Augmented Lagrangian Method for A Mean Curvature Based Image ...
50 Pages
English

Augmented Lagrangian Method for A Mean Curvature Based Image ...

-

Downloading requires you to have access to the YouScribe library
Learn all about the services we offer

Description

  • exposé
Augmented Lagrangian Method for A Mean Curvature Based Image Denoising Model Wei Zhu ∗, Xue-Cheng Tai †, and Tony Chan ‡ Abstract High order derivative information has been widely used in developing variational models in image processing to accomplish more advanced tasks. However, it is a nontrivial issue to construct efficient numerical algorithms to deal with the minimization of these variational models due to the associated high order Euler-Lagrange equations. In this paper, we propose an efficient numerical method for a mean curvature based image denoising model using the augmented Lagrangian method.
  • image signals from noisy images with lots of applications
  • lagrangian method
  • explicit solutions
  • mean curvature
  • noisy image
  • minimization
  • image
  • surface
  • model

Subjects

Informations

Published by
Reads 33
Language English

Colonial Legacy and Economic Development in Latin America1



Rafael Dobado González
Complutense University








“Such is the interest aroused by the
misfortune of a vanquished people that it
often makes men unfair to the
descendants of the victorious people.”
Humboldt (1822:1991), pp. 54-55.




1. Introduction


2 Colonialism is back in fashion again. In recent years it has
become a popular subject of study for economists and economic
historians. From among the several known forms of colonialism, the
Spanish colonial period in America is probably the one which is
drawing more attention. That is so because, for a growing literature,
there is a causal relationship between Spanish colonialism or, if you
prefer it, its colonial legacy and the past and present problems of
economic development in Latin America. The clearest expression of
those problems opinion would be the difference between economic
development in North America and in the rest of the Continent. Two

1
Draft: please do not cite or circulate.
2 It would appear that nobody is much concerned about the fact that under the
heading of “colonialism” there are being designated realities that, strictly speaking,
are incommensurable: what has Roman colonialism in pre-imperial Baetica
(Andalusia) in common with Cecil Rhodes´ activities in Zimbabwe? Or the conquest
of Tenochtitlan by Cortés in 1521 with the establishment of British rule in the
Hindustani Peninsula in 1858? Not much, in fact. Furthermore, some similar
historic episodes, with an undoubted importance and similarity with the aforesaid,
such as the invasion of India by the Moguls or the conquests in Asia, Africa and
Europe by the Ottomans are not usually associated with the idea of colonialism.
Therefore, let us accept that the idea of colonialism is generally associated with
Occidental Europe between roughly 1500 and 1960.
1 sets of works, the one by Engermann and Sokoloff (1994, 2002 and
2005) and the other by Acemoglu, Johnson and Robinson (2001a and
2002), have proved to be especially decisive. In fact, they have, in
my opinion, shaped what I term the “new orthodoxy” regarding the
relations between institutions, colonialism and economic growth.

This “new orthodoxy” is succeeding in exerting a growing
intellectual influence. In his latest book, The Mystery of Economic
Growth, Helpman devotes a whole chapter to institutions and politics,
which includes a section dealing with the influence of colonial origins
3 on economic development. In The White Man’s Burden, Easterly also
adheres to those who postulate a connection between colonialism and
4contemporary economic problems. Of more practical importance is,
perhaps, the fact that the World Bank has adopted the “new
orthodoxy” in several of its latest publications. The examination by
De Ferranti et al. (2004) of the historical roots of inequality in Latin
America basically consists in a description of the main points of the
5“Engerman-Sokoloff version” of the “new orthodoxy”. The Report on
6World Development is a monograph on equity and development.
However, in reading it, one becomes surprisingly aware of the
presence of terms closely associated with the history of colonial Latin
America such as “conquistadores”, “encomienda”, “encomenderos”
and “mita”. The “new orthodoxy” is openly defended: “The
institutions that emerged in the main Spanish colonies greatly
benefited the Spanish crown and the Spanish settler elite, but they
7did not promote prosperity in Latin America.”

