a h

a

h

a

h

=

∑

are, respectively, the within household expenditure shares of commodities and the between

household total expenditure shares of consumer unit h in area a.
- 7 -

Finally, we assume that the area aggregate expenditure function

ln ( ) ~Qex p , ,ln aa a a has a quadratic, “semi-translog” functional form in its arguments with

coefficients of second-order terms independent of location, but with possibly locationspecific coefficients on linear terms. Following CCD (1982b), then, we can derive the

following (logarithmic) index number result:

ln

ln ~ , ,ln ln ~ , ,ln ln ~ , ,ln ln ~ , ,ln

ln ~ , ,ln ln ~ , ,ln ln ln

.

ln ln

I

Qux p Qux p Qux p Qux p

Qux p Qux p p p

ab

a ab b a aa a b bb b bba a

p

a aa a

p

b bb b ba

x

=





 



 − 



 



 + 



 



 − 



 



 



 





∇ 



 



 +∇ 



 



 



 



 − 



 





∇

1

2

1

2

1

2

rrrr

r r =

 + ln ( ) ~ , ,ln ln ~ Qux p Qux p x x , ,ln a aa a

x

b bb b  r r b a 

 



 +∇ 



 



 



 



 −

(8)

Substituting (6) and (7) into (8), following CCD (1982b) again, and with reference to

Fixler and Zieschang (1992), we have

ln ln ln ln . I T w w p p w wx x ( )( ) ( )( ) ab ab

i

a

i

b

i

b

i

a

iz

a

i

a

iz

b

i

b

iz

b

iz

a

i z

=≡ + −− + −





 

 ∑ ∑  1

2 β β (9)

This formula for the bilateral index between areas is an extremely flexible result that

permits all parameters of the semi-log “hedonic” price equations to differ by area, that

fully reflects household optimization over measured product quantities and characteristics.

III. Törnqvist Multilateral (Transitive) Systems of Bilateral Index

Numbers

In another paper, Caves, Christensen, and Diewert (CCD, 1982a) noted that the

system of bilateral Törnqvist interarea indexes is not transitive, but developed a simply

calculated multilateral variant satisfying the transitivity property. Returning to lower case
- 8 -

notation for the index arguments for areas, we derive the following general implication of

transitivity for this class of index number:

PROPOSITION 1

It is necessary and sufficient for the bilateral Törnqvist item index to be transitive,

that for all a, b, there exist constant vectors w0 and ln p0 such that

wp wp w p p ( )

pw w

i

a

i

b

i

b

i

a

i

i i

b

i

a

i

i i

b

i

a

i

ln ln ln ln

ln ( )

∑∑∑

∑

−= −

− −

0

0 (10)

where

wi

0 = a reference share for index item i for the entire region, with

wi

i

0

∑ = 1.

ln pi

0 = a reference price for index item i across the entire region.

Furthermore, if this condition holds, the multilateral Törnqvist index has the form

ln ln ln ln ln T ww p p ww p p [ ( )( ) ( )( )] ab

i i

b

i

b

i

i

i i

a

i

a ≡ + −−+ − ◊ ∑ i

1

2

0 0 1

2

0 0 (11)

The proof is given in Appendix I. CCD(1982a) showed that application of the

EKS principle to a system of bilateral Törnqvist indexes yields the above formula with the

reference shares and log prices set at their simple arithmetic averages across areas.
- 9 -

Clearly, these simple averages could also be replaced with total expenditure weighted

averages. We consider still another way of estimating the reference shares and prices in

the next section.

The overall system an be adjusted to be transitive in both prices and item

characteristics by applying the principle underlying Proposition 1. This is stated in:

PROPOSITION 2

If the area-specific CPD coefficients are known, it is necessary and sufficient for

the bilateral quality-adjusted Törnqvist item index to be transitive, that for all a, b,

[ ]() ( )

( ) [ ]

wp x wp x

wx x x w w

w p p pw w

i

a

i

b

iz

a

iz

b

n z

i

a

i

a

iz

b

iz

a

i z

iz i iz

b

iz

a

iz iz

b

i

b

iz

a

i

a

i z i z

i i

b

i

a

i

i i

b

i

a

i

ln ln

ln ln ln ( )

−



 



 



 



 − −



 



 



 



 















= − −+ −

+ − +− −

∑ ∑ ∑ ∑

∑∑ ∑∑

∑ ∑

β β

β ββ 00 0

0 0

(12)

where

xiz

0 = a reference characteristic z for index item i across the entire region

βiz

0 = a reference coefficient for the characteristic z of item i in a semi-log

hedonic equation explaining specification price across the entire

region

pi

0 = a reference price for item i across the entire region

wi

0 = a reference share for item i for the entire region.

Furthermore, if this condition holds, the bilateral Törnqvist index for item group i has the

form
- 10 -

( )( ) ( )( )

( )( ) ( )( )

ln ln ln

ln ln

T w wx x w w p p

w wx x w w p p

ab

iz i iz

b

i

b

iz

b

iz

i z

i i

b

i

b

i

i

iz i iz

a

i

a

iz

a

iz

i z

i i

a

i

a

i

i

=− + − + + − −

− + −+ + −





 



 ◊

∑ ∑ ∑

∑ ∑ ∑

1

2

00 0 1

2

0 0

1

2

00 0 1

2

0 0

β β

β β 

(13)

IV. Multilateral price measurement with subaggregates of items

Let pijklmn

a be the price in area a, of which there are A areas in total, of

specification n in item group m in stratum class l in basic heading class k in group j in

major group or division i. Let qijklmn

a be the corresponding quantity purchased. The

bilateral Törnqvist index comparing the prices in areas a and b for item aggregate ijklm is

ln ln ln T ww p p ijklm ( )( ) ab

ijklmn

a

ijklmn

b

ijklmn

b

ijklmn

a

n

≡+ − ∑ 1

2

where

wijklmn

a = the value share in area a of specification ijklmn within the next-higher

group ijklm, with

w

p q

p q ijklmn

a ijklmn

a

ijklmn

a

ijklmn

a

ijklmn

a

n

≡

∑

and with qijklmn

a the quantity of the specification transacted, so that

wijklmn

a

n

∑ = 1.
- 11 -

Analysis of the contribution of subaggregates to levels of place to place indexes.

In practice, index numbers are produced for hierarchical classification trees of products,

industries, occupations, etc. Because Törnqvist indexes are linear in the log differences of

detailed specification prices, the contribution of each subaggregate, say, women’s apparel,

to the all items level ratio between two areas can be readily calculated by exponentiating

the appropriate weighted sums of log price differences. These sums would be calculated

from the transitive expression for the index given in equation (11), where it is expressed in

terms of locality weights averaged with reference weights and price differentials from

reference prices. In this case, “all items” bilateral indexes are constructed as the direct

aggregation of the specification prices as

[ ( )( )

( )( )]

ln ln ln

ln ln .

T ww p p

ww p p

ab

ijklmn ijklmn

b

ijklmn

b

ijklmn

i j k l m n

ijklmn ijklmn

a

ijklmn

a

ijklmn

≡ +−

−+ −

∑∑∑∑∑∑ 1

2

0 0

1

2

0 0

The contribution to the level of lnT ab of major commodity group i would simply be the

subordinate sum

[ ( )( )

( )( )]

ln ln ln

ln ln .

C ww p p

ww p p

i

ab

ijklmn

a

ijklmn ijklmn

b

ijklmn

j k l m n

ijklmn

a

ijklmn ijklmn

a

ijklmn

≡ +−

−+ −

∑∑∑∑∑ 1

2

0 0

1

2

0 0

The simplicity of this approach to analysis of the place to place price differentials of

subaggregates, and its focus on subaggregate change within the larger “all items” context,

has a great deal of appeal. The extension of this discussion to quality adjusted price

indexes including characteristics is straightforward and left to the reader.
- 12 -

Transitivity simultaneously across several aggregation levels. Nevertheless, when

place to place subaggregate indexes are to be published in addition to the “all items”

index, it may not be seen as sufficient to adjust only the “all items” index to be transitive.

The subaggregates would then be required not only to satisfy transitivity, but aggregate

according to an index number rule to successively higher levels. This is a property distinct

from consistency in aggregation, whereby an index formula for an aggregate calculated

directly is the same as that calculated with the same formula successively applied to

intermediate subaggregates. Rather, assuming the same index formula is repeatedly

applied at each level as in the latter case, we would like all levels of aggregation to satisfy

transitivity while preserving the aggregation rule, so that users might also combine lowlevel aggregates following the same formula and weighting and be assured of obtaining the

higher level aggregates. We show that it is possible to construct such aggregationconsistent place to place indexes under a multilevel Törnqvist aggregation rule.

Having dealt with the first level of aggregation in the Section II, we now consider

aggregation of the item indexes ijklm to the stratum level ijkl. We first observe from

Proposition that the transitivity of the item aggregate ijklm permits us to identify average

price levels for the aggregate for each area in the region as

ln ln ln p ww p p ijklm ( )( ) a

ijklmn ijklmn

a

ijklmn

a

ijklmn

n

=+ − ∑ 1

2

0 0

allowing us to rewrite the expression for the bilateral item index as:

ln ln ln Tpp ijklm

ab

ijklm

b

ijklm

a = − .

The bilateral index between areas a and b of the stratum aggregate ijkl over item groups

ijklm is

ln ln ln ln T ww T ww p p ijkl ( ) ( )( ) ab

ijklm

a

ijklm

b

ijklm

ab

m

ijklm

a

ijklm

b

ijklm

b

ijklm

a

m

=+ =+ − ∑ ∑ 1

2

1

2 .
- 13 -

Applying the Proposition to the stratum level, the transitive bilateral index between areas a

and b of the stratum aggregate ijkl over item groups ijklm is, therefore,

[ ( )( )

( )( )]

ln ln ln

ln ln .

