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HB31
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DEWEY
13
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
EVOLVING STANDARDS FOR ACADEMIC PUBLISHING:
A q-r THEORY
Glenn
Ellison, Massachusetts Institute
of Technology
Working Paper 00-13
July
2000
Room E52-251
50 Memorial Drive
Cambridge, MA 02142
downloaded without charge from the
Social Science Research Network Paper Collection at
http //papers ssrn com/paper taf?abstract_id=XXXXXX
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TECHNOLOGY
LIBRARIES
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
EVOLVING STANDARDS FOR ACADEMIC PUBLISHING:
A q-r THEORY
Glenn
Ellison, Massachusetts Institute of
Technology
Working Paper 00-1
July 2000
Room E52-251
50 Memorial Drive
Cambridge, MA 02142
downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssrn. com/paper. taf?abstract_id=XXXXXX
This paper can be
Evolving Standards for Academic Publishing:
Glenn Ellison
A
q-r
Theory
1
Department of Economics
Massachusetts Institute of Technology
.-v
June 2000
would like to thank the National Science Foundation (SBR-9818534), the Sloan Foundation
and the Center for Advanced Studies in the Behavioral Sciences for their support. I would like
to thank Robert Barro, John Cochrane, Ken Corts, Drew Fudcnberg, John Geanakoplos, Robin
Pcmantlc, Gary Saxonhonsc and various seminar audiences for helpful comments and Christine
Kiang and Nada Mora for outstanding research assistance.
J
I
Abstract
This paper develops a model of evolving standards
for
academic publishing.
It is
mo-
tivated by the increasing tendency of academic journals to require multiple revisions of
articles
and by changes
in
quality dimensions: q and
the content of articles. Papers are modeled as varying along two
r.
The former
represents the clarity and importance of a paper's
and polish. Observed trends are regarded as
increases in r-quality A static equilibrium model in which an arbitrary social norm determines how q and r are weighted is developed and used to discuss comparative statics
explanations for increases in r. The paper then analyzes a learning model in which referees
(who have a biased view of the importance of their own work) try to learn the social norm
main ideas and the
latter its craftsmanship
from observing how their own papers arc treated and the decisions editors make on papers
they referee.
The model
predicts that social
increasingly emphasize r-quality.
JEL
Classification No.: A14, D70,
C73
Glenn Ellison
Department of Economics
Massachusetts Institute of Technology
50 Memorial Drive
Cambridge,
MA
02142-1347
norms
will
gradually but steadily evolve to
Introduction
1
I
encourage potential readers of this paper to
first
put
it
down
for
through a thirty- or forty-year-old issue of an economics journal.
convey much better than
much
longer.
1
2
longer introductions.
They have
have more sections discussing extensions of the main
The
anticipate that this will
I
can how dramatically economics papers have changed over the
I
few decades. Papers today are
last
two minutes and thumb
results.
They have more
They
references.
Around 1960
process by which papers get published has also changed dramatically.
the Quarterly Journal of Economics reserved the "revise-and-resubmit" option for five or
so special cases per year.
submit
their papers,
about nine months.
takes 20 to 30
receive reports,
Today extensive
months
similar experiences.
they have received
at
I
and get a
final
norm and
in
let
still
authors
acceptance within
getting an acceptance
disciplines
have had
academic journals arc widespread and dramatic,
field
this reflects that the
changes have occurred
see only a small part of the overall picture.
develop a model to organize the observed trends and help us think about
potential explanations.
as differing along
revisions
revisions arc the
Perhaps
attention.
gradually and that researchers in each
In this paper
make
most top journals. 4 Many other academic
While the changes
little
most journals' processes
In the early 1970's
My
central premise
is
that
two quality dimensions: q and
r.
we can
I
academic papers
usefully regard
think of q as reflecting a paper's
main
ideas and r as representing other aspects of quality described by words like craftsmanship,
thoroughness and polish.
phenomenon
of a single
I
think of the various changes noted above as different aspects
— an increase
in the r-quality of published papers.
an equilibrium model of time allocation and quality standards and use
'Ariel Rubinstein's 1982
is
Econometrica
article, "Perfect
shorter than the average note in Econometrica in 2000
For example,
Amartya Sen's "The
Equilibrium
(if
in
it
I
first
develop
to discuss
what
a Bargaining Model," for example,
one accounts
for the
type
sizes).
Impossibility of a Paretian Liberal" and two other papers in the
January- February 1970 issue of the Journal of Political Economy had one paragraph introductions. No
introduction in the Feburary 2000 JPE was shorter than seven paragraphs and two were longer than Sen's
entire paper.
An extreme example here is Michael Spence's 1973 QJE paper "Job Market Signaling." It contains two
While my anectodes all relate to classic papers, old journals also contain many derivative papers
references.
making
N
'
oider contributions to long forgotten literatures. These also look very different from today's
papers.
''The one exception is the QJE where
on the duration of review process.
it
takes about 13 months. See Ellison (2000) for
much more data
might cause such an increase.
I
then develop a dynamic learning model
in
which economists
struggle to reconcile the high standards to which they arc being held with the mediocrity
they see
of their
(This occurs in part because economists have biased views of the quality
in journals
own
The model
work.)
predicts that social
norms
will
evolve gradually to emphasize
r-quality.
I
begin in Section 2 with a quick look at some data on the form of papers and the length
of the review
and revision process
in a
number
of disciplines.
Section 3 describes a static equilibrium model of the journal publishing process.
continuum of economists are endowed with one unit of time
in
which to write one paper
A
for
the one journal in the profession. Papers are described by their position along two quality
dimensions, q and
of the
main
r.
interpret the q dimension as reflecting the clarity
I
results of the paper,
and the
dimension as reflecting various other aspects
r
that are typically improved
of quality (generality, robustness checks, extensions, etc.)
and when authors "polish" papers prior to submission.
in revisions
economists make
on
r-quality.
how
is
to divide their time
A commonly
and importance
The main
decision
between the developing new ideas and working
understood social norm determines how the quality dimensions
arc weighted.
I
analyze the static model in Section
produces a reasonable outcome. Papers
4.
For a range of parameter values the model
initially
submitted to the journal can be divided
into three groups. Papers with the lowest q are determined to be of sufficiently low interest
that no feasible revision could
papers with intermediate
possible, but only
make them
q's are
acceptable.
if
Finally,
make two main observations about
are possible.
spend most of
spend very
If
the
their
little
A
second set of
papers with a sufficiently high q
they achieve a somewhat lower
always able to meet the revision standard that
I
are not revised.
marginal. These papers are revised to the greatest extent
some become acceptable.
be publishable even
They
is
r.
set for
The authors
of these papers are
them.
the static model. First, a continuum of social
community agrees that
^-quality
time developing main ideas.
If
is
will
norms
very important, then authors will
r-quality
is
very important, then authors
time on ideas and focus on revisions. Nothing in the model prevents either
extreme or something
in the
middle from being an equilibrium. Second, the marginal papers
that
fall
just short of being accepted arc relatively low in (-/-quality
/•-quality relative to the set of
that a paper's q-quality
The model makes
is
resubmitted papers. This
developed
and revisions
first
number
clear that a
is
and
a consequence of the assumption
later increase r.
of equilibrium comparative statics explanations
could be given for increases in r-quality. Such explanations, however,
in practice.
them
The observed changes
economics and other
in
requires cither a large change in
outcome
My
to an exogenous variable.
relatively high in
some exogenous
fields
may
not work well
are large. Accounting for
variable or a high sensitivity of the
impression from the empirical work I've done
the economics profession has not changed
much
is
that
over the last thirty years. (Ellison, 2000)
Equilibrium explanations arc also hard to reconcile with editors' comments that changes
were not planned or desired.
explanations
— to account
I
for
take these difficulties as motivation for exploring evolutionary
observed changes such an explanation only need sto provide
a good reason to think that each year papers
be a paragraph longer and require a
will
couple weeks more to revise than the year before.
Section 5 describes a dynamic learning model.
journal's referees
(who arc
also the authors).
The main
The
actors in the
model arc the
referees are not self-interested.
They
simply try to apply the prevailing standards of the profession in weighting 7-quality and
r-quality and in proposing a set of
improvements that would bring a paper up to the pub-
lication threshold. Referees learn the prevailing standards
of
what
revisions they arc asked to
from two sources: observations
make and observations
of
whether editors eventually
decide to accept or reject papers they have refereed. Editors are not an active force in the
model. They simply
fill
the journal's slots by accepting the fraction r of papers with the
highest average quality (weighted according to the then prevailing
model of a busy
editor.
Making
referees the driving force
comments that they abhor the trend toward
fifty
is
norm).T view
this as
a
also consistent with editors'
page papers with myriad extensions and
wish that authors would just concisely explain what ideas they have.
Section 6 discusses the dynamic model with no overconfidence bias. All of the equilibria
(if
the static model are steady-states.
standard that
is
I
note that
if
infeasibly high, then economists will
referees try to to hold authors to a
both realize that overall quality stan-
dards arc lower than they had thought and conclude that r-quality must be relatively more
important than they had thought. The latter inference
is
papers that are unexpectedly accepted are relatively low
made because
in q
and
the submarginal
relatively high in
r.
Section 7 adds in the assumption that economists are biased and think their work
than
slightly better
it
really
is.
5
The former
steady-states of the model are destabilized
as referees try to hold others to the higher standard that they perceive
to their
own
papers.
Standards can not stray
is
being applied
from the equilibrium set
far
- -
referees
would see editors accepting many papers they strongly recommended against and
would overwhelm the
What happens
e bias.
authors to a standard that
instead
is
about how economists rationalize standards that are too high
still
gradual evolution of social norms to increasingly weight r-quality.
them a candidate
the dynamics makes
for
is
good enough
There has been
notable
is
little
to
make
its
all,
tastes.
The
focus
model
is
The
result
is
The slow steady form
a
of
because the dynamics change once
work on the dynamics of standards. The most
in
which a
admission to a club. (One could think of publishing
have heterogeneous
applies.
acceptance a sure thing.
related theoretical
Sobel's (1998) analysis of a
of the previous section
explaining observed trends. In the long run the
process stops short of papers having no q-quality at
no paper's idea
this
that referees perpetually try to hold
The observation
slighly too high.
is
is
on how
series of
in
candidates work to obtain
a journal as an example.) Judges
different voting rules lead to rising, falling
or fluctuating standards.
The
general
fact that
title
I
have not to followed the current trend and given this paper an overly
and a seven page introduction should not be taken to indicate that there are not
broader lessons to be learned from
for politeness,
standards
for
it.
There are
all
kinds of social norms,
language and violence on television, hazing at
hours worked by young doctors and lawyers, years spent
of grades, etc.
Many
of these
e.g.
in
standards
fraternities,
higher education, distributions
norms have commonly perceived
trends, but other than the
In the psychology literature this is referred to as an overconfidence bias. An often discussed example is
Svenson's (1981) finding that about 90 percent of the U.S. college students in his study estimated themselves
to be safer (and more skillful) at driving than the median subject. Psychologists have reported that experts
many fields are overconfident in assessing their own ability to answer questions. Lichtenstein, Fischoff
and Phillips (1982) piovide a nice (but early) survey. Overconfidence is frequently mentioned in finance to
motivate the existence of agency problems and to justify the actions of noise traders as in De Long et al
in
(1990). Odean (1998) is a notable recent contribution with a detailed summary of psychology and finance
papers on overconfidence. Rabin (1998) discusses a number of other psychological biases and their relevance
to economics.
literature on fashion cycles, e.g.
Kami and
of the existing literature on social
Schmeidlcr (1990) and Pesendorfcr (1995), most
norms doesn't focus on change.
conclusions about other norms from
my
My
results.
view
should be expected and
On
a theoretical
level,
if
so in
what
will
not try to draw
that one would need to analyze
is
each application separately and think about how the norm
drift
I
is
learned to assess whether a
direction.
the paper's innovation
to note that
is
one can produce a model
that explains a long gradual trend by making a slight perturbation to a model with a
continuum of
equilibria.
penetrating question:
In an early presentation of this paper
'so arc
you trying to
tell
us that you're going to explain a thirty-year
trend by saying that we've been out of equilibrium the whole time?'
hope to convince readers that models of the type
Some data from
2
Table
1
The
table
lists
long as they were twenty
long
how
"Yes!"
