UNIVERSITY OF CALIFORNIA, IRVINE Essays on Corruption and Governance DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Economics by Amjad Toukan Dissertation Committee: Stergios Skaperdas, Chair Michelle Garfmkel Priya Ranjan Donald Saari 2007 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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UNIVERSITY OF CALIFORNIA, IRVINE
Essays on Corruption and Governance
DISSERTATION
Submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in Economics
by
Amjad Toukan
Dissertation Committee:
Stergios Skaperdas, Chair Michelle Garfmkel
Priya Ranjan Donald Saari
2007
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 3271334
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To determine the optimal share to sell to large shareholders (5 , the optimal
share to keep a* and the optimal share to sell to dispersed shareholders (1 - a - [1) ,
we plug in (16) and (17) into the maximization problem (15) above. Due to the
difficulty in obtaining a closed form solution, we have provided a numerical solution
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to the maximization problem as shown in figures 1.2 and 1.3 attached. Numerical
solution results show the optimal ownership structure that maximizes the expected
payoff to owners/managers for the different values of 6 (efficiency of the judiciary
and law enforcement system) and are discussed in the sections below.
Analysis of figure 1.2 attached:
Numerical solution results show that owners/managers get a higher return from
investing an additional dollar in the public firm than they would from retaining it
(except for investing in the public firm, we assume that the owners/managers earn
zero return on their money), so they reinvest the full amount of the equity sale
proceeds back into the public firm (y* =1).
In our model, we have assumed that the legal protection of outside
shareholders complements the efforts exerted by large shareholders in monitoring the
managers, so as the efficiency of the judiciary and law enforcement system improves
( Q t ), equity valuation by outside shareholders increase and the value of public firms
increase. Results obtained from our numerical solution are consistent with the
existing literature as we show that as the efficiency of the judiciary and law
enforcement system improves (0 T ), the optimal value to the owners/managers from
taking their firm public increases and the likelihood that entrepreneurs will take their
privately held firms public increases. An example with Vf 2 as the market value of
the private firm and Vq being the optimal value to the owners/managers from taking
their firm public is shown in figure 1.2 attached.
Analysis of figure 1.3 attached:
2 The value o f the private firm is exogenously determined in our model.
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In deciding to take their company public, three sources of value contribute to the
owners/managers payoff: expropriating part of the value of the public firm; retaining
part of the proceeds received from selling equity; and the value received from being
shareholders.
In a forward looking game, the owners/managers will decide on the optimal
ownership structure in stage two of the game in a manner that maximizes their
expected payoff from taking their firm public in stage three. The owners/managers
weigh the costs and benefits of expropriation of outside investors that comes with
control. Such private benefits of control, as described by Jensen and Meckling
(1976), do come at the expense of profits accruing to the outside investors (including
the owners/managers who keep a share of the firm). In legal regimes with weak
investor protection (low values of 6 ), the owners/managers can steal a firm’s profits
perfectly efficiently and no rational outsider would finance such a firm. In such legal
regimes, the cost of raising capital to entrepreneurs is high and the family firm
emerges as the value maximizing outcome where the original owners retain both
ownership and control.
As investor protection improves or the expropriation technology becomes less
efficient, the owners/managers expropriate less, and their private benefits of control
diminish. In such situations entrepreneurs obtain outside finance on better terms. In
addition to the legal protection of outside shareholders, the presence of large
shareholders restricts managers’ excessive spending and is in the best interest of
dispersed shareholders. Pagano and Roell (1998) show that the optimal ownership
structure chosen by the entrepreneur generally involves some measure of dispersion
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(more than one external investor). It may also involve a certain degree of monitoring
by a large external shareholder, because in order to obtain equity capital more
cheaply, the initial owner needs to restrain his own future tendency to stray. So in
legal regimes with intermediate investor protection (intermediate values of 6 ), the
optimal ownership structure chosen by entrepreneurs involves keeping the majority of
firm ownership while selling the rest of the company shares to large shareholders.
The family controlled firm emerges as the equilibrium outcome.
When legal protection of outside investors is very good (high values of 6),
there is no need for monitoring in equilibrium, and the widely held professionally
managed firm emerges as the equilibrium outcome.
Our results are consistent with La Porta, Lopez-de-Silanes, Shleifer and
Vishny (1998), Shleifer and Wolfenzon (2002) and Burkart, Panunzi and Shleifer
(2003) as we show that the concentration of ownership of shares in public companies
is negatively related to the legal protection of outside shareholders. In contrast with
Castillo and Skaperdas (2005), we obtain a negative and monotone relationship
between the legal protection of outside shareholders and the size of the ownership
share retained by the owners/managers.
1.4 Equilibrium choices where the partners compete with
the powers of persuasion
In stage three of the game, the competition between large shareholders and
owners/managers involves owners/managers and large shareholders devoting costly
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resources to influence the opinion of a third party: Board of Directors, Securities and
Exchange Commission or the courts in their favor [Skaperdas and Vaidya 2005].
Briefly, the functional form is derived using the following process: Managers and
large shareholders expend resources em and e]s on gathering information and
evidence. The evidence and information produced are presented to the Board of
Directors, Securities and Exchange Commission or the courts. Based on the evidence
and information presented, the Board of Directors, Securities and Exchange
Commission or the courts make an inference about the truth. They update their prior
beliefs in light of the evidence and information presented and the posterior beliefs
thus produced determine the probability of their judgment being in favor or against
the claimant.
In addition to the effect that resources have in collecting information and
uncovering evidence, the efficiency of the judiciary and law enforcement system
should have an effect on the ease or difficulty with which each side can collect
information or uncover evidence in favor of its cause. In our analysis, the higher the
efficiency of the judiciary and law enforcement system the easier it is for
shareholders to collect information or uncover evidence in their favor and the harder
it is for managers to collect information or uncover evidence in theirs.
As before, the share of the gross value of the public firm received by the
owners/managers is a function of the two kinds of effort:
q(em,es)=0.5-<l>[del , O c r r c l (18)
with em representing costly efforts exerted by the owners/managers to influence the
opinion of the Board of Directors, Securities and Exchange Commission or the courts
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in their favor, and els denotes costly efforts exerted by large shareholders to influence
the opinion of the Board of Directors, Securities and Exchange Commission or the
courts in theirs. 1 - q(em, els) represents the share of the gross value of the public
firm received by shareholders (including the owners/managers who keep a share of
the firm).
As before the parameter 6 reflects the efficiency of the judiciary and law
enforcement system in a country and it varies between 0 and 1. An increase in 6
towards 1 would indicate stronger law enforcement or a more efficient legal system.