T ww p p

ww p p

ijkl

ab

ijklm ijklm

b

ijklm

b

ijklm

m

ijklm ijklm

a

ijklm

a

ijklm

≡+ −

−+ −

∑ 1

2

0 0

1

2

0 0

We note that the expression for the transitive Törnqvist item index above would

have been obtained if the reference specification prices had been

ln ln ln ( ) ppp ijklmn

m

ijklmn ijklm

0 00 = + . Further, if the specification reference prices were so

adjusted, the transitivity of the lower level item indexes would continue to hold. Further

still, because each level’s log index is the difference between weighted log price relatives,

those components constant within group cancel, leaving only those elements varying with

members of the group. To confirm,

[ ( )( )

( )( )]

[ ( )( )

( )( )]

[ ( ) ( ) ]

[ ( )( )

( )( )]

ln ln ln ln

ln ln ln

ln ln

ln ln

ln ln

ln ln

ln ln .

T ww p p p

ww p p p

ww p p

ww p p

ww p ww p

ww p p

ww p p

ijklm

ab

ijklmn ijklmn

b

ijklmn

b

ijklmn ijklm

n

ijklmn ijklmn

a

ijklmn

a

ijklmn ijklm

ijklmn ijklmn

b

ijklmn

b

ijklmn

n

ijklmn ijklmn

a

ijklmn

a

ijklmn

ijklmn ijklmn

b

ijklm

n

ijklmn ijklmn

a

ijklm

ijklmn ijklmn

b

ijklmn

b

ijklmn

n

ijklmn ijklmn

a

ijklmn

a

ijklmn

≡ + −−

−+ −−

=+ −

−+ −

− + −+

=+ −

−+ −

∑

∑

∑

∑

1

2

0 00

1

2

0 00

1

2

0 0

1

2

0 0

1

2

0 0 1

2

0 0

1

2

0 0

1

2

0 0

 In effect, then, each level of aggregation adds a component to the reference price vector,

so that a system transitive at all levels of aggregation would require specification reference

prices of the form
- 14 -

ln ln ln ln ln ln ln ( ) p p p p p pp ijklmn

ijklm

ijklmn ijklm ijkl ijk ij i

0 0 0 0 0 00 = + + + ++ .

Finally, only the components of the reference price vector relevant to (within) a given

aggregation level enter into that level’s transitivity adjustment equation. This permits a

decomposition of the estimation procedure allowing the lowest aggregate reference shares

and reference price components to be estimated first (using the regression equation

presented in the Proposition), followed by successively higher levels in turn. Again, the

extension to quality adjusted price indexes accounting for the differences in product

characteristics across areas is straightforward.

More than one aggregation tree. Statistical price series are often published on

more than one aggregation scheme. For example, establishment data are often published

on commodities and industries (Producer Price Indexes) and occupations and industries

(Employment Cost Indexes). Multiple trees can be incorporated into the structure just

elucidated by merging the trees and defining cells by crossing the classification strata in the

two (or more) structures. There is an new consistency issue introduced; namely, that

comparable aggregates formed from differing subaggregates in the distinct classification

structures should be the same. Most obviously, the “all items” price index on

establishment data should be the same whether the subaggregates are industries or

occupations/commodities. Similarly, the Industry Division 1 labor compensation index

should be the same number, whether calculated as an aggregate of the two-digit industries

or major occupational groups within Division 1. Constraints of this type bring us much

closer to imposing a defacto requirement of traditional consistency in aggregation on the

data, but are not equivalent to imposing the property unless each elementary price is

contained in a distinct cross-cell of the two or more structures. We consider only one,

commodity aggregation tree in this paper.
- 15 -

V. Estimation of the Reference Values for Shares, Prices, and

Determinants of Quality

Adjusting for quality from place to place. Data permitting, it is standard practice

in constructing place to place price indexes to adjust for known price determining

specification characteristics using a regression of specification prices on measured

characteristics and a set of dummy variables for locality. This country-product-dummy

(CPD) approach is relatively simple to do and easily implemented. The most obvious way

of controlling for quality in constructing a place to place index is to use the intercept plus

coefficients on the area dummy variables as quality adjusted price levels in the bilateral

price index for the item group. We show in this section that the use of the CPD model in

this way is a special case of an exact Törnqvist index number that incorporates quality

characteristics when there is a known hedonic function. The special case is that the

hedonic function is the same from area to area, other than the intercept.

Suppose the characteristics of specification n in area a are given by the vector

xijklmn

a and we define the set of dummy variables

Lb A

b a a ab == =  = 







 



For 

 if 

 otherwise

2 3 1

0 ,, , , L ∆ .

A CPD regression would be run by fitting the following model:

ln p Lx ijklmn

a

ijklm ijklm

a

ijklm ijklmn

a

ijklmn

a = + ′ + ′ αα β ε + 0 .
- 16 -

As described above, the conventional technique is to use the estimates of the area

dummy parameters α$ ijklmn as the item log-prices to be used in further aggregation.

Alternatively, from equation (13) the exact bilateral Törnqvist item index between areas a

and b is

( )( )

( )( )

ln

ln ln

T w wx x

ww p p

ijklm

ab a

ijklmn

a b

ijklmn

b

ijklmnz

b

ijklmnz

a

n z

ijklmn

a

ijklmn

b

ijklmn

b

ijklmn

a

n

ijklmnz ijklmnz =− + −

++ −

∑∑

∑

1

2

1

2

β β

where the first term is a quality adjustment and the second is the familiar price index.

If the slopes are the same across areas, as in Country-Product Dummy models, the

bilateral index reduces to

ln ln ln T ww p x p x ijklm ( ) ab

ijklmn

a

ijklmn

b

ijklmn

b

ijklmnz

b

z

ijklmn

a

ijklmnz

a

n z ijklmnz ijklmnz = + − −− 



 



 



 

 ∑ ∑ ∑  1

2 β β

which is an index number of quality-adjusted specification prices. This is equivalent to the

conventional practice of using the intercept estimates for each area as the qualitycorrected area price level for the specifications within the item group, since, from the CPD

model, the area intercept coefficient for the item group can be expressed in terms of

quality-corrected prices as

αα β ε ijklm ijklm

a

ijklmn

a

ijklm ijklmn

a

ijklmn

a Lp x 0 + ′ = − ′ ln . −

Although individual hedonic models by area are desirable, there may be insufficient

data to obtain tight estimates of the coefficients, or to identify the coefficients at all. In

the first case, noisy coefficients can be estimated more accurately by blending them with a
- 17 -

pooled regional regression. An example of this approach is set out in Randolph and

Zieschang (1987) with application to a rent model for the CPI shelter component.

The EKS/CCD Approach. CCD (1982) show that application of the unweighted

Eltetö/Köves/Szulc approach to making a system of bilateral parities transitive is

equivalent to choosing the reference shares and prices as

w w

p p

ijklmn A ijklmn

a

a

ijklmn A ijklmn

a

a

0 1

0 1

=

=

∑

ln ln ∑

A (preferable) weighted version would select the reference values as the weighted average

across the area share in the next-higher level aggregate, as in the following for aggregation

of items to strata:

w sw

p sp

ijklmn ijklm

a

ijklmn

a

a

ijklmn ijklm

a

ijklmn

a

a

0

0

=

=

∑

ln ln ∑

where

s

p q

p q ijklm

a

ijklmn

a

ijklmn

a

n

ijklmn

a

ijklmn

a

a n

≡

∑

∑∑ .

When quality adjustment information is available, the reference hedonic prices (or

coefficients) and item characteristics are determined (in weighted form) by

β β ijklmnq ijklmn ijklm

a

ijklmnq

a

ijklmn

a

a

ijklmnq ijklm

a

ijklmnq

a

a

wsw

x sx

0 0

0

=

=

∑

∑ .
- 18 -

A regression approach for minimal adjustment of the data. An alternative to (or,

as noted below, a likely superclass of) the EKS/CCD approach is to apply the Proposition

1 transitivity condition directly. When this condition on the cross-weighted differences of

log regional prices is not met, the data may be minimally adjusted to satisfy transitivity by

fitting the following equation using least squares to obtain estimates [ ] w p $ , $ ijklmn ijklmn

0 0 for

each specification n in item group ijklm:

wpwpw p p ( )

pw w

ijklmn

a

ijklmn

b

ijklmn

b

ijklmn

a

ijklmn ijklmn

b

ijklmn

a

ijklmn ijklmn

b

ijklmn

a

ijklmn

ab

ln ln ln ln

ln ( )

−= −

− −+

0

0 ε

with the parameter restriction

wijklmn

n

0

∑ = 1.

2

Recalling the A is the number of areas in the region, there will be at most A A( )/ − 1 2

independent observations to estimate this equation for each specification ijklmn, and the

model would be run as a stacked regression of specifications n within the item group

ijklm.

In considering possible schemes for performing weighted estimation of the

reference share and price paramenters, each record could be weighted by the average

importance of areas a and b at the next higher level (item) aggregate; that is, by

 

2

 This restriction is not required for transitivity, but is required for aggregation consistency

at the next level up, and embodies an inherent property of the solution to the variant of the

transitivity functional equation leading to the reference shares and prices form for the

transitive system of bilateral Törnqvist index numbers.
- 19 -

( ) 1

2 s s ijklm

a

ijklm

b + .

In this scheme, areas with higher overall shares for the item across the region would carry

more weight in determining the estimated within-item specification reference shares and

prices. This is reminiscent of, if distinct from, the weighting approach suggested by

Selvanathan and Prasada Rao (1992), and is more transparent as to how a weighting

methodology would actually work in a system of transitive Törnqvist parities—it affects

the estimates of the reference shares and prices.3

When quality adjustment information is available, the reference variables would be

estimated in a way analogous to that for imposing transitivity in prices only as follows:

Estimate hedonic equations for each area as

ln p x ijklmn

a

ijklm

a a

ijklmn

a

ijklmn

a

ijklm = + ′ αβ ε + .