I
possible.
the form of an academic article has
number
five
many
years ago and have about twice; as
of references for
now than
in 1975.
The
references. Jn almost
increases are
Likewise with the exceptions of law and history, articles
references.
way
is
make such arguments
the average page length and the average
papers seem to be longer
the sciences.
more
answer
top journals in a number of disciplines. Economics papers arc roughly twice as
articles in
all fields
introduce
I
My
various disciplines
provides some statistical evidence on
changed.
Robert Barro asked a
more moderate
now tend
While economics has experienced substantial reference growth
to go to catch
many
in
to have
it
has a
social sciences.
Table 2 provides some evidence on how long
extensively they are revised for publication in a
takes longer to get a paper accepted
now than
it
takes to review papers and on
number
it
of fields.
did in 1975.
how
In almost every case
it
While Econometrica and
the Review of Economic Studies have the most drawn out publication processes
among
the listed journals, similar trends are visible in computer science, psychology, statistics,
linguistics
and
finance,
and
I've
been told that
many rounds
at the top journals in marketing, political science,
A
slowdown
is
also visible in
some
sciences, but the
of revisions are also the
and a number of other
time scale
is
norm
social sciences
completely different.
The
3
model
static
In this section
describe
I
a.
simple static model of academic publishing.
The main
the model are a continuum of economists (of unit mass). Each economist
one unit of time and
may
mass r of papers with
and
leisure time,
i.e.
write one paper. There
<
r
<
is
is
endowed with
one economics journal that publishes a
Economists preferences arc lexicographic
1.
actors in
in publications
they attempt to maximize the probability of publishing an article in
the journal; holding the probability of publication fixed they prefer more leisure to
Papers can be
dimension
is
fully described
by two dimensions of
quality, q
and
The
r.
less.
g-quality
intended to reflect the inherent importance, interest, clarity etc. of the main
ideas of the paper.
The
r-quality dimension
when they
quality that authors improve
paper's exposition, to
make
is
intended to
aspects of
reflect additional
arc asked in revisions to improve and tighten a
clear relationships to other papers in the literature, to generalize
theoretical results, to check the robustness of empirical results, to extend the analysis to
consider tela ted questions, etc.
norms
Social
Under the
aq +
(I
(a, z)-social norm.,
— a)r >
z.
papers arc regarded as worth of publication
The parameter a may
addition to reflecting what people think
while he feels that a particular high
failure to
The
it
make
should
r
still
q,
two
reflect
makes a paper
people think authors should be required to do.
in a journal,
common and commonly known.
papers are assumed to be
for evaluating
different value
valuable,
it
if
and only
judgements.
can also
reflect
is
"better" than the marginal paper
improvements required of everyone
is
While the model
illustrated below.
a.t
else.
moment
the
is
described as a four
the authors are the only ones
acting in a nonmechanical way.
1
t
=
3
Economists
Referees
Economists
Editors
choose
assess q
choose
say
q
e
[0, l]
what
For example, a referee might argue that
low r paper
step process with three groups of players,
t
In
be rejected because the good idea does not excuse the author's
timeline of the model
t=
if
report r(q)
tr
e
[o, i
-
g
yes/ no
In the first stage of the model, authors choose the fraction
t
G
q
devote to thinking up and developing the main ideas of the paper.
~
of q-quality q
t
q
F
F
Assume that
F(q\t q ).
is
Natural specifications
infinite).
mean
t
q
The
a paper
will
rn(t
[0,
result
q )]
t
is
and
q
each
>
(with m{t q )
t
q
.
or exponentially
[0, t q ]
.
model authors submit
In the second stage of the
their papers to the journal.
journal's referees correctly assess the quality q of the paper and report that
acceptable for publication
if
and only
authors are able to revise
if
aq +
quality of at least r(q) as defined by
r(q) as a
for
have the q distribution increasing in
For example, q might be assumed to be uniformly distributed on
distributed with
time to
continuously differentiablc in
has an everywhere positive density f{q\t q ) on the interval
being possibly
[0,1] of their
(1
—
a)r(q)
=
z.
it
it
The
will
be
and achieve an
r-
In practice one can think of
measure of the number of improvements rcfereees ask
for in their reports
and the
difficulty of the tasks.
amount
In the third stage authors choose the
revisions.
r
=
h(t. r )
The production
+
Assume that
h!
>
and
assume
where
rj,
is
77
of /--quality
a
random
again a
is
<
0.
To ensure
also that h'(0)
=
00,
random
tr
[0, 1
(E
is
—
t
to
q\
process. Specifically,
spend on
assume that
with a
>
0.
a decreasing returns activity with h(0)
=
0,
variable uniformly distributed on
the production of revisions
h"
of time
[0,
a]
that time will be allocated to both dimensions of quality
and
h'(l)
=
I
0.
which aq
In the fourth stage, editors accept the fraction r of papers for
+
(1
— a)r
is
highest for publication.
An
equilibrium of the model
is
a quadruple, (a,z,t*,t*(q)) such that
chosen to maximize the probability that aq
there are multiple choices that yield the
fraction of papers with
social norm,
4
if
aq +
(1
- a)r >
there exist choices of
t
q
+
(1
- a)r >
and
is
exactly
t r (q)
for
r.
I
and
t*(q) are
z (and are as small as possible
same probability
z
r*
of publication)
and such that the
will refer to (a, z) as
which
(a, z, t q
,
tr
if
(q)) is
a consistent
an equilibrium.
Analysis of the static model
In this section
I
analyze the model described in the previous section.
main observations.
First,
many
different social
norms
arc possible.
I
wish to highlight two
Second, the marginal
accepted papers tend to have relatively low ^-quality and relatively high r-quality
in the
universe of published papers.
Characterization of equilibrium
4.1
The
analysis of the equilibrium
an equilibrium
leisure, at t
3 authors will devote
r-quality unless the paper
less
time
a straightforward backward induction argument. Consider
Because of the lexicographic preference
(a, z, t* t*{q))-
=
is
all
of their remaining time to improving their paper's
sure to be rejected
is
for publications over
anyway
or
sure to be accepted even
is
if
devoted to revisions. As a result we have,
is
Proposition
In any equilibrium of the model,
1
q={z-{\- a)h{\ -
Then,
t*))/a.
q<q
let
q
=
h- l ((z-aq)/(l-a))
(For this proposition, define h~ (x)
Note that
may
q
the support of
be
less
Hence,
q.
it
is
=
if
—
(1
— a)(h(l — t*) + o~))/a and
and
(0
[
(z
x
<
if
q<q,
if
q
<
q.
0.)
may
than zero and q
be greater than the upper bound of
may
possible that either of the extreme cases
not arise for
particular parameterizations of the model.
In the first stage, the time
will
t
q
allocated to trying to develop the
main
ideas for a paper
be chosen to maximize the probability of eventual publication. Write G{z\t)
probability that
aq +
(1
— a)r
is
at
most z when
above proposition. Note that this probability
set equal to
1
—
t
q
.
G(z:t)
is
a fixed
t.
G
is
is
chosen optimally as in the
the same as
it
would be
q
maxfl,-
uniformly continuous in z and
strictly
and
rr
t,
t
if t r
was simply
Hence,
G(z;t)=J_
Note that
is
=
for the
between zero and one. Write
The equilibrium time
allocation
is
L
a
It is strictly
t.
G~
i
)f(q\t)dq
increasing in z whenever
{p;t) foi the inverse of this function for
easily described by
Proposition 2 In
any
the first stage of
the time allocated to developing q-
equilibrium.,
quality satisfies
t*
G Argm.axt G~\\ -
r\t).
Proof
In equilibrium, each economist's
satisfy G(z;t*)
=
(1
-
r).
If r*
<
accepted with probability
is
does not belong to
Argmax
£
G -1 (l
G _1 (l — r;t) > G _1 (l - r;
does maximize that expression has
increasing in z whenever
paper
G(z;
t)
which contradicts the optimality of
<
1.
t.*)
this implies that G(z,
-
=
t)
r.
Hence, z must
r;t), then
Because
z.
any
t
which
G is strictly
< G(G _1 (1 —
t; t))
=
r,
t*.
QED.
Some examples
4.2
Figure
1
illustrates the distribution of
case generated by assuming that t
for r
production
has a
=
0.5
and
is
h(t r )
=
y/t T
—
=
tr
paper qualities
03, q
is
in
a "typical" equilibrium
uniformly distributed on
/2 with a
=
0.2,
and the
social
[0,
r
9 ],
—
in this
the technology
norm forjudging papers
z as 0.504.
For those parameters, the equilibrium effort allocated to q production turns out to be
t*
~
All three possible
0.S2G.
g-quality less that q
~
outcomes of a submission occur.
0.48 realize that their papers have no chance of becoming acceptable
and do not attempt to revise them. Authors of papers with
as
much time
as possible to revising (setting
tr
=
1
—
t*
accepted with probability strictly between zero and one.
q G
[<?,
papers
m(tq)
will
The
—
t*]
Authors of papers with
x
[0.68,0.83]
%
€ (q,q)
q
0.174)
(0.48,0.68) devote
and have
their papers
Authors of papers with quality
do the minimal revision necessary to ensure that their
be accepted with probability one.
figure
shows the outline of the support of the equilibrium distribution of paper
qualities in (q, r)-space.
Paper qualities are distributed with a constant density within
these regions. Papers in the lower
papers are never accepted.
left
The upper
box are those
right region
is
for
which authors set
upper region
is,
of course, r.
tr
=
0.
These
divided into a triangle of papers thai
are revised then rejected and a trapezoid of papers that are accepted.
in this
~
The mass
of papers
.
0.6
h(l-t*)+o
\
Revised
but -
mi-*:)
rejected
--
Accepted
papers
N
N
o effort
at revision
—
9
Figure
The
1:
q~U[0,t q
:
The form
=
as
much time
0.2,
a =
q
1
q
seems to
compared
=
0.3,
0.5, z as 0.504.
reflect fairly well
observation I'd like to make'
relatively low ^-quality
The marginal
=
y/i-t/2, a
of the equilibrium
One
journal
q
equilibrium distribution of paper qualities in a "typical" equilbrium: r
h(t)
\
1
1
t*
the functioning of an economics
that the "marginal'
is
to the pool of accepted papers
—
-
7
rejected papers have
they
all
have q £
[q,q\.
rejected papers are not relatively low in /--quality. Their authors have spent
as possible revising
and achieved r-qualitics that are on a.verage superior to
those of accepted papers.
While
I
think that the case illustrated above
quent arguments focus on
authors set
tT
=
t*
the primary one of interest and subse-
the equilibrium can take other forms for different parameter
Most notably, when a
values.
all
it,
is
is
— there
sufficiently small
(i.e.
g-quality
is
of
its
The
eventual acceptance a sure thing.
for
such a case: q
~
U[0,
t
is
good enough to
following proposition formalizes this obser-
paper qualities and the acceptance
vation. Figure 2 graphs the equilibrium distribution of
and rejection regions
importance)
always be some chance that any idea, no matter how
will
vacuous, can be developed into a publishable paper and no paper's idea
make
little
q ],
= v^T —
h(t r )
tr
/2,
o
=
0.2,
a =
0.2
and
finite
and
z« 0.532.
Proposition 3 Suppose
uniformly bounded for
t*{q)
=
1
—
t*
for
all
that the upper
all
q 6
t
q
E
[0, 1].
