"PROPER QUADRATIC COST FUNCTIONS
WITH AN APPLICATION TO AT&T"
by
Lars-Hendrik ROLLER*
N° 88 / 22
* Lars-Hendrik ROLLER, Assistant Professor of Economics,
INSEAD, Fontainebleau, France
Director of Publication :
Charles WYPLOSZ, Associate Dean
for Research and Development
Printed at INSEAD,
Fontainebleau, France
Proper Quadratic Cost Functions with an Application to AT&T
by
I,
*
Lars-Hendrik Roller
INSEAD
Boulevard de Constance
77305 Fontainebleau Cedex
France
May 1987
(revised March 88)
*
Financial support was provided by the Institute for Law and Economics,
University of Pennsylvania. I am grateful to Almarin Phillips, Rafael Rob,
and Robin C. Sickles for valuable comments and discussions. All opinions
and remaining errors are mine.
Proper Quadratic Cost Functions with an Application to AT&T
by
'I
Lars-Hendrik Roller
*
Abstract
When choosing a flexible functional form to model multi-output cost
structures, one is quickly confronted with severe violations of certain
regularity conditions over large regions of output space. This problem is
particularly troublesome when the economic analysis extrapolates cost
information from such (improper) regions. This paper explicitly imposes
regional properness on the parameter space of flexible functional forms,
thereby using more of economic theory in the modelling process. The apparent
trade-off between functional flexibility and functional properness has been
identified for the case of the quadratic cost function, and it is argued,
that this trade-off should be resolved in favor of properness not
flexibility in order to obtain meaningful models of multi-output cost
structures. Using the quadratic cost function I illustrate the procedure
with an application to AT&T.
- 3 -
0. Introduction
When choosing a flexible functional form to model multi-output cost
structures, one is quickly confronted with severe violations of certain
regularity conditions over large regions of output space (for evidence of
poor global behaviour see Wales (1977), Guilkey and Lovell (1980), and
Guilkey, Lovell and Sickles (1983)). This problem is particularly
troublesome when the economic analysis extrapolates cost information from
such (improper) regions (see Roller (1987)).
One obvious suggestion is to simply choose a functional form that a priori
satisfies all conditions for a proper cost function globally.
Unfortunately, this usually implies that flexibility is sacrificed in the
process. Alternatively, one can constrain the cost inference to that region
over which the cost function is indeed well-behaved. The idea then is to
choose a functional form that satisfies the regularity conditions for the
largest possible region (see Caves and Christensen (1980), Barnett and Lee
(1985), and Barnett, Lee and Wolfe (1985,1987)). However, this regular
region may typically be too small in order to model demanding cost concepts
such as economies of scope and subadditivity.
This paper uses a different approach (see also Diewert and Wales (1987)) by
explicitly imposing regional properness on the parameter space of flexible
functional forms, thereby using more of economic theory in the modelling
process. In this fashion, this procedure allows for a meaningful (i.e.
consistent with economic theory) analysis of multi-output cost concepts. On
the other hand, some of the functional flexibility may be lost, leading to a
trade-off between the size and shape of the proper region and functional
flexibility.
The analysis is based on the quadratic cost function, because it seems
better suited for multi-output cost models than the more "popular" translog
1,
(TL) cost function. As is argued in Roller (1987), the translog functional
family performs rather unsatisfactory with respect to more demanding cost
concepts such as natural monopoly or economies of scope.
This paper is divided into two parts. First, Section 1 defines proper cost
functions, discusses how regional properness is imposed, and addresses the
properness-flexibility trade-off. Second, Section 2 discusses an
application of the procedure to AT&T using the quadratic cost function.
1. Proper Cost Functions and Flexibility
The approach in this paper is to impose certain regularity conditions upon
functional forms to ensure that they are well-behaved over the relevant
region. In particular, functional forms are constrained to be proper cost
functions. This contrasts with "traditional" analysis, where functional
forms are proper only over limited regions in output space and, thereby,
inappropriate for analyzing global cost concepts.
Proper cost functions are defined in accordance with Baumol, Panzar, Willig
(1982) as being consistent with the definition of a cost function, i.e. a
proper cost function must be nonnegative and linearly homogeneous, concave
and nondecreasing in input prices. In addition, when the assumption of free
disposal is made, a proper cost function must be nondecreasing in outputs.
1.1 Flexibility of the Quadratic Cost Function
Let C (y,w,t) denote an unknown cost function defined by the usual solution
to the program of minimizing costs, given a k-input price vector wcR
k
and an
index of technological advances denoted t, to produce a n-output vector
yeRn+ . For notational convenience, define y ni.i s t. Then the Generalized*
1
CES-Quadratic (G-CES-Q) approximation to C (y,w,t) is defined by :
(1)
n+1
C G-CES-Q(y,w)
n+1 n+1
= CES(w) [ u6 + E miyi
i(yiyi)b']
+ (1/2) E
Em
i=1
i=1 j=1
1. For a discussion about the translog approximation of C (y,w,t) to
flexibility see Appendix-B.
k
Tr (-1/0
where CES(w) . [ E ww I
i=1 "
Linear homogeneity in input prices and symmetry requires:
k
(2)
1
1.E
. 1W
= 1, for all i=1,..k
and
ce
13
= e.,
1.
for all i,j=1,...n+1
3
Nested in (1) is the CES-Quadratic functional form (CES-Q), obtained by
setting b=1. Before imposing more restrictions on the G-CES-Q, such as
monotonicity, concavity and nonnegativity, it is useful to analyze the
flexibility properties of the quadratic form.
Diewert (1974) defines a flexible functional form, C, as a second-order
differential approximation to an arbitrary twice continuously differentiable
*
cost function C that satisfies linear homogeneity in input prices at any
point (y
*
* *
2
,w ,t ). Hence, C must satisfy the following (n+k+1) +(n+k+1)+1
equations :
* * *
* * * *
C(y ,w ,t ) = C (y or ,t )
(3)
* * *
* * * *
C(y 07 ,t ) = C (y ,w ,t )
i
i
* * * *
C..(y ,w ,t ) =
(y ,w ,t )
ij
Cij
i=1,...,n+k+1
i,j=1,...,n+k+1
By imposing symmetry and linear homogeneity on C * , we can restrict
((n+k+l)(n+k)/2)+n+k+2 elements of (3). Thus, a function must have at
least:
(4)
(n+k+1)2+(n+k+1)+1 - [((n+k+1)(n+k)/2)+n+k+2] . [(n+k+1)2+(n+k+1)1/2
2.Cdenotes the first order partial derivative with respect to i, and
i
C..denotes the second order partial derivative with respect to i and j.
ij
free parameters to be flexible in the sense of Diewert. The G-CES-Q defined
2
by (1) and (2) has [(n+1) +3n+2k+7]/2 free parameters, which is strictly
less than (4) 3 . Hence, the G-CES-Q, as well as the CES-Q, are not
flexible functional forms.
In light of the rather limited flexibility of the quadratic cost function,
two different approaches may be taken. First, functional forms displaying
more flexibility could be analyzed. Diewert and Wales (1987) show how
various functional forms display considerable flexibility when linear
homogeneity, symmetry and (global) concavity restrictions are imposed.