Obtaining the estimates

$

$

α

β

ijklm

a

ijklm

a

















for each area. Then using least squares, estimate the vector

 

3

 Actually, there is probably a weighting scheme for the transitivity fitting equation that

generates the EKS/CCD versions of the transitive Törnqvist system of parities, but it does

does not seem obvious how these weights would be determined.
- 20 -

x

w

p

w

ijklmnq

ijklmnq ijklmn

ijklmn

ijklmn

0

0 0

0

0

−

−





























β

ln

by fitting the equation

[ ]( ) ( )

( ) [ ]

wp x wp x

wx x x w w

w p p pw w

ijklm

a

ijklmn

b

ijklmnq

a

ijklmn

b

q

ijklm

a

ijklmn

a

ijklmnq

b

ijklmn

a

q

ijklmnq ijklmn ijklmnq

b

ijklmnq

a

q

ijklmnq ijklmnq

b

ijklm

b

ijklmnq

a

ijklm

a

q

ijklmn ijklmn

b

ijklmn

a

ijklmn ijklmn

b

ijklmn

a

ijklmn

ab

ln $ ln $

$ $

ln ln ln ( )

−





 



 













 − − 



 



 















=− − + −

+ − +− − +

∑ ∑

∑ ∑

β β

β ββ

ε

00 0

0 0

with the parameter restriction

wijklmn

n

0

∑ = 1.

There will be at most A A( )/ − 1 2 independent observations to estimate this equation for

each specification ijklmn, and the model would be run as a stacked regression of

specifications n within the item group ijklm. The observation weighting would follow the

same scheme as in the simple case without specification characteristics and quality

adjustment.

Notice that if the hedonic slope coefficients are the same across areas for each

specification characteristic so that βββ ijklmnq

a

ijklmnq

b = = ijklmnq

0 , then the estimating equation

collapses to
- 21 -

[ ]

wp x wp x

wp x p x

p x ww

ijklm

a

ijklmn

b

ijklmnq ijklmn

b

q

ijklm

a

ijklmn

a

ijklmnq ijklmn

a

q

ijklmn ijklmn

b

ijklmnq ijklmnq

b

q

ijklmn

a

ijklmnq ijklmnq

a

q

ijklmn ijklmnq ijklmnq

q

ijklmn

b

ijklmn

a

ijklmn

ab

ln $ ln $

ln $ ln $

ln $ ( )

−





 



 













 − − 



 



 















= − −− 



 



 















+− + 



 



 















− +

∑ ∑

∑ ∑

∑

β β

β β

β ε

0 0

00 0

0 00

In this case, the coefficient on the difference between the share vectors of the two areas is

a quality-adjusted reference price vector, and no reference characteristics vector can be

separately identified. It can, if desired, be independently determined as the EKS/CCD

weighted average.

VI. An Empirical Example

An empirical example of the methodology is provided by interarea prices for U.S.

urban areas derived from hedonic regressions on data from the Consumer Price Index. The

CPI collects prices on a large sample of individual products, based on a probability sample

of those specific products consumers are most likely to purchase in specific outlets in

specific urban areas (see US DOL (1988)). This approach results in a sample which is

representative of household consumption choices, but is heterogeneous in nature. For

example, the category for instant coffee consists of observations on instant coffee

products of different sizes, brands, caffeine content, and other characteristics. In order to

compare the prices of instant coffee across cities these differences in characteristics must

be explicitly accounted for, circumstances ideal for applying a hedonic regression

approach. A recent major effort at BLS has produced such interarea price indices for most

of the major categories of goods and services for 44 U.S. urban areas; this effort is

described in detail in Kokoski, Cardiff, and Moulton (1994). A more recent application of

this approach to 1993 CPI data provided the data input for this example.
- 22 -

The estimated hedonic regression coefficients on the areas from two expenditure

classes (ECs) of food at home have been selected: EC11, fresh fruits, and EC12, fresh

vegetables. These expenditure classes are represented by several item strata (IS), each of

which consists of a single entry level item (ELI). The hierarchical classification scheme for

this example is:

EC11: Fresh Fruits

1101 Apples

11011 Apples

1102 Bananas

11021 Bananas

1103 Oranges

11031 Oranges

1104 Other fresh fruits

11041 Other fresh fruits

EC12: Fresh Vegetables

1201 Potatoes

12011 Potatoes

1202 Lettuce

12021 Lettuce

1203 Tomatoes

12031 Tomatoes

1204 Other fresh vegetables

12041 Other fresh vegetables

In this preliminary example only the first three item strata of each EC are included and are

aggregated for three areas: Philadelphia, Boston, and Pittsburgh. For purposes of

exposition, we will let the lowest level of aggregation, subscripted ijklmn, be represented

by the ELI (which, in this case, map uniquely into item strata). The next highest level,

subscripted ijklm, is represented by the expenditure class, and these two ECs will be

aggregated to a higher level ijkl which we can call “Fresh fruits and vegetables”. [This will

be expanded to the full complement of item strata within these two ECs and to all 44

geographic areas in the near future.]

A log-linear hedonic regression was performed on each of these ELIs separately,

as in Section VI above
- 23 -

ln p Lx ijklmn

a

ijklm ijklm

a

ijklm ijklmn

a

ijklmn

a = + ′ + ′ αα β ε + 0 ,

where ln pijklmn

a represents the log of the price of each item specification n in the mth ELI

for the ath area, xijklmnz

a are the variables defining the characteristics of each item

specification, including the type of outlet where priced, and La is the dummy variable

vector for area a. It has been shown (Summers [1973]) that the exponentiated coefficients

αijklm are bilateral price indices for area a relative to the reference area (arbitrarily chosen

as area a = 1). The coefficient estimates are presented in Appendix II. The expenditure

shares for this simplified example of three areas and six ELIs are provided in Table 2 of

Appendix III, where Wxxxxx is the share of expenditures on ELI xxxxx with respect to all

three ELIs in that EC for each specific area, and S(ECx) is the share of expenditures for

ECx in each area with respect to all three areas.

Employing the regression approach described in this paper for aggregation, the

transitive Tornqvist indices for the simplified example are given in Table 3 of Appendix

III. As would be expected, the index value for the aggregate Fresh fruits and vegetables

lies between the index values for each component EC for each area. The regression

coefficients obtained from the aggregation procedure are shown in Table 4, where

W0(xxxxx) is the coefficient estimate wijklm

0 for ELI xxxxx and P0(xxxxx) is the coefficient

estimate pijklm

0 for ELI xxxxx as specified in the regression equation. The regression

coefficient estimates for the equation which derives the higher level of aggregation are

provided in Table 5, Appendix II. Since there is only one ELI per stratum in our example,

we aggregate directly to the expenditure class. Here, W0 (Ecxx) is the coefficient

estimate wijk

0 for EC xx and P0 (Ecxx) is the estimated value of pijk0 , as earlier specified.

For comparison, the bilateral Tornqvist indices for each EC are provided in Table

6 of Appendix III. These may be compared with the transitive parities to show, for this
- 24 -

example, the degree of empirical adjustment required to achieve this property.

Recognizing that transitivity must be achieved at the cost of characteristicity, it is useful to

assess this difference (see Drechsler (1973)). In this case the magnitude of the difference

between the transitive Tornqvist and its bilateral counterpart is less than 2 percent of the

index value.

VII. Conclusion and an Extension

In this paper we have considered the case of a single cross section of areas within

which transitive bilateral quality-adjusted price comparisons are to be made between areas.

We have also considered commodity aggregation within this framework, whereby

transitivity is imposed while preserving a staged Törnqvist index aggregation rule. We

have applied the technique to a small subset of the commodities priced in the U.S.

Consumer Price Index.

Our approach to transitivity has been a “minimum data adjustment” criterion with

weighting specific to bilateral comparisons, and therefore differs from other methods of

imposing transitivity in a system of bilateral place to place Törnqvist index numbers.

Although our method has some appeal because we can claim to minimally purturb the data

in order to impose the transitive property with weighting sensitive to specific bilateral

comparisons, the area expenditure weighted sum of the log locality price levels will not

necessarily be equal to zero, in contrast with the EKS/CCD approach, which satisfies this

property by construction. The need for this property, as well as operational considerations

such as ease of computation and calculation of measures of precision, would need to be

weighed in deciding on an estimator for production of a regular statistical series of

interarea price indexes. Before closing, we would like to briefly describe a promising

avenue of research using this framework in a time series context.
- 25 -

The single chain link case. It has been a problem in the interpretation of data from

the International Comparisons Project that the change in the levels of real GDP implied by

the international purchasing power parities from time to time has not been the same as the

growth in national GDPs measured by direct deflation using a(n implicit) time series GDP

deflator. We consider here a remedy within the Törnqvist system of interarea and time

series index numbers by considering a system of area indexes that are transitive both

among areas within the same time period as well as between areas from differing time

periods. A direct implication of this is that the index change between two periods for a

given area, say a, can be expressed as the product of the relative level between two areas,

say, a and b, in the first period, times the relative change in b between the two periods for

any two areas a and b.

The Törnqvist item index ln , Tijklm

ab uv between area a in time period u and area b in

time period v, where uv t t , , ∈ − { } 1 , is

ln ln ln ( )( ) , T ww p p ijklm

ab uv

ijklmn

au

ijklmn

bv

ijklmn

bv

ijklmn

au

n

=+ − ∑ 1

2 .

It is straightforward to see that, for the system of between area, between period parities to

be transitive, Proposition 1 applies directly in this case, with reference share and price

vectors determined for the union of the two time periods and collections of areas. If

quality adjustments are possible using hedonic regressions, then Proposition 2 can be

applied to show the transitive form of the quality adjusted system of parities as a function

of a reference share, price and hedonic coefficients vectors across areas and time periods.

We note below that, under international decentralization of compilation, the country

hedonic regression coefficients would generally not be the same, as in the CPD approach.

An additional comparison generally computed in this case is the change over time

of the regional aggregate of areas. Examples of such indexes would be national consumer
- 26 -

price and producer price and labor compensation indexes as composites of the subnational

areas sampled to obtain the data. This index can be written as

( )

( ) ( )( )

ln ln

ln ln .