In Poverty Reduction and Growth: Virtuous and Vicious Circles
we again find, exposed explicitly, one of the basic tenets of the “new
orthodoxy”. Main contemporary economic problems in Latin America

3
“The influence of institutions imposed by colonizing powers on the development of
various territories and countries has received particular attention. Some have
argued that a colonizer has a decisive impact on the formation of its former
colony’s political, legal, and economic performance.” Helpman (2004, p. 122).
4 “This chapter argues that old conventional wisdom was correct –the previous
imperial era did not facilitate economic development. Instead, it created some of
the conditions for today’s unsuccessful interventions; failed states and dab
government.” Easterly (2006, p. 272).
5 “Following Engerman and Sokoloff (1997, 2000, 2002) and Acemoglu, Johnson,
and Robinson (2001, 2002), the authors of this chapter argue that the
contemporary situation cannot be understood without recognizing that extreme
inequality emerged soon after the Europeans began to colonize the Americas half a
millennium ago, and has been reflected in the institutions they put in place.” De
Ferranti et al. (2004, p. 41).
6
It is not by chance that the cover of the report – as a metaphor of inequality, in
my interpretation – shows a fragment of the mural by Diego Rivera entitled “Sueño
de una tarde dominical en la Alameda Central”, which is conserved in the Museo
Mural Diego Rivera, Mexico City.
7
World Bank (2005, p. 112).
2 (low income level, inequality and persistent poverty) are not
independent of the Spanish “colonial legacy”:

“Is there something intrinsic to the region that has left it with
relatively low growth and high levels of inequality and poverty?
The World Bank’s Latin American region flagship Inequality in
Latin America: Breaking with History? (…) argued that
exclusionary institutions set up during the European conquest
to exploit existing mineral wealth and indigenous populations,
and the particular crops suited to the region’s climate (such as
sugar plantations based on a slave workforce), led to highly
unequal access to land, education, and political power at least
until the late 1800s and thus had adverse consequences for
8growth and inequality for a long time,…”

Thus, the “new orthodoxy” has spread beyond the strictly
academic limits and might eventually bias future measures of
economic policy. That is the reason why the discussion of this subject
stirs up an additional interest as an adequate diagnosis is a necessary
–but not sufficient- condition for the solution to the problems of
several hundreds of millions of Latin Americans.



2. Brief description of the “new orthodoxy”


It is not easy to summarize in a few lines the ideas of
Engerman and Sokoloff (1994, 2002 y 2005). Certainly, these ideas
have been changing somewhat in the course of time, but there is a
central aspect in them. This is the decisive role assigned to extreme
inequality in explaining the economic differences between the ex-
British colonies in North America and the Spanish colonies in the rest
of the American continent.

In turn, the differences in equality would be in accordance with
those already existing in the initial endowment of factors in the
various colonies. Thus, the areas (the Caribbean and Brazil) with
favourable conditions for growing sugar cane or other that presented
scale economies would end up characterized by large
plantations based on the employment of slave labour and became
very unequal societies. Inequality in continental Hispanic America
arose from the abundance of indigenous population and from the
granting of lands, mineral deposits, native labour and taxes to the
colonial elite. These practices were influenced by pre-existing

8
Perry et al. (2006, pp. 2.3).
3 Mesoamerican and Andean institutions. The size of the elite was
limited by a restrictive immigration policy.

Contrarily, in the North American Eastern coast, the lesser
inequality resulted from the absence of an abundant indigenous
population and from local geographical features which made it
suitable only for small family-sized farming without significant
economies of scale. This greater equality promoted more democratic
political institutions, higher investment in public goods and
infrastructure, and a relatively easy access to property rights and
economic opportunities. All these circumstances promoted economic
growth and explain why Latin America fell so far behind North
America economically.

Therefore, according to Engerman and Sokoloff (1994, 2002
and 2005), the conditions prevailing originally in the colonial system
in America would exert an unavoidable influence during the following
centuries. The extremely long-lasting inertia of the most remote
colonial past, defined mainly in terms of its endowment of factors
towards 1500, is other of the central aspects in the works by these
authors.