Second, a weaker flexibility criterion, called output-flexibility may be
used. This approach is taken in this chapter. The assumption underlying
the motivation for using output-flexibility rather than flexibility is that
the analysis is primarily in output space (for example: natural monopoly).
Whenever the analysis is based on correct modelling in output space, it is
output-flexibility that is of crucial importance. In fact, outputflexibility is sufficient for substantive flexibility 4 of various cost
5
concepts .
Definitionl: C is an output-flexible functional form if and only if C is
a second order differential approximation to an arbitrary
2
3. The precise condition under which [(n+1) +3n+2k+7]/2 is strictly less
2
than (4) is 2n(k-1)+k +k>6, which is satisfied for k>1. Hence, we will
assume that C is a multi-input cost function.
4.
For a definition of substantive flexibility see Baumol, Panzar, Willig
1982.
5.
For example, cost-complementarities at a point can be positive or
negative for output-flexible forms, thereby displaying substantive
flexibility.
-E-
twice continuously differentiable cost function C * at any
* * *
admissible point (y ,w ,t ), such that C satisfies the
2
following n +n+1 equations:
* * *
C(y ,w ,t )
C i (y
**
* * * *
C (y ,w ,t )>0
*
* *
,t ) = C i (y ,w ,t )>0
* * *
* * *
C..(y ,w ,t ) = C.. (Y ,w ,t )
i=1,...,n
i,j=1,...,n
Using the symmetry conditions in (2), an output-flexible functional form
2
6
must have at least n +n+1-[(n-l)n/2] = [n 2 +3n+2]/2 free parameters .
Before analyzing output-flexibility of the quadratic cost function, we
impose two additional restrictions on (1). Assuming (2) holds, the G-CES-Q
- as well as the CES-Q - cost function is globally concave and nonnegative
in input prices if and only if:
(5)
r>-1 and 020, for all i.1,...k
Thus, the G-CES-Q, defined by (1), (2) and (5), has at least [(n+l) 2 +3n+7]/2
free parameters, whereas the CES-Q has at least [(n+1)
2
+3n+5]/2, both of
which have enough to be output-flexible. Moreover, we have the following
result:
Propositionl:
The CES-Quadratic - and consequently the G-CES-Q - cost
function defined by (1), (2) and (5) is an output-flexible
functional form.
Proof: (see Appendix-A)
In other words, imposing properness at the input side, leads to functional
forms flexible over the entire output space.
6. Linear homogeneity does not effect output-flexibility.
- 9 -
1.2 Monotonicity and Nonnegativity
A proper cost function must be nonnegative as well as monotone in output
quantities. The problem of enforcing regional monotonicity can be stated as
imposing constraints on the parameter space of a cost function, such that
over that constrained parameter space, all marginal cost schedules are
7
nonnegative for a specified region in output space . The size and shape of
the output region is determined by the objective of the analysis. For
example, if the intend is to investigate a property such as economies of
scope, it is certainly attractive to choose the output region to include
stand alone costs. However, it is important to realize, that certain
functional forms will lose their flexibility - or substantive flexibility as the constrained output region gets larger. Consequently, some functional
forms may not possess enough flexibility to analyze certain cost concepts,
when positive marginal costs are imposed.
Consider, the class of marginal cost schedules linear in A(.) with an
8
multiplicativetermF.(.) of the form :
(6)
n+1
ac
= C i (y,w) = Fi(y,w)(a.+ E b..e(y.,y.,b)), i=1,...,n
yi
1 .1
1 j=1 13
where F.(.) is nonnegative.
Note that this form includes as a special case the G-CES-Q (and the CES-Q
for b=1), defined by (1), (2) and (5). To see this let,
F i (y,w) = CES(w)
7.
Global monotonicity is imposed whenever monotonicity is imposed over
the entire output space.
8. The translog cost function also belongs to this class. For a discussion
regarding monotonicity of the translog functional form see Appendix-B.
- is-
e(Y.,Y.,b) =
(Y.Y.)
b'
/Y.,
Y. 0
I
a.1 = ce.1
b.tj = ce..b'
tj
The requirement that F i (y,w)=CES(w) is nonnegative is satisfied by (5).
Consider imposing monotonicity over a rectangular region in output space, S,
9
defined by yminen+1, y max en+1 such that :
min<y i <V,
max , for all 1)
S = ()TER n+1 10<y,
Proposition2 establishes an upper bound on the number of constraints
sufficient to impose monotonicity over region S.
Proposition2:
Let C i (y,w) be given
by (6)
n+1
and A = E b..0(y.,y.,b).
j=1 13
1
Define the set of critical points L i by:
L i = {x n+
min,ymax
i
1,A 1 ), for 1=1,...,n+1),
wre
he Ai
= fyllin yi yliaximi/ay1=0).
Then, for all w,
C i (y,w)>0 for all y€L' => C i (y,w)>0 for all ycS.
Proof: (see Appendix-A)
In other words, it suffices to impose monotonicity at the critical points,
independent of input prices w. Since L i has a large number of elements, we
9. For the G-CES-Q we require that y ml in >0 for 1=1,...,n, since marginal
cost schedules are undefined at y=0.
are left with an even larger number of constraints for monotonicity
10
.
Furthermore, it is clear from the proof of proposition 2 that only n
constraints are binding. In particular, monotonicity is satisfied if and
only if the following n constraints are met:
i
C.(x
(7)
i*
i=1,...,n
,w) > 0;
where x
i*
= argmax -A
i
(y,r i )
and
yel l
la=(a.,b,...,b.,b)
n+1
i il
Unfortunately, which n constraints are binding is unknown, since x
upon
i*
depends
ri.
The final property to be imposed for functional properness is nonnegativity
of the cost function. Assuming monotonicity is satisfied via (7), and (2)
and (5) hold as well, then the cost function is nonnegative over S if and
only if:
(8)
C(y
min
,w)>0
1.3 Proper Quadratic Cost Functions and Output-Flexibility
Propositions3 and 4 establish the relationship between output-flexibility
and properness of the quadratic cost function.
10. The exact number of elements in L i is:
n+1
t
i
T i = 2 n+1 + 2n it 2 ED i. ,
j where E = E Di_i
t
j=1
t=1
i
Di iis the cardinality of A and D=O. Thus, the number of constraints
0
t
t
to impose monotonicity is of order nTi.
Proposition3:
Let t *>0
11 ,
then the G-CES-Q proper cost function defined by
(1), (2), (5), (7) and (8) is an output-flexible functional
form.
Proof: (see Appendix-A)
In other words, the G-CES-Q, constrained to a proper functional form over
region S, is still a flexible approximation over the entire output space
(given t * >0).
Proposition4:
*
Let t eS' where S' is the complement region of S restricted
t'
to t, then the CES-Q proper cost function defined by (1),
(2), (5), (7), and (8) is an output-flexible functional
form.
