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Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 1
A Note: Are (Positive) Real Options Values
a Contradiction in Terms?
Norbert Hirschauer
*
and Oliver Musshoff
**
,
♣
♣♣
♣
* Faculty of Natural Sciences III,
Institute of Agricultural and Nutritional Sciences,
Martin-Luther-Universität Halle-Wittenberg,
Ludwig-Wucherer-Str. 2, D-06108 Halle (Saale), Germany.
** Faculty of Agricultural Sciences,
Department for Agricultural Economics and Rural Development,
Georg-August-Universität Göttingen, Platz der Göttinger Sieben 5,
D-37073 Göttingen, Germany.
First version received on 6
th
May 2004
Final version received on 30
th
June 2004
Claiming analogy with financial option pricing the real options approach assumes
that the present value of investment cash flows (or: real asset value) can be
replicated by a risk-free financial portfolio; that is, this present value is considered
to be equivalent to an asset value in a complete capital market. It would be
perfectly legitimate to ask whether the complete market assumption, which is the
fundamental base of option pricing theory, also holds for real assets. This note,
however, does not investigate the arbitrary question whether the assumptions of
the real options approach are adequate. It asks the more fundamental question
whether non-zero real option values are consistent with the very model
assumptions. We demonstrate that this is not the case. Our systematic review of
model assumptions refutes the widespread opinion that so called real options can
be valued independent of subjective risk preferences. Consequently we have to
conclude that, though computed real asset values may reflect flexibility, they never
represent option values in line with option pricing theory. JEL: C61, D80, G13.
1. Introduction
Inspired by financial option pricing theory, the
so called “new investment theory” or “real
options approach to investment” investigates
entrepreneurial flexibility (cf. McDonald and
Siegel, 1986; Dixit and Pindyck, 1994). Using
the seeming analogy with American type
financial options, the risk-free interest rate is
used – independent of investors’ risk
preferences – for determining early-exercise
frontiers (optimal exercise strategies in terms
Briefing Notes in
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Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 2
of critical present values
*
V
or trigger prices
*
P
) and real option values F for time-
interdependent business decisions under
uncertainty.
In the classical application, a flexible and
irreversible investment opportunity with
uncertain outcome is interpreted as a real
option where the possibility to delay the
investment is equivalent to an American call:
The investor has the right, but not the
obligation, to buy a real asset (investment
good) at a given strike price, I (investment
costs). The present value, V, of future
investment cash flows is interpreted as the
value of the underlying asset which can
presumably be replicated. This implies that an
investment option is only exercised if its
intrinsic value, i (the positive net present value
of an immediate investment) exceeds the
continuation value, f (the discounted net
present value of the optimal future
investment). The difference
if
−
(value of
waiting) represents the opportunity costs over
time. They are caused by the fact that
“exercising an irreversible investment option
now” competes with “exercising it later”. In
other words: The only “innovative” part of the
real options approach is its claim that –
independent of investors’ risk preferences –
the risk-free interest rate may be used for
discounting. If just an arbitrary risk-adjusted
discount rate is used, there is nothing
conceptually new in the “new investment
theory” compared to flexible investment
planning which has been dealing with the
problem of time-interdependent decision-
making under uncertainty for decades.
American (financial) call options and
investment opportunities have in fact two
essential features in common: the stochastic
development of the asset value and the
flexibility of the exercise decision. A complete
market for the underlying asset, however, is
the additional precondition for a valuation of
options independent of subjective preferences.
Otherwise a risk-less replication portfolio or
hedge portfolio cannot be constructed and an
objective option value cannot be found. At
first view it seems interesting to ask whether
the complete market assumption, which is
generally acknowledged for financial markets,
also holds for different types of real assets.
Prior to that, however, this note shows that
non-zero real option values are not consistent
with the complete market assumption per se.
Therefore, an investigation into the question
whether the complete market assumption
reproduces reality adequately is obsolete.
2. Comparison of Financial and Real
Options
Financial Options
Because the owner of a financial option has
the right, but not the obligation to exercise his
option at a given strike price, he can profit
from unexpected positive stochastic shocks to
the market value of the underlying asset. For
instance, a positive value of a European option
on a time continuous underlying asset (cf.