While Engerman and Solkoloff (1994, 2002 y 2005) deal
preferably and almost exclusively with America, Acemoglu, Johnson
and Robinson (2001a and 2002) treat the subject of colonialism in a
more global manner. However, the points of contact between the
works done by both groups of authors are notorious. As can be seen,
for our purposes, the “Acemoglu-Johnson-Robinson version” of the
relations between colonialism, institutions and economic development
is only slightly different from that of “Engerman-Sokoloff”.

In short, in the article more interesting to us, Acemoglu,
Johnson and Robinson (2002) raise the question of the difference
between “institutions of private property” and “extractive
9institutions”. In those European colonies where there was an
abundant native population, the colonizers established “extractive
institutions”, whereas those of “private property” were set up in
scarcely populated colonies. Taking population density and
urbanization as indicators, it would appear that the future colonies of

9 “…, we hypothesize that a cluster of institutions ensuring secure property rights
for a broad cross section of society, which we refer to as institutions of private
property, are essential for investment incentives and successful economic
performance. In contrast, extractive institutions, which concentrate power in the
hands of a small elite and create a high risk of expropriation for the majority of the
population, are likely to discourage investment and economic development.
Extractive institutions, despite their adverse effects on aggregate performance,
may emerge as equilibrium institutions because they increase the rents captured by
the groups that hold political power.” Acemoglu et al. (2002, p. 1.235).
4 the former type (Mongol, Inca and Aztec empires, for example) would
not only be richer than those of the latter (Canada, U.S.A. and New
Zealand) towards 1500, they would also be among the most
10prosperous areas of the world. Paradoxically, three centuries later,
the pre-colonial situation has already been inverted as a consequence
of the “institutional reversal” caused by colonialism. As was to be
expected by following this line of argument, Spanish colonialism and,
11as usual, the mining sector particularly are negatively judged. The
“reversal of fortunes” between North America and the rest of the
Continent would have dramatically altered the relative situation
prevailing there 500 years ago and it would have been explained by
12the “institutional reversal” caused by colonialism.

With an unquestionable intellectual appeal, the “conjecture of
inequality” of Engerman and Sokoloff and the “institutional reversal
hypothesis” of Acemoglu, Johnson and Robinson present an important
basic similarity between them: Both of them ascribe a decisive and
lasting role to the institutions in the explanation of the different
economic results achieved by human societies in the long term. In
both cases, the “weight of history” is conspicuously present. They
also share a difficult and ambitious aim: no less than making

10 “This paper documents a reversal in relative incomes among the former
European colonies. The Mughals in India and the Aztecs and Incas in the Americas
were among the richest civilizations in 1500, while de civilizations in North America,
Canada, New Zealand, and Australia were less developed. Today the United States,
Canada, New Zealand and Australia are an order of magnitude richer than the
countries now occupying the territories of the Mughals, Aztec and Inca Empires.
Today the United States, Canada, New Zealand, and Australia are an order of
magnitude richer than the countries now occupying the territories of the Mughals,
Aztecs, and Inca Empires.” (Ibídem, p. 1.231).
11
“… while in a number of colonies such as the United States, Canada, Australia,
New Zealand, Hong Kong, and Singapore, Europeans established institutions of
private property, in many others they set up or took over already existing
extractive institutions in order to directly extract resources, to develop plantation
and mining networks, or to collect taxes. Notice that what is important for our story
is not the “plunder” or the direct extraction of resources by the European powers,
but the long-run consequences of the institutions that they set up to support
extraction. The distinguishing feature of these institutions was a high concentration
of political power in the hands of a few who extracted resources from the rest of the
population. For example, the main objective of the Spanish and Portuguese
colonization was to obtain silver, gold, and other valuables from America, and
throughout they monopolized military power to enable the extraction of these
resources. The mining network set up for this reason was based on forced labor and
the oppression of the native population.” (Ibidem, p. 1264).
12
“In fact, historical and econometric evidence suggests that European colonialism
caused an “institutional reversal”: European colonialism led to the development of
institutions of private property in previously poor areas, while introducing extractive
institutions or maintaining existing extractive institutions in previously prosperous
places.” (Ibidem, p. 1235).
5 institutions “endogenous”. Institutions would be explained either
directly -Engerman and Sokoloff- or indirectly, via wealth -Acemoglu,
Johnson and Robinson- by the size of the native population in contact
with the colonizers. Thus, this variable plays a very important role in
both cases.