Proof: (see Appendix-A)
Proposition4 demonstrates a trade-off between the size of the proper cost
region 'and the size of the flexible cost region. As the size of S
increases, Si decreases and vice versa. In the limit, as the region of
properness (flexibility) becomes the entire admissible output space, the
region of flexibility (properness) becomes empty. A similar trade-off is
apparent for the G-CES-Q, when assumption t >0 is replaced by t min >0 in
Proposition3. Both of these conditions are rather weak, yet they show that
the G-CES-Q is either flexible or proper, but not both, at t=0.
*
min
11. t >0 can be replaced by t
>0; see the proof of Proposition3 in
Appendix-A.
- 13 -
2. The Proper Quadratic Cost Function: An Application
In this section, we present an application of the analysis in Section 1 to
the cost structure of AT&T. As described above, we are particularly
interested in imposing properness in order to analyze demanding cost
concepts, such as natural monopoly and economies of scope, in a meaningful
fashion. Furthermore, the CES-quadratic cost function described above is
used, whereas all previous studies for AT&T have stayed within the TL world.
The CES-quadratic cost function is defined in (1). Using Shepherd's lemma
we obtain the cost share equations:
(aCES(w)/awdw iOiwir
(9)
S11
CES(w)
_
i=1,...,k
k
-r
E 8.w .
j=1
3
In addition to (2) and (5) we impose nonnegativity defined by (8). Since
CES(w) > 0 by (5), nonnegativity for the quadratic cost function is implied
by:
n+1
(10)
min
m6 > - E cey.1
1
i=1
n+1 n+1
,
min min b
-(1/2) iE
)
6 'x i4kY . Y.
3
=1 j=1 J 1
Note, that if y min .0, (8) simplifies to a6>0. Finally, monotonicity is
imposed by:
(11)
n+1
b'
>0,
m: + E ce.b'(y.y.)
/y.
1
1
1
13
j=1
Note that:
i
.
for ya , 1=1,...,n.
- 14 -
0,
A .
j
for
j i
n+1
(((1+b')/(ceii(2b'-1)) E
j
Thus, for the G-CES-Q, L
i
has 2
n+1
+2
n
b
' (b'-1)]
1/b'
),
elements, leading to 3n2
for monotonicity. For the CES-Q form (b=1), we have Al
j.
Consequently, L
i
has 2
n+1
for
j=i
13 3
elements, resulting in n2
n
constraints
(), for all i and
n+1
constraints for
monotonicity.
2.1. Data and Estimation
The data used (annual time series fro 1947-1978) are described in Evans and
Heckman (1984) and have been used in a number of studies analyzing the
question of natural monopoly for AT&T. With this data set, I first estimate
the CES-Q functional form using three-inputs (k=3) and two-outputs (n=2).
Inputs are capital, labor and materials, whereas outputs are local and toll
telephone service (aggregated over five reported outputs). Second, a threeoutput model (n=3) is estimated: outputs are local, intra- and interstate
telephone service.
Since the analysis includes stand alone cost extrapolation (e.g. natural
monopoly), I choose ymin =0 and
y max
equal to the largest values observed in
the sample, thereby ensuring that all the analysis is over a proper region
(see Appendix-D).
Imposing properness for the two-output model requires 4 equality constraints
for (2), 4 inequality constraints for (5), 1 inequality constraint for (10)
and 16 inequality constraints for (11). For the three-output model
properness requires 7 equality constraints for (2), 4 inequality constraints
for (5), 1 inequality constraint for (10) and 48 inequality constraints for
(11).
- 15-
It must be emphasized that local, toll and, indeed, technology are highly
colinear. This colinearity problem makes the econometric results extremely
sensitive to the functional form, the estimation procedure, the data, and
the variable chosen to represent technology. Nonetheless, I continue to
explore essentially methodological issues.
Assuming normality, the system of equations defined by (1) and (9) is
estimated by nonlinear full-information maximum likelihood. The invariance
property of maximum likelihood estimation allows us to delete one share
equation without affecting the results. First-order serial correlation in
each equation is specified, yet no correlation across equations is
allowed
12
. The constraints for properness, i.e. (2), (5), (10) and (11),
are imposed on the likelihood function via a penalty function of the form:
nc
P = h E log(Gi),
i=1
where h is a shrinkage factor and G i >0 are nc constraints. The sequence of
solutions for successively smaller values of h will converge to the
constrained optimum13
2.2. Results
The estimated CES-Q cost surface is plotted in Graphsl-4 (see Appendix-D),
demonstrating visually that it is indeed proper. Contrary to a TL
12.
The correlation coefficient in each of the cost share equations is
constrained to be indentical, in order to use the invariance property of
maximum likelihood (see Berndt and Savin, 1975).
13.
See F.A. Lootsma (1972) and A.V. Fiacco and G.P. McCormick (1964).
- IV -
functional form, stand alone costs (i.e. costs along the axis) are not zero
or infinite
Table 1 reports estimates of local cost concepts evaluated at observed
sample points. As can be seen, strong overall economies of scale are
identified, ranging from 1.28 to 1.56 for the two-output model and 1.68 to
2.75 for the three-output model. These results are very much in line with
other studies. However the cost-complementarity estimates are substantially
different from other studies. I find cost-complementarities at all sample
points between all outputs suggesting efficiencies from joint production.
Table 2 reports estimated economies of scope. Since the estimated cost
surface is proper, unlike the TL world stand alone costs are not degenerate,
and the results in Table 2 are at least consistent with the definition of a
cost function. Economies of scope seem to be present at all sample points
for the two- as well as three-output model, thereby satisfying a necessary
condition for multi-product natural monopoly.
Due to the global properness of the cost surface, we are now in a position
to test for natural monopoly not only via satisfaction of necessary
conditions (i.e. regional subadditivity tests), but apply a necessary and
sufficient test (i.e. global subadditivity tests)
15
. The test I use is
analogous to Evans and Heckman (1984). In particular, consider an output
level y=(y l ,y2 ) for the case n=2 (the test for n=3 is analogous). Then the
14. The TL specification can be shown to go to zero or infinity as one
output approaches zero.
15. Finding a natural monopoly globally implies, of course, a regional
natural monopoly.
- 17 -
cost surface is subadditive up to y with respect to 2 hypothetical firms if
and only if
16
max Cost(wy l ,py2 ) + Cost((1-w)y i ,(1-p)y 2 ) - Cost(y i ,y2 ) < 0
0.),(3
where 0<w<1, 0<p<1
Note that this test requires cost extrapolations for all output levels up to
y. Table 3 reports the maximum (over w and p) percentage gain from
divestiture in each year. Since all gains from divestiture are negative in
all years for both the two- and the three-output model, it is concluded that
the cost structure is that of a natural monopoly.
3. Conclusion
This paper attempts to use more of economic theory in the modelling process,
in particular when appropriate data are not available and global cost
concepts are analyzed. The apparent trade-off between functional
flexibility and functional properness has been identified for the case of
the quadratic cost function, and it is argued, that this trade-off should be
resolved in favor of properness not flexibility in order to obtain
meaningful models of cost structure.
16. To be a truly sufficient test, we need to do the same test for more
than just 2 hypothetical firms.
