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von Haefen, Phaneuf, and Parsons: Estimation and Welfare Analysis 197
increases in consumption of other goods. This in turn limits the richness of substitution patterns that can be captured with this
preference structure. For perspective, it is instructive to compare these implica-
tions with those that arise from the separability assumptions embedded in discrete choice RUM models. These models de-
compose the time horizon of choice into separable choice occasions on which the individual makes discrete choices.
Consumer behavior across each of the choice occasions is un- coordinated and, thus, diminishing marginal utility of consump-
tion for a good is absent from these models. Although discrete choice RUM models can generate fairly rich substitution pat-
terns among goods, they assume that on a given choice occasion all goods are quality-adjustedperfect substitutes and income ef-
fects are absent for a notable exception, see Herriges and Kling 1999.
The additively separable empirical demand system specica- tions estimated in this article can be nested within the following
general structure:
U.x; Q; z; ¯; D
M
X
j
1 ½
j
9.s; d
j
;
¡Á.q
j
x
j
C µ
j
¢
½
j
C 1
½
z
z
½
z
;
ln 9.s; d
j
; D .± C
± T
s C .³ C
³ T
d
j
C
j
;
ln Á.q
j
D °
T
q
j
; 7
where s and d
j
are vectors of individual specic demographic variables and site-specic dummy variables, respectively; µ D
[µ
1
; : : : ; µ
M
]
T
0I ½ D [½
1
; : : : ; ½
M
; ½
z
] 1I ±; ³ , and ° are
estimable parameters;
±
;
³
represent unobserved hetero- geneity that varies randomly across individuals in the popula-
tion; and .
1
; : : : ;
M
represent unobserved heterogeneity that varies randomly across individuals and goods.
Our preference structure is a close relative of the linear ex- penditure system employed by PKH but differs in three im-
portant respects. First, our specication can be interpreted as a more general specication because, in the limit as all elements
of ½ approach 0, our specication nests the linear expenditure system, that is,
lim
½ M
X
j
1 ½
j
9.s; d
j
; ¡
Á.q
j
x
j
C µ
j
¢
½
j
C 1
½
z
z
½
z
D
M
X
j
9.s; d
j
; ln
¡Á.q
j
x
j
C µ
j
¢ C ln z: 8 Second, PKH assumed, using our notation in 7, that a good’s
quality attributes enter preferences through 9 instead of Á. This approach to introducing quality implies that weak complemen-
tarity i.e., U=q
j
D 0 if x
j
D 0; 8 j; see Mäler 1974; Bradford
and Hildebrandt 1977 for discussions is not, in general, satis- ed unless µ
j
D 0 when ½
j
6D 0 and µ
j
D 1 for the limiting case
when ½
j
D 0; 8 j. As a result a potentially large component of
the total value associated with a quality change will be indepen- dent of the consumer’s use of a particular commodity, a concep-
tually troubling implication for many applications. Because our specication introduces quality through the simple repackaging
Á
parameters Griliches 1964, weak complementarity is satis- ed for all parameter values; thus, only use-related values will
arise from our model. Finally, our specication allows the para- meters for the demographic and site-specic dummy variables
entering the 9 parameters to vary randomly across individuals in the population. As discussed later, this feature of our model
allows us to introduce a more exible structure for unobserved heterogeneity.
Maximizing the utility function in 7 with respect to p
T
x C
z D y and the nonnegativity constraints implies a set of rst-
order conditions that, with some manipulation, can be written as
j
· ¡.± C
± T
s ¡ .³ C
³ T
d
j
C ln
p
j
Á .q
j
C .½
z
¡ 1 ln. y ¡ p
T
x
C . 1 ¡ ½
j
ln
¡Á.q
j
x
j
C µ
j
¢ 8 j:
9 These weak inequalities, along with assumptions for the dis-
tributions of D .
±
;
³
;
1
; : : : ;
M
, permit estimation of the structural parameters using maximum likelihood techniques. In
our application we assume that each
j
is an independent and identically distributed draw from the Type I extreme-value dis-
tribution with common scale parameter ¹. Dening the right side of 9 as g
j
.
±
;
³
, the likelihood of observing a particular
vector of choices x conditional on .
±
;
³
can be written as