Ranking of economic journals: A statistical survey and analysis.
Ramrattan, Lall B. ; Szenberg, Michael
I. Introduction
The literature has focused on two prominent features of economics
journals. One group has documented several underlying qualitative
criteria in order to rank the journals. The other has attempted to make
inferences from the compensation characteristics of the editors and
editorial staff of the journals. In addition to these efforts, modem
literature has assessed the expansion of economics journals to the
domain of the Internet, and examined the shifting of their subject
matter from the abstract to the less technical. Unfortunately, there are
additional questions relating to the early concerns that remain
unanswered. Successful rankings in the past have only considered the
demand side viewpoint, ignoring the production characteristics of the
journals. The lack of adequate data limits one's ability to
estimate significant results of an econometric model. The purpose of
this paper is to present the results of a larger survey in order to
challenge some of the hypotheses in current literature, and to shed new
ligh t on modern concerns about the technical competence of
practitioners in economics and the effects of editorial compensation on
the journals.
Several well-known surveys and studies have adequately documented
the initial concerns. An early study by Liebowitz and Palmer (1984) used
the number of citations a journal was credited with in the literature in
order to rank them. A survey by Laband and Piette (1994) expanded this
methodology to include the number of pages published and allowed for
entry and exit of journals over time. A more recent article has shown
how to use such a page-counting methodology to rank not only journals,
but also the economics departments from which the articles originated
(Dusansky and Vernon, 1998). These studies examined objective
characteristics of the journal. A citation was viewed as the ". . .
scientific community's version of dollar voting by consumers for
goods and services" (Laband and Piette, 641). However, the supply
side, production, or input characteristics, such as the magnitude and
arrangement of the production staff, can also be used to establish the
value of the journals. This paper collected such data to en able a
supply side ranking.
A previous study (Lee and Szenberg, 1988) addressed the concern of
literature on the effect of compensation of journal editors and
editorial staff on the cost of journals to libraries and other
subscribing institutions. Using the results from a survey of 50
economics journals, it explored the relationship between compensation of
editors and editorial staff and circulation, controlled by qualitative
characteristics such as institutional affiliations- government,
university, and other. Among its results, it found that the elasticity
between circulation and compensation was about 0.35, implying that a one
unit percent increase in circulation would have a 35 percent increase in
the editor's compensation. However, that study did not have
significant t-values, implying that a larger sample or an improved
specification was required. The present study utilized a larger sample,
and concentrated on an improved specification guided by careful data
exploration techniques. Factor analysis was used to sort out and create
i ndices of colinear variables, in order to enhance modeling of the
hypotheses.
Over the last two decades, the literature has documented a movement
away from the technical and formalist writing style to a more practical
and business oriented style within the discipline of economics. One such
study by the Commission on Graduate Education in Economics (COGEE, 1991)
was concerned with "what they see as 'empty formalism in the
profession today." COGEE prescribed that the technical nature of
the subject matter must be explained and justified, and not just
exorcised from the discipline. In response, instructors of economics and
their colleagues "... are relying on The Journal of Economic
Perspectives (JEP) and The Journal of Economic Literature (JEL) to stay
current in areas in which they may not specialize" (Becker, 1998,
128).
The advent of the Internet has caused a paradigm shift in the way
journals distribute their literature and cut costs. The services of
JSTOR, for instance, which include providing current and back issues of
economics journals on the web, has been a strategic cost saving move for
libraries and sponsor institutions. As Varian documented, the cost to
digitize journal articles is about 50 cents per page. If capital costs
are added for storing printed journals, he concluded, "... there
may be considerable savings to digitization" (Varian, 1997, 97).
Within the new Internet environment, Goffe and Parks (1997, 79) have, in
a sense, resuscitated the pricing question raised by Lee and Szenberg
(1988) that "editorial text editing costs do not change much in the
electronic world." They proceed to argue that cost reduction of
journals is a function of editorial work completed, implying that an
explanation can be found within a model that accounts for staff inputs,
including variables such as editorial assistants, secretar ies, and
other salaried help. This study accommodates such gaps in the
literature.
This paper proposes to answer questions noted above via the results
of a survey of various economics journal editors. The next section
describes the sample design, followed by data exploration techniques.
The ranking section provides an alternative way of ranking the journals
from the production characteristics end. The last section explains how
an econometric model can be built to answer questions regarding both the
cost and quality aspects of journals.