, , T ss T

ss w w p p

ijklm

R uv

ijklm

au

ijklm

av

ijklm

aa uv

a

ijklm

au

ijklm

av

ijklmn

au

ijklmn

av

ijklmn

av

ijklmn

au

a n

= +

=+ + −

∑

∑ ∑

1

2

1

2

1

2

By period to period and interarea transitivity

ln ln ln ( )( ) , T ss p p ijklm

R uv

ijklm

au

ijklm

av

ijklmn

av

ijklmn

au

a

=+ − ∑ 1

2

where

ln ln ln p ww p p ijklm ( )( ) au

ijklmn ijklmn

au

ijklmn

au

ijklmn

n

=+ − ∑ 1

2

00 00

The aggregate time series index under period/area transitivity between the two periods is,

therefore, a weighted average of the relative change in a set of area price levels, insuring

consistency between the levels within period across area and rates of change between

periods within area.

Time series/cross section transitivity over multiple periods. Clearly, the single

chain link, two period case can be extended to the multiple period case by pooling the data

for multiple periods. A distinct advantage of the application of this procedure is that the

problem of chain drift is eliminated over the multiple period epoch being adjusted, while

maintaining much of the period specificity of the weight and price components of the

Törnqvist index formula. The reason is that transitivity eliminates drift, which is usually

defined as the persistent deviation of a direct index between nonadjacent periods as

compared with the product of adjacent period chain links covering the multiple period

interval. An issue to be resolved in applying this technique is that it refers to a moving

window of a fixed time duration. Data passing outside the window would not exactly

satisfy the transitive property. Choosing the window as a long enough period could be

expected to result in very slow change in the reference prices and shares, however, so that
- 27 -

the effect could be minimized, at the cost of providing less of Drechsler’s (1973)

“characteristicity” for relatively recent time periods.

Decentralized computing of international parities while controlling for the quality

of goods available in different countries. The methodology outlined here, which uses a

hedonic, characteristics-based quality adjustment procedure, permits decentralized, within

country estimation of the hedonic equation coefficients. This is especially attractive in

view of the great, and generally justified reluctance with which most statistical offices

grant access to the micro data sources of their price indexes. The prerequisite for this

would be that a standard product classification would have to be adopted by all countries,

and also, with each product class, a standard list of product characteristics or specification

measures would have to be adopted. One such set of standards might be derived by

merging of the U.S. CPI specification file, listing the characteristics measures for some

365 product categories, with a standard international commodity classification, such as the

Central Product Classification or CPC of the United Nations, itself a superset of the now

standard Harmonized classification for internationally traded commodities.

A compilation strategy such as this for the ICP would have a distinct advantage

over the current approach of pricing a long, detailed list of narrowly specified items. The

number of product strata required would be smaller, and the countries could use the

estimates for their own, internal quality adjustment needs for time series and within

country geographical comparisons.
- 28 -

VIII. Appendix I: Proofs of Propositions

Proof of Proposition 1:

The proof of this proposition follows methods used in, for example, Aczel (1966),

and Eichhorn (1978). First, we establish the following solution of the transitivity

(functional) equation for all single-valued functions g of two vectors of identical

dimension in an argument set D that satisfy an identity condition gxx ( ) , = 0 :

gxy gyz gxz gxx xyz D

iff

gxy hy hx

(, ) (,) (,) (, ) (,,)

( , ) ( ) ( ).

+ = =∀ ∈

= −

 and , 0

Let y y = 0

. Then for all x and z in the domain of g

gxy gy z rx hz gxz (, ) ( ,) () () (,) 0 0 + =+=

Substituting this back into the transitivity equation,

rx hy ry hz gxz () () () () (,) +++= .

By identity

gyy ry hy ( ) , () () =+= 0

and hence
- 29 -

ry hy () () = −

We can now express gxz ( , ) in terms of h as

gxz hz hy (,) () () = −

yielding the desired result.

From this, transitivity of the Törnqvist bilateral relative requires that, for all a, b

ln ( , ) ( , ). T hw p hw p ab b b a a = − rr rr

Expanding the bilateral relative expression, we have

( )( )

( )

ln ln ln

ln ln ln ln

( , ) ( , ).

T ww p p

w pw pw pw p

hw p hw p

ab

i

a

i

b

i

b

i

a

i

i

b

i

b

i

b

i

b

i

a

i

b

i

b

i

a

i

bb aa

≡+ −

= −+−

= −

∑

∑

1

2

1

2

v r rr

We set b = 0solve for hw p a a (,) r r in terms of reference area 0 as

hw p hw p w p w p pw

w p

a a

i i

i

i i

a

i

i i

a

i

i

a

i

a

i

( , ) ( , ) ln ln

.

rr rr = − 



 



 + −

+

∑∑ ∑

∑

0 0 1

2

0 0 1

2

0 1

2

0

1

2

Substituting this into the expanded equation for the transitive bilateral log parity,

multiplying through by 2, and subtracting w pw p i

b

i

b

i

a

i

a ln ln − inside the summations from

both sides, we have
- 30 -

( )( )

( )

w pw p w p p

pw w

i

a

i

b

i

b

i

a

i

i i

b

i

a

i

i i

b

i

a

i

ln ln ln ln

ln .

−= −

− −

∑ ∑

∑

0

0

The expression for the transitive Törnqvist bilateral parity obtains by substituting this

expression for the cross product between the area weights and prices into the expanded

expression for the parity, adding and subtracting the term w p i i

i

0 0 ∑ ln , and collecting

terms.

QED

Proof of Proposition 2:

The proof follows very closely that of Proposition 1. It is easy to see from this

that the price level for each area now has a price and quality adjustment component.
- 31 -

IX. Appendix II: Hedonic Regression Results for Fruits and

Vegetables

Table 1. ELI 11011: Apples

Mean of dependent variable: log price -2.8886

Adjusted R2 .3329

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD

BOSTON-LAWRENCE-SALEM, MA-NH -0.11302

PITTSBURGH-BEAVER VALLEY, PA -0.07054

BUFFALO-NIAGRA FALLS, NY -0.20282

NEW YORK CITY 0.06071

NEW YORK-CONN. SUBURBS -0.05384

NEW JERSEY SUBURBS -0.02993

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI 0.06099

DETROIT-ANN ARBOR, MI -0.04564

ST. LOUIS-EAST ST. LOUIS, MO-IL -0.02697

CLEVELAND-AKRON-LORAIN, OH -0.16546

MINNEAPOLIS-ST. PAUL, MN-WI -0.00094

MILWAUKEE, WI 0.01006

CINCINNATI-HAMILTON, OH-KY-IN -0.08656

KANSAS CITY, MO - KANSAS CITY, KS -0.01494

WASHINGTON, DC-MD-VA -0.01403

DALLAS-FORT WORTH, TX -0.05908

BALTIMORE, MD -0.04353

HOUSTON-GALVESTON-BRAZORIA, TX -0.11871

ATLANTA, GA -0.00259

MIAMI-FORT LAUDERDALE, FL -0.03459

TAMPA-ST. PETERSBURG-CLEARWATER, FL 0.05230

NEW ORLEANS, LA -0.02976

LOS ANGELES COUNTY, CA -0.17093

GREATER LOS ANGELES, CA -0.20649

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.19800

SEATTLE-TACOMA, WA 0.19215

SAN DIEGO, CA -0.17869

PORTLAND-VANCOUVER, OR-WA -0.17181

HONOLULU, HI 0.00481

ANCHORAGE, AK -0.10670

DENVER-BOULDER, CO -0.03535

NORTHEAST REGION, B SIZE PSUS -0.04942

NORTHEAST REGION, C SIZE PSUS -0.09681

NORTHEAST REGION, D SIZE PSUS -0.08744

NORTH CENTRAL REGION, B SIZE PSUS 0.01421

NORTH CENTRAL REGION, C SIZE PSUS -0.05190

NORTH CENTRAL REGION, D SIZE PSUS -0.15361

SOUTH REGION, B SIZE PSUS -0.01420

SOUTH REGION, C SIZE PSUS -0.10217

SOUTH REGION, D SIZE PSUS -0.04820

WEST REGION, B SIZE PSUS -0.11932

WEST REGION, C SIZE PSUS -0.12937
- 32 -

Table 1. ELI 11011: Apples

Mean of dependent variable: log price -2.8886

Adjusted R2 .3329

Variable Coefficient

WEST REGION, D SIZE PSUS -0.07509

Rotation group (ref=same sample as previous month)

NEW SAMPLE -0.03224

Month of collection (ref=JAN, 11 months of data)

FEB 0.03022

MAR 0.04515

APR 0.05623

MAY 0.10186

JUN 0.15730

JUL 0.19332

AUG 0.20836

SEP 0.17460

OCT 0.01422

NOV 0.03296

Outlet type (ref=CHAIN GROCERY)

INDEPENDENT GROCERY STORES -0.07482

FULL SERVICE DEPARTMENT STORES -0.11568

PRODUCE MARKET -0.18148

CONVENIENCE STORES 0.05972

COMMODITY ORIENTED OUT NEC -0.41615

OUTLET NOT ELSEWHERE CLASSIFIED -0.41217

Package type (ref=OTHER)

PACKAGING: LOOSE -0.07769

PACKAGING: MULTI-PACK -0.33425

PACKAGING: SINGLE ITEM, INDIVIDUALLY -0.43312

Package size (ref=0-10 POUNDS)

ABOVE 10 POUNDS 0.01042

SIZE REPRESENTS: WEIGHED ONE MULTI-PK -0.09754

SIZE REPRESENTS: WEIGHT LABELED -0.03956

SIZE: WEIGH 2 APPLES -0.05256

SIZE: OTHER OMITTED

Grade (ref=OTHER GRADE/GRADE NOT AVAILABLE)

U.S. EXTRA FANCY 0.01337

Variety (ref=OTHER)