Conversely a movement of 6 toward 0, would indicate weaker law enforcement or a
less efficient legal system. The function ea is positive, increasing and strictly
concave. The parameter (j) is taken as exogenous in our model and it varies between
0 and 0.5. In a more fully articulated model, it would be an increasing function of the
likelihood of conviction of the managers of the firm given that there is legal evidence
against them.
Solving for Equilibrium:
Large shareholders and owners/managers choose their equilibrium efforts
simultaneously and in a manner that maximizes their total payoffs in stage three of
the game. Given values of the owners/managers share in the public firm ( a ), large
shareholders share ( f t ) and the value of the public firm to both large and dispersed
shareholders ( S ) we solve for the owners/managers equilibrium efforts by
differentiating equation (1) above with respect to em and setting it equal to zero. The
owners’/managers’ equilibrium efforts are given by equation (19) below:
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em = ( ( ! - « ) ( ! - # ) ?* O '^ ) (|“ff)5 O 9)
In order to solve for large shareholders’ equilibrium efforts, we differentiate
equation (3) above with respect to e,s and we set it equal to zero. Large shareholders’
equilibrium efforts are given by equation (20) below:
e;=(pe<|>aVp)< \ (20)
Substituting equations (19) and (20) into equations (1) and (2) above we get
the equilibrium payoffs to the owners/managers and to shareholders respectively:
V'm =Vp +0.5(a - l )Vp + ( a - 1 ) ^ 9 ) ^ (J3 V
- ((1 - a )(l - (21)
r;=O.5(l-a)F,+(l-aX00)W iP o r ) ^ V ^ c t ) < t > ( \ - V
- ( p 0 t < r ) & V & (22)
Choosing the optimal ownership structure to owners/managers:
Owners/managers choose the proportion of shares to sell to large shareholders ( f t ),
the proportion to keep ( a ) , the proportion to sell to dispersed shareholders
(1 - a - (5 ) and the fraction ( y ) of the equity sales proceeds to keep in a manner that
maximizes their expected payoff from taking their company public.
Max(V;t(a,j3,yS) + (\-y)V:(a , j3 ,y)) (23)a,p,y
Due to the complexity in solving the maximization problem above, we will
illustrate by an example as shown below:
Example:
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We assume that that the value of the public firm is determined through a Cobb-
Douglas-like form:
Vp(yS) = K ( y S f 5 whereK > 0 (24)
Substituting (24) into (22) above and in the special case of o - 0.5 , we get:
S = v;{a,p,yS) =----------------- ----------- W ~ a y K ' y ------ ...(25)[ 4 - 2 ( l - a ) p e 2f - K y + 2 ( l - a ) 2f - ( l - d ) - K 2r + J32<l>2e 2K 2r f
To determine the optimal share to sell to large shareholders , the optimal
share to owners/managers a* and the optimal share to sell to dispersed shareholders
(1 - a -/?)* , we plug in (24) and (25) into the maximization problem (23) above.
Due to the difficulty in obtaining a closed form solution, we have provided a
numerical solution to the maximization problem as shown in figures 1.4 and 1.5
attached. Numerical solution results show the optimal ownership structure that
maximizes the expected payoff to owners/managers for the different values of 6
(efficiency of the judiciary and law enforcement system) and are discussed in the
sections below.
The choice of the constant K depends in part on the value of ^ and both
values of ^ and K should be chosen in a manner that would be consistent with what
is observed in the real world. For our analysis we have chosen K to equal 20 and (f
to equal 0.25. Future work is required to get an empirical estimation for both K and
</>.
Analysis of figure 1.4 attached:
In our model, we have assumed that the legal protection of outside shareholders
complements the efforts exerted by large shareholders in monitoring the managers, so
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as the efficiency of the judiciary and law enforcement system improves (9 T ), equity
valuation by outside shareholders increase and the value of public firms increase.
Results obtained from our numerical solution are consistent with the existing
literature as we show that as the efficiency of the judiciary and law enforcement
system improves ( 0 T ), the optimal value to the owners/managers from taking their
firm public increases and the likelihood that entrepreneurs will take their privately
held firms public increases. An example with V( 3 as the market value of the private
firm and Vq being the optimal value to the owners/managers from taking their firm
public is shown in figure 1.4 attached.
Analysis of figure 1.5 attached:
Numerical solution results show that owners/managers get a higher return from
investing an additional dollar in the public firm than they would from retaining it
(except for investing in the public firm, we assume that the owners/managers earn
zero return on their money), so they reinvest the full amount of the equity sale
proceeds back into the public firm ( y* =1).
Upon deciding to take their privately held company public, the
owners/managers have to find the particular combination of concentrated and
dispersed ownership that maximizes their wealth. Three sources of value contribute
to the owners/managers payoff: expropriating part of the value of the public firm;
retaining part of the proceeds received from selling equity; and the value received
from being shareholders.
3 The value o f the private firm is exogenously determined in our model.
26
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In legal regimes with weakest shareholder protection, relatively low values of
6 , the value of the private firm exceeds its value being public (Fig. 1.4) and the
original owners decide against taking their privately held firm public. Ownership
stays with the original founders and the family owned corporation emerges as the
equilibrium outcome.
In legal regimes with intermediate shareholder protection, values of 6
midway between 0 and 1, the value of the public firm exceeds its value being private
(Fig. 1.4) and the original owners decide to take their privately held firm public.
Majority ownership stays with the original founders and the family controlled
corporation emerges as the equilibrium outcome (a* > 0.5).
In legal regimes that successfully limit the expropriation of shareholders, 6
approaching 1, the value of the public firm exceeds its value being private (Fig. 1.4)
and the original owners decide to take their privately held firm public. The widely
held corporation emerges as the equilibrium outcome.
1.5 Concluding Remarks
Our results are consistent to a large extent with the existing literature on Corporate
Governance as Burkart, Panunzi and Shleifer (2003) and Shleifer and Wolfenzon
(2002) show that firms are more valuable, shareholder expropriation is lower and
ownership concentration is lower, with better protection of shareholders. Our results
are also consistent with Burkart, Panunzi and Shleifer (2003) as they show that in
legal regimes that successfully limit the expropriation of minority shareholders, the
widely held professionally managed corporation emerges as the equilibrium outcome.
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In legal regimes with intermediate protection, management is delegated to a
professional, but the family stays on as large shareholders to monitor the manager. In
legal regimes with the weakest protection, the founder designates his heir to manage
and ownership remains inside the family. In Western Europe for example, many
publicly traded firms are family controlled through a majority ownership while in
emerging markets such as the Middle East, both ownership and control tend to stay
with the family. In the United States, separation of ownership and control occurs at
an early stage where the original founder and his family retain only marginal
ownership.