II. Sample Design
The sample design was a simple random survey of economics journals.
We pulled a random sample of 250 out of the 600 journals (excluding the
50 or so governmental publications) for which the Journal of Economic
Literature publishes articles in its "Contents of Current
Periodicals" (Volume XXXVII (1), March 1999, 344-401). Sampling was
conducted using a mailed questionnaire, email, telephone, and written
follow-ups. The sample size of responses necessary to be considered
significant varies depending on the proportion of expected responses for
this type of survey. If we assume a 50:50 chance of receiving a
response, then with a universe of 550, we would expect 226 responses
received to be within a 95% confidence interval. The survey had 90
responses, which puts it at a 90% confidence level. (1) The "Report
of the American Economic Association (ABA) Committee on the
Journals" actually received 635 out of 1,100 or a response rate of
57.6% (AEA Papers and Proceedings, Volume 90 (2), May 2000, 528). The
AEA also doe s a "Universal Academic Questionnaire" (UAQ)
survey. In May 1999, it received 331 responses and in May 2000, 305
responses (ibid. 534). The universe of that survey is not given, but
knowing that its membership (Regular, Junior, Life, and Honorary)
exceeds 20,000, the response rate cannot be substantial. Using the AEA
response percentage for the "AEA Committee on the Journals"
study would require slightly less than 222 responses to reach a 95
percent confidence level, but compared with the UAQ study, our response
rate is very attractive according to Snedecor and Cochran (1959).
The questionnaire had six parts corresponding to general,
editorial, secretarial, professional, compensatory, and refereeing
characteristics. The general section asked five questions regarding
publications, circulation, invited articles, subscribers, and sponsors.
The next two sections asked three questions regarding the number of
editors, type of editors, (associate, assistant, and managing) and
secretaries (part-time, full-time and others). The professional section
had four questions seeking information regarding graduate assistants,
copy editors, proofreaders and others. The section on compensation asked
for four types of compensation data. The compensation for referees was
designated as a dummy variable to equal "yes" if referees were
paid.
The descriptive statistics in Table 1 show that average circulation
is about 4,855 per year, with approximately 2,761 accounted for by paid
subscription. About 80 percent of the journals have an institutional
sponsor, and they publish an average of 4 or more issues per year. The
study did not aim at a stratification of sponsors by institutional
affiliations, such as government and universities. The expected number
of invited articles is only about 20 percent. On average, the journals
have about 7 associate editors. There are ten times as many associate
and three times as many assistant as managing editors.
Data on compensation to editors was sparse. We had to supplement
compensation figures with estimates for the reduction in teaching time
for editors. The methodology we use is consistent with Lee and Szenberg
(1988). We used the May 2000 figure of $90,068 from the ABA UAQ survey
for tenured or tenure-track academic economists as equivalent to that of
a representative editor. That figure was decreased by the percentage of
teaching reduction indicated by the respondents.
We used factor analysis for data exploration. Factor analysis has
the advantage of reducing the data to a few central variables and
revealing something about how the data cluster. It helps identify
relationships between observed values that cannot be discerned in an
obvious way. Table 2 shows our extraction of five factors from the
sample survey. The numbers indicate factor loading and explain how
closely the 17 variables are correlated with the five factors. (2) The
last row shows that the five factors combined explain about 53 percent
of the variance in the data. The last column, the communality or
[h.sup.2], demonstrates what percentage of variation in a variable is
explained by the five factors taken together. We see that 81 and 86
percent of the variation in subscription and circulation, respectively,
is accounted for by the five factors taken together.
The first factor is loaded in variable 2 (circulation). We have a
priori knowledge that circulation has some relationship to subscription,
which is brought out by the second highest loading on paid subscription
(variable 3) with circulation. However, factor analysis also brings out
the less obvious relationships like the association of other types of
assistants (variable 12) and percent of invited articles (variable 4) to
heavily circulated or heavily subscribed journals. A similar analysis
shows that factor 2 is loaded in copy editors (variable 14) and in
proofreaders (variable 15), and is bi-polar with the number of issues
(variable 1). Factor 3 is loaded in the technical nature of the journals
(variable 11), which is associated with managing editors (variable 8),
and is not in concert with the percentage of invited articles (variable
3). Factor 4 is loaded in payments to referees (variable 17) and in the
number of full-time secretaries (variable 10), and factor 5 is loaded in
graduate assistants (variable 13).