Black and Scholes, 1973) requires a non-zero
probability that the value of the underlying
asset at expiration exceeds the strike price. It
should be noted that the expected profit of
“buying a financial option at its market price
and exercising it according to the optimal
strategy” is zero, because the option value is
computed as a fair price resulting from
homogenous expectations in a complete
market. This is equivalent with the statement
that all assets in a complete market yield the
risk-free interest. More formally: In the
absence of transaction costs the computed
value of an option
F
must be equivalent to its
market price
M
due to arbitrage:
MFMF
=
⇒
=
−
0
.
Real Options and
Industry Wide Uncertainty
Contrary to financial options, real options are
not traded on markets. Hence, there is no
certified right to buy a real asset at a given
strike price, I, which may eventually be
exceeded by the market value of the asset, V.
An investor (owner of a real option) cannot
profit from stochastic shocks to an underlying
asset value if they are experienced by all
market participants, that is, if it is a complete
market. Today, and in all future periods, he
just has the right to acquire the present value
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 3
of investment cash flows at exactly the
price
VI
=
. The investment decisions of
competitors will always entail a zero-profit
market environment because they already
invest at a critical exercise value, V
*
= I.
Consequently we know a priori that risk-
neutral valuation in combination with the
absence of a traded title forces the value of
waiting and the value of a real option to be
zero.
Dixit and Pindyck, whose book “Investment
under Uncertainty” (1994) triggered all recent
publications on real options, take account of
perfect competition using the term “industry
wide shock”. They do not concentrate on the
fact that this is, per se, equivalent with non-
existing real option values and critical exercise
values
IV =
*
. Instead they emphasise how
critical exercise values can be computed in
terms of critical prices P
*
. Their line of
thought runs as follows (cf. chapter 8): They
assume a stochastic demand which may be
described by geometric Brownian motion
(GBM). Due to market entries and exits, the
corresponding stochastic price process in a
perfectly competitive market is a regulated
GBM. Its parameters can be computed if
functional relationships (e.g. the demand
function) are known.
1
They essentially come
to the conclusion that the investment strategy
of a “myopic planner” who accounts for the
correct parameters of the price process, but
ignores the fact that it is a regulated process, is
correct in terms of critical prices P
*
.
Consequently, an analytical calculation of
optimal strategies is possible because it is not
necessary to consider the unmanageable
regulated process.
To avoid misunderstanding of this
theoretically consistent (“option”) approach it
1
In their basic thought experiment Dixit and
Pindyck implicitly assume that the elasticity of
demand is one, and that variable costs and the
rate of depreciation are zero. In this setting the
demand process translates one to one into the
price process, except for the fact that the latter is
a regulated GBM.
should be noted, that it is not exploring a time-
interdependent decision problem at all. There
are no opportunity costs over time because the
implicit assumptions (inputs to the model) are
already: V
*
= I, i = 0, f = 0 and F = 0. The
approach only answers the (technical) question
of how an initial value P
*
(which ensures that
capitalized future prices equal the given
investment cost I) may be computed, if we act
on the assumption that the price process is to
be described by a regulated GBM.
The figure, further below, provides an
overview of the results of the thought
experiment of Dixit and Pindyck which are
often subsumed as “optimality of myopic
planning”:
• Myopic and non-myopic planners will
derive the same critical exercise value in terms
of a critical price P
*
which exceeds the
annualised investment costs k per unit of
output.
• The myopic planner misinterprets this
critical price
kP >
*
and believes that
investing at
*
P
is equivalent to a present
value of the investment
*
V
which exceeds the
investment costs
I
. However, competitors
invest as soon as investment costs are covered,
and this produces a regulated price process
which in fact reduces the effective
*
V
to the
level of
I
.
• The myopic planner wrongly thinks that
he enjoys a positive option value
F
and
therefore “superprofits”. Due to competition,
however, the option value is in fact zero.
At first sight the myopic planning principle
seems to be very useful. Nevertheless, we
cannot use it for practical applications: Being
able to neglect the fact of a regulated process
is no remedy to the strategy problem in terms
of trigger prices because we are not able to
derive the correct parameters (drift and
standard deviation) of the process in the first
place: Neither the parameters of the original
stochastic demand process nor the functional
relationships between demand and price
(elasticity of demand etc.) can easily be
estimated empirically. Hence, we have to fall
back on empirical price series which are
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 4
regularly available. However, using price
series from a presumably competitive market
leaves us with the problem of finding correct
estimators for regulated time series.