Even though our findings are consistent to a large extent with the existing
empirical literature, measuring the correct level of legal protection of outside
shareholders ( 6 ) for different countries would be vital in interpreting empirical
results. Conflicts between shareholders and managers are not the only situations
where agency costs are incurred. We can think of the company’s overall value as a
pie that is divided among a number of claimants. These include management,
shareholders, company workforce, banks, creditors and the government. Work is
currently underway to analyze the situation where the owners raise cash from both
equity and debt financing to fund the firm’s investment decisions.
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Optimal Value to Owners/Managers
0.6
0.4P u b l i c F i r m s
0.2
0.1 0.2 0.8 0.9 10.3 0.4 0.5 0.6 0.7
Theta
Figure 1.2: The partners compete in an asymmetric contest for control
(Vo*) Optimal Value toOwners/Managers
(Vf) Value of PrivateFirm
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Optimal Ownership Structure to Owners/Managers1 -
0.9 |I
I0.7 4
0.6 -
0.5
0.4 -f—
0.3
0.2 4—
[
0.1
o L0.1
p*
0.2 0.3
1
0.4 0.7 0.8 0.9 10.5 0.6
Theta
Figure 1.3 : The partners compete in an asymmetric contest for control
Owners/Managers(Alpha*)
Large Shareholders (Beta*)
Dispersed Shareholders (1- Alpha*-Beta*)
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Optimal Value to Owners/Managers
1.2 -
1 -
0.8
0.4 ■
0.2 -
/P u b l i c F i r m s
0 V 0 V <5 o - O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O ' O '
Theta
Figure 1.4: The partners compete with the powers of persuasion
(Vo*) Optimal Value to Owners/Managers
(Vf) Value of Private Firm
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Optimal Ownership Structure to Owners/Managers
Owners/Managers
■— Large Shareholders
Dispersed Shareholders
0.2
1 - a * -|3
- 0 .2 J
Theta
Figure 1.5: The partners compete with the powers of persuasion
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Chapter 2
Risk of Expropriation and the Rybczynski Theorem
2.1 Introduction
Based on the Heckscher-Ohlin (HO) Model of international trade (see for example
Bhagwati, Srinivasan and Panagariya 1998), we can derive growth paths for
production and trade in terms of a country’s capital-labor ratio. As a country grows, it
will accumulate more capital relative to the world leading to an increase in the output
of its capital-intensive goods relative to the output of its labor-intensive goods. This
is the ladder-of-development or product-cycle hypothesis: a country's output mix
depends on its stage of development, with countries moving from agriculture to labor-
intensive manufactures to high-tech manufacturing and services as their aggregate
labor productivity increases [James Harrigan and Egon Zakrajsek, 2000]. Rybczynski
theorem formally states that “If a factor endowment in a country rises (falls), and if
prices of the outputs remain the same, then the output of the good that uses that factor
intensively will rise (fall) while the output of the other good will fall (rise).”
Harrigan (1995) and Bernstein and Weinstein (1998) used the Heckscher-
Ohlin (HO) general equilibrium model with factor price equalization to provide
empirical confirmation of Rybczynski theorem. Harrigan (1995) use data on
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manufacturing output and factor endowments for 20 OECD countries from 1970 to
1985 and show that under well-known conditions, there will be a linear Rybczynski
relationship between sectoral outputs and factor endowments across countries.
Bernstein and Weinstein (1998) use data on production patterns and factor
endowments at the regional level for both OECD countries and Japan to verify the
Rybczynski theorem. In a recent paper, Xu [2002] focuses on developing countries,
finding capital abundance to be statistically significant in determining production
patterns in 18 of 28 examined industries. In his panel data regressions controlling for
time and country fixed effects as well as industry skill level (proxied by industry
average wage rate relative to the US), the value-added shares of 11 of the 12
relatively labor-intensive industries increase with country capital abundance, with
five of them statistically significant, and the value-added shares of 10 of the 16
relatively capital intensive industries decrease with country capital abundance, with
four of the 10 statistically significant. This finding contradicts the predictions of
Rybczynski theorem and presents the author with a puzzle.
The starting point of departure of this paper is to ask how corruption and risk
of expropriation affect the Rybczynski predictions. A preliminary analysis,
comparing data (1980-1983) for two countries with similar capital stock per worker
(K/L), reveals that the ratio of the output of capital intensive goods to the output of
labor intensive goods is higher for countries that have less corruption and higher
bureaucratic efficiency [The relevant data on corruption and the bureaucratic
efficiency index were taken from Mauro’s 1995]. Both indices, (recorded by country
representatives in each country) are subjective. The bureaucratic efficiency index is
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the average of the judiciary system, red tape and corruption indices. The preliminary
analysis comparing data for Japan and Venezuela is shown in table 2.1 below:
Country Year K/L C/L BEI Country Year K/L C/L BEI
JPN 1981 23,345 1.72 9.08 VEN 1981 21,635 0.45 5.42
JPN 1982 24,614 1.70 9.08 VEN 1982 21,603 0.52 5.42
JPN 1983 25,785 1.70 9.08 VEN 1983 21,606 0.48 5.42K /L = capital stock per workerC/L = (value added o f capital intensive goods) / (value added o f labor intensive goods)BEI = Bureaucratic efficiency index
Table 2.1: Comparison table for Japan and Venezuela
In this paper, we use the Heckscher-Ohlin (HO) general equilibrium model to
test empirically the hypothesis that Rybczynski predictions are less likely to hold in
countries with higher risk of expropriation and higher incidence of corruption. Risk
of expropriation and incidence of corruption by corrupt government officials are
higher in the case of capital-intensive projects due to the larger size of the prize
(larger size of the pie). So in countries where the risk of expropriation and the
incidence of corruption are high, investors prefer to invest in labor-intensive projects
instead of capital-intensive projects.
Many economists argue that it is easier for a corrupt government official to
expropriate large non-standard capital-intensive projects as opposed to smaller,
standardized labor-intensive projects. Kaufmann [1998] suggests that bribing and
rent-seeking exact a significant economic cost. Corrupt bureaucrats tend to favor
non-standard, complex, and expensive capital-intensive projects that make it easier to
skim significant sums. Coolidge and Rose-Ackerman [1997], argue that kleptocrats
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will differentially support projects that generate large corrupt payoffs. And if
revelations of corruption would destabilize the regime, the kleptocrat will favor
projects where payoffs can be easily hidden. Examples of such projects are
specialized capital-intensive projects with one of kind designs such that no one would
be able to locate a reliable cost benchmark. Coolidge and Rose-Ackerman [1997]
also point out that lacking credible commitment mechanisms, such as independent
law enforcement institutions, the corrupt autocrat may have difficulty convincing
investors to make capital investments since they may fear expropriation or
confiscatory tax and regulatory systems. The only investors willing to commit funds
may be those with a short term, get rich-quick attitude.