18-
-
*
Table 1 - Local Cost Concepts
Estimated Cost-Complementarities and Overall Returns to Scale (ORS)
for 1974-1978
n=2
Year
CC
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
-
*
11
CC
-
12
n=3
CC
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
22
ORS
1.56
1.52
1.49
1.47
1.44
1.42
1.41
1.39
1.37
1.36
1.34
1.33
1.32
1.31
1.31
1.30
1.29
1.29
1.28
1.28
1.28
1.28
1.28
1.29
1.29
1.30
1.30
1.31
1.32
1.33
1.34
1.36
CC
11
-
CC
12
CC
-
-
13
CC
-
22
CC
-
23
CC
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
33
ORS
1.99
1.92
1.87
1.84
1.81
1.78
1.76
1.74
1.72
1.69
1.68
1.68
1.68
1.68
1.69
1.70
1.71
1.73
1.76
1.80
1.84
1.89
1.93
1.98
2.03
2.10
2.17
2.26
2.35
2.46
2.60
2.75
CC.denotes the sign of the cost-complementarity between output y.1 and
13
2
For the two-output model
outputy.i.e.thesignofCC ii =0 C/3y.By.).
1 3
3,
(n=2) we have (y ,y )=(Local,Toll); for the three-output model (n=3) we
1 2
have (y1,y2,y3)=(Local,Intra,Inter). ORS denotes overall returns to scale
as defined by Baumol, Panzar and Willig (1982).
- 19 -
Table 2 *
Estimated Economies of Scope for 1947-78
*
Year
SCOPE%
(n=2)
SCOPE%
(n=3)
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
34
32
30
29
27
26
25
24
23
21
20
20
18
17
17
16
15
14
13
13
12
11
11
11
10
10
10
9
9
9
9
9
95
89
86
84
81
79
77
75
72
69
67
66
64
63
62
62
61
62
62
63
64
65
65
66
67
65
69
71
73
75
78
80
SCOPE% denotes degree of economies of scope, i.e.
100*[Cost(0,y2 )+Cost(y 1 ,0) - Cost(y 1 ,y 2 )]/Cost(y i ,y 2 ), for the two-output
model (n=2), and
100*[Cost(0,0,y 3 )+Cost(0,y 2 ,0)+Cost(y 1 ,0,0) - Cost(y1,y2,y3)]/Cost(y1,y2),
for the three-output model (n=3). In other words, SCOPE% is the percentage
loss from having each product be produced by a single firm.
-20-
Table 3
Maximum Percentage Gain from
Divestiture for 1947-1978
*
Year
two-output model
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
-34
-32
-30
-29
-27
-26
-25
-24
-23
-21
-20
-19
-18
-17
-16
-16
-15
-14
-13
-12
-12
-11
-10
-10
-10
-9
-9
-8
-8
-8
-8
-7
three-output model
-47
-44
-43
-42
-40
-39
-38
-37
-35
-34
-33
-32
-31
-31
-30
-30
-30
-30
-30
-30
-30
-30
-30
-30
-30
-30
-30
-31
-31
-32
-32
-32
The entries in the table are the solution to the program
max Cost(coy i ,py 2 ) + Cost((1-0y 1 ,(1-p)y 2 ) - Cost(y 1 ,y 2 ) < 0
04P
where 0<w<1, 0<p<1
as describe in the text above. The test for the three-output model is
analogous.
-21-
Appendix-A
Proof of Propositionl:
We need to show that C defined by (1), (2), (5) and b.1 can satisfy
2
the n +n+1 equations in (3).
(5). Set b=1.
* * * *
C (y ,w ,t )
Step3:
Step2:
Steps:
Let Oi and r satisfy (2) and
Let a6 solve the equation:
n+1
+
E aiyi
CES(w Ma6
+
i=1 E
n+1 n+1
(1/2) E
j.1
Let ai solve the n equations:
n+ 1
* * * *
* * b' *
*
C.(y ,w ,t ) = CES(w He + E a!.b1(y.y.) /y.[,
ij
1
1
1
1
j=1
Step4:
1 .1,...,n
Let a!. solve the n(n-1)/2 equations:
1j
* * * *
(y ,w , t )
c ij
Let
* * b'
ai4(yiyi) ]
solve
cc.
11
*
2 *
(b'-1)]
,
CES(w M ab'
..
(y y)
1
i=1,...,n; j>i
the n equations:
n+ 1
*
*
* *
*.(2W-2)
*(b'-2) *b'
*
1,
1..b1(2b1-1)y
C. .(y ,w , t ) = CES(w )[ E ce..b'(b'-1)y.
.+0e1
yj
1
1
11
j=1 13
i *.j
i=1,....,n
Steps:
The remaining n2+n+1-[(n(n-1)/2)+2n+1]
n(n-1)/2 equations are
satisfied by the symmetry restrictions. q.e.d.
Proof of Proposition2:
Let xs cS and x s not cL i . By construction of L 1 we have:
i s
i i*
i*
i
A (x ) > A (x ), where x cL = argmax-A .
y cL1
By hypothesis,
- 22 -
i i*
C (x ,w) > 0
=>
a.+A(x
1
i*
by assumption on F
) > 0
i
i s
a.+A (x ) > 0
i s
C (x ,w) > 0. q.e.d.
.>
Proof of Proposition3:
We need to show, that the G-CES-Q cost function can satisfy (2), (5),
(7) and (8), as well
as
the n 2 +n+1 equations in Definition) at the
* * *
admissible point (y ,w ,t ).
Stepl:
Let pi and r satisfy (2) and (5).
Step2:
Let a!. solve
13
the n(n-1)/2 equations:
* * * *
C..(y ,w , t )
*
2 * * (b'-1)]
CES(w Moe..b' (y y )
,
j
i=1,...,n; j>i
Let a solve the n equations:
11
n+ 1
*
*
* *
C (y w
t )
"
*(b'-2) *b'
y],
CES(w )[
1
j=1
*j
1
i.1,....,n
Step3:
Let a! satisfy the n constraints given by(7):
1
i i*
i* i* b' i*
a! > -A (x ) . -E a!.b'(x. x. ) /x.
1
13
1 3
1
(al)
Thus, given (al), we need to be able to solve:
* * * *
(a2)C.(y ,w ,t )
1
n+1
CES(w Hat +
1
* * *
Note,thatifC.(y ,w ,t )
1
be satisfied, since
a' can
b=0, then:
(al) <=> a! > 0
1
* * b' *
E a!.b'(y.y.) /y.] > 0;
j=1 13
13
i=1,...,n
* * *
0 is satisfied, any C.(y ,w ,t ) > 0 can also
always be increased without violating (al). Let
- Li -
*
* * * *
(a2)<=>C. (y ,w ,t ) = CES(w )a!
i
* * * *
Seta=0=>C(y ,w ,t ) = 0.
i
i
Step4:
Let acsatisfy (8), i.e. C
G-CES-0
(y
min
,w)>0 if
n+1 n+1
n+1
min
min min '
E a!.(y. y. )b
a' > -E cy.