[0, rn.(t*)],
bound of the
q- distribution,
Then, there exists
i.e.
all
a >
m(t q ).
such that for
is
all
a €
(0,
a),
papers are reuised to the greatest extent possible
10
h{l-t*)
+o
Accepted
papers
0.6 -•
h(i-t;)
Revised
but
rejected
t*
q
Figure
T
=
2:
0.3, q
An example
~
q
\
a" equilibrium:
of the equilibrium quality distribution in a "low
U[0, t q ), h(t)
and no paper achieves
q
=y/i-
t/2,
a =
a =
0.2,
0.2, z tv 0.532.
a level of q- quality sufficient to ensure that
it
will be accepted with
probability one.
Proof
To
see that q
<
note that
if
a paper with q
and gets the best possible draw on r-quality
=
is
revised to the greatest extent possible
its overall
quality will be (1
— a)h(l —
t*)
+ a.
In equlibrium,
Probjary
+
(1
- a)r >
(1
-
a){h(l -tl)
7
+ a)} <
Prob{r >
a
<
1
For
a
sufficiently small the expression is less
of the paper with q
=
than
r,
Ml -
—>
•m{t*)f<j
q'
-a
+a
1
as
q —
»
-m(t*)}
H
—a
0.
'"
and hence there
is
a positive probability
>
m(t*) note that
if
a paper with g-quality m(t*)
the greatest extent possible but gets the worst possible draw on r-quaHty
+
(1
- a)h(l -
Pvob{a<7+
(1
- a)r > am(i!) +
am{t*)
¥
being acceptable.
Similarly, to see that q
level is
tl)
t*)
revised to
is
its overall
quality
and
(1
- a)Wl -
t*)}
>
Prob{r > h(l -
t*)
H
+
1
>
<xm(t* )
1
q
cr(l-a)
11
1
as
a
—a
-»
0.
H
Hence,
the best r
<
any r
for
is
the probability that a paper with g-quality m(t*)
1
strictly positive
a
if
is
fails
to be
among
sufficiently small.
QED.
Some
of the results
I'll
give later will
the statements of these results
I
depend on the form
will give the
To
of the equilibrium.
simplify
forms pictured in the figures (and a couple of
other forms) names.
Definition
q
It
1
< m(t*} and
r(m.(t.*))
>
has the "som.ewhat low
0<q<q<
an equilibrium
/ will say that
0.
An
a"
form, if
m(t*) and r(m(t*))
The somewhat low a form
is
"typical" or has the typical
is
a"
equilibrium, has the "low
<
<
<
q
m,(t*)
<
q.
form,
It
is
if
<
q
if
<
<
m(t*)
q
<
<
q.
a" form
"high
of the
if
0.
similar to the low
a
form, with the only difference being
The
that in the former authors of the lowest q papers do not revise their papers.
is
form
similar to the typical form, but the highest q papers are so
good that
r(q)
high,
a form
negative,
is
i.e.
they revised the paper to
make
it
be publishablc. The authors of these papers obviously exert no
effort
on revisions and have
referees
tell
die authors that even
if
their papers accepted with quality to .spare. In the
a
—
0.2
and r
=
0.3 the equilibrium has the low
low a form for
a G
high a form for
a £
a form
for
(0.2286,0.3363), the typical form for
(0.5870,
1).
q
if
the distribution of q
is
~
a €
U[0,
t
q \,
would
it
h(f)
=
still
\/i—
r/2,
somewhat
(0,0.2285), the
a €
In other specifications for the
take on other forms. For example,
will
model with
worse
(0.3364,0.5869) and the
model the equilibrium can
unbounded
(or r
is
large)
we
simultaneously see papers of the lowest g-quality being resubmitted and papers of the
highest g-quality being accepted with no revisions.
4.3
In the
The
multiplicity of consistent social
model described above not
all
norms arc
social
in the journal for a small fraction of papers,
Thi.v however,
community
is
really the only constraint.
norms
consistent.
If
there
is
only room
then the quality threshold z must be high.
.Nothing in the model restricts the weight the
places on 7-quality versus r-quality. There are a continuum of consistent social
norms with any a being
possible.
The
following proposition gives a formal statement to this
12
effect,
h{t)
=
and Figure
s/i.
-
t/2,
3 graphs the set of consistent social
a
=
Proposition 4 In
0.2
=
and r
is
for the
model with
~
q
U[0,
t
q ],
0.3.
the m.odel described above, for
such that (a,z*(a))
norms
any a 6
[0, 1]
there exists
an unique z* (a)
a consistent social norm,.
Proof
For any fixed a,
Because
for all
G
is
z*(a) to H(z)
It is
G{z;t) be the
uniformly continuous,
is
II
t,
let
continuous with H(0)
=
1
—
t.
(a, 2*(q))
is
CDF of aq+(l-a)r
t is
an agent setting
t.
q
H(z)
=
inf t G(z;t).
chosen from a compact set and lim 2 _4oo G(z;
=
and lim z _oo^(z)
=
1.
Hence there
t)
—
1
a solution
is
a consistent social norm.
not possible for both (a, z) and (a,
In that case,
as above. Let
z')
to be consistent social
norms with
z
equal to the the equilibrium choice under the (a,z')
would surpass the z threshhold with piobability greater than
<
z'.
norm
r.
QED.
z
i
0.5 --
I
Figure
r
=
3:
0.3.
Consistent social norms (a, z) in the model with q
and a
=
Explanations
My
view of the trends
for
in
observed increases
=
y/t
-
t/2,
clear that a
in /-quality
economics papers mentioned
be thought of as aspects of an increase
makes
U[0,t q ], h(t)
0.2.
4.4
all
~
a
number
in
in the
introduction
is
that they can
the r-quality of published papers.
The model
of different explanations for such a change are possible.
13
The explanation
published papers
I
focus on in the latter half of this paper
will increase
if
a
decreases,
i.e.
if
norms
social
that the r-quality of
is
shift to place; relatively less
emphasis on q-quality and relatively more emphasis on r-quality. This raises the r-quality
of published papers for
two reasons: economists react by allocating more of
their time to
producing r-quality; and when choosing from the pool of resubmitted papers the journal
places
more emphasis on
r-quality.
Other plausible explanations do not require a change
and
One
r.
is
in social
that the technologies for producing q and r
norms
may have
shifted over time. For
example, one could argue that economists have begun to exhaust the set of
and model
change
this as a
in F{q\t q ) that
one could argue that advances
in
latter explanation
reducing r has two
A
q
Similarly,
.
second potential explanation
may have become more
is
competitive.
not straightforward, so
First,
effects.
it
I'll
discuss
more
allows the journal to be
from the pool of resubmitted papers. Second,
of
f
We
is
that
might think of the
in r.
and
this
might
standards in both dimensions. 6
raise quality
If
possible ideas
computer technology or accumulated knowledge allow
growth of the profession and other factors as equivalent to a decrease
The
all
reduces the marginal benefit of
authors to produce more r-quality per unit time.
publishing in the top journals
for trading off q
it
affects authors'
it
Intuitively,
further.
selective
when choosing
time allocation decisions.
authors react to increased competition by gambling on bold projects that require a
t.
q
.
the second effect could offset the
first
and make the
overall effect of competition
lot
on
r-quality ambiguous.
Formally,
C _1 (l — r;
is
t
q
)
should note
I
first
that nothing in the assumptions so far guarantees that
(which plays the role of the economists' objective function when
quasi concave.
If,
for
example, q
~
[/[0, kt?}\
with n
>
1,
a discussion as
by
just
I
t* will
change discontinuously
in the
Ellison (2000) notes that
moderate, but that decreases
is
such that
t*
is
the
relative status ol the top journals
number
may have
I
To provide
will avoid
in the profession
also contributed to
will
as simple
such complications
t)
=
over the last 30 years has been
some top journals and an increase in the
a more substantial increase in competition.
of articles published by
14
selected)
the unique solution to ^(z*(a.r);
by many measures the growth
in
is
and some higher value of t q
parameters.
can of the potential effects of r on r-quality,
assuming that F(q:t)
q
then the production of g-quality
would involve increasing returns. In some cases, both both
be local optima and
t
among, values of
standard
is
which G{z*{a,r)\f) <
for
t
strictly
concave at the optimum,
and that the probably of achieving the
1
T (z"(a,T):t*) >
i.e.
0.
^gj
Recall that t*{r) solves
dG
~(z*(r);t*q (r))=0.
dt
Differentiating with respect to r gives
z*
is
always decreasing
in
r and we have assumed that ^p~
§^§i{z"'{r);t*(T))
<
To think about the
decreasing in r
if
that |J(z;
the density of the overall quality distribution.
t
q
is
)
0.
more spread out when authors spend more time thinking
of r-quality
is
which case the Jj^f
negative. In this case,
is
the overall effect of r on r quality
For
a.
more
is
q.
is
is
marginal
rr
new
t* will
ideas
more
functional form like F{q\t q )
sensitive to
t
q
tT
only shift the
for a
mean
be decreasing
increase as r decreases, and
authors setting a times the effect of
When
the journal
is
is
~
more
t
q
cm
their luck being
highly nonselective,
When
the journal
on getting nearly as a good a draw as possible on
(7[0,
t
q ],
the higher percentiles of the q distribution
investcments. Hence the return to
on the paper being marginal
be
and the production
conditioning on getting a very bad draw from the q distribution.
With a
will
the q distribution becomes
on r-quality conditional on
the journal.
for
extremely selective, the conditioning
are
t* reflects
- a) times the effect of
(1
such that their paper
this
If
for the density to
is
t*
may be ambiguous.
direct intuition note that
q-quality equal to
outcome
Hence,
sign of this derviative note
a more deterministic: process in which increases in
r-quality [as we've assumed), then the natural
in tg, in
of
positive.
is
t
q
is
greater
when one conditions
selective journal.
Figure 4 illustrates the effects of changes in r on time allocation and quality in a model
with q
~
(7[0,fJ, h{t)
= Vt -
monotonically decreasing,
right panel
shows the
i.e.
t/2,
/*
effect of r
a
=
0.2,
and a
=
0.5
increases as the journal
on the mean
q-
The
left
panel shows that
t* is
becomes more competitive.' The
and r-quality of the published papers. The
The shape of the figure when r is near zero is sensitive to the distributional assumptions. \Vi<h the
uniform specification the maximum possible return to /, is bounded and t" is bounded away from one as T
q
approaches zero. If q had been specified as exponentially distributed with parameter t q the effect of r, on
,
—
t1
percentile of the q distribution would grow without bound as r approaches zero
spent on revisions would decrease all the way to zero in the limit.
the
1
15
and the time
beween r and r-qnality
relationship
is
nonmonotonic. At some points the
effect of r
on
t*
dominates, while at others the effect of journal selectivity dominates.
$
T
1
Time
Figure
5
A
The
static:
4:
Effect of journal selectivity
model above has a continuum of equilibria corresponding to
I
describe a dynamic model of the evolution of norms.
common
common
The model
belief.
who
The model
are trying to learn and apply the profession's
Instead, the
beliefs at every point in
to learn the prevailing
all
different social
when one hears the term
"learning model"
not model agents as arriving with different beliefs and examine whether there
convergence to a
t,
r
quality of published papers
on time allocation and observed paper quality
standards. In contrast to what one might think
have
r
dynamic model of evolving norms
involves a population of author-referees
will
q
Mean
1
Mean
allocation
norms. In this section
I
Mean
norm
model
time and
involves a discrete set of time periods
it
as in the static
receive via referee reports
This focus
is
and
game
is
of Section 2
nol intended to suggest that whether a
on
and Fudenbeig (2000), the common
will
on whether agents' attempts
8
t
=
0, 1, 2,.
(at,zt).
.
.
and serve as a
community
.
At the
They then
editorial decisions will suggest to
effects of belief or preference heterogeneity
in Ellison
be constructed so that agents
will focus
I
lead to a shift in norms.
economists believe that that the social norm
try to publish
will
is
start of period
write a paper and
referee.
The data they
them that the
will reach a
social
norm
common norm and
the
he evolution of social norms are not interesting. Instead, as
beliefs learning model is motivated solely by the desire for a
I
tractable model that highlights an important effect.
16
is
in fact, (at, z t ).