Furthermore, we cannot neglect variable costs
in an adequate model. Instead of modelling
stochastic prices, we have to make sure that
capitalised stochastic investment cash flows
equal the investment costs. Due to the fact that
cash flows may be negative at times, we
cannot assume that they follow a (regulated)
GBM. Instead, we have to use open-ended
statistical tests based on empirical time series
in order to derive the most suitable cash flow
process. Because we can no longer assume a
regulated GBM with well-known parameters,
the myopic planning principle cannot be used.
Nevertheless, the theoretical model provides a
valuable structural insight: The critical value
of the stochastic cash flow will differ from
annualized investment costs for all processes
where expected future values do not equal the
present one (e.g. regulated Brownian motion,
Brownian motion with non-zero drift etc.).
Such a finding must not be confounded with
the existence of opportunity costs over time.
On the contrary, it exactly brings forth a value
of waiting and a real option value of zero
consistent with the assumptions for risk-
neutral valuation.
Real Options and
Firm-Specific Uncertainty
Using the term “idiosyncratic shock” or “firm-
specific shock” Dixit and Pindyck (1994,
p. 249) describe a different set of assumptions.
They now assume that individual firms may
suffer or profit from individual shocks.
Intuition is given by examples such as “a shift
of fashion in an industry with differentiated
products” or “a chance improvement in
entrepreneurial skills”. In other words: They
allow for individual cash flows and individual
asset values
indiv
V
instead of a general market
value
IV
=
. The assumption that the
individual asset value may exceed investment
costs (
VIV
indiv
=>
) is equivalent with the
assumption that a firm may enjoy a
comparative advantage. Nevertheless
assuming that the risk neutral valuation
principle can be used, they calculate positive
real option values in the case of firm-specific
uncertainty whenever there is a non-zero
probability that the individual asset value
exceeds the investment costs. However, due to
arbitrage considerations, computing positive
real option values conflicts with the fact that
there is no market price for real options in the
first place.
Proposition: It follows from a positive
probability for
IV
indiv
>
that the underlying
real asset is not fully replicable and that the
risk-neutral valuation principle cannot be used
if no market price is paid for this comparative
advantage.
Proof: If we accepted the risk-neutral
valuation principle, we would compute a
positive “option” value whenever there is a
positive probability for
IV
indiv
>
. However, a
computed positive option value needs to be
matched by a positive option price. Otherwise
it is not an arbitrage-free market we would
have to conclude that the individual real asset
earns an interest rate above the risk-free
interest (“superprofits”). This, in turn, would
be a violation of the essential option pricing
assumption of complete markets and fully
replicable assets. In brief: if no price is paid
for a real “option”, there can be no “option”
value either.
Conclusion: Contrary to a complete market
where the underlying asset and the option are
traded allowing for a consistent use of
contingent claim analysis, the risk-free interest
rate cannot be justified any more with the risk-
neutral valuation principle, but only with the
simplifying model assumption of risk-neutral
decision-making. Therefore, the term “real
option value” is rather misleading in the
context of firm-specific shocks. In order to be
more precise, one should term F the “value of
a flexible investment opportunity for a
presumably risk-neutral decision-maker”.
With financial option contracts we can indeed
determine the fair price for the option and
anticipate its future value. When the option is
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 5
traded, its market price coincides with the
computed value (apart from transaction costs).
With individual entrepreneurial opportunities
we would have to make the following
loophole reasoning if we wanted to “save” the
risk-neutral valuation principle: “The real
option does not yet exist, but will be brought
to existence if we pay the computed option
price.” Paying that price would then be
equivalent with procuring the comparative
advantage of a positive probability that the
individual asset value exceeds the investment
costs.” Obviously, this is neither a sensible
way out nor the perspective taken by those
who valuate real “options”.
3. Contribution of the Real Options
Approach to Investment Theory?