It is worth observing if any variable loads highly in more than one
of the factors. Almost all the variables fit this criterion. Their
influence is spread broadly across several factors. The number of issues
a journal publishes annually (variable 1) is bi-polar between factors 3
and 4, vs. factor 2. Sponsors (variable 5) is positively loaded in
factors 4 and 5. While associate editors (variable 6) is loaded in
factor 3, assistant editors (variable 7) is loaded in factors 2 and 4.
III. Ranking of Journals
In this section we propose a ranking of journals based on their
production characteristics (Table 3). Unlike the demand side ranking
mentioned above, this ranking is based on the journals' supply side
characteristics. The method extracted the principal components of the
set of variables identified in Table 1 and ranked the journals on a
weighted average of their scores. Because the literature does not
identify weights, we decided to give each variable equal weight in the
ranking. There are two sets of rankings because the inclusion of the
compensation variable severely limits the number of journals on which
scores are available. However, if the compensation variable is excluded,
we can rank 72 out of the 92 journals, 20 being excluded for having no
data in some of their cells. When compensation is included, we can only
rank 41 journals. The first column in Table 3 presents the ranking
excluding compensation and the second column displays the ranking
including compensation.
When compensation is included, the Journal of Economic Perspectives
(JEP) is ranked first. Laband and Piette (1994, Tables 1 and A1) ranked
the JEP fourteenth, based on citations in articles, and eleventh based
on citations per character. Having started in the 1980s, it may appear
that the JEP has worked its way up the ladder over time. However, time
does not appear to be the influential factor. As Becker (1998) has
pointed out, the JEP may have moved up in rank by providing the
practitioners in the field with a non-technical source to stay abreast
of the literature. Additionally, the table below shows that when
compensation is left out of the editorial picture, the JEP ranking falls
to number sixty-one, implying that having a strong and deep pocketed
sponsor like the American Economic Association (AEA) is essential for
the high quality of the journal.
IV. Model and Estimation
In this section, we specify and estimate a model to explain some
current and ongoing questions in the literature. In particular, we will
address two central issues: cost and the technical nature of journals.
A. A priori Specifications
The factor analysis above helps identify an econometric model to
further explain the data. The cluster of Factor 1 among circulation,
subscription, and percentage of invited articles indicates that those
variables are, in a sense, redundant, as they are found to have
significant causal links. We can choose one or the other, or have an
index of them based on their degree of colinearity. To use all of them
in an econometric model would add surplus meaning to the data.
Therefore, we make the following specifications of the model to be
estimated:
Lcomp = c(1) + c(2) * Lcir + c(3) * secpt + c(4) * gass + c(5) *
prass + c(6) * cass (1)
Tech = c(7) + c(8) * Linvpct + c(9) * Lasso + c(10) * secft (2)
Issues = c(11) + c(12) * refbin + c(13) * Lass + c(14) * prass (3)
The variables are defined in Tables 1 and 4. L represents their
logarithmetic value, and c(*) is the coefficient to be estimated. The
list of instrumental variables we use represents the following
modification of the data set. All independent variables, such as
circulation, percentage of invited articles, and the index of
assistants, were excluded.
Our a priori knowledge of Equation 1 draws from the work of Lee and
Szenberg (1988), who used circulation as a prominent predictor variable for compensation, controlling for a variety of sponsorship variables
such as university, government, and association in the background. We
now attempt to improve that specification by keeping the sponsor in the
background as an instrumental variable, and by explicitly adding a set
of other effort variables.
The specification of Equation 2 is aimed at ascertaining whether
the journals are maintaining their technical formalism, considering the
recent call to be more pragmatic and business oriented. A validation of
this specification would tell us that the goals, as expounded in the
Journal of Economic Literature survey (COGEE, 1991), of keeping the
essential technical aspects of economics, while making it somewhat
user-friendly, would be asserted. We think that the technical journals
would most likely be the ones to search for the best article and not
necessarily invite an article. This has a two-pronged implication.
First, reaching out to persons specialized in their field can produce a
technical product. However, reaching out can also guarantee publication,
regardless of whether or not the product is scientific. Technical
journals would reach out to the more mature thinkers and, therefore, be
more affiliated with associate rather than assistant or managing
editors, and have a negative association with the percen tage of invited
articles.