This leads them to alter their beliefs aceording to
-a
a t+ i
-
zt+i
for
some constant
gather and
What
First,
A:
>
To complete
0.
t
,
zt
the specification
must describe what data economists
I
inferences (d ( z t ) from the data.
how they draw the
,
data do economists get?
assume that economists get two types of data points.
I
when an author submits a paper
of quality at least q
I
assume that the
he or she receives give him or her a data point of the form
should
on the
all lie
line
a
t
q
+
{1
- a
t
)r(q)
=
zt
.
I
will allow,
In particular,
I'll
r(q))
9
These datapoints
however, for the possibility
when judging the
that economists arc subject to an overconfidence bias
own work.
(q,
referee reports
quality of their
assume that they overestimate the r-quality of
their initial
submission and this leads them to believe that they have been required to achieve an
quality that
r-
10
In this
higher than what they have actually been required to achieve.
is e
—a
=
+
—a
q
+
(1
Second, whenever an economist referees a paper that
is
of sufficiently high quality to
case, the (q,r(q)) datapoints actually
lie
on the
line
a
t
t
)r(q)
zt
(1
t
)e.
be
1112
Economists
resubmitted he or she gets a data point of the form (g,r, Accept/Reject).
expect to sec
all
papers lying above the line atq
papers lying below this
If
line
finite
number
To keep the model tractable
Note that
as to
make
it
in a slight
list
it
Q/)r
=
zt
being accepted and
all
I
if
they entered the model with
common
avoid this by invoking word-of-mouth communication.
departure from the static model I've assumed that journals do not provide the
make the paper publishable if the paper's q-quality is so low
of revisions sufficient to
inconceivable that a revision will be publishable.
of journal practices.
because
—
of data points, then their analyses would lead
to a divergence in the second period beliefs even
author with a
(1
being rejected.
economists each saw a
beliefs.
+
I
I
believe that this
is
a good description
did not try to incorporate such behavior by referees in the static model, however,
seemed a needless complication and because it creates a possibility for another type of equilibrium
I did not feel was important: authors won't save time for revisions if referees won't ask for
multiplicity that
large revisions because they don't think they're feasible.
Given that the acceptance fronteir is downward sloping in q-r space this assumption is almost equivalent
assuming that authors believe their papers to be of slightly higher q-quality than they actually are, or
to assuming that have biased views of both the q- and r-quality of their work. I've chosen the formulation
above because it makes some results a little cleaner (especially those about small a behavior.)
Another important data source for real world economists is reading journals. Given the word-of-mouth
assumption below, this would just provide redundant observations on all of the acceptances. For this reason,
nothing would be changed if 1 included this data source in the model.
An ambiguity in the model is what happens if the assumed standards is so excessively high that fewer
than r papers are resubmitted. In the simulations in the next section I assume that in this case editors
accept some papers that aie not resubmitted and that these acceptances are observed by the referees.
to
17
I
talks to every other economist in each period
assume that each economist
sees
all
author's
of the data points that were generated in that period.
While
experiences a measure zero subset of his or her datasct,
own
I
this
and thereby
makes each
do not want to
lose
the possibility of inferences being affected by the authors' misperceptions of the quality of
their
own work.
I
thus assume that the {q,r(q)) observations economists receive by hearing
others taik about the referee reports they received are contaminated by the author's bias
(and that the listeners do not realize
What do
this).
economists do with the data they obtain each period? Fitting the (a,
involves estimating the slope and intercept of a line that
fits
z)
model
the {q,r(q)) data and divides
the acceptance and rejection regions. Typically, no line will do both jobs perfectly.
I
assume
that this does not cause economists to lose faith in their model of the world and that they
go ahead and try to
Formally,
I
fit
13
the data as well as possible with the («, z) model.
assume that economists' period
(d
where L(a,z)
is
describing the
(q,
fit
I
,
a loss function
r(q)) points
the hypothesis that
Specifically,
t
all
zt
)
analyses take the form
= argminLfa, zj/zi,^),
a, z
tha.t
describes
and a measure
referees
t
\i 2
how
poorly the the data (a measure
describing the
(q, r.
/.i\
Accept /Reject) points)
and the journal editor are applying the
(a, z) social
norm.
assume that
L(a,
z;
m, fi 2 = Li(a,z;m) + L 2 (a,z;fi 2 ),
)
where
Li(a,
is
z;
fj,i)
=
/
(r{q)-
—
2
^
d/zi(g),
I
a
J
a standard mean squared deviation measure of the distance
the {q,r(q)) data points and the line 0*7
L z {a,z:n2 )=
iRu A
(
V
—- a
1
+
(1
- a)r =
r)d/.i 2 {q,r)+
)
z
(in
the r-dimension) between
and
('"--7
Jr vr
\
I
-a
M/*2(g,r).
J
Formally, economists are estimating a misspecified model.
A justification for not worrying about
economists noticing the misspecification is that in a more realistic model economists would only receive
a finite number of datapoints and there would be a random component to each observation, so the form
of the misspecification would not be so appaient. The idea that economists struggle to reconcile haid-toreconcile observations while maintaining biased self images does not
18'
seem
unrealistic to
me.
where
Rua
failing to
is
the set of
meet the
which papers were "unexpectedly accepted" despite
r) values for
(17,
standard and
(ct,z)
Rur
i
s
'he set of '"unexpectedly rejected" papers
that met the (a, z) standard but were rejected. L2 can be thought of as the product of the
fraction of accept/reject decisions that are inconsistent with the (a, 2)
(in the
age degree of error
model and the aver-
r-dimension) that appears to be embodied in the "unexpected"
decisions.
Obviously other
loss functions
would be reasonable. The most natural would probably
be the negative of the log likelihood of the data under a hypothesis involving referees and
the editor trying to apply the (a, 2)
norm but making
idiosyncratic errors in judging the
quality of each paper. Analyzing such a specification would require cxaminining integrals of
CDF's and PDF's, however, and
in
I
felt
that the specification above was the best compromise
terms of reflecting a similar goodness-of-fit notion and being tractable.
6
Analysis of the dynamic model with no overconfidence bias
(e
=
0)
In this section
dynamic model when economists do not have
discuss the behavior of the
I
an inflated view of the quality of their own work. The main observations arc that consistent social
norms arc steady
states of the
model and that when
referees are too
demanding
economists infer both that their standards were too high and that g-quality must be
tively less
important than they had thought.
6.1
Steady states
When
there
is
no overconfidence bias
the static model
is
Then, (a
t
,
it is
easy to see that any consistent social
norm
of
a steady state of the dynamic learning model.
Proposition 5 Suppose
norm..
rela-
zt
)
=
e
=
in the
(ocq, zq)
for
all
dynamic model and
(oq, zq)
is
a consistent social
t.
Proof
All points (q, r(q)) in the
c*o<7+ (1 -cto)r(q)
=
z
.
The
data obtained from
referees' reports lie exactly
editor's decisions are also consistent with
19
on the
imposing the
line
(0.0, 20)
standard,
+
a$q
i.e.
all
— ao)r —
(1
the ^-distribution
zq
is
always nonnegative)
=
(ao,zo)
— Q'o) r
rejected papers have ao<7+ (1
>
~ zo
<
and
Hence, both L\ and L2 are zero for (a,
0.
nonatoinic on a continuous support, L\
for
all
any other
(a, z).
is
accepted papers have
z)
=
(c*o, zo)-
Because
strictly positive (and
The unique minimum
of the loss function
is
L2
is
thus
(ao, zo)-
QED.
Disequilibrium dynamics
6.2
In this section
I
discuss the disequlibrium behavior of the
in this section (and in the
for (/-production, q
~
remainder of the paper)
The whole
U[0,t q }.
what
of
want
norm
The
figure
was constructed by solving the model numerically
the figure
is
~
U[0,1 q ], r
=
0.3,
14
figure at
To
a =
a
—
and
0,2
help organize the dynamics
0.3363. This
is
I
—
o?, z/ + ]
—
zj)
for various initial beliefs
h(t)
the locus of consistent social norms (a, z*(a)).
are proportional to the change in beliefs (a/ + i
beliefs.
of economists' beliefs about
(a, z) outside of equilibrium follows the pattern illustrated in Figure 5.
under the assumption that q
line in
results
to say in this section can be
summarized concisely by saying that the dynamic evolution
the social
The
concern the uniform technology
will
I
dynamic model.
=
The
yjl
—
t/2.
vectors in the figure
that occurs for various initial
have also placed a vertical dashed
where the equilibrium
shifts
The sohd
line in the
from the somewhat low a form
to the typical form.
The
regions.
locus of consistent social
norms and the dashed
line divide (a,z)
In three of the four regions the learing process
is
space into four
mostly just a straightforward
adjustment of the overall quality threshold: when referees try to impose a standard that
would not allow the editor to
that they must reduce
2;
when
fill
the journal they infer from the unexpected acceptances
referees are too soft
and the editor has to turn down some
papers they recommend they learn to choose a higher
14
The speed
z.
15
is determined by an arbitrary scaling parameter k.
Note that unlike all other graphs in this paper the x and y axes in this figure do
not have thf same scale. The j/-axis has been magnified by a factor of 1.5. These choices reflect an attempt
to maximize ihe visibility of the directions and minimize clutter.
I5
The dynamics in the 2 < z*(q) and a large region fit this desciiption only if a is not too large. I discuss
what happens in the "high o" case at the end of this section.
The
with which beliefs change in the model
figure uses k
=
0.6.
20
0.2
0.1
Figure
What
is
0.3
The
5:
high.
i.e.
''typical'''
z
most important
>
z'(a).
0.7
to
my main argument
5.
is
what happens
Suppose that the (a
t
,Zt)
0.9
0.8
norms when
disequilibrium evolution of social
the upper right part of Figure
-
0.6
0.4
f
=
a
1
0.
in the fourth region
standard
is
unreasonably
Suppose also that the distribution of resubmitted papers has the
form. Economists will then (correctly) perceive that referees are asking
them
to
meet a very high standard and that some papers that they thought were submarginal are
being accepted. The conflict in this data leads economists to do two things: to believe that
quality standards are less
is
relatively
To
demanding than they had thought; and to
believe that r-quality
more important than than they had thought.
illustrate
why economists make
this inference, Figure 6 contains
of the data economists get in one such case. 16
The
apoints they get from referee reports.
quality distribution. All papers above
The bold
outlined area
and to the
an enlarged view
line represents the (q,r(q)) datis
the support of the (uniform)
right of the bold line are accepted.
The
journal editor also accepts papers in the shaded region (to the surprise of the referees).
Lower quality papers are
The
Hid
z
=
rejected.
The
figure graphs the quality distribution
0.53417 with q
~
U[0A. q
}
t
h(l)
=
y/i
-
lines
below the g-axis and to the
and the best fit (d, £) when
t/2, a = 0.2 and r = 0.3.
21
left
of the r-axis
initial beliefs are
that a
=
0.5
support of the q and r distributions
illustrate the
among resubmitted
papers.
have used
I
bold lines to show the support of the quality distribution for the unexpectedly accepted
papers. These papers are at the low end of the q distribution and at the high end of the r
distribution. Economists' rationalize these acceptances in part
be more important than they had thought. The dashed
that best
gives a
fits
good
The
the data.
fit
flatter line
accounts for
line
by concluding that
r
must
graphs the social norm (a,
many unexpected
z)
acceptances and
to the high q part of the [q,r(q)) data.
(q,r(q)) data
-t*)
/?(1
+a
Expected
acceptances
/?.(]
-t
Best
5
Figure
6:
2
-1
«
1
9
q
fit
Economists' inferences when standards are too high: the "typical" case
Figure 7 contains a similar diagram illustrating economists inferences
beliefs
(a t ,z
t
)
a
are unreasonably tough and
t
resubmitted papers has the "low a" form -devote the same
maximum
is
sufficcntly
all
fit is
when
papers are resubmitted and
effort to their revisions.
referees'
low so that the distribution of
all
authors
Here, the "unexpectedly accepted"
papers are uniformly distributed in the q dimension, and the dotted
best
to data
line illustrates that the
obtained by slightly lowering z while leaving the slope of the line unchanged.