Likewise, the ones as well as the others “de-hispanicize” the
question. Thus, their explanations are opposed to those of a
Neoweberian “Landes-type”, which may be grouped together under
the heading of “culture matters” and emphasize the burden that the
13Iberian culture would impose on economic development. An
extreme version of this line of thought is given by Harrison (2000):
“In the case of Latin America, we see a cultural pattern, derivative of
traditional Hispanic culture, that is anti-democratic, anti-social, anti-
progress, anti-entrepreneurial, and, at least among the elite, anti-
14work.” Neither do they exactly coincide with the “North-type”
institutionalism. According to this author, the contrast between the
results of North America and Latin America would also reflect the
15long-term effect of the institutional differences. However, this would
be the end of the coincidences. North seems to believe that
institutions would be exogenous, not endogenous, as they end up by
16being determined by the beliefs.

In spite of their undeniable improvements with respect to what
could be termed “old institutional orthodoxy” regarding Spanish
colonialism in America, neither the “conjecture of inequality” of
Engerman and Sokoloff nor the “institutional reversal hypothesis” of

13 “Max Weber was right. If we have learned anything from the history of the
economic development, it is the culture makes all the difference” Landes (2000, p.
2). In Landes (1998) a chapter –“The South American Way”- is devoted to show
the cultural limitations of the imitation of the Iberian society that Latin America
would be.
14 Harrison (2000, p. 165).
15 “Some of the contrasting performance can be explained by the standard factor
endowments analysis from neo-classical economics. Endowments were clearly a
driving force in the pattern of European colonization. But the endowments
argument must be fundamentally supplemented by the powerful consequences of
the path dependent results of colonial inheritance, the institutions of slavery and
the encomienda system, and contrasting institutional evolutions that occurred as a
consequence of this blend of economic and institutional forces over the two
centuries.” (Ibidem).
16
“The source of these contrasting institutional patterns was the fundamental
beliefs of the key players in each case. (…) That belief system, carried over to the
American colonies, provided the basic source of the adaptively efficient institutions
that evolved. In contrast, the beliefs underlying the institutions promulgated by the
Spanish Crown have provided two centuries of instability, turmoil, personal
exchange, and limited development.” (Ibidem, pp. 114-115). In fact, one may ask
whether there is any substantive difference between the viewpoints of North and
Landes.
6 Acemoglu, Johnson and Robinson are free from weak points. Some of
them are briefly examined subsequently.

This work, which is not intended to be exhaustive, criticizes
some of the fundamental ideas exposed in the two sets of works. I
base my arguments, mainly but not exclusively, on the case of
Mexico. In my opinion, the “new orthodoxy” is not consistent with the
evidence furnished by the Pre-Hispanic, colonial and post-colonial
economic history. The excessive generalization is also a deficiency.
Latin America is not only very heterogeneous economically but
Mexican regions themselves are very unequal. Another shortcoming
is the oversight of the fact that colonialism has its own “history”, that
is to say, there occurred things, of no little importance, between the
th thbeginnings of the 16 and 19 centuries.

No less surprising is the overlooking of the important fact that
history continued after 1820. On the other hand, it has not yet been
proved that economic institutions in colonial Mexico (New Spain)
should have given rise to an extremely unequal society or that they
should be exclusively “extractive”, that is to say, inefficient from the
viewpoint of economic development. What we know about New
Spanish mining –the economic sector that would better represent
Spanish colonialism in America according to the “new orthodoxy”–
does not permit maintaining such interpretation of the colonial
economic institutions, at least, in New Spain.

