Will democracy engender equality

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Will democracy engender equality?
May 8, 2006

• John E. Roemer
• Yale University

Adapted from Democracy, education, and equality
(CUP, 2006)
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• Equality of opportunity life chances are
  independent of the wealth of parents
• Education as the central institution to rectify
  disadvantage of family environment
• Democracy with party competition, where parties
  represent different interest groups (classes?)
  in society
• Will democracy implement the kind of educational
  policy which will, in the long-run, eliminate
  influence of family background on human capital
  of dynasties?

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The society

• Adults with children adults derive utility from
  own consumption (after-tax income) and childs
  future wage

Tax policy and investment in children are
political and public decisions

• Society exists for many generations

4

• Educational technology

Returns to education are private with this
technology

• Childs human capital influenced by family
  culture and by explicit investment
• assume all children have equal abilitywish to
  focus on socially generated inequality

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Adults policy preferences

• Each adult cares only about household consumption
  her childs wage

household consumption is the same as after-tax
income human capital has a consumption value,
too note no value to leisure
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Political competition

• Political struggle must settle four issues

1. How much tax revenue to collect
2. How to partition revenues into two budgets,
one for redistn consumption, the other for
educational investment
3. How to redistribute income among adults as a
function of adult wage, h (tax transfer
incidence)
4. How to target investment in children by SES
of family (incidence of investment)
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Dynamics under Laissez-Faire

( C-D utility fcn ) Let h2gth1 .
Then the ratio of the sons HC will be After t
dates the ratio of human capitals will be So
wage ratios converge to zero if bclt1
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bc1
However if bc1, then the distribution of HC
does not change with Laissez-Faire, except for a
multiplicative constant because Consequently, we
study the case bc1, as it separates neatly the
effects of democracy from technology. Any
convergence which takes place must be due to
political competition.
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Convergence to equality
We say that a sequence of distribution functions
converges to equality if where CV(F) is the
coefficient of variation of F equivalently, for
almost all pairs of quantiles we have
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Party formation

• Two parties will form, representing the rich
  and the poor. A political equilibrium will
  ensue, in which each party proposes a platform, a
  policy. One party wins the election and
  implements its policy.This entails a distribution
  of wages in the next generation.

• This process repeats, ad infinitum.

• Question What is the asymptotic distribution of
  wages/human capital of this dynamic process?

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I. Unidimensional policy space

• Denote - total
  resource fcn
• Parties each propose an affine function of h as
  the total-resource function.
• Hotelling-Downs equilibrium both parties propose
  ideal policy of voter with median human capital
• dynamics?

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Theorem 1(unidimensional, Downs)

• Let bc1. Convergence to equality of human
  capital occurs asymptotically iff the date-0
  distn F is strongly skewed

(called strong skewness because this conditions
implies skewness, i.e.,
by Jensens inequality
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Individual optimization
A voter has an optimal tax rate of 0 iff her
income is less than the mean and an optimal tax
rate of 1 iff her income is greater than the mean.
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Proof of theorem 1

• If then the ideal policy of median
  voter is a1no taxation. Thus CV(F1 )CV(F2 )
  and the distribution stays the same forever,
  except for a mult. constant.
• If then a0. Then
• The question becomes when is
• Equivalently
  for all
• Theorem
• 6. Hence convergence to equality iff
  

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Remark
That is, strong skewness is a nec and suff
condition for convergence to equality. In
particular, the distribution will be strongly
skewed at every date iff it converges to
equality! This seems inconsistent with
empirical reality the most egalitarian
distributions the Nordic countries are also the
least skewed in the world. We will recall
this anomaly later.
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II. We now introduce an - dimensional
Policy Space

• A policy must satisfy three conditions
• 1. The social budget constraint
• 2. A social norm
• 3.? and r are continuous

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• There are no other restrictions on these
  policies they need not be linear, for example.
  They are drawn from an infinite-dim space of
  pairs of functions. This models the idea that
  political competition is ruthless, no-holds
  barred (except for the social norm, which is a
  traditional restriction)

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How to conceive of political equm?