Even with the simple
loss function I've chosen, getting analytic expressions for the
optimal inference given an inconsistent (q
(
zt
,
)
is difficult.
Proposition 6
is
a characteri-
zation of the dynamics that brings out the main observations I've mentioned above.
proposition characterizes the dynamics for
i.e.
for zt close to
z*(a
t
).
Parts
(a)
and
initial beliefs
that are close to being consistent,
(b) note that in the low
22
The
a and somewhat low
J
L
r
{q,r{q)) data
U.
/
—
/
«.
"
0.6
-
U.o
-
Expcc:ted
/ acceptances
^^-^-^-Ct^r^: --^1^.
:
Suprise acceptances
,J1^
Best
fit
to data
.
Expected rejections
1
t*
g
Figure
a
7:
when standards
Inferences
a standard that
toward z*(a
is
t
Part
).
(c)
my main
a
notes that
(at least
when
approximately) and adjust
referees' beliefs
correspond to
too low the dynamics are similar in the "typical" case: the dynamics are
approximately vertical when the social norm
to
are too high: the- "low a" case.
cases economists do not adjust their estimate of
their estimate of z
Q
0.5
observation.
notes that
It
involve both a reduction in
a and
counting for the change that
is
when
is
approximately consistent. Part (d) relates
zt is
slightly larger
than z*(at) the dynamics
a reduction in the overall quality standard (after ac-
induced mechanically by the change
two parameters arc comparable
in
The
in a).
magnitude. The proof of the proposition
is
shifts in the
contained in
Appendix A.
Proposition 6 Consider
the
dynamic model described above with F(q\t q )
~
(7[0, t q }.
tq(a.z) be economists' optim.al time allocation when, they believe that the social
(a,z).
(a)
Write b(z)
sa
a{z
—
z*(a)) as shorthand for lim,^,.( Q )
Suppose that for a given Q( £
has the low a form,.
(0, 1) the
i
zt+\
-
t
=
zt
=
Then, there exists a constant a
o.(z*(a
t
)
-
2
(
x
=
)
23
>
such that for
zt
norm
is
a.
unique equilibrium for the social
of z*(q() the dynamics have
a t+ - a
T _,'f (
Let,
norm
(at, z*(cxt))
in a neighborhood
(b)
Suppose that for a given at £
has the somewhat low
a form and
there exists a constant a
Q't
zt+i
For
(c)
a*
~
~zt
~
-
+i
(0, 1) the
>
-
o.(z*(a t )
<
has the "typical" form, and z t
t
t
«
zt
Rs
-a
+i
zt+\
-
to
z*{a
at.
the
t )
t
=
t
(a ,z*(a
t
q
t
)).
Then
dynamics have
—
= 0.
unique equilibrium, for the social
Then
z*(at).
aj
norm
>
there exists a constant a
(at, z*(at))
such that for
zt
dynamics have
-
a.(z*(a,)
has the ''typical" form, and z
z,),
t
(0, 1)
>
the unique equilibrium, for the social norm, (at, z*(at))
z*(a t ).
Let
>
Then, there exist constants a\
l-oc.
strictly positive
dynamics have at+\
(0, 1) the
Suppose that for a given at 6
(d)
is
zt )
Suppose that for a given at G
close to z*(a{) the
—^-
such that for z t close
larger than. z*(at) the
zt slightly
a
that
unique equilibrium for the social norm, (at,z*(ctt))
M
=
q
and «2 >
(q(at,z t
)
+
t
q
(at.z t ))/2 and
such that for z
t
M
T
=
close to z*(at) the
dynamics have
q, + 1
z t+ i
t
«
-ai(z - z* (a
zt
«
a 2 (z* (a
-a
-
The one notable
is
is
a form
for
-
zt
)
))
+
(a t+ i
- a )(Mq t
z
<
z*(a) and
a
is
I
M
have
apparent from the figure that
why economists conclude
when standard
r
)
left
out of the discussion so far
sufficiently high so that the equilibrium
in this case
more important than they had thought.
relatively
argument
It is
t )
t
feature of the Figure 5 that
what happens when
the high
q
t
that r
is
economists conclude that
The argument
is
similar to the
more important than they had thought
are too high in a typical equilibrium.
The unexpectedly
rejected papers
arc relatively low q papers and hence a steeper line allows referees to account for
the unexpected rejections while maintaining a good
I
fit
have not discussed this case in more detail because
here seems less plausible.
First,
it
has
many
of
to the r(q) data for high q papers.
in
a couple of ways the argument
involves economists mistakenly not achieving levels of
24
r-quality that they could have achieved. Second, the effect derives from economists trying
to
datapoints with
fit
negative.
The overconfidence
7
In this section
I
and gradual evolution
bias
show that adding a
to place ever
in
which
more emphasis
r-quality.
e-perturbations of dynamics with a continuum of steady-states
7.1
Before discussing the model,
dynamic model
is
of the
it is
instructive to discuss
~t+i
(pi,z)
= argmm QjZ
L(a,
~
zt
z.\a. t ,zt).
_
\
\
where
more
stucturc in
its
generality.
The
form
a t+ - a t
is
produces a model
slight overconfidence bias
norms can slowly and steadily evolve over a long period
social
on
r(ij)
,
a ~
/
J
\
A
social
t
zi.
at
zt
norm
(at,z
t
is
)
a steady-state only
if it
a solution to
—-{a u zf,a u zt) =
aa
dL
<
-T-K^L-,zuat,zt)^
OZ
This
is
—
n
a system of two equations in two unknowns. Ordinarily, one would expect such a
system to have one solution (or zero or a few). The fact that the dynamic model of the
previous section has a continuum of equilibria indicates that
What happens
it
slightly?
if
it is
we take a dynamic model with a continuum
The answer
depends on how the system
of course
is
somewhat
special.
of equilibria
pertubed.
and perturb
To take a simple
example, consider a dynamic of the form above with the loss function
L(a,
z;
au z
t )
=
{a
-a
This model has every point on the line z
happen with an c-pertuibation
is
t
2
t
+
)
= a
(z
t
an f-order shift
-
z,)
2
+
(z
-
a)
2
as a steady state.
in
.
One
thing that can
the set of steady states. For example,
While I earlier defined L as depending on the measures fx\ and jj.7 describing the two types of data, /<]
and H2 are themselves functions of a and z
I use a
and z as arguments of L in this section to clarify
the nature of the dynamic.
t
t
.
t
9.F,
t
if
wc perturb the
loss function
above to
L(a,z;a t ,zt,e)
=
-
(a
2
a,)
+
(2
-
zt
2
)
the system has a continuum of steady states given by z
With a
if
wc instead perturb the system
L(a,z;a t ,zt ,e)
the only remaining steady-state
example, the
The
first
-
(z
(a
=a +
t
+
e))
2
,
e.
generic perturbation, however, the continuum of steady states will disappear.
For example,
this
t
+
6
=
is
-a
(a
at
=
2
t
zt
to
-
2
+
(z
=
0.
What happens
zt
)
+
-
)
(2
a)
2
+
ez
2
,
to the former equilibria? In
perturbed dynamics are
3
+
2f
3
+
2f
3
+
zf
3
+
ze
terms on the right hand sides of these equations
tell
us that from any
condition the dynamics lead quickly to a neighborhood of the nearly stable locus z t
The system then
evolves at an
state. If the initial condition
is
e
initial
=
a>.
rate in a neighborhood of this locus toward the steady
very from the steady state a long gradual evolution would
be observed.
Obviously, the most natural
way
to account for a long gradual trend in an economic
variable will usually be to view the trend as reflecting a continuous shift in the equilibrium
of a
is
model due
to a trending
intended to convey
continuum
7.2
is
of equilibria
Social
norms
exogenous variable. The most general idea the dynamic model
that the disequilibrium dynamics in perturbations of models with a
may
for
provide an alternate method
for
explaining some such trends.
academic publishing
My main observation about the model
with no overconfidence bias was that
if referees
try to
hold authors to an unreasonably high standard, then social norms will evolve to place more
weight on r-quahty This disequilibrium shift
observed shifts in academic standards
be incomplete
in that
for
we have no reason
is
not an appealing candidate for explaining
two reasons.
First,
such an explanation would
to expect initial beliefs to be too
26
demanding
as
opposed to too undemanding. Second, and more importantly, the model does not
gradual trend. Instead, social norms
in
much
further
movement along the
set.
The dynamics with an
When
ovcrconfidence bias are qualitatively different.
e
are far from the equilibrium set, the e-pcrturbation has
impact
little
confidence then becomes important. In the typical case
economists'
initial beliefs
The
over-
destabilizes the former equilibria.
it
correspond to a consistent social norm, then their mispercep-
tions of the referee reports they receive will lead
standards must be higher than they had thought
will
beliefs
— we again see rapid
convergence to a neighborhood of the set of equilibria of the unperturbed model.
If
a long
such a model move; very quickly to a neighborhood
of the equilibrium set and then converge slowly without
equilibrium
fit
them
to conclude that overall quality
z
perpetually try to hold authors to a standard that
is
—
(i.e.
>
zt
0.)
For this reason, referees
slightly higher
than
is
feasible.
The
e-overconfjdcncc does not affect the argument that economists will conclude that r-quality
is
more important than they had thought whenever standards are higher than
Hence, when the equilibrium has the typical form we
social
norms through the near equilibrium
Musi-
we look forward
the answer
is
no.
In the
overconfidence bias
to
is
to
a.
(/-quality
observe a gradual evolution of
whatsoever? In
neighborhood of a consistent
make economists think
had thought. In the low a and somewhat low
feasible.
toward lower a values.
set
world with no
will
is
social
norm
my model
at least,
the effect of a small
that z must be slightly higher than they
a cases, when
the standard
is
slightly too high
economists infer that z must be slightly lower than they had thought. For any such a, the
two
effects
turn out to exactly offset for some z slightly greater than z*(a).
The e-pcrturbed
model has a continuum of steady-states lying just above the low a and somewhat low a
portions of the set of steady states of the unperturbed model.
the evolution of social norms will
that no paper's idea
is
come
good enough to
The model thus
to a halt as soon as r
let its
is
sufficiently
author be sure that he or she
predicts that
important so
will eventually
be able to get an acceptance.
Figure 8 illustrates the dynamics of the system with a small overconfidence bias.
figure
was generated by solving the model numerically
assumption that q
~
U[0,t q ], r
=
0.3,
a
=
0.2, h(t)
27
=
for various initial beliefs
y/t
-
t/2 and
e
=
0.01.
The
under the
The
thick
solid curve
on the
side of the figure
left
is
the locus of steady states (a, z f (a)).
Ou
side of the figure I've graphed eight curves illustrating the evolution of social
While the curves appear to join together
eight initial conditions.
the
the right
norms from
well before they reach
endpoint, they actually remain separate over the whole range and in an extremely
left
now appears
magnified figure what
From
of nearly parallel curves.
down and
to the
left
to be one central curve
initial
would be revealed to be a
conditions with z large the system initially evolves
toward the set of nearly stable norms and then moves along
until the
somewhat low a region
an
evolution up toward the nearly stable set, and then again a
initial
along the nearly stable
The arrows on
From
reached.
is
set
initial
this set
conditions with z small there
movement
is
to the left
set.
the curves give a feeling for the speed of movement.
The arrows mark
the beliefs that prevail after one period of evolution and then after every ten additional
periods.
18
The
fact that the
arrows are
movement toward the nearly
initial
initially far
stable set
is
apart on each curve reflects that the
rapid -- from most starting points the
curves get sufficiently close to the nearly stable set to be indistinguishable lo the naked
The
eye within ten or twenty periods.
fact that,
arrows then become closely and regularly
spaced as norms evolve along the nearly stable set reflects that this evolution
steady.
with a
Here, the evolution from a near equilibrium with a
=
0.4 takes
=
is
slow and
0.8 to a near equilibrium
about two hundred periods.
