Matthew Effect
as a Reflexive System
metsyS evixelfeR a sa
tceffE wehttaM
Yaroslav Prytula
Dept. International Economic Analysis and Finance,
Lviv Ivan Franko National University, Ukraine
IREX Visiting scholar at George Mason University
Outline
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What is the Matthew Effect?
Evidences and logic of the Matthew Effect
Modelling of the Matthew Effect
Is the Matthew Effect a natural law?
Self-fulfilling prophesy
Reflexivity and the Matthew Effect
Ukrainian proverb
+
Poor
Fool
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Matthew Effect
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Robert K. Merton: the phenomenon when “the rich get
richer and the poor get poorer”
Other words – this is the phenomenon of accumulated
advantages.
Although originally developed by Merton to explain
advancement in scientific careers, cumulative advantage
is a general mechanism for inequality across any
temporal process in which a favorable relative position
becomes a resource that produces further relative gains.
(DiPrete and Eirich, 2006)
Saint Matthew’s Gospel (25:29):
For unto every one that hath
shall be given, and he shall
have abundance: but from him
that hath not shall be taken away
even that which he hath
Matthew Effect in science and research
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Newton, Leibniz and calculus.
‘Nobel prize’ effect (Zuckerman 1972, Merton 1988): ”the world
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Brain drain effect (Schott 1998)
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is peculiar in this matter of how it gives credit. It tends to give the credit
to already famous people.”
 ‘Harvard’ effect (Medoff, 2006): “Ceteris paribus, an article written
by an economist affiliated with Harvard University or the University of
Chicago had significantly (statistically and numerically) greater peer
recognition than if it was written by an economist affiliated with a less
prestigious university.”
 Matilda effect (Rossiter 1993, 1995): “an effect in science that has
historically promoted cumulative male advantage and female disadvantage
through the operation of old-boy networks and other discriminatory
practices.”
Matthew Effect in technology
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QWERTY effect
‘Increasing returns’ (Arthur 1996): product gains value with every
additional unit produced.
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‘Winner take all’ effect (Schiller 2004): current information
technologies may produce winner-take-all effect.
No limit to the size of technological gap
Matthew Effect in economic
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Hysteresis in unemployment (Heckman & Borjas 1980):
previous unemployment creates future unemployment.
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Compensation/bonuses for top managers (Frank & Cook,
1996): in 1974 the average CEO’s compensation of a large US company
was 35 times higher then the compensation of average manufacture
worker, in became 120 times higher in 1990s, 500 – in 2000 and reached
1000 in mid 2000 declining after 2007-08 criticism.
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Flat or progressive tax rate, Flat or regressive taxes lead to
redistribution of wealth to upper income groups creating ME, at the same
time progressive taxation often lead to tax avoidance or tax evasion and
also may create ME.
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Wealth accumulation, compound interest rate.
Wealth accumulation,
power of compounding
Difference in investing $100 and $1000 for 50 years with 5%
compounding interest rate.
12000
10000
8000
6000
4000
2000
48
45
42
39
36
33
30
27
24
21
18
15
12
9
6
3
0
0
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Matthew Effect in health
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Health accumulation
The Status Syndrome (Marmot 2008): our social standing directly
affects our health and life expectancy. Socio-economic position is an
important determinant for health outcomes.
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Marmot argues that we should make our society more
participatory and inclusive in order to increase overall public
health.