We have to state that contingent claim analysis
and therefore the risk-neutral valuation
principle is not consistent with the existence of
positive real options values. Instead of a
problem solving new approach which justifies
the utilisation of the risk-free interest rate
independent of individual risk attitudes, we are
again facing the old problem of how to
determine the individual risk attitude. We need
to know the individual risk attitude and
therefore the risk adjusted discount rate in
order to determine the optimal investment
strategy and the value of flexibility. If we use
– for the sake of simplicity – the risk-free
discount rate, we are only able to determine
the optimal strategy and the value of flexibility
for a presumably risk-neutral decision-maker.
That is, we are not able to differentiate which
part of an initially computed value of waiting
is in fact due to opportunity costs over time,
and which part would be eliminated if we
correctly accounted for individually required
risk premiums.
To summarize our argumentation briefly: (i) It
seems not to be realistic, but it would be
consistent with the risk-neutral valuation
principle of option pricing theory to assume
industry wide uncertainty and complete
markets for real assets. However, in spite of
the widely used term “real option approach”
for such settings, we know a priori that
positive values of waiting and real option
values cannot exist. (ii) It seems to be realistic,
but it is not consistent with option pricing
theory to assume firm-specific shocks and
therefore incomplete markets for real assets. In
spite of the widely used term “real option
approach” for such settings, the risk-free
interest rate cannot be justified with the risk-
neutral valuation principle, but only with the
simplifying assumption of risk-neutral
decision-making. Hence, we are back to
flexible investment planning and the problem
of how to estimate individual risk attitudes.
4. Conclusion
The objective of our review was to investigate
the potential of the real options approach in
order to avoid misinterpretations. Realising the
limitations of the so called real options
approach gives us the chance to assess its
effective contribution to time-interdependent
decision-making in general and flexible
investment planning in particular:
First of all, powerful technical procedures
have been developed recently for pricing
American type options and other complex
financial options. Some of them integrate
stochastic simulation of the state variable into
a general backward-recursive framework of
option pricing. Others use e.g. stochastic
simulation connected with genetic algorithms.
Sparked off by the real option discussion,
many economists dealing with dynamic
decision problems now make use of these
procedures in other fields than option pricing.
This generates a great advantage compared to
traditional decision tree approaches and
enables them, for instance, to solve the time-
interdependent problem of flexible investment
planning more easily. It also allows for
practical problem solutions even if real world
complexities such as non GBM-processes
and/or multiple stochastic variables and
correlations have to be considered.
Secondly, the real option discussion enhanced
the conceptual understanding of the
interactions between uncertainty, flexibility
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 6
and irreversibility. It generated valuable
insights into the structure of time-
interdependent decision problems, regardless
of what the actual discount rate is. The effects
of various determinants (such as the standard
deviation of the underlying asset, the interest
rate etc.) upon the value of entrepreneurial
flexibility can be easily demonstrated. Thus,
the real options approach to investment has
increased the awareness that there is an
economic value to flexibility, and that
investment decisions are time-interdependent
problems. Equally helpful are the easy-to-
understand terms “continuation value”, “value
of waiting” and “real option value”, always
taking into account that their naming cannot
be justified by the risk-neutral valuation
principle.
To conclude this review: Given the state of the
academic discussion it may be sensible to
settle on using the terms “real option” and
“real option value” in the context of flexible
investment planning, although, strictly
speaking, they are a contradiction in terms.
However, if we do so, we should always be
aware of the fact that - contrary to financial
option pricing - these terms are not to be
justified by the risk-neutral valuation
principle.
* * * * * * * * *
Figure 1: The myopic planning principle: Critical price P
*
, critical present value V
*
, and option
value F for myopic and non-myopic planners.
x
x
x x
from the myopic planner’s point of view
from the non-myopic planner’s point of view (perfect competition)
x
m* nm**
F
x
I
k
critical price P
*
critical net present
value
V
*
option value F
m* nm** m* nm**
*
**
V
*
P
*
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 7
References:
Black, F. and M. Scholes, “The Pricing of
Options and Corporate Liabilities”, Journal
of Political Economy, 81: 637 – 659, 1973.
Dixit, A.K. and R.S. Pindyck, Investment
under Uncertainty, Princeton: Princeton
University Press. 1994.
McDonald, R. and D. Siegel, “The Value
of Waiting to Invest”, Quarterly Journal of
Economics, 101: 707 – 728, 1986.