Equation 3 is specified to account for the wide range of the number
of issues published by a journal, which, as Table 1 noted, may range
from 2 to 12 per year. As the average number of issues exceeds four per
year, the amount of work required to publish them is more challenging.
The potential increase in the number of issues would necessarily engage
the whole range of editors (associate, assistant, and managing), which
we combined into an index called "Lass," which should have an
overall positive effect. On one hand, the higher rate of production,
measured by more frequent issues, could justify the journals'
efforts to make payments to referees as well, and should also have an
overall positive effect. On the other hand, greater emphasis on
proof-reading would diminish the number of issues published, and have an
overall negative effect.
B. Results and Implications
The estimated coefficients and their statistical properties are
listed in Table 4, below. We obtained the best results using
simultaneous equations with the GMM estimating technique (Greene, 2000).
All the variables show significant t-values, which are mostly
significant at the 99 percent confidence level.
The result of Equation 1 is most striking. It demonstrates that the
elasticity between circulation and compensation to editors is 0.64,
almost double that of the earlier estimate of 0.35 in the Lee and
Szenberg (1988) study. On the one hand, part-time secretaries and
graduate assistants tend to reduce compensation. On the other hand,
proof-readers and copy editors enhance compensation, which would be
apparent if all those functions were consolidated in the same person.
We note here the manner in which this result can shed some light on
the issues considered in the Lee and Szenberg (1988) study, namely, that
rising journal costs, in turn, escalate the costs of library items. As
mentioned previously, if we interpret the predictor variables as a
dollar value vote for the journal, then we can make some implications
for pricing. Elasticity could be used to ascertain mark-ups above cost
under conditions of profit maximization. Defining Markup = (Price -
Cost)/Cost, and using the notion that marginal revenue, marginal cost,
and price are the same for profit maximization under perfect
competition, we obtain the optimal markup for the journals by the
formula: 1/(1-inverse elasticity) - 1. Because we are dealing with an
inelastic case, i.e., the elasticity for circulation is 0.65, the
formula will not allow a markup. To that extent it underscores the
earlier finding that journals do not escalate production costs of
library items. We note that while our conclusion did not change from the
previous study, the forces that enable it are different. Our results
have incorporated the state of the economy wherein the advent of the
Internet has put a downward pressure on costs, as we cited above.
The results of Equation 2 validate the hypothesis that technical
journals would be the most likely to have associate editors, and not
likely to invite articles. This provides a significant explanation for
the existence of technical journals in the face of rapid changes towards
the practical side of business. We can speculate that the conditions for
the existence of this state of affairs can be ascribed to the journals
being more user-friendly and keeping technical aspects contained in
their pages to the essentials. The rise of the Journal of Economic
Perspectives to the number one position illustrates this trend.
The signs of the results of Equation 3 are in accordance with what
we expected. On the one hand, the more the referees (Retbin) are
compensated and the higher the index of assistants (Lass), the more
likely the journals are to have multiple issues. On the other hand, an
emphasis on proofreading, or an equivalent increase in proofreaders,
slows down the frequency of journal publications, as hypothesized.
V. Conclusions
This paper sets out to revisit methods to rank and assess cost and
quality of economics journals via a statistical survey. The data allowed
a ranking from the production or supply side of the journals as opposed
to only the demand side ranking that was previously used in the
literature. We were also able to get significant estimates to validate
some hypotheses regarding editor compensation and the technical nature
of the subject. In particular, we found that the elasticity of
compensation with respect to circulation, i.e., 0.65, confirms the
finding in the literature.
Regarding quality, this article validates some propositions
discussed by the Commission on Graduate Education in Economics. The
results indicate that while there have been complaints that the subject
matter of economics has become increasingly technical, the journals have
not abandoned essential formalism in their content. The Journal of
Economic Perspectives' rise in rank to the number one position
supported this finding as well. The JEP has risen to fill the major
function of providing the specialist with a non-technical source to keep
abreast of the literature. Finally, the significance of the production
side viewpoint is underscored by the results of Equation 3, which show a
significant relationship between administrative efforts and a
journals' quality.
TABLE 1
Descriptive Statistics
Variables N Mean Min. Max.