Matthew Effect in education
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Reading ability (Stanovich 1986) “slow reading acquisition has
cognitive, behavioral, and motivational consequences that slow the
development of other cognitive skills and inhibit performance on many
academic tasks”
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Skills beget skills (Heckman 2006) “Skill begets skill. Motivation
begets motivation. If a child is not motivated and stimulated to learn and
engage early on in life, the more likely it is that when the child becomes an
adult, it will fail in social and economic life”
Matthew Effect in sports
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Confusion of ability with
maturity (Gladwell 2008)
Soccer clubs like superstar
universities
Source: www.sportsscientists.com/2009/01/mattheweffect.html
Matthew Effect in Life
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Monopoly game
Winner take all
Too big to fail
Economy of scale
Migration patterns
Bank run
Urban population growth
Use of English language
Use of limited number of words for communication: Zipf’s
law
Opportunity structures
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Opportunities are not randomly distributed
Merton defines opportunity structures as
“the scale and distribution of conditions that provide various probabilities for
acting individuals and groups to achieve specifiable outcomes”
and
“the interacting processes of individual self-selection and institutional social
selection affect successive probabilities of access to the opportunity
structure”
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Example: time and place are important (Gladwell 2008): Out of
75 riches people in human history 14 were born during 9 years of
Industrial revolution
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Another example: oligarchs in Russia and Ukraine
Picture of Ukrainian oligarch
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Male
Average age – 47 years
Higher education
Place of doing business: Kyiv (40%), Eastern Ukraine
(52%)
Picture of Russian oligarch
Male
 Lives in
Moscow
 Average age
– 50 years
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Ecclesiastes, 9:11
I have seen something else under the sun:
The race is not to the swift
or the battle to the strong,
nor does food come to the wise
or wealth to the brilliant
or favor to the learned;
but time and chance happen to them all.
Other names for the Matthew Effect
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Cumulative advantages
Path-dependent increasing returns
First-mover advantage
Positive feedback loop
Success breeds success
Multiplier effect
Gibrat's rule of proportionate growth
Lock-in
Halo effect
Self-fulfilling prophecy
Preferential attachment
Merton’s Matthew Effect and
Myrdal’s circular causation
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Myrdal (1944) provides very similar analysis of cumulative
(dis)advantage (circular causation) to Merton works.
While Merton was inclined to ascribe to social systems a
natural tendency toward stable equilibrium, Myrdal was rather
skeptical of the existence of natural equilibrium of any kind
(Rigney 2010).
Myrdal points out that dynamism and instability are the
natural order of things in economics and other social systems:
“circular causation has validity over the entire field of social relations. It
should be main hypothesis when studying economic underdevelopment
and development”
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The last proposition is quite similar to Soros’s (1987) concept
of reflexivity in social systems.
Analytical formulation of Matthew Effect
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Usually ME is modeled as a differential equation of
exponential growth, i.e.
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that implies
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or in discrete case
Analytical formulation of Matthew Effect
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Adding possible exogenous influence X and stochastic term e:
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Merton argued that previous success does not directly cause
current success, but it rather increases one’s level of
resources that (in combination with other factors) increases
current success, i.e.
Analytical formulation of Matthew Effect
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Combining last two equations gives us:
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That is the same as previous representation.
Adding varying
we can derive evidence consistent
equation with growing level of inequality over time.
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Merton vs. Mincer
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Mincre’s human capital earning equation:
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States that shock has temporary effect while in Merton
cumulative advantage model it has long-lasting effect.
Merton vs. Dickens & Flynn
social-multiplier effects
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Dickens and Flynn proposed a sophisticated explanation for
the considerable rise in measured IQ between the early
1950s and the early 1980s in the Netherlands and nearly 20
other countries.
They show that the social-multiplier effects (link between IQ
and the local environment) in their model allow relatively small
exogenous changes in the environment to cause surprisingly
large changes over time in a population’s mean IQ. Their
model is, essentially:
What limits the Matthew Effect?
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Merton (1968, 1988):
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Limit of resources or capacity to expand
External factor, government interventions (redistribution)
ME will always fail to unfold in communication systems fraught with
extreme noise
Morality, altruism
Reflexivity
What reins in the Matthew Effect?
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Podolny’s (1993) points out that status-erosion occurs as
the consequence of a high-status organization’s choice to
expand in market share by encroaching on a lower-status
competitor’s niche.
What reins in the Matthew Effect?
In their article “When Do Matthew Effects Occur?” Bothner et
al. built a model of status-based competition in which actors
always experience the Matthew Effect at the micro level. They
studied what happens on macro level.
 Their findings reveal the importance of a single factor
governing whether the Matthew Effect operates freely or is
circumscribed. This factor is the
degree to which status diffuses through social relations.
 When actors’ status levels are strongly influenced by the
status levels of those dispensing recognition to them (i.e.,
status diffusion occurs), then in due course the top-ranked
actor is nearly matched in status by the actor she endorses,
i.e. no ME.
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What reins in the Matthew Effect?