In conducting panel data regressions (16 developing countries over a period of
eight years 1984-1991), controlling for time and country fixed effects as well as
incidence of corruption and risk of expropriation, I find a negative and not
statistically significant relationship between capital stock per worker and the ratio of
the value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries. In the case of developing countries,
lack of statistical significance between capital stock per worker and the ratio of value
added share of capital intensive goods to the value added share of labor intensive
goods contradicts the predictions of the Rybczynski Theorem. A positive and
statistically significant relationship obtains between the Corruption and Expropriation
Index (the higher the Corruption and Expropriation Index the higher the incidence of
corruption and risk of expropriation) and the ratio of the value-added share of the
relatively capital-intensive industries to the value-added share of the relatively labor-
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intensive industries. This supports the notion that the risk of expropriation and the
incidence of corruption are important factors in determining of the shape investment
structure in a country. In countries where the risk of expropriation and the incidence
of corruption are high, investors prefer to invest in labor-intensive projects instead of
capital-intensive projects.
In conducting panel data regressions (22 developed OECD countries over a
period of eight years 1984-1991), controlling for time and country fixed effects as
well as incidence of corruption and risk of expropriation, I find a positive and
statistically significant relationship between both independent variables (capital stock
per worker and the Corruption and Expropriation Index) and the ratio of the value-
added share of the relatively capital-intensive industries to the value-added share of
the relatively labor-intensive industries.
In the next section I will suggest a modification to the Heckscher-Ohlin model
where I will allow for international variability in corruption and risk of expropriation.
The modification to the Heckscher-Ohlin model is intended to explain cross country
differences in the ratio of capital-intensive output to labor intensive output and is not
intended to explain the contradiction in the predictions of Rybczynski theorem.
Results predicted by the model show that a negative relationship exists between the
risk of expropriation by corrupt government officials and the ratio of capital-intensive
output to labor-intensive output.
2.2 The Model
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We assume that we have two countries. Each country produces two final goods, X
(capital intensive) and Y (labor intensive) using two factors of production labor and
capital. We will consider two approaches to solving our model where the same result
of higher taxation of the capital intensive good relative to the labor intensive good
obtains.
In our first approach, capital-intensive output and labor-intensive output are
subject to an expropriation tax t imposed by corrupt government officials. Risk of
expropriation by corrupt government officials is higher in the case of capital-intensive
projects due to the larger size of the prize (larger size of the pie), so we assume that
capital-intensive output is taxed at a higher rate than labor intensive output. Capital-
intensive firms maximize the following profit function:
M a x ( \ - t x )Px f x (Kx ,Lx ) - r K x - w L x (1)KX ’LX
Labor-intensive firms maximize the following profit function:
Max(\ - ty )Py f y (Ky , Ly) ~ rK y ~ WLy (2)K y ,Ly
where t x > t Y (good X is effectively taxed at a higher rate than good Y)
In our second approach, we examine the specific case of a Cobb Douglas
production function, and from our argument in section I above we assume that it is
easier for corrupt government officials to expropriate the capital endowment of firms
rather than their labor endowment. Capital-intensive firms maximize the following
profit function:
Max Px [(1 - t)(Kx ) f [Lx ]*-“ - rKx - wLx
= M a x { \ - t ) aPx [Kx ]a[Lx t a ~ r K x - w L x (3)KX’LX
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Labor-intensive firms maximize the following profit function:
MaxPY[ ( \ - t ) (K Y)Y[LYt P - rKY - w L YK y , L y
= MOX( 1 ~ t ) PPy [Ky ] P [Ly ]'~fi ~ rK y ~ WLy (4)K y , Ly
a > ft , to guarantee that good X has a higher capital intensity than good Y
(1 - 1)“ > (1 - t)/f (good X is effectively taxed at a higher rate than good Y)
From the two approaches illustrated above, we can show that taxing the output
of individual firms effectively translates into a reduction in the relative price of the
labor intensive good X to the price of the labor intensive good Y. The effective
reduction in the relative price of good X to the price of good Y, results in an increase
in the capital to labor ratio for both goods X and Y as shown in Figure (2.1) below.
In figure 2.1 below we have equilibrium initially, with the goods-price ratio
Py Wexchanging (-J—) X for Y and with the factor-price ratio (—) at ABCD. FactorPx r
K Kproportions in X and Y are indicated by points B and C respectively with —— > ——
Lx Ly
pat all factor-price ratios. An increase in the effective goods-price ratio (— ) results
Px
in the upward shift of good X isoquant. The new equilibrium factor-price ratio is at
EFGH and it is tangential to the new (—— ,y^P--)X isoquant and the Y isoquant.0 — tx ~)Px
wThe above implies that we must have a higher factor-price ratio (—) and thus higher
r
K ratios in both sectors.L
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Facto
r K
For any finite factor-price ratio, there must be full employment of both factors
in equilibrium. Furthermore, the overall factor-endowment ratio must be a weighted
average of the factor ratios in the two sectors, X and Y. This is shown in the identity:
( f ) = ( ^ X ~ L) + ( | L) ( ^ ) (5)J-j X Y
Where,
L "I- Ly — L
K X + K Y = K
and —^ and — are weights adding up to unity.
O Factor L
Figure 2.1: Equilibrium analysis
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The effective reduction in the relative price of good X to the price of good Y
P K( — i ), results in an increase in the capital to labor ratio for both goods ( —— T ) and
PY L x
Y
A change in the effective goods-price ratio does not alter the amount of capital
Kand labor available in the economy and hence the ratio -j— stays the same. In order
for equation (5) to hold, we must have a decrease in the weight relative to theL
weight — . In other words Lx has to decrease and LY has to increase. From above, L
we know that —- is increasing and since LY is increasing then K Y must be LY
increasing and K x must be decreasing.
So an effective reduction in the relative price of good X to the price of good Y
p( — -I), results in a decrease in K x and Lx and an increase in K y and Ly. This
Py
implies that the output of capital-intensive goods decreases and the output of labor-
intensive goods increases.
The same result can be reached using an algebraic representation as shown in
the derivation below. Capital-intensive firms solve the following optimization
problem.
Max Px f x (K x , Lx ) — rK x — wLxKx ,PX
The first-order conditions are
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d ° f x ( K x , L x ) _ u .
X SLX
p dfx (Kx ,Lx ) X SKX
dfx ( K x , Lx )MPT...