* Dr. Norbert Hirschauer is acting
Professor of Farm Management at the
Institute of Agricultural and Nutritional
Sciences of the Martin-Luther-Universität
Halle-Wittenberg. He has written
extensively on decision support in
investment/finance and risk management.
His current research and his recent
publications are focused on behavioral risks
in the agro-food business and on innovative
hedging instruments including weather
derivatives.
** Oliver Musshoff is Professor of
Agricultural Economics at the Universität
Göttingen. His main areas of research are
business management and operations
research. He has published numerous
articles on investment, finance and risk
management. His current research interests
are focused on the optimization of
production decisions and the use of hedging
instruments. Oliver Musshoff thanks the
German Research Foundation for its
financial support.
* * * * * * * *
♣
♣♣
♣
The views expressed here are personal
to the authors and do not necessarily
reflect those of the other staff, faculty or
students of this or any other institution.
**********
Book Review:
William Easterly. (2006) The White Man’s
Burden: Why the West’s efforts to aid the
rest have done so much ill and so little good.
Published by the Penguin Press. New York.
PP 436. ISBN 1-59420-037-8.
In the past six decades, richer countries have
directed over $2 trillion of foreign aid to
poorer countries. In the last decade of the
twentieth century alone, the latter have
received $50-60 billion of aid every year.
Still today nearly half of the world’s
population lives on less than two dollars a
day and has no access to sanitation.
According to a recent influential book by
Jeffrey Sachs entitled The End of Poverty:
Economic Possibilities for Our Time, a
fundamental problem is that much of the
world’s poor are caught in a poverty trap. In
order to help remedy this situation, Sachs
suggests a “big push” through substantial
increases in aid – as well as better
coordination of this aid. Since its publication
in 2005, Sachs’ book has received much
attention in both academic and government
circles.
Against this backdrop, Easterly’s new book
enters the stage with a remarkably simple,
yet sagacious question: If it is so easy to end
poverty, why has it not been done? Thus,
Easterly spends over 400 pages persuading
us why the solution is more profound than
simply having to spend even more money on
aid. Easterly can hardly be accused of being
anti-development aid since he is one of the
world’s most respected development
economists. Even without his impressive
qualifications (former senior economist at
World Bank, now a professor at NYU), his
central message is quite logical: When one
has repeatedly done something that has not
worked in the past, one cannot just keep on
doing more of the same.
Easterly criticizes past aid strategies on
several fronts. First, donors often boast
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 8
about how much aid they have given instead
of paying adequate attention to how well it
has worked. Second, just as the demise of
the former Eastern Bloc showed us that
central planning does not work, analogously
aid should not be centrally planned –
without enough attention to the agents,
markets, and circumstances on the front
lines. Solutions to end poverty, rather than
being centrally planned, have to be
innovative, include trials and errors, and
involve supporting individuals and markets
that work well. A good example of this type
of support is the creation of economic and
social initiatives from below such as those
provided by the Grameen Bank – whose
founder won the Nobel Peace Prize in 2006.
Related to this is the issue of monitoring.
Inadequate monitoring can lead to disastrous
outcomes. Consider a case where an
administrative fiat by a bureaucratic central
planner is issued to build a school, with
good intention to improve literacy in a
region. However, little else is done, such as
procuring enough teachers to staff it or
ensuring that those who are available
continue to show up for work. The members
of the local community know that the
project has failed. Nonetheless, the donor
extols its generosity to its constituents on
how well the project must be doing. The
bottom line is that the locals and aid workers
at the grass roots are in a better position to
monitor aid projects and judge their failures
and successes than the bureaucrats in suits.
On this basis, Easterly suggests that donor
agencies create and finance an independent
international evaluation body with trained
staff from both rich and poor countries to
evaluate random samples of an agency’s
efforts.
Easterly then turns to several studies which
conclude that “aid works if there is good
governance in poorer countries” – a notion
which has become widely accepted in many
circles. Based on his own recent work
published in journals and those of some
other economists, Easterly argues that this
conclusion is deeply flawed and does not
stand up to additional empirical scrutiny.
Throughout the monograph Easterly is
careful not to claim that he has all the
answers to the woes of aid. Above all, he
denounces the complacent and patronising
attitude of donors who think they know how
to solve poorer peoples’ problems better
than the stakeholders themselves. One of his
blunt messages is that donors should not try
to transform governments and societies or
waste time with more summits and
declarations. Rather, he suggests that aid
should aim to make individuals better off.