Proposition 7 provides a formal description of some properties of the system.
(a) notes that the
somewhat low a
2
is
is
no steady
slightly higher
q
state:
the
when a
is
at (a,z*(a)) the
than z*(a) the
Proposition 7 Consider
t
continuum of equilibria covering roughly the low a and
a.
ranges. Part (b) notes that
typical form there
when
model has
Part
fit is
such that the equilibrium has the
data
is
better
improved by reducing
fit
by increasing
a.
dynamic model described above with F(q\t g )
(a,z) be economists' optimal time allocation when they believe
z;
that,
~
U[0,
q \.
Let
the social norm, is
(a,z),
(a)
Suppose
with
1
e
=
that,
for a given
has the low
a
In constructing the figure
a G
(0, 1) the
unique equilibrium for the social norm. (a,z*(n))
or somewhat low
I
took k
=
a
0.5
28
form..
Suppose that
^r
is strictly
positive
Figure
at
t.
—
t
q
0.3
0.2
1
8:
The
is
(
(b)
a
a steady state of the
c
case z (a)
e
e sufficiently
—
>
a
1
0.
such that
model with e-overconfidence
2(1
When
has the typical form.
the loss function has -g^{a, z;a, z)
=
—
z*(a)
— a)ae when
~
ae
when
e is
e is sufficiently
small. In
small.
the unique equilibrium for the social
(0, 1)
>
that. z (a)
+
exactly equal, to z*(a)
small there exists a z
f
such
a,
c
>
norm
we have ^(a, z*(a);a, z*(a)) <
0.
z*(a) for which the distribution of paper qualities
and expectedly and unexpectedly accepted papers has
and
e
(
Suppose that for a given a €
(o,z*(a)) with
For
is
norms when
sufficiently small there exists a value of z, z (a)
Further, there exists a positive constant
the low
0.9
0.8
0.7:
disequilibrium evolution of social
(a,z*(a)). Then, for
(a,2 f (a))
0.6
0.5
0.4
the typical
For any such
0.
form pictured
f^(«, z;a,z)
z,
<
0.
in
Figure 6
Hence, the
system, does not have a steady state where the distribution of paper qualities has the typical
form.
Let z ( (a) be the smallest value of z such that
constants a and b such that z t (a)
For those
who do not
- z*(a)
ss
^(a,z;a,z)
ae
and ^(a.
=
(
0.
Then there
(
z (a); a, z (a))
exist positive
w — be
for small
believe that academics suffer from overconfidence bias (and those
29
who
are wondering
of such s bias),
I
if
observed changes in standards should be taken as providing evidence
would
like to
note that a gradual evolution toward lower a norms can
be generated by many small modifications to the basic dynamic model. Essentially, any
perturbation that makes referees perpetually try to hold authors to a slightly infeasibly high
standard
to
will
do the same
make up more
thing.
extensive
lists
One example would be an assumption
of revisions than
is
that referees try
standard to impress editors with their
thoroughness. Another would be an assumption that referees arc competitive (or spiteful)
and try to hold back others
in their field
by imposing standards that are
slightly higher
than the norm (perhaps because making requests that are even more demanding would
expose their
spite).
In a standard one-dimensional
by a cost of revisions or
in
model where the optimal
level of revisions is
determined
a one-dimensional learning model where referees are learn z by
observing referees' reports and editors' decisions, an p-pcrturbation
a mode! in which the original equilibrium (or steady-state)
dimensional learning model, however,
e
is
like these just
shifted by
c.
produces
In the two-
changes can greatly change the equilibrium set and
create steady long-term disequilibrium evolution.
8
I
Conclusion
have proposed that
it
is
helpful to think
lishing process with a two-dimensional q-r
model
is
about observed changes
model of
quality.
The
see in journals.
The model
by spending
and
'less
less
economics pub-
idea behind the dynamic
that social norms for weighing different aspects of quality
struggle to reconcile the high standards being applied to
in the
may
shift as
economists
them with the mediocrity they
predicts a long gradual shift in standards.
Academics react
time developing new insights and more and more time polishing
papers.
Among
the
many
possible extensions to the model,
I
view the incorporation of random-
ness in the assessment of quality and in economists' data samples as the most intriguing.
Referees
who
receive signals suggesting that standards arc higher than they arc
clude that r-quality
is
more important than they thought, while
referees
who
may
con-
receive signals
suggesting that standards arc lower than they are will not draw the opposite conclusion.
30
Even without an ovcrconfidcnce
Sobel's (1908) work suggests that
may have more
What
wc may sec increasing emphasis placed on
randomness
due to heterogeneity
in assessments
in tastes
subtle effects.
model, because individual preferences over q and r do not appear.
arc time invariant, then welfare changes as standards evolve.
increasing or welfare decreasing depends on
optimum
how
If
preferences
Whether changes
are welfare
the prevailing social
norm
from the
differs
given authors' and readers' preferences.
The changes
of the last few decades
have had a substantial impact on economists.
young economists report spending as much time revising old papers
Guiding larger and more frequent revisions
If
r-quality.
are the welfare effects of changes in publication standards? There are no answers
my
within
bias
is
as working on
new
Many
ones.
an additional burden on referees and editors.
many
the changes that have occurred were accidental and
possible, then a discussion in the profession of
ether social norms arc really
what standards we would
like to
have would
be valuable.
While
have emphasized the model of learning with ovcrconfidencc. other explanations
observed changes are possible. Indeed, one of the main motivations for the
for the;
model
I
is
to clarify
how
static-
the growth of the economies profession, changes in the set of ideas
waiting to be discovered and other factors might alter the publication process. Ultimately,
which of the potential explanations are most important
is
an empirical question.
I
attempt
to begin this sorting out in Ellison (2000).
How
else
might one examine the evolutionary model empirically?
one could directly examine
experiences as authors.
is
A
referees'
demands and
see
general premise of the model that
that learning occurs within communities of referees.
to observe whether a
how they
random shock
appointment of a new editor who
A
With
are affected
may be more
ideal
by
easily
good empirical
test
referees'
examined
would be
to a particular field at a particular journal, e.g.
likes revisions, affects
how papers
data
the
in the field are treated at
other journals. Another feature that distinguishes the evolutionary model from equilibrium
models
is
that transitory shocks have permanent effects. For example, even after a revision-
loving editor
is
replaced, the fact that referees learned a high revision
publication remains slow for years to come.
31
norm
will
ensure that
In addition to trying to change
tried to
make
Comparative
how people
think ahout academic publishing,
I
have
the general point that a long run trend can be a disequilibrium phenomenon.
statics of equilibria will
remain the standard
for explaining trends,
that models like that I've developed here will find other applications.
32
but
I
hope
A
Appendix
Pi oof of Proposition 6
(a) In the
low a case for (z,t q )
= ~ 2 g(i'- -o
This function has Jp
^f =
—h"[\ —
t
q
>
)
a neighborhood of (z*(a t ).t q (at, z*(a t )))
in
"^
^'^
all
z t in a neighborhood of z*(at).
-a
1
~~
)
and hence
0,
The
t
w ^ich
*?)>
independent of
is
neighborhood of z*(at),
in a
for the level of r-quality that
Write r a {q;a t z t )
,
(at,z t )
when
=
,
in Figure
r{q\a t ,z*{a
When
7.
<
zt
all
z*(at) the situation
describe economists' inferences,
is
The
situation
similar,
and
a
Z
w —
'
1
is
\ _a
M
m
of the loss function over
ee (t.q(at,zt )
q
+
w
and
where
z t )))/2.
q holds for
t ,
Because
z t ).
is
thus
that pictured
like
line.
of variables
m = ^^
and analyze the
the slope of the line
is
mean
>
some
^-quality,
z*(q
{
).
The
signs reversed.
the change of variables L\ takes on a very simple form. 19
w)
L-l-(m,
rt q (n t ,zt)
=
M
{m(q -
/
q
Jo
+w-
)
M
{m{q -
/
q)
tq(<Xt,Zt) JO
1
By making
z,)
,
2
a few comparisons
w >
w <
wt, or for
outside the interval
[r a (0;
t
at
—
5
,
zt ))~
1
-dq
—
)
—
-A^o)
w-
+
(m
t
(q
-
M
q)
+ w )Y dq
t
t
3
h
(m -
m
t
)(w
-w
t
)(q
-
M
q
2
)
+ (w - w
)
1
jttq (at
achieved for
9 (q
m
tq(a tl z t
r(q;
t.g(a t ,z t )
fti(<*t,zt)
1
is
(a
carry out the calculations for z t
I'll
calculations in the opposite case are identical but with
With
is
the level of r quality required of a paper with the
max(0, q{a tl
<
q)
but involving a parallelogram of
make a change
I'll
independent of
is
m.{t
has
actually necessary for an editor to
is
unexpectedly rejected papers lying just above the (q,r(q))
minimization
<
<
It also
z.
authors revise to the greatest extent possible.
near z*(a t ).
for z t
))
t
(at,zt )
q
the population believes the standard
independent of zt and
locally
is
r a (q;a t z*)
To
t
continuity of the thresholds implies that the ordering q
accept a paper of ^-quality q
q
\
'
2;.
t
a
we have
{m it is
ra
m
2
r )
+
(w -
w
2
t )
easy to sec that the
(Mq ,at,zt),
or with a slope
at, z ),r(0; at, zt)\. (For
t
minimum
m
of L\
for
+
which
Lo can not be
iv
+ m( — Mq
)
example, to show the second note that
any such w, L(m,,w) > L{m ,r a {Mq ,at,zt)) because L\ is smaller at (m ,r a (Mq ,at,zt ))
and L2 has its global minimum there.) In the range containing any potential minumum,
L2 turns out to also be a simple quadratic.
for
t
rt q (at.zt)
L-2{m.iu)
=
To make
also omit
t
,zt)+{m-Tn t )(q-Mq)
1
r—dr—
Jo
cf
f
q
]
-dq
(a t ,zt)
more readable
the formulas
and
arguments of
(Mq ;a
/
lo
are determined by q (
ru--r a
t
M
zt
9
,
,
so
I'll often omit the /j] and
and /xo
f.12 arguments of L\ and L2. /Ji
sometimes substitute a and 2, (or m and w ) as arguments. I will
and q to improve readability.
I'll
f,, q,
also
t
33
t
t
*>
t
)-q
q
(a t
.
rt q (a t.,z
,z t )
fiq(a
1
-
(w
/
ra
2at q (a t zt ) Jo
la
{Mq au z ) +
\
(m.
t
- m,)(q -
M
z
q ))
dq
,
t
r
Zia
q
(a t ,zt )
2
{m -
rn t )
1
2
+ --(w lo
(Mq :a
ra
t
,z t ))
2
.
Hence.
=
L(rn,,w\m t ,w t )
m
-
-t q (at zt ) 2 (m
,
2
The minimum clearly involves m = mt. This
The minimizing value for w is w = "^
z t in a neighborhood of z*(a t ).
...
ra
(M9
v
;
,
t
-a
I
= a
2+1"
t
t
and zt
t ))
q
V
'
at Z
'
Recall that r a
-
.
a = at
gives the first part of the conclusion:
=
M
-a
1 - a
zt
1
w
+
[2o
identities at
2
t,
;
.
independent of
is
g
Substituting this into the expression for
Using the
+ —(w - ra {Mq
2
iv t )
M
z*(a t )-zt
=
-
{w
thus have
Z*(Qt)-Q
1 — at
=
ot z£ )
We
+
t )
q
z*(a t )
=
1
t
-
-a
zt
h
W
t
.
t
gives
-a
ly(l
+
at_Afq
f )
— 0.7)^
(1
allows us to conclude as desired
that
7
-t+\
(b)
of
The
G
is
~
zt
=
k
=
fc(l
proof for the
t
(a
q
t
,
This would cause
z*(a t )),
many
w
t
m
Write Ta (zt )
=
k (a t
——
fc-
lo
case
is
h
M
q
+
-(z*(Qf)
(1
-
- a )w - a
t
t
very similar.