Additionally, my work gives some broad outlines of what could
eventually end up by providing an alternative explanation for the
“new orthodoxy”. It includes contributions from various areas of
knowledge, such as Geography, Archaeology, Anthropology, History
and Economic Development


3. Criticism of the “new orthodoxy” in outline


3.1. Some general questions:

In the first place, the “new orthodoxy”, particularly in the
“Acemoglu-Johnson-Robinson version” generalizes excessively.
In Latin America, such different economic situations coexist that they
cannot be classified into a single taxonomic category. That is to say,
from a strictly economic viewpoint, it is perfectly legitimate to feel
doubtful about the existence of such a sufficiently homogeneous Latin
America as to be recognized as a separate entity endowed with
sufficient realism and operating capacity. While the per capita GDP of
Argentine, Chile and Uruguay is on a level with that of Eastern
Europe, in Bolivia and Honduras is similar to the one of some poor
7 countries in Asia and Africa. In the confines of South America –see
Map 1- we find an illustrative example of the extremely economic
heterogeneity of contiguous or nearby countries. But it so happens
that the differences between Mexico and some Central American
countries (especially, Honduras and Nicaragua) are certainly striking.
How is it possible to reconcile such a wide diversity of results with
only one common explicative cause? Would it not be necessary more
particularization?

Furthermore, some Latin American countries are by themselves
extreme cases of economic heterogeneity. Mexico is a good example:
in 2004, the factor of difference between the per capita GDP of the
first five states (16.7% of population) and the last five ones (15.8%)
was five. In reality, the intra-Mexican differences are so considerable
that these five “richest” states have, in PPP, an average product that
is slightly lower than the Spanish one and similar to that of Korea,
Israel, Greece, Slovenia or Portugal, whereas that of the “poorest”
states is near the one of Guatemala, Philippines, Sri Lanka or Egypt.

Even more striking is another fact that frequently passes
unnoticed. The per capita GDP of the 16 millions of inhabitants of the
five richest Mexican states is only slightly lower than that of the five
poorest North American states. Thus, these richest Mexican states
are economically nearer to the poorest North American states than to
the poorest states of Mexico. Then, the border line between the
“success” of North America and the “failure” to the South of Bravo
River somewhat fades away if the respective economies are broken
down into their component parts.

In the second place, even though the “new orthodoxy”
emphasizes the role of history in the explanation of contemporary
problems, it turns out that the economic history of Latin America, or
of other ex-colonies, hardly appears either in the works by Engerman
and Sokoloff or in those by Acemoglu, Johnson and Robinson. In this
respect, it suffices to take a look at the bibliographies accompanying
their works. In my opinion, theirs is a history without facts, only
time: in their view, there is no change worthy of mention between
the initial conditions existing towards 1500 and the final conditions
thprevailing at the beginning of the 19 century. Regarding Mexico, it is
simply inconceivable to admit tacitly or expressly that the structures
arising in the first decades of the colonial period should remain
unchanged up to the Independence or that they only should give rise
to others no less unequal.

There were complex agrarian structures in wide rural areas of
Central-Southern New Spain which changed in the course of the
colonial period. Besides, specially in the North, sparsely populated at
ththe beginning of the 16 century, the mining centres, the agrarian
8 and commercial areas intended to provide for their needs, and the
cities and their agrarian environments, constitute radical novelties
with respect to the old cliché representing the situation immediately
after 1521, which Engerman and Sokoloff made extensive to the
three subsequent centuries. These novelties are hardly admissible by
the concept of an extreme economic polarization between an elitist
white minority elite and an indigenous majority. As to ethnicity,
mestizos were far from irrelevant. In economic terms, intermediate
groups, who did not lack resources, performed fundamental functions
in the New Spanish economy, especially during the late colonial
period. On the other hand, many institutions in New Spain were
genuinely of “private property”.