DELICIOUS 0.00968

GOLDEN DELICIOUS -0.03918

RED DELICIOUS -0.04676

OTHER DELICIOUS OMITTED

GRANNY SMITH 0.03385

GRAVENSTEIN -0.17583

JONATHAN -0.17352

MCINTOSH -0.05280

ROME BEAUTY (RED ROME) -0.03041

STAYMAN -0.11321
- 33 -

Table 1. ELI 11011: Apples

Mean of dependent variable: log price -2.8886

Adjusted R2 .3329

Variable Coefficient

WINESAP 0.06369

YORK (YORK IMPERIAL) 0.74756
- 34 -

Table 2. ELI 11021: Bananas

Mean of dependent variable: log price -3.5118

Adjusted R2 .3314

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD )

BOSTON-LAWRENCE-SALEM, MA-NH -0.01941

PITTSBURGH-BEAVER VALLEY, PA -0.18766

BUFFALO-NIAGRA FALLS, NY -0.01421

NEW YORK CITY 0.01522

NEW YORK-CONN. SUBURBS -0.02748

NEW JERSEY SUBURBS -0.00491

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI -0.02261

DETROIT-ANN ARBOR, MI -0.22780

ST. LOUIS-EAST ST. LOUIS, MO-IL 0.04932

CLEVELAND-AKRON-LORAIN, OH -0.14305

MINNEAPOLIS-ST. PAUL, MN-WI -0.23664

MILWAUKEE, WI -0.11808

CINCINNATI-HAMILTON, OH-KY-IN -0.18154

KANSAS CITY, MO - KANSAS CITY, KS -0.10477

WASHINGTON, DC-MD-VA 0.01819

DALLAS-FORT WORTH, TX -0.25484

BALTIMORE, MD -0.05988

HOUSTON-GALVESTON-BRAZORIA, TX -0.12477

ATLANTA, GA -0.30016

MIAMI-FORT LAUDERDALE, FL -0.50646

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.31348

NEW ORLEANS, LA -0.00361

LOS ANGELES COUNTY, CA -0.02534

GREATER LOS ANGELES, CA -0.10411

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.08328

SEATTLE-TACOMA, WA 0.12307

SAN DIEGO, CA -0.17004

PORTLAND-VANCOUVER, OR-WA -0.12146

HONOLULU, HI 0.55898

ANCHORAGE, AK 0.43803

DENVER-BOULDER, CO 0.08929

NORTHEAST REGION, B SIZE PSUS -0.05294

NORTHEAST REGION, C SIZE PSUS -0.13774

NORTHEAST REGION, D SIZE PSUS 0.06198

NORTH CENTRAL REGION, B SIZE PSUS -0.18972

NORTH CENTRAL REGION, C SIZE PSUS -0.23027

NORTH CENTRAL REGION, D SIZE PSUS -0.08938

SOUTH REGION, B SIZE PSUS -0.20297

SOUTH REGION, C SIZE PSUS -0.22290

SOUTH REGION, D SIZE PSUS -0.04390

WEST REGION, B SIZE PSUS -0.05745

WEST REGION, C SIZE PSUS -0.09631

WEST REGION, D SIZE PSUS -0.27655

Rotation group (ref=same sample as previous month)

NEW SAMPLE -0.01012
- 35 -

Table 2. ELI 11021: Bananas

Mean of dependent variable: log price -3.5118

Adjusted R2 .3314

Variable Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB 0.09711

MAR 0.27093

APR 0.22156

MAY 0.23920

JUN 0.15363

JUL 0.12148

AUG -0.08925

SEP -0.04995

OCT -0.14127

NOV -0.05280

Outlet type (ref=CHAIN GROCERY)

INDEPENDENT GROCERY STORES -0.04932

FULL SERVICE DEPARTMENT STORES -0.23667

PRODUCE MARKET -0.13124

CONVENIENCE STORES 0.39717

COMMODITY ORIENTED OUT NEC -0.23223

OUTLET NOT ELSEWHERE CLASSIFIED -0.60950

Package size (ref=WEIGHED ONE BUNCH)

SIZE REPRESENTS: WEIGHT LABELED -0.03506

Grade (ref=OTHER GRADE/GRADE NOT AVAILABLE)

STORE SECONDS OR OTHER THAN 1ST QUALITY 0.06409

1ST QUALITY OR CLASS 0.01581
- 36 -

Table 3. ELI 11031: Oranges

Mean of dependent variable: log price -2.8848

Adjusted R2 .3403

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD

BOSTON-LAWRENCE-SALEM, MA-NH 0.06634

PITTSBURGH-BEAVER VALLEY, PA 0.03833

BUFFALO-NIAGRA FALLS, NY -0.00287

NEW YORK CITY 0.13458

NEW YORK-CONN. SUBURBS -0.02681

NEW JERSEY SUBURBS -0.12221

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI 0.23166

DETROIT-ANN ARBOR, MI 0.01161

ST. LOUIS-EAST ST. LOUIS, MO-IL 0.06972

CLEVELAND-AKRON-LORAIN, OH 0.02411

MINNEAPOLIS-ST. PAUL, MN-WI 0.07582

MILWAUKEE, WI 0.01591

CINCINNATI-HAMILTON, OH-KY-IN 0.01295

KANSAS CITY, MO - KANSAS CITY, KS 0.44553

WASHINGTON, DC-MD-VA -0.00686

DALLAS-FORT WORTH, TX -0.14995

BALTIMORE, MD -0.02344

HOUSTON-GALVESTON-BRAZORIA, TX -0.22791

ATLANTA, GA 0.11588

MIAMI-FORT LAUDERDALE, FL -0.36500

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.65656

NEW ORLEANS, LA -0.02918

LOS ANGELES COUNTY, CA -0.08845

GREATER LOS ANGELES, CA -0.07800

SAN FRANCISCO-OAKLAND-SAN JOSE, CA 0.06305

SEATTLE-TACOMA, WA 0.05389

SAN DIEGO, CA -0.04144

PORTLAND-VANCOUVER, OR-WA 0.10993

HONOLULU, HI 0.22252

ANCHORAGE, AK 0.35183

DENVER-BOULDER, CO 0.21348

NORTHEAST REGION, B SIZE PSUS 0.01369

NORTHEAST REGION, C SIZE PSUS -0.03222

NORTHEAST REGION, D SIZE PSUS 0.18581

NORTH CENTRAL REGION, B SIZE PSUS 0.19250

NORTH CENTRAL REGION, C SIZE PSUS 0.09794

NORTH CENTRAL REGION, D SIZE PSUS -0.11770

SOUTH REGION, B SIZE PSUS 0.01788

SOUTH REGION, C SIZE PSUS -0.08665

SOUTH REGION, D SIZE PSUS -0.06157

WEST REGION, B SIZE PSUS 0.06924

WEST REGION, C SIZE PSUS 0.04585

WEST REGION, D SIZE PSUS -0.02118

Rotation group (ref=same sample as previous month)

NEW SAMPLE -0.04340
- 37 -

Table 3. ELI 11031: Oranges

Mean of dependent variable: log price -2.8848

Adjusted R2 .3403

Variable Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB 0.08286

MAR 0.12605

APR 0.14488

MAY 0.14072

JUN 0.25007

JUL 0.29341

AUG 0.34215

SEP 0.39708

OCT 0.23935

NOV -0.04562

Outlet type (ref=CHAIN GROCERY)

INDEPENDENT GROCERY STORES -0.10642

FULL SERVICE DEPARTMENT STORES -0.00639

PRODUCE MARKET -0.15877

CONVENIENCE STORES 0.01025

COMMODITY ORIENTED OUT NEC -0.61553

OUTLET NOT ELSEWHERE CLASSIFIED -0.95862

Package type (ref=OTHER)

PACKAGING: MULTI-PACK -0.19648

PACKAGING: SINGLE ITEM, INDIVIDUALLY -0.06804

Package size

WEIGH 2 ORANGES -0.22778

WEIGHED 1 MULTI-PACK -0.11644

WEIGHT LABELED -0.10879

Grade (ref=OTHER GRADE/GRADE NOT AVAILABLE)

U.S. FANCY 0.01961

Variety

NAVEL 0.29912

TEMPLE -0.11816

VALENCIA 0.14359

TANGELO 0.28032

TANGERINE 0.44601
- 38 -

Table 4. ELI 11041: Other fresh fruit

Mean of dependent variable: log price -2.7285

Adjusted R2 0.5932

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD

BOSTON-LAWRENCE-SALEM, MA-NH -0.03617

PITTSBURGH-BEAVER VALLEY, PA -0.10519

BUFFALO-NIAGRA FALLS, NY -0.20930

NEW YORK CITY -0.01446

NEW YORK-CONN. SUBURBS -0.02877

NEW JERSEY SUBURBS -0.05622

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI -0.00033

DETROIT-ANN ARBOR, MI -0.16026

ST. LOUIS-EAST ST. LOUIS, MO-IL -0.02078

CLEVELAND-AKRON-LORAIN, OH -0.01462

MINNEAPOLIS-ST. PAUL, MN-WI -0.09512

MILWAUKEE, WI -0.04899

CINCINNATI-HAMILTON, OH-KY-IN -0.00455

KANSAS CITY, MO - KANSAS CITY, KS -0.05681

WASHINGTON, DC-MD-VA 0.08002

DALLAS-FORT WORTH, TX -0.03552

BALTIMORE, MD 0.03504

HOUSTON-GALVESTON-BRAZORIA, TX -0.18318

ATLANTA, GA 0.01898

MIAMI-FORT LAUDERDALE, FL -0.31861

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.07724

NEW ORLEANS, LA -0.00581

LOS ANGELES COUNTY, CA -0.12754

GREATER LOS ANGELES, CA -0.07642

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.02541

SEATTLE-TACOMA, WA 0.15074

SAN DIEGO, CA -0.12074

PORTLAND-VANCOUVER, OR-WA 0.01383

HONOLULU, HI 0.11750

ANCHORAGE, AK 0.12539

DENVER-BOULDER, CO 0.02031

NORTHEAST REGION, B SIZE PSUS -0.03246

NORTHEAST REGION, C SIZE PSUS -0.13600

NORTHEAST REGION, D SIZE PSUS 0.06941

NORTH CENTRAL REGION, B SIZE PSUS -0.03791

NORTH CENTRAL REGION, C SIZE PSUS -0.09401

NORTH CENTRAL REGION, D SIZE PSUS -0.20600

SOUTH REGION, B SIZE PSUS -0.07499

SOUTH REGION, C SIZE PSUS -0.10318

SOUTH REGION, D SIZE PSUS -0.08453

WEST REGION, B SIZE PSUS 0.02278

WEST REGION, C SIZE PSUS -0.05945

WEST REGION, D SIZE PSUS -0.08199

Rotation group (ref=same sample as previous month)