- (1/2) E
(a3)
ij 1
J
0
i 1
i=1
i=1 j=1
Given (a3) we have to solve:
(a4)
n+1
* * * *
*
*
C (y ,w ,t ) . CES(w )[a' + E ay
0
i=1 i i
n+1 n+1
* * b'
E a!.(y.y.)
+ (1/2) E
I
i=1 j=1 13 1
* * *
* min
Ify=y,thensetceC(y ,w= ,t )>O, thereby satisfying (a3) and (a4).
* min
; substituting (a3) into (a4) yields:
Let y oy
n+1
* * * *
*
* min
-y. )
C (y ,w ,t )/CES(w ) > E a(yii
i
1=1
n+1 n+1
m in min b'
* *
I,
)
E a!.[(y.y.)b' - (y. y.
+ (1/2) E
1
J
1 J
i=1 j=1 l i
*
or a!
if y
>0
which can be satisfied by an appropriate choice of a'
1,n+1
n+1
n+1
*
min
min
or yn+1>0 (Note that satisfaction is guaranteed for y n+1 .5, n+1 >0,
* min
since y Oy
).
Step5:
2
The remaining n +n+1-[(n(n-1)/2)+2n+1] = n(n-1)/2 equations are
satisfied by the symmetry restrictions. q.e.d.
Proof of Proposition4:
We need to show, that the CES-Q cost function can satisfy (2), (5), (7) and
(8), as well as the n 2 +n+1 equations in Definitionl at the admissible
point (y*,w*,t*)eS'. Stepl , Step2 and Step5 are identical to Proposition3,
except set b=1.
Step3:
Let a satisfy the n constraints given by (7):
i
- 24 -
n+1
-E
j=1 1.3
i
a: > -A (x)
(a5)
Thus, given (a5), we need to be able to solve:
(a6)
C i (y
*
,w ,t
*
n+1
) = CES(w)[ai +
E
> 0;
i=1,...,n
j=1 1.3
* * *
* * *
Note that if Ci(y ,w ,t )=0 is satisfied, any Ci(y ,w ,t )>0 can also be
satisfied, since at can always be increased without violating (a5).
Furthermore,
i
aA
ac.
i,n+1
* * *
ac.07 ,w ,t )
i*
and
- x
n+1
am:
i,n+1
*
Yn+1
Thus, assuming (a5) holds strictly, the total derivative is:
* * *
dC.(y ,w ,t )
-- x
n+1
Yn+1
dm!
i,n+1
* * *
is not in S
since y
lienceC.(y ,w ,t ) is strictly monotonic in a:
n+1
1,n+1'
* * *
suchthatC.(y ,w ,t ) = 0.
by assumption. Therefore, we can choose a:
i,n+1
Step4:
(a7)
Let
a6
satisfy (8), i.e. C
CES-Q
(y
min
n+1 n+1
n+1
min
E
- (1/2) E
a'
> - E a:y.
0 i=1 j=1
i=1
,w)>0 if
min m in
y.
)
a:.(y.
Given (a7) we have to solve:
(a8)
* * * *
C (y ,w ,t ) = CES(w
*
n+1 n+1
**
E al4(yiyi)]
aiy i + (1/2) E
1=1 j=1
1=1
n+1
)[116 + E
Assuming equality on (a7) and substituting into (a8) yields:
n+ 1
* * * *
* min
C (y ,w ,t )/CES(w ) > E a:(y.-y. )
i=1 "
- 25 -
n+1 n+1
+ (1/2) E
1=1
* *
E ce..[(y.)
y.
j=1 I" j
min m in
(y. y.
)],
1 3
*
min
which can be satisfied by an appropriate choice of a' , since y
-y
#0
n+1
n+1 n+1
by assumption. q.e.d.
- 26-
Appendix-B
Monotonicity, Nonnegativity and Flexibility:
The Case of the Translog Cost Function
The Translog (TL) approximation to C * (y,w,t) is:
log(C
TL
n+1 k
k
n+1
E a„log(yi)log(w.)
(y,w))ao + E a.log(y) + E 0,log(w,) + E
1
i= " i=1 " i=1 j=1 1J
(A)
k k
n+1 n+1
(w.)
E 0..log(wi)log
E a..log(y i )log(y.) + (1/2) E
+ (1/2) E
i=1 j=1 13
i=1 j=1 13
Linear homogeneity in input prices requires:
(b2)
k
k
k
E0..=0,
for
j=1,...k
and
E
a..=0, for i=1,...,n+1
E O.=1,
1.1
j=1
j=1 3
j=113
Symmetry:
aii,
for i,j=1,...,n+1
(b3)
ji ,
o
for
The TL functional form defined by (bi), (b2) and (b3) does have exactly
(n+1)(n+2)/2 + nk + k(K+3)/2 parameters and can be shown to be flexible
(see Woodland,1976 or Khaled, 1978). However, it loses its flexibility when
concavity in input prices is added (see Diewert 1987). Since primary
emphasis is put upon output analysis, we will concentrate on imposing
properness with respect to outputs.
The TL form also belongs to the class described by (6). Using nonnegativity,
the marginal cost schedule of CTL is equivalent to (6) by setting:
Fi(y,w)=C
TL
(y,w)/yi
3(y.,y.b)=10 g(y .)
1
k
a.= a. + E a..log(w.)
1
ij
1
j=1
(evaluated for some w)
-
13
LI -
13
Therefore we have:
. n+1
A i = E a..lo
.)
j=1 13 g(Y3
(A i ) = (), for all 1.1,...,n+1 and i=1,...,n
1
n+1
Li has only 2
elements for each i.
=>
.>
From Proposition2 we know, that monotonicity over the rectangular region S
is guaranteed if for i=1,...,n:
(b4)
J
.L(y,w) > 0, for yeLi
1
Finally, note that the TL cost function is by definition globally
nonnegative, i.e. for any parameter vector C
Proposition-B1: Let
t
*
c(t
min
,t
max
TL
> 0.
), then the TL cost function defined by
(bl), (b2), (b3) and (b4) is an output-flexible functional
form.
Proof: We need to show, that the TL cost function can satisfy (bl), (b2),
(b3), and (b4), as well as the n 2 +n+1 equations in Definition) at the
* * *
admissible point (y ,w ,t ).
Step):
Leta..solve the n(n+1)/2 equations:
13
* * * *
TL * * *
C ii (y ,w ,t ) = C ii (y ,w ,t )
Step2:
Let at) satisfy:
C
Step3:
(b5)
*
T1, * * *
* * *
(y ,w ,t ) = C (y ,w ,t)
Leta.satisfy the n constraints:
1
n+1
k
a. + E a..log(w.) > -E a..log(x. )
3 13
1 j=1 13
3
j=1
- Lb -
Thus, given (b5), we need to be able to solve:
n+1
k
*
*
* * * *
* *
.) ] > 0; i=1,...n
(b6) C i (y ,w ,t ) = C /y. [a. + E a..log(w.) + E a.lo
j=1 13
j=1 13 g(Y3
3
Substituting (b5) into (b6) yields:
* * *
C.y./C=
1 i
k
i*
* n+1
E a..(log(w.)-log(w.)) + E a..(log(y.)-log(x. )),
J
J
J
j1 13
j=
1 13
Which can be solved, given that y
i*
*
, which is satisfied by
x
n+1
n+1
assumption.