1. Issues per Year (Issues) 92 4.848 2 12
2. Circulation (Cir) 85 4,855 200 80,000
3. Paid Subscriptions (Sub) 91 2,761 0 40,000
4. Pct.. of Invited Articles 84 19.92 0 100
(Invpct
5. Sponsor Binary (1 = Yes) (Spon) 89 0.7978 0 1
6. Associate Editors (ASSO) 92 7.15 0 40
7. Assistant Editors (ASSI) 92 2.359 0 41
8. Managing Editors (Mng) 92 0.7554 0 6
9. Part-time Secretary (SECPT) 92 0.5027 0 4
10. Full-time Secretary (SECFT) 92 0.1984 0 1
11. Technical Binary (1 = Yes) 89 0.5393 0 1
(Tech)
12. Other Assistants (OASS) 92 0.2609 0 2
13. Graduate Assistants (GASS) 92 0.375 0 10
14. Copy Editors (CASS) 92 0.4565 0 1
15. Proof Readers (Prass) 92 0.3098 0 5
16. Teaching Reduction (Teachcut) 90 0.553 0 25
TABLE 2
Rotated Factor Loadings and Communalities Varimax Rotation
Variable Factor 1 Factor 2 Factor 3 Factor 4 Factor 5
1. Issues -0.082 -0.648 0.242 0.276 -0.104
2. Cir 0.928 -0.000 -0.016 -0.029 -0.021
3. Sub 0.891 0.048 -0.024 -0.036 -0.119
4. Invpct 0.208 0.167 -0.625 -0.148 -0.188
5. Spon -0.226 0.043 0.003 0.321 0.287
6. ASSO -0.192 -0.419 0.353 -0.023 -0.49
7. ASSI 0.037 0.261 -0.298 0.194 -0.088
8. Mng 0.138 0.045 0.534 0.061 -0.111
9. SECPT -0.178 0.154 0.123 -0.423 -0.445
10. SECFT 0.016 0.188 -0.101 0.652 -0.102
11. Tech -0.027 0.121 0.733 -0.271 -0.036
12. OASS 0.694 -0.106 -0.022 0.103 0.238
13. GASS -0.040 0.003 0.133 -0.137 0.765
14. CASS -0.128 0.689 0.028 0.323 0.038
15. Prass -0.096 0.749 0.199 0.099 -0.081
16. T. cut -0.110 -0.350 0.3 12 0.138 -0.321
17. Refbin 0.028 *** -0.022 *** 0.069 0.735 -0.029
Variance 2.3683 1.9414 1.6732 1.6253 1.3666
% Var 0.139 0.114 0.098 0.096 0.08
Variable Communality/[h.sup.2]
1. Issues 0.572
2. Cir 0.863
3. Sub 0.812
4. Invpct 0.52
5. Spon 0.239
6. ASSO 0.578
7. ASSI 0.204
8. Mng 0.322
9. SECPT 0.447
10. SECFT 0.481
11. Tech 0.628
12. OASS 0.56
13. GASS 0.623
14. CASS 0.598
15. Prass 0.626
16. T. cut 0.354
17. Refbin 0.548
Variance 8.9748
% Var 0.528
TABLE 3
Ranking of Economic Journals Principal Component Method on Production
Characteristics
Rank Variables (Excluding Variables (Including Compensation)
Compensation)
1. Am. Journal of Agri. Econs. J. Economic Perspectives
2. Small Business Econs. J. Regulatory Economics
3. J. Scient. Beh. and Org. Finance Practice and Education
4. J. Urban Economics Eastern Economic Journal
5. Science and Society Journal of Env. Econs. and
Management
6. Review of RPE Journal of Urban Economics
7. The Antitrust Bulletin Journal of Macroeconomics
8. J. Human Resources Review of Black Political Economy
9. J. Public Economics Small Business Economics
10. Review of Social Economy J. of Economics
11. J. World Business Economic Perspective
12. J. Multinational Fin. The Accounting Review
Management
13. J. Cultural Economics Regulation
14. Review of Political Economy FRB Richmond Quarterly
15. J. Intl. Fin. Markets, Inst. Industrial Relation
16. The Energy Journal J. Future Markets
17. Regulation Canadian Public Policy
18. J. Env. Econs. and Management J. Public Economics
19. Finance Practice and Education Review of Regional Studies
20. Marketing Science Atlantic Economic Journal
21. J. Consumer Affairs Review of Social Economy
22. Car. Rochester Conf. Series on Growth and Change: AS. of Urb/Reg.
Pub. Policy
23. Social Science Quarterly The Energy Journal
24. Int. Trade and Public Finance J. Scientific Beh. and Org.
25. J. of Regulator Econs. Review of Radical Poll Econ.
26. Review of Agri. Economics Economics of Education Review
27. Rand Journal of Economics Intl. Adv. in Economic Research
28. Economics of Education Review J. Development Economics
29. Growth and Change: a J. of Am. J. of Agricultural Economics
Urb/Reg.