(6)w _ dLx _ MPLX
7 ~ 8fx (Kx ,L x r MPKx
dKx
Labor-intensive firms solve the following profit maximizing problem:
MaxPY f Y(KY,Ly) ~ rKY - wLy
the first-order conditions are
p dfY( K Y, L Y) _1 y ---------------------------------- W
dLy
dfY( K y , L Y)Y 6Ky
dfY( K Y, LY)
w _ dLy _ MPLy ^r 8fy (Ky , Ly ) MPKy
SKy
In a competitive equilibrium, each output price must equal its marginal cost,
which under the assumption of constant returns to scale equals the average cost.
Therefore we have the equations of production equilibrium:
L xP* = r ~ ^ +W^ <8)
P r E jL + w h L (9)Y Y
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where X and Y are the outputs of the capital-intensive and labor-intensive goods
P rrespectively. Now, we define the relative prices n = — and Q = — . Dividing
PY w
equation (8) by equation (9) above, we have a functional relationship between relative
output-prices and relative factor-prices:
Q K X | Lx X XK = -
ClKy Ly
Y Y
To see whether the relative goods-price ratio is increasing or decreasing in the
relative factor-price ratio, we take the logarithms of both sides and differentiate. This
yields:
Ly Lx1 dn Ky K x
71X1 (h + K-m + K)K X Ky
Therefore a higher Q T (— T) corresponds to a higher n t (— t ) if andW Py
K Konly if —— > —— which is always true since good X is more capital-intensive than
Lx Ly
good Y.
The above also implies that an effective reduction in the relative price of good
X to the price of good Y ( —X J ,) wjH result in an increase in — AnPY Q r
Wincrease in — T will result in an increase in the marginal product of labor relative to r
the marginal product of capital for both capital-intensive and labor-intensive goods as
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can be seen from equations (6) and (7) above. An increase in the marginal product of
labor relative to the marginal product of capital for both goods X and Y implies that
K Kthe capital to labor ratio will increase for both goods ( —— t ) and ( —— T ).
Lx LY
Adopting the same argument we used under the geometric representation above, an
increase in the capital to labor ratio for both goods X and Y will result in a decrease
in the output of capital-intensive goods and an increase in the output of labor-
intensive goods.
Our model developed above is useful in explaining cross-country differences
in the ratio of capital-intensive output to labor-intensive output. Our model predicts
that countries (with similar capital stock per worker) with higher incidence of
corruption and higher risk of expropriation have a lower ratio of capital-intensive
output to labor-intensive output. This implies that the spread of corruption and the
weak enforcement of property rights can have adverse effects on a country’s
development predicted by the ladder-of-development or product-cycle hypothesis: a
country’s output mix depends on its stage of development, with countries moving
from agriculture to labor-intensive manufactures to high-tech manufacturing and
services as their aggregate labor productivity increases [James Harrigan and Egon
Zakrajsek, 2000]. In section IV below, we use panel data collected for 22 developed
and 16 developing countries to show that an increase in the incidence of corruption
and the risk of expropriation can render the Rybczynski predictions statistically not
significant. We start by providing an illustration of the Rybczynski theorem.
The Rybczynski theorem predicts that holding product prices constant, an
increase in the relative supply of capital increases the relative output of the capital-
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intensive good so much that the output of the labor-intensive good decline. As can be
Kshown from equation (5) above, an increase in the relative supply of capital ( — T )L
will lead to an increase in the weight -L- relative to the weight —E . In other wordsL L
L x has to increase and Ly has to decrease.
K KIf prices are constant then ( ——) and ( —- ) remain unchanged and from the
Lx Ly
goods-output ratio shown in equation (10) below, an increase in Lx relative to LY
will lead to an increase in the relative output of the capital-intensive good to the
labor-intensive good.
Y , / * ( — ->!)— = ( - ^ - ) -------- - A ( 1 0 )Y T KY Ly f A r , i)
L y
Equation (10) above defines the relationship predicted by Rybczynski theorem
which formally states that “If a factor endowment in a country rises (falls), and if
prices of the outputs remain the same, then the output of the good that uses that factor
intensively will rise (fall) while the output of the other good will fall (rise).”
2.3 Data Description
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In this section we provide a description for the panel data collected for 22 developed
1 2(OECD) and 16 developing countries used in the empirical estimation of the model.
Subsection III.l provides a description of the corruption and risk of expropriation
index and section III.2 provides a description of the remaining variables.
2.3.1. IRIS-3 File of International Country Risk Guide (ICRG) Data - The data files
provided by the IRIS-3 file contain annual values for indicators of the quality of
governance, 1982-1997, constructed by Stephen Knack and the IRIS Center,
University of Maryland, from monthly ICRG data provided by The PRS Group.
Currently, IRIS-3 provides annual ratings for the following indicators: Corruption in
government, rule of law (law and order tradition), bureaucratic quality, ethnic
tensions, repudiation of contracts by government, and risk of expropriation. To
measure the incidence of corruption and risk of expropriation in a country, I took the
simple average of the risk of expropriation and corruption indices. The IRIS Center’s
definitions of these indices are reported below:
1- Risk of Expropriation: This variable evaluates the risk of outright
confiscation and forced nationalization of property. Lower ratings are given to
countries where expropriation of private foreign investment is a likely event (Knack,
Stephen [principal investigator(s)] / PRS Group [distributor], 1982-1997).
2- Corruption: Lower scores indicate that high government officials are likely
to demand special payments and that illegal payments are generally expected
throughout lower levels of government in the form of bribes connected with import
' List o f developed (OECD) countries: Australia, Austria, Canada, Denmark, Finland,France, Germany, Greece, Ireland, Italy, Japan, Korea, M exico, Netherlands, N ew Zealand, Norway, Portugal, Spain, Sweden, Turkey, UK, and U SA .2 List o f developing countries: Argentina, B olivia, Chile, Colombia, Ecuador, Guatemala, Honduras, India, Iran, Kenya, M alawi, M orocco, Panama, Peru, Philippines, and V enezuela.
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and export licenses, exchange controls, tax assessment, police protection, or loans
(Knack, Stephen [principal investigator(s)]/'PRS Group [distributor], 1982-1997).
From the definitions above, it can be seen that the two indices are closely
related. There may be measurement error in each individual index, and taking the
simple average of the two yields a better estimate of the determinants of the
confiscatory tax imposed by corrupt government officials. I will label the average of
the two indices the Expropriation Index (El), where the higher the El the lower the
incidence of corruption and risk of expropriation.
2.3.2. Value added data for 28 three-digit ISIC manufacturing aggregates were drawn
from the UNIDO INDSTAT3 database, available from the United Nations. The
dependent variable (value-added share of the relatively capital-intensive industries to
the value-added share of the relatively labor-intensive industries) used in the panel
data regressions below, was constructed by dividing the total value added output of
the 14 most capital-intensive industries by the total value added output of the 14 most
labor-intensive industries. Classification of labor-intensive and capital-intensive
industries wwas done in accordance with Schott [2001], where sectors were ordered
in terms of increasing capital intensity according to maximum observed value added
per worker.