Step4:
The remaining n2+n+1-[(n(n+1)/2)+n+1] = n(n-1)/2 equations are
satisfied by the symmetry restrictions. q.e.d.
- 29 -
Appendix-C
On the Choice of S
The shape and size of the region over which the cost function is proper is
crucially dependent upon the objective of the analysis. I will next discuss
how various objectives may influence the construction of the region S.
Criterion 1: Analysis up to a point.
When the intent is to properly model and estimate stand alone cost concepts,
it becomes necessary to allow for a well-behaved cost surface "close" to the
axis. Thus, it is appropriate to choose y
up to a point
ymax.
min
=0, thereby ensuring properness
By doing so, for example, estimation of economies of
scope extrapolates cost information only from a proper cost function.
Similarly, tests for subadditivity up to a point exclusively use cost
information from a proper cost surface, conforming with economic theory.
(Note: To include the sample in S, one must obviously set y
max
equal to the
largest values observed.)
Criterion 2: Analysis around sample such that the largest (smallest) output
ratios in S are equal to the largest (smallest) output ratios
observed in the sample.
This criterion may be used, whenever regional extrapolation is constrained
to be around the observed sample. For example, the regional test for
subadditivity suggested by Evans and Heckmann (1984), falls in this
category. To fulfill criterion 2 we need:
(c l)
max
Y.
min
Yj
max
- R..
13
and
min
Y.i
ymax
max
min
- R ij n '
-30-
where
R.ma x
. is the largest sample ratio of y/y.
i
13
min i
R..s the smallest sample ratio of y /y.
13
i
min
max
Bychoosing.at
some arbitrary value (perhaps sample minimum), all y.
Yi
aredeterrainedby(m.Furthermore,using(coand.
min y.
max, ymax
Yj
1 must
J
satisfy the following conditions:
max
min
13
min
max
< min '
Yi
Yi
Yi
R
13
for all j
min
Yj
The precise choice of max
For
example, S is a square in i,j space whenever:
max
Yi
1)R7x
min ' 13
min
13
Yi
min max
R.. (R.. + 1)
13
13
Choose,
max
R. + 1
min 1
max
Yl..--Y.1
min
R.. + 1
13
and S will be a rectangular region in i,j space "extended" towards the data
with the highest spread. Note that this construction of S will not
necessarily include the sample. In fact it is impossible ,in general, to
satisfy criterion 2 as well as have the sample included.
Appendix-D
Graphl
• Estimated CES-Q Cost Function for AT&T (two-output model)
(Q1=local telephone service, Q2=toll telephone service)
--4
Graph2
Estimated CES-Q Cost Function for AT&T (three-output model)
(01.1ocal telephone service, Q2=intrastate telephone service)
01
A
(SI
11‘.
cn
01
tA
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1111
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03
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.10
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Graph4
Estimated CES-Q Cost Function for AT&T (three-output model)
(02.intrastate telephone service, Q3=interstate telephone service)
to
CD
-35-
References
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I/
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INSEAD WORKING PAPERS SERIES
1985
85/01 Jean DERMINE
"The measurement of interest rate risk by
financial intermediaries", December 1983,
Revised December 1984.
85/02 Philippe A. NAERT
and Els GIJSBRECHTS
"Diffusion model for new product introduction
in existing markets* .
85/03 Philippe A. NAERT
and Els GIJSBRECHTS
"Towards a decision support system for
hierarchically allocating marketing resources
across and within product groups" .
"Market share specification, estimation and
validation: towards reconciling seemingly
divergent views" .
85/04 Philippe A. NAERT
and Marcel WEVERBERGH
85/05 Ahmet AYKAC,
Marcel CORSTJENS,
David GAUTSCHI
and Ira HOROWITZ
"Estimation uncertainty and optimal
advertising decisions",
Second draft, April 1985.
85/06 Kasra FERDOWS
"The shifting paradigms of manufacturing:
inventory, quality and nov versatility", March
1985.
"Personality, culture and organization".
85/17 Manfred P.R. KETS DE
VRIES and Danny MILLER
85/18 Manfred P.R. KETS
DE VRIES
"The darker side of entrepreneurship".
85/19 Manfred F.R. KETS DE
VRIES and Dany MILLER
"Narcissism and leadership: an object
relations perspective".
85/20 Manfred F.R. KETS DE
VRIES and Dany MILLER
"Interpreting organizational texts".
85/21 Hervig M. LANGOHR
and Claude J. VIALLET
"Nationalization, compensation and wealth
transfers: France 1981-1982" 1, Final version
July 1985.
85/22 Hervig M. LANGOHR and
B. Espen ECKBO
"Takeover premiums, disclosure regulations,
and the market for corporate control. A
comparative analysis of public tender offers,
controlling-block trades and minority buyout in
France", July 1985.
85/23 Manfred P.R. KETS DE
VRIES and Dany MILLER
"Barriers to adaptation: personal, cultural
and organizational perspectives".
85/24 Spyros MAKRIDAKIS
"The art and science of forecasting: an
assessment and future directions".
85/25 Gabriel HAWAVINI
"Financial innovation and recent developments
in the French capital markets", October 1985.
85/26 Karel O. COOL and
Dan E. SCHENDEL
"Patterns of competition, strategic group
formation and the performance case of the US
pharmaceutical industry, 1963-1982",
October 1985.
85/27 Arnoud DE MEYER
"European manufacturing: • comparative study
(1985)".
85/07 Kasra FERDOWS,
Jeffrey G. MILLER,
Jinchiro NAKANE and
Thomas E.VOLLMANN.
"Evolving manufacturing strategies in Europe,
Japan and North-America"
85/08 Spyros MAKRIDAKIS
and Robert CARBONE
"Forecasting when pattern changes occur
beyond the historical data" , April 1985.
85/09 Spyros MAKRIDAKIS
and Robert CARBONE
"Sampling distribution of post-sample
forecasting errors" , February 1985.
85/10 Jean DERMINE
'Portfolio optimization by financial
intermediaries in an asset pricing model".
85/11 Antonio M. BORCES and
Alfredo M. PEREIRA
"Energy demand in Portuguese manufacturing: a
two-stage model".
86/01 Arnoud DE MEYER
"The B i D/Production interface".
85/12 Arnoud DE MEYER
"Defining a manufacturing strategy - a survey
of European manufacturers".
86/02 Philippe A. NAERT
Marcel WEVERBERGH
and Guido VERSWIJVEL
"Subjective estimation in integrating
communication budget and allocation
decisions: a case study", January 1986.
85/13 Arnoud DE MEYER
"Large European manufacturers and the
management of R i D".
86/03 Michael BRIMM
"Sponsorship and the diffusion of
organizational innovation: a preliminary view".
85/14 Ahmet ATRAC,
Marcel CORSTJENS,
David GAUTSCHI and
Douglas L. MacLACHLAN
"The advertising-sales relationship in the
U.S. cigarette industry: a comparison of
correlational and causality testing
approaches".