• There is no median voter theorem in this model.
  There are no Condorcet winners in the policy
  space. So if two parties each try to choose
  policy to defeat the other, there is no Nash Eqm.

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Probability of Victory
policies
But we say the true vote for t1 is where ? is a
R.V. uniformly distributed on -?,? . So
?(t1,t2)PrF(H(t1,t2)) ?gt.5
All thats important is that ? is an increasing
fcn of vote share
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Factions

• The party has preferences over policies. Its
  virtual utility function is the average of the
  utility functions of its members. But there are
  factions

• The Opportunists wish only to max the probability
  of partys victory

• The Reformists wish to max the partys expected
  utility

• The Militants wish only to announce a policy as
  close as possible to the partys ideal policy
  (max utility, not expected utility)
• display payoff functions here

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Political equilibrium

• A PUNE (party unanimity Nash equilibrium) is
• 1. a partition of citizen types into two
  constituencies

3. Neither party can deviate from its policy in a
way to satisfy all three factions, given the
policy of the other party (Nash equilibrium in
party competition)
4. Every member of each party (weakly) prefers
his partys policy to the other partys policy
(party stability) Formal definition HERE
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At a PUNE, the factions of each party have
bargained To a policy proposal, facing the
oppositions policy We use only the fact that
bargaining engenders Pareto Efficient solutions
among the class of bargainers
A PUNE (one can show) is Nash-equilibrium between
parties and a pair of Nash-bargaining solutions
(with generally unequal powers) between factions
In fact we can dispense with Reformists. So the
bargaining In each party is characterized by one
relative bargaining power (of, say, the
Opportunists).
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the UPS of M-R-O in a party, given other partys
policy
Ms util


origin is utility value when other party wins for
sure
Rs util
Os util
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Existence of equilibrium

• Fact Regardless of the dim of the policy space,
  many PUNEs exist (indeed, a 2-dim manifold)
• Multiplicity of equilibria is associated with
  different pairs of relative strengths of factions
  in internal bargaining

• Virtue of factional modelpolitical equilibria
  exist, regardless of dim of policy space.
• Thus the resolution of non-existence of political
  equm in many dimensions is to recognize
  intra-party bargaining problem

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Left and Right policies at PUNE
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Proportionality

• the consumption allocation, investment
  allocation, and total-resource allocation are all
  proportional . If X(h) is total resources
• so the previous graph is graph of r,? as well

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The manifold of PUNEs

• on upper boundary the Opportunists are decisive
• on lower boundary, the Militants are decisive
• in interior both Opps and Mils have some power

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Note that the mapping from parents h to childs
h is increasing for all policies. So each
dynasty occupies an unchanging rank in the HC
distribution, across time
We study intertemporal sequences of PUNEs where
the pivot type is in the same dynasty, at every
date. This implies that the probability of
victory of Left(Right) is constant over time
each party represents same dynasties forever.
We study two such sequences One where at each
date the PUNE is on the upper boundary of
manifold the other, on the lower boundary
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The beginning of dynamics
note that any chord on either policy graph cuts
the ordinate(vertical) axis above the origin
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We assume hereforth that bc1.
Let let eqn ofchord through
be denoted
. Know dgt0 m0. So
Critical here is dgt0. So wage ratios decrease
and the CV of wages decreases, regardless who
wins the election.
The question is Do wage ratios decrease to unity
or to some larger number? Does CV approach 0 or
a pos number?
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Dynamics of human capital
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Opportunist politics,
Large policy spaceTheorem 2Let bc 1. Let
A(h) be the intertempororal sequence of PUNEs
with dynasty h always the pivot, and lying at
each date on the upper boundary(opporst
politics) of the equilm manifold. Then the
limit CV of human capital is positive.
So opportunist politics never generate EOp in
LongRun. Unlike the unidim model.
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Dynamics with partisan politics