Capital Stock per worker data in 1985 prices were collected from version 5.6
of the Penn World Table. The Penn World Table displays a set of national accounts
economic time series covering many countries. Its expenditure entries are
denominated in a common set of prices in a common currency so that real quantity
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comparisons can be made, both between countries and over time. The table also
provides information about relative prices within and between countries, as well as
demographic data and capital stock estimates.
Gross enrollment ratios for primary, secondary and tertiary levels of education
were collected from the UNESCO Institute for Statistics. Total enrollment in a
specific level of education, regardless of age, is expressed as a percentage of the
official school-age population corresponding to the same level of education in a given
school-year.
Finally, oil production data were collected from the CIA World Factbook.
The data are used to construct a dummy variable which takes on a value of 1 for a
country if it is one of the top 30 oil producing nations or a 0 if it is not.
2.4 Empirical Results
In this section we use panel data for 22 developed (OECD) and 16 developing
countries to test the relationship between capital stock per worker and the ratio of the
value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries. Subsection 2.4.1 focuses on OECD
countries where I find a positive and statistically significant relationship between
capital stock per worker and the ratio of the value-added share of the relatively
capital-intensive industries to the value-added share of the relatively labor-intensive
industries. The relationship remains positive and statistically significant even after
controlling for the expropriation index, education index and the oil dummy variable.
Subsection 2.4.2 focuses on developing countries where I find a negative and not
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statistically significant relationship between capital stock per worker and the ratio of
the value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries. The relationship remains negative
and not statistically significant even after controlling for the expropriation index,
education index and the oil dummy variable.
To test my hypothesis I use panel data regressions. Below is the regression
equation for my estimation:
LN(C, / Z.) = a + fi lLN(Ki /L ,) + fi2LN(EI i) + fi-iLN(OILi) + fiALN(EDUi) + u, ,
where C / L represents the ratio of the value-added share of the relatively capital-
intensive industries to the value-added share of the relatively labor-intensive
industries, K / L represents capital stock per worker, El represents the risk of
expropriation index, OIL represents the oil production index and EDU represents
the level of education index.
2.4.1. OECD Countries - In Table 2.2 below, we report our results from estimating
the Rybczynski effects for a sample of 22 OECD countries using both fixed-effects
and random-effects methods. The results are similar between the two methods. The
Hausman test supports the hypothesis of no correlation between the independent
variables and the country specific effects, so the random-effects estimator is valid.
Table 2.2 shows that there is a positive and statistically significant relationship
between capital stock per worker and the dependent variable (ratio of the value-added
share of the relatively capital-intensive industries to the value-added share of the
relatively labor-intensive industries), both in the random-effects and fixed-effects
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methods. Controlling for the risk of expropriation (expropriation index), I find a
positive and statistically significant relationship between both independent variables
(capital stock per worker and the expropriation index) and the dependent variable
(ratio of the value-added share of the relatively capital-intensive industries to the
value-added share of the relatively labor-intensive industries). Overall the R-square
increases from 0.346 to 0.415 for the random effects model and from 0.346 to 0.427
for the fixed effects model. The increase in the R-square implies that the
expropriation index plays an important role in explaining variations in the ratio of the
value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries.
Controlling for the level of education (education index), oil production (oil
dummy variable) and risk of expropriation (expropriation index) we find a not
statistically significant relationships between two independent variables (the
education index and the oil dummy variable) and the dependent variable (ratio of the
value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries), while the relationships between the
remaining two independent variables (capital stock per worker and the expropriation
index) and the dependent variable (ratio of the value-added share of the relatively
capital-intensive industries to the value-added share of the relatively labor-intensive
industries) remain positive and statistically significant.
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Table 2.2Estimating Rybczynski effects for a sample of 22 OECD Countries
Dependent variable: LN(value-added share o f the relatively capital-intensive industries / value-added share o f the relatively labor-intensive industries)
*** = significant at the 0.01 level, * = significant at the 0.10 level** = significant at the 0.05 level, Standard error in parenthesisHo (Hausman Test): Difference in coefficients not systematic
Overall the R-square drops from 0.415 to 0.374 for the random effects model and
from 0.427 to 0.406 for the fixed effects model.
2.4.2. Developing Countries — In Table 2.3 below, we report our results from
estimating Rybczynski effects for a sample of 16 developing countries using both
fixed-effects and random-effects methods. The results are similar between the two
methods. The Hausman test supports the hypothesis of no correlation between the
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independent variables and the country specific effects in almost all cases, so the
random-effects estimator is valid. Table 2.3 shows that there is a negative and not
statistically significant relationship between capital stock per worker and the ratio of
the value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries, both in the random-effects and fixed-
effects methods. Controlling for the risk of expropriation (expropriation index), I find
a positive and statistically significant relationship between the expropriation index
and the dependent variable (ratio of the value-added share of the relatively capital-
intensive industries to the value-added share of the relatively labor-intensive
industries) while a negative and not statistically significant relationship maintains
between capital stock per worker and the dependent variable. Overall R-square
increases from 0.006 to 0.011 for the random effects model and from 0.006 to 0.018
for the fixed effects model. The significant increase in R-square implies that the
expropriation index plays a very important role in explaining the variation in the ratio
of the value-added share of the relatively capital-intensive industries to the value-
added share of the relatively labor-intensive industries. The low level of R-square
with capital stock per worker as the only independent variable implies that capital
stock per worker plays a minor role in explaining variations in the ratio of the value-
added share of the relatively capital-intensive industries to the value-added share of
the relatively labor-intensive industries.
Controlling for the level of education (education index), oil production (oil
dummy variable) and risk of expropriation (expropriation index) we find not
statistically significant relationships between three independent variables (capital
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stock per worker, the education index and the oil dummy variable) and the dependent
variable (ratio of the value-added share of the relatively capital-intensive industries to
the value-added share of the relatively labor-intensive
Table 2.3Estimating Rybczynski effects for a sample o f 16 developing countries
Dependent variable: LN(value-added share o f the relatively capital-intensive industries / value-added share o f the relatively labor-intensive industries)
*** = significant at the 0.01 level, * = significant at the 0.10 level** = significant at the 0.05 level, Standard error in parenthesisHo (Hausman Test): Difference in coefficients not systematic
industries) while the relationship between the expropriation index and the dependent
variable remains positive and statistically significant in the fixed-effects method.