86/04 Spyros MAKRIDAKIS
and Michele HIBON
"Confidence intervals: an empirical
investigation for the series in the MCompetition" .
85/15 Arnoud DE MEYER and
Roland VAN DIERDONCK
"Organizing a technology jump or overcoming
the technological hurdle".
86/05 Charles A. WYPLOSZ
"A note on the reduction of the workweek",
July 1985.
85/16 Hervig M. LANGOHR and
Antony M. SANTOMERO
"Commercial bank refinancing and economic
stability: an analysis of European features".
1986
86/06 Francesco GIAVAllI,
Jeff R. SHEEN and
Charles A. VYPLOSZ
"The real exchange rate and the fiscal
aspects of a natural resource discovery",
Revised version: February 1986.
86/22 Albert CORHAY,
Gabriel A. HAVAVINI
and Pierre A. MICHEL
"Seasonality in the risk-return relationships
some international evidence", July 1986.
86/07 Douglas L. MacLACHLAN
and Spyros MAKRIDAKIS
"Judgmental biases in sales forecasting",
February 1986.
86/23 Arnoud DE MEYER
"An exploratory study on the integration of
information systems in manufacturing",
July 1986.
86/08 Jose de la TORRE and
David H. NECKAR
"Forecasting political risks for
international operations", Second Draft:
March 3, 1986.
86/24 David GAUTSCHI
and Vithala R. RAO
"A methodology for specification and
aggregation in product concept testing",
July 1986.
86/25 H. Peter GRAY
and Ingo WALTER
"Protection", August 1986.
86/26 Barry EICHENGREEN
and Charles VYPLOSZ
"The economic consequences of the Franc
Poincare", September 1986.
86/27 Karel COOL
and Ingemar DIERICKX
"Negative risk-return relationships in
business strategy: paradox or truism?",
October 1986.
86/09 Philippe C. HASPESLAGH "Conceptualizing the strategic process in
diversified firms: the role and nature of the
corporate influence process", February 1986.
86/10 R. MOENART,
Arnoud DE MEYER,
J. BARBS and
D. DESCHOOLMEESTER.
"Analysing the issues concerning
technological de-maturity".
86/11 Philippe A. NAERT
and Alain BULTEZ
"Prom "Lydiametry" to "Pinkhamization":
misspecifying advertising dynamics rarely
affects profitability".
86/12 Roger BETANCOURT
and David GAUTSCHI
"The economics of retail firms", Revised
April 1986.
86/29 Manfred KETS DE VRIES
"Why follow the leader?".
86/13 S.P. ANDERSON
and Damien J. NEVEN
"Spatial competition A la Cournot".
86/30 Manfred KETS DE VRIES
"The succession game: the reel story.
86/31 Arnoud DE MEYER
86/14 Charles VALDMAN
"Comparaison Internationale des merges brutes
du commerce", June 1985.
"Flexibility: the next competitive battle",
October 1986.
86/15 Mihkel TOMBAK and
Arnoud DE MEYER
"Nov the managerial attitudes of firms with
VMS differ from other manufacturing firms:
survey results", June 1986.
86/31 Arnoud DE MEYER,
Jinichiro NAKANE,
Jeffrey G. MILLER
and Kasra FERDONS
"Flexibility: the next competitive battle",
Revised Version: March 1987
86/16 B. Espen ECKBO and
Hervig M. LANGOHR
"Les primes des offres publiques, la note
d • information et le marche des transferts de
contrAle des societes".
86/32 Karel COOL
and Dan SCHENDEL
Performance differences among strategic group
members", October 1986.
86/17 David B. JEMISON
"Strategic capability transfer in acquisition
integration", May 1986.
86/33 Ernst BALTENSPERGER
and Jean DERMINE
"The role of public policy in insuring
financial stability: a cross-country,
comparative perspective", August 1986, Revised
November 1986.
86/18 James TEBOUL
and V. MALLERET
"Towards an operational definition of
services", 1986.
86/34 Philippe HASPESLAGH
and David JEMISON
"Acquisitions: myths and reality",
July 1986.
86/19 Rob R. VEITZ
"Nostradamus: a knowledge-based forecasting
advisor".
86/35 Jean DERMINE
"Measuring the market value of a bank, a
primer", November 1986.
86/20 Albert CORHAY,
Gabriel HAVAVINI
and Pierre A. MICHEL
"The pricing of equity on the London stock
exchange: seasonality and size premium",
June 1986.
86/36 Albert CORHAY and
Gabriel HAVAVINI
"Seasonality in the risk-return relationship:
some international evidence", July 1986.
86/21 Albert CORHAY,
Gabriel A. HAVAVINI
and Pierre A. MICHEL
"Risk-premia seasonality in U.S. and European
equity markets", February 1986.
86/37 David GAUTSCHI and
Roger BETANCOURT
"The evolution of retailing: a suggested
economic interpretation".
86/38 Gabriel HAVAVINI
"Financial innovation and recent developments
in the French capital markets", Updated:
September 1986.
"Interpreting organisational texts.
86/28 Manfred KETS DE
VRIES and Danny MILLER
87/13 Sumantra CHOSHAL
and Nitin NOHRIA
"Multinational corporations as differentiated
networks", April 1987.
87/14 Landis GABEL
"Product Standards and Competitive Strategy: An
Analysis of the Principles", May 1987.
87/15 Spyros MAKRIDAKIS
"METAFORECASTINC: Rays of improving
Forecasting. Accuracy and Usefulness",
May 1987.
"FMS as indicator of manufacturing strategy",
December 1986.
87/16 Susan SCHNEIDER
and Roger DUNBAR
"Takeover attempts: what does the language tell
us?, June 1987.
86/43 Damien NEVEN
"On the existence of equilibrium in hotelling's
model", November 1986.
87/17 Andre LAURENT and
Fernando BARTOLOME
"Managers' cognitive maps for upward and
downward relationships", June 1987.
86/44 Ingemar DIERICKR
Carmen MATUTES
and Damien NEVEN
"Value added tax and competition",
December 1986.
87/18 Reinhard ANGELMAR and
Christoph LIEBSCHER
"Patents and the European biotechnology lag: a
study of large European pharmaceutical firms",
June 1987.
87/19 David BEGG and
Charles VYPLOSZ
"Why the EMS? Dynamic games and the equilibrium
policy regime, May 1987.
86/39 Gabriel HAWAWINI
Pierre MICHEL
and Albert CORHAY
"The pricing of common stocks on the Brussels
stock exchange: a re-examination of the
evidence", November 1986.
86/40 Charles VYPLOSZ
"Capital flows liberalization and the EMS, a
French perspective", December 1986.
86/41 Kasra FERDOWS
and Wickham SKINNER
"Manufacturing in a nev perspective",
July 1986.
86/42 Rasta FERDOWS
and Per LINDBERG
1987
87/01 Manfred KETS DE VRIES
"Prisoners of leadership".
87/20 Spyros MAKRIDAKIS
"A new approach to statistical forecasting",
June 1987.
87/02 Claude VIALLET
"An empirical investigation of international
asset pricing", November 1986.
87/21 Susan SCHNEIDER
"Strategy formulation: the impact of national
culture", Revised: July 1987.