NEW SAMPLE 0.04082
- 39 -

Table 4. ELI 11041: Other fresh fruit

Mean of dependent variable: log price -2.7285

Adjusted R2 0.5932

Variable Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB -0.04646

MAR -0.06279

APR -0.01630

MAY -0.01466

JUN -0.05689

JUL -0.14868

AUG -0.26625

SEP -0.23102

OCT -0.18405

NOV -0.13335

Outlet type (ref=CHAIN GROCERY)

INDEPENDENT GROCERY STORES -0.04624

FULL SERVICE DEPARTMENT STORES 0.24117

PRODUCE MARKET -0.14419

CONVENIENCE STORES -0.00807

COMMODITY ORIENTED OUT NEC -0.00207

OUTLET NOT ELSEWHERE CLASSIFIED -0.72177

Package type

PACKAGING: MULTI-PACK 0.00157

PACKAGING: SINGLE ITEM, INDIVIDUALLY 0.04563

Package size

WEIGH ONE MULTI-PACK -0.39775

WEIGH 2 FRUITS -0.31620

WEIGHT LABELED -0.33027

Grade (ref=OTHER GRADE/GRADE NOT AVAILABLE)

U.S. EXTRA FANCY 0.04234

Variety

AVOCADOS 0.19300

BERRIES 0.28592

BLUEBERRIES 0.25617

CRANBERRIES -0.02272

RASPBERRIES 0.99209

STRAWBERRIES -0.30166

CHERRIES (SWEET/TART) 0.28835

GRAPEFRUIT -0.90631

PINK GRAPEFRUIT -0.03686

RED (RUBY) GRAPEFRUIT -0.06126

WHITE (YELLOW) GRAPEFRUIT -0.12095

GRAPES -0.18645

RED (FLAME) SEEDLESS GRAPES -0.00638

EMPEROR OR TOKAY GRAPES -0.05662

REBIER GRAPES 0.04156

CONCORD GRAPES -0.00026

THOMPSON SEEDLESS 0.05003

LEMONS -0.26529
- 40 -

Table 4. ELI 11041: Other fresh fruit

Mean of dependent variable: log price -2.7285

Adjusted R2 0.5932

Variable Coefficient

LIMES -0.28323

MELONS -0.82440

WATERMELON -0.71551

CANTALOUPE MELONS -0.19234

HONEYDEW MELONS -0.01389

CASABA MELONS -0.07582

CRENSHAW MELONS 0.29155

PERSIAN MELONS 0.26967

SANTA CLAUS MELONS -0.08431

PEACHES -0.44508

PEARS -0.13922

ANJOU PEARS -0.46646

BARTLETT PEARS -0.45497

BOSC PEARS -0.34758

SECKEL PEARS 0.01742

PINEAPPLES -1.02458

PLUMS -0.21393
- 41 -

Table 5. ELI 12011: Potatoes

Mean of dependent variable: log price -3.7367

Adjusted R2 0.6228

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD )

BOSTON-LAWRENCE-SALEM, MA-NH -0.06387

PITTSBURGH-BEAVER VALLEY, PA -0.23146

BUFFALO-NIAGRA FALLS, NY -0.07529

NEW YORK CITY -0.11552

NEW YORK-CONN. SUBURBS -0.08816

NEW JERSEY SUBURBS -0.07603

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI 0.15525

DETROIT-ANN ARBOR, MI -0.20893

ST. LOUIS-EAST ST. LOUIS, MO-IL 0.17335

CLEVELAND-AKRON-LORAIN, OH -0.15117

MINNEAPOLIS-ST. PAUL, MN-WI -0.44411

MILWAUKEE, WI -0.18660

CINCINNATI-HAMILTON, OH-KY-IN -0.10455

KANSAS CITY, MO - KANSAS CITY, KS -0.12530

WASHINGTON, DC-MD-VA 0.03654

DALLAS-FORT WORTH, TX -0.18926

BALTIMORE, MD -0.14338

HOUSTON-GALVESTON-BRAZORIA, TX 0.04671

ATLANTA, GA -0.05600

MIAMI-FORT LAUDERDALE, FL -0.15124

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.04608

NEW ORLEANS, LA -0.31242

LOS ANGELES COUNTY, CA -0.06874

GREATER LOS ANGELES, CA -0.02597

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.03646

SEATTLE-TACOMA, WA -0.21794

SAN DIEGO, CA -0.26552

PORTLAND-VANCOUVER, OR-WA -0.19012

HONOLULU, HI 0.57928

ANCHORAGE, AK 0.31145

DENVER-BOULDER, CO 0.07387

NORTHEAST REGION, B SIZE PSUS -0.02074

NORTHEAST REGION, C SIZE PSUS -0.08409

NORTHEAST REGION, D SIZE PSUS -0.00174

NORTH CENTRAL REGION, B SIZE PSUS -0.16171

NORTH CENTRAL REGION, C SIZE PSUS -0.18821

NORTH CENTRAL REGION, D SIZE PSUS -0.35833

SOUTH REGION, B SIZE PSUS -0.16423

SOUTH REGION, C SIZE PSUS -0.11572

SOUTH REGION, D SIZE PSUS -0.16923

WEST REGION, B SIZE PSUS -0.27332

WEST REGION, C SIZE PSUS -0.15643

WEST REGION, D SIZE PSUS -0.28844

Rotation group (ref=same sample as previous month)

NEW SAMPLE -0.02658
- 42 -

Table 5. ELI 12011: Potatoes

Mean of dependent variable: log price -3.7367

Adjusted R2 0.6228

Variable Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB 0.01009

MAR -0.00178

APR 0.02363

MAY 0.06245

JUN 0.16776

JUL 0.17522

AUG 0.11864

SEP 0.01893

OCT -0.07231

NOV -0.09234

Outlet type (ref=CHAIN GROCERY)

FULL SERVICE DEPARTMENT STORES -0.61027

INDEPENDENT GROCERY STORES -0.02169

PRODUCE MARKET -0.12607

CONVENIENCE STORES 0.27450

COMMODITY ORIENTED OUT NEC -0.39201

OUTLET NOT ELSEWHERE CLASSIFIED -0.31633

Package type

PACKAGING: LOOSE 0.78494

PACKAGING: MULTI-PACK, WEIGHT: GREATER T -0.51911

PACKAGING: MULTI-PACK, WEIGHT: 0-9.999 L 0.35237

Package size

WEIGHED 2 POTATOES -0.32016

WEIGHT LABELED -0.10378

Variety

WHITE POTATO -0.11197

ROUND OR LONG RUSSET -0.12073

ROUND OR LONG WHITE -0.08151

ROUND RED 0.13440

BAKING POTATO 0.07752

YAM -0.25983

SWEET POTATO/YAM 0.28265

SWEET POTATO -0.45422

UNABLE TO DETERMINE VARIETY -0.40993
- 43 -

Table 6. ELI 12021: Lettuce

Mean of dependent variable: log price -3.1222

Adjusted R2 0.5385

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD

BOSTON-LAWRENCE-SALEM, MA-NH -0.29268

PITTSBURGH-BEAVER VALLEY, PA -0.25850

BUFFALO-NIAGRA FALLS, NY -0.23543

NEW YORK CITY -0.04737

NEW YORK-CONN. SUBURBS -0.14394

NEW JERSEY SUBURBS -0.12854

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI -0.08079

DETROIT-ANN ARBOR, MI -0.25233

ST. LOUIS-EAST ST. LOUIS, MO-IL -0.10762

CLEVELAND-AKRON-LORAIN, OH -0.36251

MINNEAPOLIS-ST. PAUL, MN-WI -0.37324

MILWAUKEE, WI -0.28823

CINCINNATI-HAMILTON, OH-KY-IN 0.04950

KANSAS CITY, MO - KANSAS CITY, KS -0.19183

WASHINGTON, DC-MD-VA -0.05585

DALLAS-FORT WORTH, TX -0.10340

BALTIMORE, MD -0.15619

HOUSTON-GALVESTON-BRAZORIA, TX -0.04106

ATLANTA, GA -0.22134

MIAMI-FORT LAUDERDALE, FL -0.27921

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.33078

NEW ORLEANS, LA -0.37557

LOS ANGELES COUNTY, CA -0.42383

GREATER LOS ANGELES, CA -0.46923

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.42209

SEATTLE-TACOMA, WA -0.31179

SAN DIEGO, CA -0.63145

PORTLAND-VANCOUVER, OR-WA -0.36026

HONOLULU, HI 0.11241

ANCHORAGE, AK 0.24406

DENVER-BOULDER, CO -0.01414

NORTHEAST REGION, B SIZE PSUS -0.15127

NORTHEAST REGION, C SIZE PSUS -0.13739

NORTHEAST REGION, D SIZE PSUS -0.05323

NORTH CENTRAL REGION, B SIZE PSUS -0.25840

NORTH CENTRAL REGION, C SIZE PSUS -0.27277

NORTH CENTRAL REGION, D SIZE PSUS -0.31699

SOUTH REGION, B SIZE PSUS -0.15786

SOUTH REGION, C SIZE PSUS -0.16706

SOUTH REGION, D SIZE PSUS -0.05474

WEST REGION, B SIZE PSUS -0.39816

WEST REGION, C SIZE PSUS -0.30573

WEST REGION, D SIZE PSUS -0.43150

Rotation group (ref=same sample as previous month)