> z*(a
M
q
(1
-
0.7)10,)
z t ).
One
difference
G
is
that the form
will not be strictly
,
To avoid them.
t
I've just
q (at,z)
is
assumed
=
z*(a t ).
the proposition
in
differentiable in z at z*(a t ).
case then proceeds exactly as above to
t )
+
(a t zt ) might not be differentiable at zt
q
This ensures that
0.
t
1
possible that the second derivative of
complications.
>
zt )
show that
=
=
o
la
+r
r a{hiq \a t ,z,)
By
- w
t ).
1
= 1 — G(zj; t q (at, zt))
the inital beliefs.
rjzt)
=
iu t )
which case
in
analysis of the z t
a —a
it
-
&)u>
somewhat low a
that -Q^-{a t ,t q (at, z*(a t )))
The
-
(1
- a t )(u> -
This makes
different.
positive at
{aMg +
for the fraction of
papers achieving the
the envelope theorem
we know that
—(z
l
dz
t
q
i
{a r ):t q {a, z*{a ))(z t
:
(a ,z (q
t
(1
-
(
))
-q{a
t
,z*(a t ))
at)at q {a ,z*{at))
t
34
-
in a
z*(a t ))
zt
standard given
neighborhood of z*(a t
).,
-
z*(a+)
ra
(h
I""
is
1
neighborhood of z*{a
dz. Hence, in a
,
(Mq ;a u z )-
-a
^__L(r
(1
=
Wt
t
t
the standard from z*{at) to
when he lowers
of extra papers the editor accepts
The mass
)at q
.
.
B («)
t )
we have
.
-
r)
-
z t ),
-Qj)
(1
This gives
-
zt+l
= jAt
for a
t
)
as desired.
-- the formula
s*(a«) case adds another slight complication
bounded by {q,h{l slightly different because there are no papers in the triangle
z ))/a u h(l-t q )+a) that
a). (q,r a (q,at,zt)),^d(q+{l-at){.r a {q,auzt)-r{q,a tl t
unexpectedly rejected. The loss function thus takes the form
for
The
L 2 is
t
+
q)
~a{z*{a
zt
analysis of the
<
z,
can be
2a
+
1
,
,
9/
,
2
1
..\2
,,,.
.
r.„
,
„
nr...
,.AA2
24cr
'
>
7(7-
r(<?;
m,
io))(r
-
r(g;
m, w))dqdr,
indicator function.
where 7 is the triangle bounded by the three points above and I is the
a 6 such that
exists
there
c>
any
To show that at+i a t « it suffices to show that for
for all z,
that
\m - m,\ < c(z*{a t ) - zt) whenever zt 6 (z*{a t ) - 6, z*(a t )). To see this note
< m., - c{z*{a - z )
in some interval below z*(a ) we have for any
m
t
« (m
,.)
»
-jA_£ /
-
.
?£!«,
<
-^-tl(*,-8) 2 4z> t )-*)
-
,)
(m -
,„,,
t
t )
/(r
> rfc ,, -))(r -
rfe;
r
1Z<7
l
+
;
where ,4(T)
a
r{q;
q
t
,
z t ))
is
2
.
.
1-^— I(r>r{q;m,w)){r-r{q;m,w))\,
°m
q) (q,r)er
The
the area of the triangle T.
The
farthest from
is
sup
'
-
<?(tq
effect of
M
q
.
a
dm
in
m
on
r(q;
m,
to) is
<j
-
71/,,
^^-{ra (q;at ,Zt) which is largest when
is
This gives
2
l^-Kto) < - -^±{tq -
dm
change
area of the triangle
12c
2
q)
~~
-
c(z*(a t )
zt)
+ ±f^(r a (q;a
4atcr
t
,
-
zt )
r(q-a t ,z
2
t
))
.
a second order effect in z*(a )-zt Hence, -^{m.,w) <
< m. t -c(z*{a ) - zt ) when z t sufficiently close to z*(at ). Combining this with a
for all
> t + c{z*{at ) - z,) allows us to conclude that
similar calculation of the derivative for
The
(r a (q: a,, z t )-r(q; a,, z t ))
m
2
term
is
t
t
m
m
m
e {mi
A
-
.
c{z*{at )
-
z
t
w, + c{z*{a - z )) as desired.
shows that the result on zt+\ - zt
),
similar calculation
t )
t
order change in the loss function.
35
is
also unaffected
by the second
m
.
„))
J
When
(c)
the equilibrium has the typical form G(z\f q )
(l-a,)(h(l -t q )+a/2)
=
G(z;tq )
given by
is
a
t
tq
2
An
in
two derivatives of
explirit calculation of the first
this function
d G,
shows that ^&r{z;
a neighborhood of {z*{at)-,t q {a t ,z*{at))). This again implies that -g^(a t ,z*(a
and that the distribution of paper qualities has the typical form
for z t in
t
q
>
exists
))
t
)
some neighborhood
of z* (a t ).
The
and the
(q,r{q)) line
form here as
<
in z t
unexpectedly rejected papers have exactly the same
set of
z*{a t ) case of part (b) of the proposition. The result
thus identical
is
to the result for that case.
(d)
As above
comes has the
t
The
differentiable in z at z*(at).
is
q
typical
form pictured
in
Figure 6 for
distribution of paper qualities and out-
all
z t in some neighborhood (z*(at), z*(at)-
5).
wa
Write
for r a
{Mq ;at
1
z t ).
first
I
note that a number of simple comparisons imply
is less important than they had
and w 6 {w n w ). To see this, note first that
the line given by (rh,w) can not be entirely above the (in ,u' ) line over the whole range
[q(at,Zt),tq(at,zt)] of (/-qualities of resubmitted papers. From any such estimate both L\
and Lo are decreased by moving the line down until there is an intersection. Next, note
that economists must infer that standards arc lower and'g
thought. Specifically,
m
we must have
>
m
t
,
t
t
t
that
minimum
also impossible for the
it is
the (m. t .wt) line at q 6
fitted line
[<?,f<j].
about the point were
reduces w.
The
and setting
m
to have
In this case, L\
intersects the line r
it
m. t reduces L\
t
=
w < wa
estimate's also can not have
=
w>w
with the (m,w) line intersecting
and Li are both reduced by rotating the
.
and makes L2 equal to
r a (q;
m
t
,
wt) in the direction that
In this case increasing u> to
global
its
minimum. This
wa
gives
£ (r n (Mq ;at,zt ),wt). It is then easy to see that m > mt- Otherwise, slightly reducing m,
would reduce L\ and also reduce L2. (The latter is because the gain from to improving the
fit in (<7, min(g,
is greater than the loss from worsening the fit in the (possibly empty)
q ))
w
M
interval
\Mq ,q\.)
Finally, all of the
extreme values (m
= m
t
,
w —w
t
w = wa
and
)
can be
ruled out by looking at derivatives of the loss function.
To obtain
the proposition's further conclusion that the changes in
—
m
w
and
are both
Even
examine the first
after the discussion above there remain a few possibilities for exactly where the best fit line
may intersect the other lines in the figure: it may be above or below r a (q;a z ) at the left
edge and may be above or below r(t q ;at, zt) at the right edge. The first order conditions
are slightly different in the four cases. I will work out the equations for the simplest case:
assuming that the best fit line is strictly between r a (q;a z and r(q;a ,z ) throughout
first
order in z
t
z*(a
t )
order conditions of the loss function.
I
t
t
the interval
[q,
t.
with
t )
t
t
q \.
In this case, the loss function
The
,
t
,
is
very similar to the loss function in the cases above.
only differences are that the set of unexpectedly accepted papers does not have papers
(-/-qualities
above q and
is
also missing a second-order triangle in (q, r)-space
below
a t, zt)). As above, the second-order triangle can be ignored. The estimates have
the same asymptotics as those obtained by minimizing loss functions given by integrals
identical to those in part (a) but with different lower and upper bounds. Specifically we
{qi
r {q\
36
L=
can examine the minimizer of
+ L2
L\
where
m
= —{t q - qf{m -
Li(m, w)
2
+
t)
w
[w -
t)
and
——
L 2 (m,w) =
(Note that
24cr
)
-
m + 03(11)
t
)
2
-l
—
—
a
=
-
7
,
.
=
=
w')
2a(t q
/
positive constants: C]
=
- wa )
c 2 (ib
-q)w, + (q-q)w
—2a(f)+(~-~)—
w =
arguments of
)
t
q
q
,
and q to improve read-
±(f q
-
w and w a and
2
~
.
q)
+ -^ ij^J +
t
\{q
Adding C2/C3 times the second equation
2a (f g -
-
cij,
2a(tg
-
q)
Q)( f q ~Jl)\ ^2
c\, c 2
=
and
\j{t q -q)
C3 are
;
ancI
to the first gives
g)
+
(q
-
q)
minimum has m > ?n and that iu/ > w a so the first order conditions
give the true minimum if the constant in this expression is positive.
that the true
of this case can only
(
,
also give
2
c2
_
CiC
w-w =
t
g-g
-_
32a{u _ q)+{ ql)
(w t
\
-
C1C3
From the
2
a wei g"tcd average or
.
1S
C1C3
The equations
t
0,
c2 c3
We know
t
[w-wa -(m- m )——
q \
order conditions for this minimization arc of the form
rn f
—c2 {rh —
C3
q
+ *-- —
2a t q
t)
q
t
ability.) Trie first
where
m
=-{m -
—
omitted the arguments (a ,z
I've
C\{m -
t
- w a ),
c\
minumum
discussion above this can be the true
only
the leading constant
if
is
negative.
The
order in
fact that wt
—
Zi
t
last
The
z*(at).
z-z
The
— wa ~
term
=
aM
=
(1
=
(1
(z t
—
z*(at))/(l
—
at) implies that
longer expression for zt+i
M
—
m — nit
z t follows
and
w — wt
are
first
from the calculation
+ (l-a)w - (a q + (1 -a )w
- a )(w - w + Mq (a - a - w(a - a
- a )(w - wt ) + (Mq - r ){a - a,) + (MT - w)(a - at )
t
q
in this
t
t )
t
)
t )
t
)
M
t
expression
t
is
second order
in zt
—
z*(c*t).
QED.
Proof of Proposition 7
(a) Recall
from the proof of Proposition 6 that
t.
q
(a t z
,
t
)
is
differentiablc in z at z*(a t )
that the distribution of paper qualities will also have the low
for 2, in a
neighborhood of z*(a t ). The same computation as
37
a
or
and
somewhat low a form
in the
proof of part (b) of
Proposition 6 shows that for zt in some neighborhood (z*(a
is
),
t
z*(a t
)
+ 5)
the loss function
L = L\ + L 2 with
of the form
1
^(t q
Li{m,w;m t ,wt)
L 2 (m.,w;m ,w
t
12'
(m t ,w
Differentiating,
1
=
)
t
t
,->,
,.
^r~(*9
24a" q
~ ?)
(
-
previous proof we also saw that
m,)
2
(w - (w t
+
m _ rn'""
,9
+
e))
1
+ ^"C"
2 <T
'*)
~~ r a
7
2
(Mq ;a
tj
zt
))
{Mq ;a
t
zt
)
'
a steady state
is
)
-qf{m-
w —
if
ra
t
and only
(Mq ;a
t
,
w —
if
t
m
zt )
ra
j^-(zt —
,
=
2 *(»f))-
In the
2<tc.
Hence,
for e
we can find a z > z*(at) that satisfies the equation for a steady state.
i
In the somewhat low a case the equations above give z {a) — z*{a) ~ 2(1 — a)ae. In
the low a case we saw earlier that the expression wt — r a (Mq Qt.,z = ,_ a (zt — z*(at)) is
e
exact when z is sufficiently close to z*(a ), and hence the expression for z (a) — z*(a) is
sufficiently small
t
t )
;
t
t
an equality as
Again
(b)
well.
for a given
For
close to z*(a t ).