• Theorem 3. Let B(h) be a sequence of
  intertemporal PUNEs with pivot dynasty h, at
  every date located on the lower envelope of the
  equilibrium manifold.
• If then with
  probability 1, the CVHC converges to a positive
  number.
• (conjecture) If
  then there is a positive probability, less than
  1, that CVHC converges to zero.

an irony Convergence to equality only if the
distn is strongly skewed at every date!
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Simulations of convergence
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Strong skewness w.r.t. the pivot
of the initial distribution remains a necessary
but no longer sufficient condition for
convergence to equality.
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Downsian analysis is misleading.

• Thus the unidimensional model misrepresents the
  true dynamics of democracy
• There is no guarantee that democracy will
  produce, in the long run, equality of
  opportunity.
• essential intuition Whats ideal for the median
  voter is also ideal for the poor with a 1-dim
  policy space. Untrue on the infinite dim space.

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On the upper envelope of the PUNE manifold, both
parties play the ideal policy of the pivot voter.
This policy looks like this But in unidim
policy space the ideal policy of the median voter
(if median lt mean) is equal investment in all
children
h
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Relaxing public-ness of educn

• Historically, it is a democratic victory that
  education be public, and a further one that
  education be only public. What happens if we
  allow adults to top off public education with
  further privately funded education?
• One might expect that the Right party would
  advocate low taxes and no public education.
• In fact, we get exactly the same investment in
  children. The fraction of investment which is
  public is indeterminate.
• We will see this is consequence of there being
  only private returns to education

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Endogenous Growth
The first model can only handle exogenous
growth
We now introduce endogenous growth

• Here, we model dependency of wage on RD, and
• of technology on skill of workers.
• There are social returns to education

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Theorem 4 Let A(h) be a sequence of PUNEs
over time With constant pivot, and opportunist
politics. (Upper Boundary of the PUNE
manifold.) If d/c is sufficiently large then
wages converge to equality. Roughly speaking,
suffices.
Thus, I conjecture that we get convergence to
Equality of wages with all PUNEs, with
constant Pivot in this case.
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In the solution, every parent would like to
redistribute from her familys educational
resources to consumption. So public education is
important. It is simultaneously true that the
policy is constrained Pareto efficient.
?
r
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Education is compulsory

• evidence that dgt0.
• Because many parents would prefer to send their
  child to work instead of to school. But there
  are social returns to schooling.
• Child labor laws, school-leaving age laws
• Whether equality is generated in the LR depends
  upon the value of d/c. Difficult to estimate
  d. An attempt in DEE, Chapter 6, without
  success. But d may be quite large.

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Or externality in consumption
Suppose that That is, mothers care about other
mothers children, too. This will have a similar
effect to putting the externality in technology.
Will push towards equality.
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Conclusions

• Democracy with self-interested dynasties brings
  no guarantee of equality of opportunity in the
  long run.
• Two necessary conditions for the possibility of
  equality
• strong skewness of initial distribution
• relatively (highly?) partisan politics.

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Two alternatives
If there are social return to education , or
if mothers care about the children in other
dynasties, then the possibility of equality in
the LR increases.
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Other reasons for non-convergence

• Random talent ( or effort) element

• Imperfectly representative democracy (only 3
  generations with full suffrage)

• policies are less progressive because of labor
  supply elasticity

• exogenous shocks to wage distrns

• race/religious/ethnic issues dilute
  redistributive politics
• END here.

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The main lesson

• For democracy as such to bring about convergence
  to equality
• of human capital requires either significant
  externalities in edu-
• cational investment OR inter-dynasty solidarity
• The fact that we see that the countries which are
  most egalitarian
• are ones where strong skewness FAILS indicates
  that the assump-
• tion of self-interestedness if falseor there are
  strong externalities
• in the educational technology (social
  interactions?)
• Research topic what degree of solidarity is
  necessary to guarantee
• that democracy will produce convergence to
  equality?