87/03 David CAUTSCHI
and Vithala RAO
"A methodology for specification and
aggregation in product concept testing",
Revised Version: January 1987.
87/22 Susan SCHNEIDER
"Conflicting ideologies: structural and
motivational consequences", August 1987.
87/04 Sumantra GHOSHAL and
Christopher BARTLETT
"Organizing for innovations: case of the
multinational corporation", February 1987.
87/23 Roger BETANCOURT
David CAUTSCHI
"The demand for retail products and the
household production model: new views on
complementarity and substitutability".
87/05 Arnoud DE MEYER
and Kasra FERDOWS
"Managerial focal points in manufacturing
strategy", February 1987.
87/24 C.B. DERR and
Andre LAURENT
87/06 Arun K. JAIN,
Christian PINSON and
Naresh K. MALHOTRA
"Customer loyalty as a construct in the
marketing of banking services", July 1986.
"The internal and external careers: a
theoretical and cross-cultural perspective",
Spring 1987.
87/07 Rolf BANZ and
Gabriel HAVAVINI
"Equity pricing and stock market anomalies",
February 1987.
87/25 A. K. JAIN,
N. K. MALHOTRA and
Christian PINSON
"The robustness of MDS configurations in the
face of incomplete data", March 1987, Revised:
July 1987.
87/08 Manfred KETS DE VRIES
"Leaders who can't manage", February 1987.
87/26 Roger BETANCOURT
and David GAUTSCHI
"Demand complementarities, household production
and retail assortments", July 1987.
87/09 Lister VICKERY,
Mark PILKINGTON
and Paul READ
"Entrepreneurial activities of European MBAs",
March 1987.
87/27 Michael BURDA
"Is there a capital shortage in Europe?",
August 1987.
87/28 Gabriel HAWAVINI
87/10 Andre LAURENT
"A cultural view of organizational change",
March 1987
"Controlling the interest-rate risk of bonds:
an introduction to duration analysis and
immunization strategies", September 1987.
87/11 Robert PILDES and
Spyros MAKRIDAKIS
"Forecasting and loss functions", March 1987.
87/29 Susan SCHNEIDER and
Paul SHRIVASTAVA
"Interpreting strategic behavior: basic
assumptions themes in organizations", September
1987
87/12 Fernando BARTOLOME
and Andre LAURENT
"The Janus Head: learning from the superior
and subordinate faces of the manager's job",
April 1987.
87/30 Jonathan HAMILTON
"Spatial competition and the Core", August
W. Bentley MACLEOD and 1987.
Jacques-Francois THISSE
01/31
"On the optimality of central place:;",
Martine OUINZII and
Jacques-Francois TIIISSE September 1987.
87/32 Arnoud DE MEYER
"German, French and British manufacturing
strategies less different than one thinks",
September 1987.
87/33 Yves DOZ and
Amy SHUEN
"A process framework for analyzing cooperation
between firms", September 1987.
87/34 Kasra FERDOwS and
Arnoud DE MEYER
"European manufacturers: the dangers of
complacency. Insights from the 1907 European
manufacturing futures survey, October 1901.
87/35 P. J. LEDERER and
J. F. THISSE
"Competitive location on networks under
discriminatory pricing", September 1907.
87/36 Manfred KETS DE VRIES
"Prisoners of leadership", Revised version
October 1987.
87/37
Landis GABEL
87/38 Susan SCHNEIDER
"Privatization: its motives and likely
consequences", October 1987.
"Strategy formulation: the impact of national
culture", October 1987.
87/39 Manfred KETS DE VRIES "The dark side of CEO succession", November
1987
87/40 Carmen MATUTES and
Pierre RECIBEAU
"Product compatibility and the scope of entry",
November 1987
87/41 Gavriel HAVAVINI and
Claude VIALLET
"Seasonality, size premium and the relationship
between the risk and the return of French
common stocks", November 1987
87/42 Damien NEVEN and
Jacques-F. TIIISSE
"Combining horizontal and vertical
differentiation: the principle of max-min
differentiation", December 1987
87/43 Jean GABSZEVICZ and
Jacques-F. THISSE
"Location", December 1987
87/44 Jonathan HAMILTON,
Jacques-F. THISSE
and Anita VESKAMP
"Spatial discrimination: Bertrand vs. Cournot
in a model of location choice", December 1987
87/45 Karel COOL,
David JEMISON and
Ingemar DIERICKX
"Business strategy, market structure and riskreturn relationships: • causal interpretation",
December 1987.
87/46 Ingemar DIERICKX
and Karel COOL
"Asset stock accumulation and sustainability
of competitive advantage", December 1987.
88/01
Michael LAWRENCE and
Spyros MAKRIDAKIS
"Factors affecting judgemental forecasts and
confidence intervals", January 1988.
88/02
Spyros MAKRIDAKIS
"Predicting recessions and other turning
points", January 1988.
88/03
James TEBOUL
"De-industrialize service for quality", January
1988.
88/04
Susan SCHNEIDER
"National vs. corporate culture: implications
for human resource management", January 1988.
88/05
Charles WYPLOSZ
"The swinging dollar: is Europe out of step?",
January 1988.
88/06
Reinhard ANGELMAR
"Les conflits dans les canaux de distribution",
January 1988.
88/07
Ingemar DIERICKX
and Karel COOL
"Competitive advantage: a resource based
perspective", January 1988.
88/08
Reinhard ANGELMAR
and Susan SCHNEIDER
"Issues in the study of organizational
cognition", February 1988.
88/09
Bernard SINCLAIRDESGAGN4
"Price formation and product design through
bidding", February 1988.
88/10
Bernard SINCLAIRDESGAGNA
"The robustness of some standard auction game
forms", February 1988.
88/11
Bernard SINCLAIRDESGAGNe
"When stationary strategies are equilibrium
bidding strategy: The single-crossing
property", February 1988.
88/12
Spyros MAKRIDAKIS
"Business firms and managers in the 21st
century", February 1988
88/13
Manfred KETS DE VRIES
"Alexithymia in organizational life: the
organization man revisited", February 1988.
88/14
Alain NOEL
"The interpretation of strategies: a study of
the impact of CEOs on the corporation",
March 1988.
88/15
Anil DEOLALIKAR and
Lars-Hendrik ROLLER
"The production of and returns from industrial
innovation: an econometric analysis for a
developing country", December 1987.
88/16
Gabriel HAVAWINI
"Market efficiency and equity pricing:
international evidence and implications for
global investing", March 1988.
88/17
Michael BURDA
"Monopolistic competition, costs of adjustment
and the behavior of European employment",
88/18
Michael BURDA
"Reflections on "Vast Unemployment" in
global investing", November 1987, revised
February 1988.
88/19
M.J. LAWRENCE and
Spyros MAKRIDAKIS
"Individual bias in judgements of confidence",
March 1988.
88/20
Jean DERMINE,
Damien NEVEN and
J.F. THISSE
"Portfolio selection by mutual funds, an
equilibrium model", March 1988.
88/21
James TEBOUL
"De-industrialize service for quality",
March 1988 (88/03 Revised).