NEW SAMPLE -0.00552
- 44 -

Table 6. ELI 12021: Lettuce

Mean of dependent variable: log price -3.1222

Adjusted R2 0.5385

Variable Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB -0.17981

MAR -0.27424

APR -0.19154

MAY -0.10586

JUN -0.02842

JUL -0.29127

AUG -0.32081

SEP -0.29942

OCT -0.28473

NOV 0.02991

Outlet type (ref=CHAIN GROCERY)

FULL SERVICE DEPARTMENT STORES 0.12446

INDEPENDENT GROCERY STORES -0.02528

PRODUCE MARKET -0.08024

CONVENIENCE STORES 0.30320

COMMODITY ORIENTED OUT NEC -0.49838

OUTLET NOT ELSEWHERE CLASSIFIED -0.66851

Package type

PACKAGING: MULTIPACK -0.12828

Package size

SIZE REPRESENTS: WEIGHED ONE MULTI-PK 0.17900

Variety

BIBB 0.59326

BOSTON 0.13274

BUTTERHEAD 0.91953

COS/ROMAINE 0.36190

GREEN LEAF 0.60410

RED LEAF 0.64647
- 45 -

Table 7. ELI 12031: Tomatoes

Mean of dependent variable: log price -2.7011

Adjusted R2 0.1991

Label Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD

BOSTON-LAWRENCE-SALEM, MA-NH 0.01678

PITTSBURGH-BEAVER VALLEY, PA -0.05929

BUFFALO-NIAGRA FALLS, NY -0.13822

NEW YORK CITY -0.02569

NEW YORK-CONN. SUBURBS -0.13951

NEW JERSEY SUBURBS -0.00121

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI -0.05506

DETROIT-ANN ARBOR, MI -0.12991

ST. LOUIS-EAST ST. LOUIS, MO-IL -0.24150

CLEVELAND-AKRON-LORAIN, OH -0.33654

MINNEAPOLIS-ST. PAUL, MN-WI -0.19602

MILWAUKEE, WI -0.30839

CINCINNATI-HAMILTON, OH-KY-IN -0.04369

KANSAS CITY, MO - KANSAS CITY, KS -0.15001

WASHINGTON, DC-MD-VA 0.00536

DALLAS-FORT WORTH, TX -0.27754

BALTIMORE, MD -0.09699

HOUSTON-GALVESTON-BRAZORIA, TX -0.10590

ATLANTA, GA -0.05248

MIAMI-FORT LAUDERDALE, FL -0.50285

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.16919

NEW ORLEANS, LA -0.14505

LOS ANGELES COUNTY, CA -0.32307

GREATER LOS ANGELES, CA -0.39316

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.25084

SEATTLE-TACOMA, WA -0.29454

SAN DIEGO, CA -0.52545

PORTLAND-VANCOUVER, OR-WA -0.17875

HONOLULU, HI 0.04541

ANCHORAGE, AK 0.13065

DENVER-BOULDER, CO -0.11228

NORTHEAST REGION, B SIZE PSUS -0.06827

NORTHEAST REGION, C SIZE PSUS -0.13375

NORTHEAST REGION, D SIZE PSUS 0.19425

NORTH CENTRAL REGION, B SIZE PSUS -0.12224

NORTH CENTRAL REGION, C SIZE PSUS -0.22069

NORTH CENTRAL REGION, D SIZE PSUS -0.24259

SOUTH REGION, B SIZE PSUS -0.20441

SOUTH REGION, C SIZE PSUS -0.28840

SOUTH REGION, D SIZE PSUS -0.21121

WEST REGION, B SIZE PSUS -0.31270

WEST REGION, C SIZE PSUS -0.28317

WEST REGION, D SIZE PSUS -0.46059

Rotation group (ref=same sample as previous month)

NEW SAMPLE -0.02653
- 46 -

Table 7. ELI 12031: Tomatoes

Mean of dependent variable: log price -2.7011

Adjusted R2 0.1991

Label Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB -0.06562

MAR 0.03005

APR 0.24313

MAY 0.38750

JUN 0.54470

JUL 0.20950

AUG -0.19194

SEP -0.18685

OCT -0.25130

NOV -0.12365

Outlet type (ref=CHAIN GROCERY)

FULL SERVICE DEPARTMENT STORES -0.19366

INDEPENDENT GROCERY STORES -0.05455

PRODUCE MARKET -0.25519

CONVENIENCE STORES 0.57844

COMMODITY ORIENTED OUT NEC -0.73586

OUTLET NOT ELSEWHERE CLASSIFIED -0.69563

Package type

PACKAGING: MULTI-PACK 0.16951

PACKAGING: SINGLE ITEM, INDIVIDUALLY 0.48149

Package size

SIZE REPRESENTS: WEIGHED 2 TOMATOES -0.14385

Variety

UNSPECIFIED VARIETY -0.05647

FIELD GROWN/VINE-RIPENED -0.30496

HOT HOUSE OR GREENHOUSE -0.26962

UNABLE TO DETERMINE TYPE -0.26013
- 47 -

Table 8. ELI 12041: Other vegetables

Mean of dependent variable: log price -3.0502

Adjusted R2 0.4872

Variable Coefficient

Area (ref=PHILADELPHIA-WILMINGTON-TRENTON, PA-DE-NJ-MD

BOSTON-LAWRENCE-SALEM, MA-NH -0.18035

PITTSBURGH-BEAVER VALLEY, PA -0.19013

BUFFALO-NIAGRA FALLS, NY 0.16605

NEW YORK CITY 0.08782

NEW YORK-CONN. SUBURBS -0.11219

NEW JERSEY SUBURBS -0.07710

CHICAGO-GARY-LAKE COUNTY, IL-IN-WI 0.07671

DETROIT-ANN ARBOR, MI -0.23765

ST. LOUIS-EAST ST. LOUIS, MO-IL 0.04041

CLEVELAND-AKRON-LORAIN, OH -0.25811

MINNEAPOLIS-ST. PAUL, MN-WI -0.06638

MILWAUKEE, WI -0.10271

CINCINNATI-HAMILTON, OH-KY-IN -0.04813

KANSAS CITY, MO - KANSAS CITY, KS -0.01079

WASHINGTON, DC-MD-VA 0.05914

DALLAS-FORT WORTH, TX -0.03080

BALTIMORE, MD -0.13070

HOUSTON-GALVESTON-BRAZORIA, TX -0.21465

ATLANTA, GA -0.16305

MIAMI-FORT LAUDERDALE, FL -0.15624

TAMPA-ST. PETERSBURG-CLEARWATER, FL -0.16947

NEW ORLEANS, LA -0.12714

LOS ANGELES COUNTY, CA -0.30328

GREATER LOS ANGELES, CA -0.30388

SAN FRANCISCO-OAKLAND-SAN JOSE, CA -0.25710

SEATTLE-TACOMA, WA 0.28713

SAN DIEGO, CA -0.41637

PORTLAND-VANCOUVER, OR-WA -0.41273

HONOLULU, HI 0.52045

ANCHORAGE, AK 0.34271

DENVER-BOULDER, CO 0.04067

NORTHEAST REGION, B SIZE PSUS -0.09467

NORTHEAST REGION, C SIZE PSUS -0.23278

NORTHEAST REGION, D SIZE PSUS -0.12643

NORTH CENTRAL REGION, B SIZE PSUS -0.18928

NORTH CENTRAL REGION, C SIZE PSUS -0.10230

NORTH CENTRAL REGION, D SIZE PSUS -0.33089

SOUTH REGION, B SIZE PSUS -0.11132

SOUTH REGION, C SIZE PSUS -0.15629

SOUTH REGION, D SIZE PSUS -0.06746

WEST REGION, B SIZE PSUS -0.38406

WEST REGION, C SIZE PSUS -0.13431

WEST REGION, D SIZE PSUS -0.21889

Rotation group

NEW SAMPLE -0.07898
- 48 -

Table 8. ELI 12041: Other vegetables

Mean of dependent variable: log price -3.0502

Adjusted R2 0.4872

Variable Coefficient

Month of collection (ref=JAN, 11 months of data)

FEB -0.04138

MAR -0.06361

APR 0.04834

MAY -0.03054

JUN 0.01922

JUL -0.07667

AUG -0.14672

SEP -0.17824

OCT -0.18042

NOV -0.10289

Outlet type (ref=CHAIN GROCERY)

FULL SERVICE DEPARTMENT STORES 0.02692

INDEPENDENT GROCERY STORES -0.03887

PRODUCE MARKET -0.12645

CONVENIENCE STORES 0.21838

COMMODITY ORIENTED OUT NEC -0.35484

OUTLET NOT ELSEWHERE CLASSIFIED -0.55401

Package type

PACKAGING: MULTI-PACK 0.36462

TRIMMED -0.02206

Package size

WEIGHED ONE MULTI-PACK -0.44977

Variety

RADISHES WITH TOPS -0.01645

RADISHES WITHOUT TOPS -0.76580

YELLOW CORN -0.50855

WHITE CORN -0.13763

ARTICHOKES 0.56677

ASPARAGUS 0.58202

BEAN SPROUTS 0.04937

MINIATURE CARROTS 0.11278

GREEN SNAP BEANS -0.01606

POLE BEANS -0.05602

YELLOW WAX BEANS 0.42235

LIMA BEANS 0.60288

DOMESTIC (GREEN) CABBAGE -1.01275

SAVOY (CRINKLED LEAF) CABBAGE -0.68162

CHINESE (CELERY) CABBAGE -0.12622

HEARTS OF CELERY -0.02623

YELLOW ONIONS -0.95681

WHITE ONIONS -0.38899

PICKLING CUCUMBERS -0.04579

SPAGHETTI SQUASH -0.49575

YELLOW STRAIGHTNECK SQUASH -0.08479

YELLOW CROOKNECK SQUASH 0.06090

BUTTERNUT SQUASH -0.31871
- 49 -

Table 8. ELI 12041: Other vegetables

Mean of dependent variable: log price -3.0502

Adjusted R2 0.4872

Variable Coefficient

ACORN SQUASH -0.29270

ZUCCHINI (ITALIAN) SQUASH -0.11483

GREEN PEPPERS 0.20108

REGULAR MUSHROOMS -0.27425

SPANISH ONION -0.52453

RED ONION -0.11692
- 50 -

X. Appendix III: Sample Index Calculation for Fruits and

Vegetables

Table 1: CPD results for Bilateral relatives for Fruits and vegetables Entry Level Items