Easterly invites us to get back to the basics
and asks that aid agents: 1) be held
accountable for their actions; 2) not be
afraid to search; 3) experiment by trial and
error and learn from past experiences; 4)
receive adequate feedback from the poor;
and 5) reward successes and penalize
failures.
It is hard to think what more Easterly could
have said to stir up further debate on foreign
aid. I wish he could have spent more time
condemning the practice of the tying of aid –
which many economists see as a major
impediment to the effectiveness of aid.
Easterly sees tying as merely a rich-country
hypocrisy. I also wish that he could have
taken a more forceful approach in linking
the outcome of aid to trade issues. High
levels of subsidies, especially by donors like
the United States and the European Union,
depress prices and effectively shut out
producers from developing nations. If aid is
to generate economic growth or alleviate
poverty, it ought to be taken in tandem with
the removal of farm subsidies and opening
of markets to facilitate export growth by
developing countries.
Overall, time will prove this to be one of the
most influential books ever written on the
subject of foreign aid, its past failures, and
possible paths to its future.
B. Mak Arvin
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 9
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Nobuyoshi Yamori (Nagoya) and many others.
* * * * * * * *
Recent published research of interest:
Abhijit V. banerjee and Esther Duflo:
‘What is Middle Class about the Middle
Classes around the World?’, Journal of
Economic Perspective, Volume 22, 2.
J. Steven Landefeld, Eugene P. Seskin and
Barbara M. Fraumeni: ‘Taking the Pulse of
the Economy: Measuring GDP’, Journal of
Economic Perspective, Volume 22, 2.
Briefing Notes in Economics – Issue No. 77, June/July 2008 Norbert Hirschauer and Oliver Musshoff 10
Orley Ashenfelter: ‘Predicting the Quality
and Prices of Bordeaux Wine’, The Economic
Journal, Volume 118, 529.
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Online resources of interest (courtesy
of intute.ac.uk)
The Key Indicators of the International Labour
Market is “a critical step toward the
development of a set of tools for evaluating
and designing labour market policies in
relation to labour force participation,
employment, unemployment, educational
attainment, wages and compensation cost,
productivity and labour cost, as well as
poverty and income distribution.” The site
outlines the 18 key indicators by introducing
them, giving definitions and sources and
highlights of the data. There is a link to
working papers and publications and
information about the background of the key
indicators. The data is gathered by the ILO
(International Labour Organization).
http://www.ilo.org/public/english/employment
/strat/kilm/index.htm
The Manchester Institute of Innovation
Research combines the two former research
centres PREST (Policy Research in
Engineering, Science and Technology) and
CRIC (Centre for Research on Innovation and
Competition), to form a new centre for
innovation research in 2007, based at the
University of Manchester. The Institute has a
focus on innovation across both the public and
private sectors. Their website includes brief
details of their work including news and event
information, with links to papers and
presentations from their seminar series, a list
of working papers, information about the
postgraduate courses taught at the Institute and
a list of staff.
http://www.mbs.ac.uk/research/innovation/
The Consultative Group to Assist the Poor
(CGAP), with offices in Paris and
Washington, DC, is a " ... a consortium of 33
public and private development agencies
working together to expand access to financial
services for the poor in developing countries."
Agencies involved with this project include;
the World Bank, European Commission,
African Development Bank, Japan Bank for
International Cooperation and the Bill &
Melinda Gates Foundation. The website
contains useful information on a wide range of
related matters, including their poverty
assessment tools, microfinance regulation and
documents on how to train people in
understanding microfinance lending, CGAP
publications and a helpdesk for further
guidance.
http://www.cgap.org/
Economics of Education is part of the World
Bank website and draws together the various
activities, publications and research they
undertake in this area. They work in five key
topic areas: economic analysis of education
interventions, finance and expenditures in
education, public-private partnerships in the
education sector, school-based management
and impact evaluation. Each topic area
includes an overview, key issues, publications,
projects and learning/event information.
Reports are made available as PDF downloads.
As this is a World Bank resource, the
emphasis is on international, comparative and
developmental education in developing
countries.
http://go.worldbank.org/78EK1G87M0