Overall R-square increases from 0.018 to 0.059 for the random effects model and
from 0.011 to 0.030 for the fixed effects model. The increase in R-square implies that
the education level plays an important role in explaining variations in the ratio of the
value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries.
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Results from the panel data regressions are consistent with the theoretical
results obtained in the analytical section of the paper. Controlling for the level of
education (education index), oil production (oil dummy variable) and risk of
expropriation (expropriation index), a not statistically significant relationship obtains
between capital stock per worker and the dependent variable (value-added share of
the relatively capital-intensive industries to the value-added share of the relatively
labor-intensive industries) for a sample of 16 developing countries while a positive
and statistically significant relationship obtains between capital stock per worker and
the dependent variable (value-added share of the relatively capital-intensive industries
to the value- added share of the relatively labor-intensive industries) for a sample of
22 developed (OECD) countries. The not statistically significant relationship
obtained for the 16 developing countries implies a statistically not significant rate of
change in the ratio of capital-intensive output to labor intensive output caused by a
change in the capital stock per worker, while the statistically significant relationship
obtained for the 22 developed countries implies a positive and significant rate of
change in the ratio of capital intensive output to labor intensive output caused by a
change in the capital stock per worker.
The positive and statistically significant relationship between the
expropriation index and the dependent variable (ratio of the value-added share of the
relatively capital- intensive industries to the value-added share of the relatively labor-
intensive industries) for both developed and developing countries implies that risk of
expropriation in a country plays a significant role in explaining the variation in the
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ratio of the value-added share of the relatively capital-intensive industries to the
value-added share of the relatively labor-intensive industries.
Finally we conduct robustness checks regarding our measures of industry
classification and our measures of education level. To check our measure of industry
classification, we ran panel data regressions using the eight most factor intensive
industries instead of the 14 most factor intensive industries used in our analysis
above.
Our results did not change qualitatively. For developing countries, the
relationship between capital stock per worker and the dependent variable (ratio of the
value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries) remained negative and statistically
not significant while the relationship between the expropriation index and the
dependent variable (ratio of the value-added share of the relatively capital-intensive
industries to the value-added share of the relatively labor-intensive industries),
remained positive and statistically significant. For OECD countries, the relationship
between both independent variables (capital stock per worker and the expropriation
index) and the dependent variable (ratio of the value-added share of the relatively
capital-intensive industries to the value-added share of the relatively labor-intensive
industries) remained positive and statistically significant.
To check our measure of education level, we ran panel data regressions using
separate gross enrolment ratios for each of the primary, secondary and tertiary levels
of education. Our results did not change qualitatively. For developing countries, the
relationship between capital stock per worker and the dependent variable (ratio of the
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value-added share of the relatively capital-intensive industries to the value-added
share of the relatively labor-intensive industries) remained negative and statistically
not significant while the relationship between the expropriation index and the
dependent variable (ratio of the value-added share of the relatively capital-intensive
industries to the value-added share of the relatively labor-intensive industries),
remained positive and statistically significant. For OECD countries, the relationship
between both independent variables (capital stock per worker and the expropriation
index) and the dependent variable (ratio of the value-added share of the relatively
capital-intensive industries to the value-added share of the relatively labor-intensive
industries) remained positive and statistically significant. So we can conclude that
our panel data regressions results are robust to changes in both our measures of
industry classification and education level.
2.5 Concluding Remarks
From our model developed above, we were able to provide an explanation for cross
country differences in the ratio of capital-intensive output to labor intensive output
(for countries with similar capital stock per worker). We were also able to provide an
explanation as to why certain developing countries (higher incidence of corruption
and higher risk of expropriation) are slower in climbing the ladder of comparative
advantage that a country will climb as it accumulates capital relative to the world. In
the second part of the paper we used a sample of 16 developing countries, 28
manufacturing industries and eight years, to find evidence contradicting the
predictions of Rybczynski theorem. Our empirical findings suggest that Rybczynski
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predictions could seize to hold in countries with high incidence of corruption and
high risk of expropriation. It is important to mention that the model developed in this
paper is intended to explain cross country differences in the ratio of capital-intensive
output to labor intensive output and is not intended to explain the contradiction in the
predictions of Rybczynski theorem arri ved at in the empirical part of the paper.
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Chapter 3
Contests with a Generalized Difference Form*
3.1 Introduction
The literature on rent- seeking games has expanded quite rapidly in the past two
decades. According to Anderton (2001), one of the necessary building blocks of a
unifying micro-theory of conflict economics is the contest success function (CSF),
which specifies how the appropriative efforts of agents lead to an appropriative
outcome. To date, two families of CSFs have been developed. The first family of the
CSF comes from the Tullock (1980) rent-seeking game in which a contestant’s
winning probability depends on the ratio of fighting efforts. In the second family of
success functions, called “ difference-form” success functions, a contestant’s
probability of winning depends upon the difference of fighting efforts (Hirshleifer
1995).
The game-theoretic rent-seeking model studied by Tullock (1980) marked a
starting point for numerous studies on the subject. Perez-Castrillo and Verdier (1992)
stressed the importance of the shape of the players’ reaction curve in order to
* This chapter is co-authored with Stergios Skaperdas.
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understand the impact of the technology4 of rent-seeking on the structure of the
outcome of the game. Their findings indicate that, in the case when the rent-seeking
technology displays constant or decreasing returns to scale5, the reaction curve of the
agent is continuous in the bets of the other agents, increasing at first when the outside
competition is weak and decreasing continuously as the outside competition
increases. In the case of increasing returns to scale, a sharp discontinuity in the
reaction curve obtains. This discontinuity is essentially due to the nonconvexity of
the profit function of the agent. Based on the type of technology of rent-seeking, the
authors also characterize the type of pure strategy equilibria that can result in the
game. With constant or decreasing returns to scale and for a fixed number of agents,
there exists a unique Nash equilibrium which is symmetric. With increasing returns
to scale, if the number of agents is not too large, there also exists a unique symmetric
Nash equilibrium. However, if the number of agents is too large, then there exists a
multiplicity of equilibria, which are asymmetric with some agents devoting the same
amount of resources to rent-seeking and the remaining agents remain inactive.
Nitzan (1994) surveys alternative ways of modeling rent seeking contests,
focusing primarily on the relationship between the extent of rent dissipation6 and the
underlying contest characteristics: for example the number of players, the degree of
4 Following Tullock (1980) contestant i ’s probability o f winning a contested prize isN
P j = e ' ! { e \ + , w hen contestants) = 1, ,N expend “effort” C - > 0 . A ccording to Perez-7=1j * i
Castrillo and Verdier (1992), r > 0 characterizes the returns o f scale o f the technology o f rent- seeking.5 When r < 1 the technology o f rent-seeking may be considered with decreasing returns o f scale while when r > 1 the technology is with increasing returns.6 Rent dissipation is defined as the ratio between total rent-seeking outlays in equilibrium and the value o f the contested rent.