ELI Description AREA1 (PHILA) AREA2 (BOSTON) AREA3 (PITTSBG)

11011 Apples 1.0000 0.89618 0.96884

11021 Bananas 1.0000 0.98656 0.83609

11031 Oranges 1.0000 1.04715 1.05667

12011 Potatoes 1.0000 0.95105 0.81712

12021 Lettuce 1.0000 0.78312 0.75877

12031 Tomatoes 1.0000 1.03136 0.95217

Table 2: Expenditure shares within and across areas

Share Type AREA1(PHILA) AREA2 (BOSTON) AREA3 (PITTSBG)

ELI shares by area

W11011 0.39638 0.40456 0.52877

W11021 0.33412 0.27270 0.31936

W11031 0.26950 0.32273 0.15187

W12011 0.41063 0.36953 0.35684

W12021 0.29234 0.34244 0.37069

W12031 0.29704 0.28803 0.27247

Expenditure class shares by area

S(EC11) 0.46262 0.33328 0.20410

S(EC12) 0.42243 0.38425 0.19331

Table 3: Multilateral Törnqvist indexes

Item TORN12 TORN13 TORN21 TORN23 TORN31 TORN32

EC11 0.96610 0.93711 1.03509 0.97000 1.06711 1.03093

EC12 0.90929 0.82722 1.09976 0.90974 1.20877 1.09921

EC11+EC12 0.93193 0.88096 1.07305 0.94531 1.13513 1.05786
- 51 -

Table 4: Estimated reference shares and prices at the ELI level

EC ELI Variable: Coefficient Estimate:

Fruits Apples W0 (11011) 0.4391

Bananas W0 (11021) 0.3094

Oranges W0 (11031) 0.2515

Apples P0 (11011) 0.0458

Bananas P0 (11021) 0.0585

Oranges P0 (11031) -0.0318

Adjusted R2 = 0.9708

Vegetables Potatoes W0 (12011) 0.3803

Lettuce W0 (12021) 0.3331

Tomatoes W0 (12031) 0.2866

Potatoes P0 (12011) 0.0780

Lettuce P0 (12021) 0.1671

Tomatoes P0 (12031) 0.0041

Adjusted R2 = 0.9980

Table 5: Estimated reference expenditure shares and prices at the Expenditure class level

EC Variable: Coefficient Estimate:

Fruits W0 (EC11) 0.5041

P0 (EC11) 0.0609

Vegetables W0 (EC12) 0.4959

P0 (EC12) 0.1735

Adjusted R2 = 0.9947
- 52 -

Table 6: Unadjusted bilateral Törnqvist indexes

EC TORN12 TORN13 TORN21 TORN23 TORN31 TORN32

EC 11 0.96622 0.94033 1.03496 0.98959 1.06346 1.01052

EC 12 0.91564 0.83279 1.09213 0.91505 1.20078 1.09284
- 53 -

XI. Appendix IV. Fruits and Vegetables Calculation for 44 CPI

Areas

Table 1: Regression Coefficients for EC11:

Variable Coefficient Estimate

W0_11011 0.1759

P0_11011 0.0530

W0_11021 0.1697

P0-11021 0.0871

W0-11031 0.0881

P0_11031 0.0014

W0_11041 0.5663

P0_11041 0.0449

Restriction -0.000095

Adjusted R-square= 0.9832

Table 2: Regression Coefficients for EC12

Variable Coefficient Estimate

W0_12011 0.1470

P0_12011 0.0951

W0_12021 0.1268

P0_12021 0.2001

W0_12031 0.1316

P0_12031 0.1704

W0_12041 0.5946

P0_12041 0.1219

Restriction 0.000287

Adjusted R-squared= 0.9918
- 54 -

Table 3: Regression Coefficients for Fresh Fruits and Vegetables

Variable Coefficient Estimate

W0_11 0.5209

P0_11 0.0939

W0_12 0.4791

P0_12 0.2637

Restriction -3.3956 E-15

Adjusted R-squared= 0.9942
- 55 -

Table 3: Fruits and Vegetables Törnqvist Indexes for 44 Areas

Area Area Name EC11 EC12 Both

1 Philadelphia 1.000 1.000 1.000

2 St. Louis 0.999 1.006 1.005

3 Cleveland 0.975 0.797 0.870

4 Minn-St Paul 0.922 0.828 0.890

5 Milwaukee 0.980 0.856 0.921

6 Cincinnati 0.962 0.957 0.960

7 Kansas City 1.011 0.912 0.966

8 Washington 1.050 1.031 1.043

9 Dallas-Ft Wort 0.912 0.884 0.893

10 Baltimore 0.989 0.863 0.927

11 Houston 0.831 0.856 0.834

12 Boston 0.979 0.839 0.898

13 Atlanta 0.967 0.853 0.898

14 Miami 0.743 0.795 0.764

15 Tampa 0.857 0.857 0.852

16 New Orleans 0.986 0.822 0.895

17 LA County 0.909 0.753 0.832

18 Greater LA 0.898 0.736 0.817

19 San Francisco 0.936 0.775 0.852

20 Seattle 1.165 1.062 1.109

21 San Diego 0.863 0.641 0.745

22 Portland OR 0.962 0.689 0.817

23 Pittsburgh 0.921 0.824 0.870

24 Honolulu 1.196 1.391 1.279

25 Anchorage 1.175 1.319 1.237

26 Denver 1.048 1.012 1.030

27 NE B-size 0.979 0.923 0.942

28 NE C-size 0.903 0.820 0.869

29 NE D-size 1.055 0.966 1.004

30 NC B-size 0.975 0.840 0.905

31 NC C-size 0.928 0.860 0.896

32 NC D-size 0.856 0.751 0.799

33 South B-size 0.930 0.873 0.903

34 Buffalo 0.875 1.033 0.945

35 South C-size 0.881 0.845 0.853

36 South D-size 0.925 0.909 0.902

37 West B-size 0.969 0.711 0.836

38 West C-size 0.947 0.822 0.881

39 West D-size 0.889 0.729 0.805

40 New York City 1.021 1.017 1.018

41 New York- CT 0.965 0.885 0.918

42 New York-NJ 0.947 0.910 0.924

43 Chicago 1.041 1.056 1.046

44 Detroit 0.887 0.806 0.849
- 56 -

XII. References

Aczel, J. 1966. Lectures on Functional Equations and Their Applications. New

York: Academic Press.

Caves, W., L. Christensen, and W. Diewert. 1982a. “Multilateral Comparisons of Output,

Input, and Productivity Using Superlative Index Numbers,” The Economic

Journal 92, 73-86.

Caves, W., L. Christensen, and W. Diewert. 1982b. “The Economic Theory of Index

Numbers and the Measurement of Input, Output, and Productivity,”

Econometrica 50, 1393-1414.

Cuthbert, J., and M. Cuthbert. 1988. “On Aggregation Methods of Purchasing Power

Parities,” OECD Department of Economics and Statistics Working Paper 56,

Chapter 3.

Diewert, W. 1976. “Exact and Superlative Index Numbers,” Journal of Econometrics

4, 114-145.

Diewert, W. 1986. “Micro Economic Approaches to the Theory of International

Comparisons,” National Bureau of Economic Research Technical Paper 53.

Diewert, W. 1987. “Index Numbers,” in The New Palgrave Dictionary of Economics,

J. Eatwell, M, Milgate, and P. Newman, Eds. New York: The Stockton Press.

Drechsler, L. 1973. “Weighting of Index Numbers in Multilateral International

Comparisons,” Review of Income and Wealth, Series 19(1), 17- 34.

Eichhorn, W. 1978. Functional Equations in Economics. Reading, Massachusetts:

Addison-Wesley.

Fixler, D., and K. Zieschang. 1992. “Incorporating Ancillary Measures of Process and

Quality Change into a Superlative Productivity Index,” Journal of Productivity

Analysis 2(2), 245-267.

Fixler, D., and K. Zieschang. 1992. “Erratum,” Journal of Productivity Analysis 2(3),

302.
- 57 -

Kokoski, Mary, Pat Cardiff, and Brent Moulton. 1994. “Interarea Price Indices for

Consumer Goods and Services: An Hedonic Approach Using CPI Data,” BLS

Working Paper 256, July.

Moulton, B.R. 1995. "Interarea Indexes of the Cost of Shelter Using Hedonic Quality

Adjustment Techniques." Journal of Econometrics 68(1), 181-204.

Randolph, W., and K. Zieschang. 1987. “Aggregation Consistent Restriction Based

Improvement of Local Area Estimators,” American Statistical Association

Proceedings of the Section on Business and Economic Statistics.

Summers, R. 1973. “International Comparisons with Incomplete Data,” Review of

Income and Wealth, Series 19(1), March, pp. 1-16.

Selvanathan, E., and D. Prasada Rao. 1992. “An Econometric Approach to the

Construction of Generalized Theil-Törnqvist Indices for Multilateral

Comparisons,” Journal of Econometrics 54, 335-346.

U.S. Department of Labor, Bureau of Labor Statistics. 1988. “The Consumer Pirce

Index,” in BLS Handbook of Methods, Bulletin 2285, April, pp. 154-184.

Zieschang, K. 1985. “Output Price Measurement When Output Characteristics Are

Endogenous,” BLS Working Paper 150. (Revised 1987).

Zieschang, K. 1988. “The Characteristics Approach to the Problem of New and

Disappearing Goods in Price Indexes,” BLS Working Paper 183.