30. Ecological Economics J. Empirical Economics
31. Explorations in Economic Intl. Trade and Public Finance
History
32. J. of Health Economics Economic Development Qrt.
33. Economic Development Qrt. Resource Policy
34. Review of Black Political J. Intl. Fin. Markets, Institutions
Economy
35. Industrial Relations Agri. Economics
36. Economic Policy Review J. Multinational Fin. Management
37. J. Asian Economics Exploration in Economic History
38. J. Transnational Mgt. Journal of Cultural Economics
Development
39. Review of Industrial Russian and East European Finance
Organization and Trade
40. Papers in Regional Science Journal of Health Economics
41. J. Health Policies Policy and Review of Industrial Organization
Law
42. Human Resource Development Qrt.
43. J. of Macroeconomics
44. J. Labor Economics
45. Russian and E. European Fin.
and Trade
46. Population and Dev. Review
47. Resource Policy
48. J. Futures Markets
49. Canadian Public Policy
50. J. of Policy Modeling
51. National Tax Journal
52. Canadian Public Policy
53. J. of Development Economics
54. The Canadian J. Regional
Science
55. The Accounting Review
56. Economic Development and Cull
Change
57. Agri. Resource Econ. Review
58. J. Intl. Business Studies
59. Economic Perspectives
60. Review of Regional Studies
61. J. of Economic Perspectives
62. FRB Richmond Econ. Qrt.
63. Intl. J. of Qual. and Rel.
Mgmt.
64. J. Empirical Finance
65. Atlantic Economic Journal
66. Intl. Advances in Economic
Research
67. J. Money Credit and Banking
68. J. of Political Economy
69. J. of Economics, MVEA
70. Eastern Economic Journal
71. Economic Inquiry
72. Finance and Development
TABLE 4
Generalized Method of Moments: Simultaneous Equation Results
Log (Compensation)
Description Equation 1 t-Values
Constant Terms 5.04 (4.71)
Log (Circulation) 0.64 (4.42)
Part-Time Secretaries -0.31 (-1.82) **
Graduate Assistants -0.21 (-5.08)
Proofreaders 0.38 (3.25)
Copy Editors 1.07 (3.94)
Log (Invited Articles)
Log (Associate Editors)
Full-Time Secretaries
Referees
Compensation
Index of Assistants
Proofreaders
Observations 47
R-Square .28
D-W 2.62
Technical Journals Number of Issues
Description Equation 2 t-Values Equation 3 t-Values
Constant Terms 0.80 (4.24) 1.31 (24.60)
Log (Circulation)
Part-Time Secretaries
Graduate Assistants
Proofreaders
Copy Editors
Log (Invited Articles) -0.15 (-2.92)
Log (Associate Editors) 0.11 (1.63) *
Full-Time Secretaries -0.34 (-2.48)
Referees 0.18 (2.06)
Compensation
Index of Assistants 0.058 (2.13)
Proofreaders -0.11 (-2.53)
Observations 44 80
R-Square .15 .06
D-W 2.42 1.47
Note: * t values are at the 90% confidence interval
** t values are at the 95% confidence interval
All the other t values are significant at the 99% confidence interval
Notes
(1.) The American Economist was excluded from the survey to avoid
any appearance of biasing the estimates.
(2.) A negative loading should be interpreted with a negative
connotation, i.e., with the preamble that the "respondent tends not
to..." As a general rule though, "...it is customary to
'reflect' (change all) the signs of a factor on which the
highest loadings are negative. As long as all the signs in the column
are changed, it is the absolute size of the loadings, rather than the
signs, that count" (Wells and Sheth, 1974, 2-458). The columns with
the three asterisks are so adjusted.
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Lall B. Ramrattan * and Michael Szenberg **
* University of California, Berkeley
** Lubin School of Business, Pace University, New York, NY 10038,
Email: mszenberg@pace.edu