Furthermore, what about the post-colonial economic history?
This hardly exists in the “new orthodoxy” except for showing the
force of the “path dependency” which appeared very early in the
beginning of the colonial period. Does it mean that what happened in
th ththe 19 and 20 centuries did not either respond to other factors that
were not present in the colonial period? Evidently, the answer must
be in the affirmative: there are other long-lasting factors that were
not present among the initial conditions of the colonial system, which
are not a mere result of the “path dependency”. In my opinion,
relevant examples in this respect are the following: the long phase of
internal and external conflicts after the Independence; the “export-
thled growth” in the last decades of the 19 century and the beginning
thof 20 century; the “inward-looking development”; the cold war. The
laudable intention -on the part of the “new orthodoxy”, particularly in
the “Acemoglu, Johnson and Robinson version”-, of making the
institutions endogenous lacks some precision and adequacy for the
changing known facts. The extractive institutions -not well defined,
by the way – would arise where there is an abundant indigenous
population in accordance with pre-existing patterns or introducing
17new ones. As a component of the initial factor endowment, the
abundance of indigenous population has almost a similar importance
for the emergence of institutions that generate extreme inequality in
18the “Engerman-Sokoloff version”. However, we know that the
aboriginal population was much unequally distributed throughout the

17
“…, a large population and relative prosperity made extractive institutions more
profitable for the colonizers; for example, the native population could be forced to
work in mines and plantations, or taxed by taking over existing tax and tribute
systems.” Acemoglu et al. (2002, p. 1.235).
18
“Extreme inequality in wealth and human capital came to characterize much of
Spanish America as well. The inequality arose here from the endowment of large
populations of Native Americans surviving the initial impact with the diseases the
Europeans brought with them, and from the Spanish practices (which were
influenced by pre-existing Native-American organizations in Mexico and Peru) of
awarding claims on land, native labor, and rich mineral resources to members of
the elite (whose number were limited by restrictive immigration policies).”
Engerman y Sokoloff (2005, p. 4).
9 American continent before the arrival of the Iberian conquistadors.
Not only Argentine, Uruguay and Costa Rica were sparsely populated,
as Engerman and Sokoloff (2005) recognize. The same can be said
about a great part –the greatest part in fact– of the American
continent. Then, why can almost all of it be characterized by
extractive institutions and extreme inequality? Why would they
present similar contemporary economic problems?

On the one hand, we also know that a major disaster followed
the Conquest and that it was especially intense in the more densely
19populated areas. How could institutions arising from an initial
abundance of indigenous remain unharmed by the sinking of that
population? Furthermore, Carmagnani (2004) reckons that “the
persistent deficit of labour force” is one of the main characteristics of
the “economic refundation” of Latin America during the last third of
th th 20the 16 century and the first half of the 17 century. And in
addition to the above, there is the abundance of natural resources.
That is the reason why in order to exploit them in a situation of
labour shortage it was decided by “the proprietors to introduce
21compulsory work under coercion” For this author, big states were
predominant only from the middle of the 17th century and would also
respond to the demographic sinking: “Its development, in fact,
appears strongly conditioned by the existence of enormous areas of
land abandoned after the destruction of the indigenous population,
and of lands that were not used productively in the areas of tribal
22predominance,…” Thus, in some cases, the cause of the unequal
and/or extractive institutions, would exactly be the opposite to the
one suggested by the “new orthodoxy”.

On the other hand, Carmagnai (2004) also draws attention to
an aspect of the matter which has scarcely been discussed above. It
is the question of the importance of intermediate economic groups in
some areas where natives or mestizos –more rarely whites, I would
add– perform an important role and who must be integrated into the
excessively polarized scheme presented by the “new orthodoxy”
which, otherwise, would become too simplistic:

“The reality of the American colonial world therefore differs
from the common image of a society composed by a few
23dominating and many dominated people.”


19
A recent work, which could however be said to have a rather “classical”
inspiration, meaning as such the one appearing with Bora and Cook, is Livi-Bacci
(2006).
20 Carmagnani (2004, pp. 47-69).
21 Ibidem, p. 55.
22
Ibidem.
23
Ibidem, p. 87.
10