(m
t
,
w
t )
m
with
<
a the
w
vn-t
distribution of papers has the typical form
t
,
t
in
a neighborhood of
w>
r(Mq ;a
t
and (m, w)
,z t )
wt the expression for the loss function
is
zt
if
is
sufficiently
sufficiently close to
again a slight variant
of that in the previous proposition:
1
—{t q -
Li(m,w\m t wt )
,
L 2 {m,
12
I've written
m
wa
e))'
t
i
q
where again
(m - m,) 2 + (w - (w +
— f q-q
—
24cr \t -
~
w; m. t ,vit )
2
q)
\
(m ,
m
,
2
t)
—
2at
!
+
qj
q
-
~—
q (
- - (m =
—w
wa
q\
q
for r a (A/g ;o/, zj) to save space.
,
I
A
,
t
;
;
,
f
We will find fj
rameterized by (m, w).
=
if
and only
tq
with z t
this has a solution z t
u>a
= 2a—
~
q
=
=e
q-q
— z*(at) ~
2(1
0.
—a
t
)a-S—^€. This establishes the next
—
claim in part (b) and ihe fact that the smallest solution has z e (at)
>
z*(a
t
)
~
ae for
some
0.
If
(mt.Wt) were a steady state of the dynamics
qualities
had the typical form
it
which the distribution of paper
would have to satisfy the first-order condition above and the
any m. and
t
of wt and for
L 2 {m. Wt\m.
The
first
above
q,
t
,
m
w The w FOC
.
t
<
Wt)
can only be
m. t sufficiently close to
= —
—
1
a Vq ~
—q)
/
/('9-£)/2
/
in
We know that Q^(m
satisfied for w > r(Mq a z
=
additional constraint that §^(mt,Wt;m.t;wt)
for
corresponds to a
)
if
t
a
t
with L parameterized by (a, z) if and only if |^ =
when L is paA simple calculation of derivatives shows that §^(?"«, Wt\ m t,wt) =
w ~
As above
Jq-q
computation shows
direct
wt ) =
and g^jfVnt, W/.;mt> Wt) <
when (m ,w
that jj^ (m w
consistent social norm. This is the first result mentioned in part (b).
t
rn,
0.
;
t
t
,
t
,wt;rn
t
).
t
;w
t
)
=
For such values
mt we have
i(m.-m. t )q
/
\./max(0,9-A/,) Vo
f{t<,-q)/2
rdrdq
+
/
'
q
-q
r
/
Wt— wn — (m.— m, )q
^
rdrdq
'0
term is the surprise due to the unexpected acceptance of papers with ^-qualities
and the second is the suprise due to the unexpected acceptance of papers with
;-;,s
lower g-qualities. Evaluating the integrals and differentiating gives
0L 2/
——{m.t,w,:,m,t,wt )
=
(t
q
-
dm,
The
is
Looking
at the
a
is
:
q
t
,
z t ;a t z t )
,
numerator
«
-
q
t
a ).
q)
(b).
It
is
also
(1
— a
2
.
t )
This
immediate from the
be.
in the equation for
^ we can
reducing a vanishes as we approach the somewhat low
a approaches one and
M f {w -w
simply this expression divided by
the second conclusion of part
is
expression that Q^(a
- l(q -
—7-
orr{t.
derivative with respect to
negative, which
2
q)
q approaches q.)
QED.
39
a
also see that the gain from
region and q approaches
t
q
(or as
References
Dc Long.
J.
Bradford, Andrei
Slilcifer,
Lawrence H. Summers and Robert
(1990): "Noise Trader Risk in Financeial Markets," Journal of Political
J.
Waldrnann
Economy
98, 703-
738.
Ellison,
Glenn (2000): "The Slowdown of the Eeonomics Publishing Process," mimeo.
Glenn and Drew Fudenberg
Economic
Theory 90, 84-115.
of
Ellison,
(2000): "Learning Purified
Mixed
Equilibria," Journal
Kami, Edi and David Schmcidler (1990): "Fixed Preferences and Changing
ican Economic Review 80 (2), 262-267.
Tastes,"
Amer-
Baruch Fischhoff and Lawrence Phillips (1982): "Calibration of Probabilities: The State of the Art to 1980." In Judgement under Uncertainty: Heuristics and
Biases, edited by Daniel Kahneman, Paul Slovic and Amos Tversky. Cambridge: Cam-
Lichtcnstein, Sarah,
bridge University Press.
Odean, Terrance (1998;: "Volume, Volatility, Price, and Profit
Above Average." Journal of Finance 53 (6). 1887-1934.
nomic Review 85
(4),
771
All Traders Are-
"Design Innovation and Fashion Cycles," American Eco-
Pcscndoifer, Wolfgang (1995):
-
When
792.
Rabin, Matthew (1998): "Psychology and Economics," Journal, of Economic Literature 36,
11-46.
Rubinstein, Ariel (1982): "Perfect Equilibrium in a Bargaining Model," Econometrica 50,
97-109.
Sen,
Amartya
omy
78, 152-157.
(1970):
Sobel, Joel (1998):
"The Impossibility of a Paretian Liberal," Journal of
"On the Dynamics
Political,
of Standards," University of California at
Econ-
San Diego
Discussion Paper 97-15R.
Spence, A. Michael (1973):
"Job Market Signaling," Quarterly Journal of Economics 87,
355-374.
Svenson, Ola (1981): "Are
We
All Less
Risky and More
Acta Psychologica 47, 143-148.
40
Skillful
than Our Fellow Drivers,"
9
Tabic
1:
Mean
references per nonrcvicw article
Pages
1975
1999
Field
Journal
Accounting
Anthropology
Anthropology
Accounting Review
Current Anthropology
Amer.
and average page lengths
Jrn. of Physical
"
-
20.9
17.8
61.4
8.9
14.0
26.6
Biology
Cell
9.1
11.5
35.4
Chemistry
Journal of the Amer. Chemical Soci
Journal of Communication
IEEE Transactions on Info. Theory
Journal of the
Communications of the
6.4
7.9
9.0
18.6
32.8
10.0
7.3
13.7
29.0
15.0
Communication
Computer Science
Computer Science
Computer Science
Demography
Ecology
Economics
Economics
Economics
Economics
Education
Education
Eng.
-
Aero.
Eiig-
-
Elec.
Eng. - Materials
Eng. - Mcch.
Finance
Geography
Geology
Geology
History
History
ACM
ACM
17.5
57.3
47.3
49.0
38.6
52.7
23.9
37.8
7.6
7.0
14.6
6.9
Demography
13.7
13.5
16.9
Ecology
Econometrica
14.8
37.5
56.2
27.2
9.8
Journal of Political Economy
Quarterly Journal of Economics
Review of Economic Studies
American Educational Research Journal
Harvard Educational Review
AIAA Journal
IEEE Transactions on Electron Devices
Journal of Materials Science
Journal of Eiig. Mechanics and ASCE
Journal of Finance
Ann. of the Assoc, of Amer. Geographers
Geology
33.0
31.1
15.1
18.0
23.8
29.7
36.7
23.5
36.4
26.8
47.2
5.8
7.8
11.5
6.6
7.2
7.7
7 8
13.9
18.0
14.9
22.2
'
15.5
-
12.9
15.0
15.3
34.8
24.4
13.9
12.7
15.9
12.2
194
15.0
37.1
4 -
4.0
Journal of Geology
17.8
15.3
American Historical Review
Journal of American History
Harvard Law Review
22.5
56.2
18.8
21.6
22.7
31.0
28.4
92.4
85.4
a
30.1
35.0
34.6
156.6
165.9
30.9
4.0
7.2
23.0
Law
Law
Yale
Linguistics
Language
Mathematics
Mathematics
Medicine
Medicine
Oceanography
Annals of Mathematics
[nventiones Mathematicae
New England Journal of Medicine
Journal of the Amer. Medical Assoc.
Limnology and Oceanography
Paleontology
Philosophy
Physics
Physics
Physics
Political Science
Political Science
Psychology
Psychology
Psychology
Journal of PaleontologyPhilosophy of Science
Physical Review Letters
Physical Review B
Physical Review D
American Journal of Political Science
American Political Science Revii
Psychological Review
Journal of Personality and Social Psych.
Sciences
Sciences
Sociology
Sociology
12.0
32.4
11.2
12.1
Anthropology
References
:
Lav.-
Journal
22.8
59.1
19.8
35.7
55.
75.2
18.0
16.1
4.1
6.6
9.5
10.2
26.5
15.8
11.3
12.8
20.6
3.3
4.0
15.4
8.9
8.5
25.4
8.9
10.7
24.2
27.6
13.8
16.9
12.7
a
19.2
16.0
22.9
16.1
37.1
30.3
51.4
8.3
14.4
7.8
11.5
21.6
a
Developmental Psychology
Nature
4.2
5.7
23.8
12.6
17.8
Science
7.7
5.5
23.3
29.7
31.2
29.2
50.7
43.7
21.4
17.7
21.6
19.2
30.8
67.1
25.2
50.7
62.7
65.9
47.7
59.1
61.2
28.4
25.2
24.9
24.2
42.3
45.4
32.3
20.8
28.6
31.5
37.2
51.0
60.0
59.3
45.8
25.8
28.5
49.2
15.5
17.2
22.7
39.3
35.8
26.2
Statistics
American Sociological Rev;
American Journal of Sociology
Journal of the Amer. Statistical Assoc.
5.9
11.5
13.5
28.3
Women's Studies
Signs
22.1
31.0
22.5
48.5
Notes: a
-
Data not adjusted
for larger
page
size.
60.1
Tabic
Duration of the review process at various journals: 1975 and 1999
2:
Mean
1975
Journal
Field
Mean
delay
:>,•."'
submission-final resubmission time
1.2
2.2
6.9
13.6
10.4
21.0
Econometrica
9.3
26.3
AIAA
Journal
5.3
8.7
Elec.
IEEE
Transactions on Electron Devices
4.6
6.0
-
Elec.
Proceedings of the
2.6
6.9
-
Materials
Journal of Materials Science
1.5
5.2
6.5
18.6
Biology
Cell
Computer Science
Computer Science
IEEE
Economics
Eng.
-
Aero.
Eng.
-
Eng.
Eng.
Transactions on Info. Theory
Journal of the
ACM
IEEE
a
Finance
Journal of Finance
Mathematics
Mathematics
Annals of Mathematics
2.0
5.5
Invcntiones Mathematicae
1.3
10.8
Philosophy
Philosophy of Science
0.9
5.8
Physics
Physical Review
0.4
1.3
Political Science
American Journal of Political Science
Psychological Review
Annals of Statistics
Journal of the Amcr. Statistical Assoc.
6.0
7.6
Psychology
Statistics
Statistics
B
1.7
18.8
15.0
18.0
10.1
18.6
Stat.
-
Bio.
Biometrika
5.3
15.1
Stat.
-
Psych.
Psychometrika
8.1
16.8
Mean
submission-acceptance time
Ecology
Ecology
Economics
Economics
Geology
Oceanography
Quarterly Journal of Economics
8.9
Review of Economic Studies
Geology
Limnology and Oceanography
Mean
b
9.2
8.5
13.0
12.1
28.8
4.6
2.2
7.0
c
8.8
submission-publication time
Astronomy
Astrophysical Journal
Chemistry
Journal of the Amer. Chemical Society
7.8
6.2
Geology
Journal of Geology
12.4
10.6
Linguistics
Language
12.8
24.S
Philosophy
Philosophy of the Social Sciences
13.8
22.1
Physics
Physical Review Letters
2.1
5.S
Psychology
Developmental Psychology
Nature
9.S
24.1
4.3
4.3
Sciences
Notes: a
-
Data
for 1979.
occurred for about
40%
6
-
10.7
Dees not include time for post-acceptance revisions (which
- Docs not include time for post-acceptance revisions
of papers.) c
(which occurred for about
7.9
90%
of papers.)
42
52 36
^7
U O
Date Due
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