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A case of status diffusion, is in the well-known account of
Baron de Rothschild’s endorsement of a friend who
requested a loan: “Reputedly, the great man replied, ‘I
won’t give you a loan myself; but I will walk arm-in-arm
with you across the floor of the Stock Exchange, and you
soon shall have willing lenders to spare”’ (Caldini, 1989).
Is Matthew Effect a natural law?
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Sloman and Dunham (2004): ME usually is present in
biological competition within species.
Arthur (1996) New business environment makes increasing
returns model (namely ME) more and more applicable.
Myrdal (1944): circular causation has validity over the entire
field of social relations. It should be main hypothesis when
studying economic underdevelopment and development
Dannafer and Gannon (2005): ME is sufficiently pervasive,
obdurate and irrepressible social tendency as to be
considered a sociological law.
Taleb (2007) criticised the “naivety” of the Matthew Effect by
pointing out that it can not explain the decline of civilizations.
Self-fulfilling prophecy and Matthew Effect
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A prediction that directly or indirectly causes itself to become
true.
Merton: “The self-fulfilling prophecy is, in the beginning, a false definition
of the situation evoking a new behaviour which makes the original false
conception come 'true'.”
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Thomas theorem (1928):”if men define situations as real, they are
real in their consequences”
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Keynes’s Beauty Contest Theory (1936)
Goodhart's law (1975): once a social or economic indicator or
other surrogate measure is made a target for the purpose of conducting
social or economic policy, then it will lose the information content that
would qualify it to play such a role.
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Examples in finance, consumer behavior, voting.
Self-fulfilling prophecy and
economist profession
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Raghuram Rajan (Chicago Univ.) on causes of recent crisis:
Could it be corruption? Some academic economists consult for
banks or rating agencies, give speeches to investor
conferences, serve as expert witnesses, and carry out
sponsored research. It would be natural to suspect us of bias.
The bias could be implicit: our worldview is shaped by what
our friends in industry believe. Or it may be an explicit bias:
an economist might write a report that is influenced by what a
sponsor wants to hear, or give testimony that is purely
mercenary.
Source: www.project-syndicate.org/commentary/rajan14/English
Reflexivity
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Reflexivity = An act of self-reference or
self-feedback.
Soros (1987): the biases of individuals
enter into market transactions, potentially
changing the perception of fundamentals
of the economy.
Umpleby (2007): Reflexivity occurs in
social systems when an actor observes
and thinks about his or her actions and
their consequences and then modifies his
or her behavior
Sourse: Umpleby 2007
Reflexivity and Matthew Effect
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Matthew Effect may be a feedback mechanism of observation
into observation, like, compounding interest rate.
Matthew Effect may be a feedback of observer to observer’s
social group back to observer, like social-multiplier effect.
Also, Matthew Effect may be a feedback of observation to
observer to observer’s (or observer’s group) behaviour to
observation, like the Facebook.
Proposition 1: Extending the notion of
Reflexivity in social science
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Weak Reflexivity refers to automatic feedback mechanism of
an object (observer) to itself when no information is needed to
initiate the mechanism. Example: compounding interest rate as
positive feedback. Many psychological heuristics represent weak reflexivity.
Keynes's Animal Spirit.
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Semi-strong Reflexivity refers to a feedback mechanism of an
object (observer) to the social group it represents. In order to
semi-strong reflexivity to occur the information between
object, social group and/or the whole society needed to
circulate. Example: income inequality, urban-rural migration.
Strong Reflexivity refers to a feedback mechanism when
observer is included in the domain of observation. Both
information and knowledge are needed for strong reflexivity to
occur. Example, economic policy making , financial crisis.
Social mechanism
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Merton(1968) defines Social mechanisms as “social processes
having designated consequences for designated parts of the
social structure.”
Other words (Hendstrom and Swedberg 1998) can be
depicted as
Inputs -> Social Mechanisms -> Outputs
Merton considered Matthew Effect as one example of social
mechanism.
Proposition 2:
Matthew Effect  Reflexivity
1. Matthew Effect is a partial case of broader notion of
Reflexivity, and
2. Reflexivity is a partial case of social mechanisms.
Ukrainian proverb (revised): what to do?
+
Poor
Fool
+
Ukrainian proverb (revised)
Poor
Intelligent
+
Thank you