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asymmetry between the players, and the nature and source of the rent. He showed that
the extent of rent dissipation is increasing in the number of rent seekers and in the
marginal return to lobbying outlays.
Hirshleifer (1989), studied difference-form contests with two contestants,
obtaining results that are different from those of the Tullock game. Hirshleifer
pointed out that a crucial flaw of the traditional ratio model is that neither one-sided
submission nor two-sided peace between the parties can ever occur as a Cournot
equilibrium. In contrast, both of these outcomes are entirely consistent with a model
in which success is a function of the difference between the parties' resource
commitments. Che and Gale (2000) characterized equilibria for all parameter values
for a particular class of difference-form contest success function, namely the
piecewise linear function. In their work, they find similarities between general
difference-form contests and all-pay auctions.
Skaperdas and Vaidya (2005) propose a general class of “difference-form”
contests for settings in which rent-seeking involves persuasion. Examples of such
settings include litigation, advertising, lobbying, electoral campaigning or
argumentation in policy debates where contending parties expend resources to
persuade an audience of the correctness of their view. They examine how the
probability of persuading the audience depends on the resources expended by the
parties, so that persuasion can be modeled as a contest. In the present work we
attempt to explore the properties and implications of the functional form proposed by
Skaperdas and Vaidya (2005) by providing a complete characterization of the
players’ reaction functions and the pure strategy equilibria. We also discuss the
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relationship between the extent of rent dissipation and the underlying contest
characteristics: the nature of the contested rent, the number of players, the cost per
unit of persuasion activity, and the force of the evidence.
Our results for the case of two players show that when the persuasion function
is symmetric, the reaction curve of each agent is independent of the efforts of the
other agent and the non-cooperative (persuasion) equilibrium is symmetric in the
equilibrium efforts expended by both agents. Moving to more complicated cases with
asymmetric cost functions and asymmetric contestable rents, the non-cooperative
persuasion equilibrium is asymmetric in the equilibrium efforts expended by both
agents. The agent with the relatively lower cost of persuasion per unit of her
valuation of the contestable rent expends greater effort in equilibrium. The increase
in the agent’s equilibrium effort is due to the concavity of the evidence production
function and to the decrease in her marginal cost relative to the marginal cost of the
other agent. With asymmetric evidence production functions, the non-cooperative
persuasion equilibrium is also asymmetric in the equilibrium efforts expended by
both agents, with the agent on the side of the truth expending greater persuasion effort
in equilibrium. In this case, the agent’s greater equilibrium persuasion effort is due to
the increase in her relative advantage in the production of evidence at the margin.
We also characterize the type of pure strategy equilibria that may result in the
game. First we discuss the case where the total number of agents potentially
interested in persuasion is fixed to some number, which can exceed 2, and the
persuasion function is symmetric. If the number of agents is such that the positive
profits condition is satisfied then there exists a unique Nash Equilibrium which is
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symmetric. However, if the number of agents is too large and the positive profits
condition is no longer satisfied, then there exists a multiplicity of equilibria, which
are asymmetric. Some agents devote the same amount of resources to persuasion and
the remaining agents choose not to participate. In contrast to the literature surveyed
by Nitzan (1994), we show that the extent of rent dissipation is non-monotonic in the
number of rent seekers N. We also show that the extent of rent dissipation is non
monotonic in the contestable rent and in the cost per unit of persuasion activity while
increasing in the force of the evidence presented to a third party audience. The
greater the force of the evidence presented to the third party audience, the greater the
return to the resource investment by both contestants and the higher is the amount of
persuasion effort expended by all parties in equilibrium.
Finally we examine the case when the persuasion function is asymmetric. Our
results show that the reaction curve of our agent is determined by the amount of effort
expended by the other agent and by the degree of asymmetry between the likelihood
ratios of judgment held by the third party audience. The reaction curve of each agent
is continuous in the efforts of the other agent with the reaction curve of the favored
agent increasing continuously as the outside competition increases while the reaction
curve of the other agent decreases continuously as the outside competition increases.
The paper is organized as follows. Section 2 describes an alternative to the
Tullock functional form proposed by Skaperdas and Vaidya (2005). Section 3
outlines the model under symmetry and characterizes the non-cooperative pure
strategy equilibrium with two agents. Sections 4 through 8 focus on the symmetric
7 One agent is favored in terms o f the force o f the evidence presented to the third party audience and in terms o f the negative bias in judgm ent b y the third party audience.
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case and characterize: the non-cooperative pure-strategy equilibrium with asymmetric
cost functions and asymmetric contestable rents, the non-cooperative persuasion
equilibrium with asymmetric evidence production functions, the non-cooperative pure
strategy equilibria with N agents, persuasion with a fixed number of agents N, and the
relationship between the extent of rent dissipation and the underlying contest
characteristics. Section 9 examines the non-cooperative persuasion equilibrium with
asymmetry. Section 10 concludes.
3.2 Persuasion Function as an Alternative to the Tullock
Functional Form
To lay out the building blocks of persuasion, Skaperdas and Vaidya (2005) examine
an evidence production process. Two players, player 1 and player 2, compete to
gather and present evidence so as to influence the verdict of a third party audience in
their favor. With discrete evidence production, Player 1 can either produce evidence
in her favor denoted by Ex, or offer no evidence, denoted by { }. Similarly, Player 2
can either produce evidence in her favor, denoted by E2, or offer no evidence, { }.
The production of such evidence is not deterministic. The amount of resources
enhances the probability of finding a favorable piece of evidence. The authors let
h(r}) denote the probability that player 1 will find evidence in her favor. This
probability is increasing in rx, the resources expended on finding that evidence.
Similarly h(r2) denotes the probability that player 2 will find evidence in her favor,
with that probability also increasing in the resources r2 expended by the player. Thus
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in terms of evidence there are four possible states of the world that can be faced by
the third party audience: (EX,E2),(EX,{ }),({ },E2),and({ },{ }) occurring with the
following probabilities: h(rx )h{r2), h(rx )[1 - h(r2)], [1 - h{rx )]h(r2), and
[1 - h(rx )][1 - h(r2)] respectively. Given the posterior probability of player 1 winning
(and of player 2 losing) that will be induced by each realized combination of evidence
and given the function h(.), the ex ante probability of player 1 winning (and of player
2 losing) can be straightforwardly calculated:
where n represents the third party audience’s posterior probability of winning for
player 1 and n represents the third party audience’s prior. T and 6 are defined