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                The EconomicDynamics Newsletter

                Volume 3, Issue 1, November 2001

A free electronic supplement to the Review of Economic Dynamics
distributed through the EconomicDynamics mailing list and also available
on the web at http://www.EconomicDynamics.org/

In this issue:

- The Research Agenda: José-Víctor Ríos-Rull on the Determinants of
Inequality
- EconomicDynamics Interviews Mehmet Yorukoglu on Economic Revolutions
- Society for Economic Dynamics: Letter from the President
- Society for Economic Dynamics: Call for Papers, 2002 Meetings
- Society for Economic Dynamics: Call for Papers, 2002 CV Starr/RED
  Conference on Finance and the Macroeconomy
- Review: Kotlikoff's Essays on Saving, Bequests, Altruism, and
  Life-Cycle Planning
- Impressum 
- Subscribing/Unsubscribing/Address change 

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The Research Agenda: José-Víctor Ríos-Rull on the Determinants of
Inequality

José-Víctor Ríos-Rull is Professor of Economics at the University of
Pennsylvania. His main interests lie in distributional issues in
macroeconomics, public economics and demographic economics.

I want to take advantage of this opportunity that the EconomicDynamics
Newsletter provides me to discuss some questions that interest me, and
some tools that we are developing in addressing those questions. 

A good part of my research has dealt with the determinants of inequality.
A large dose of the effort in public policy is aimed to redistribute
resources among persons, and this can only be done effectively if we
understand what is it that makes people different in the first place. In
this respect, we (Castaneda, Díaz-Gimenez and Ríos-Rull (2000)) have
estimated a model with temporary (but autocorrelated) shocks to earnings
capabilities that generates a distribution of labor earnings and wealth as
well as a set of macromagnitudes and a tax system that is similar to that
of the U.S. In this model all agents share the same preferences and they
differ in age, wealth and in the realization of the earnings shock. The
model essentially estimates the properties of a stochastic process for
earnings opportunities. This process has built in some life cycle features
and some potential for intergenerational transmission of earnings. Our
findings state that most of the differences in earnings potential are
already there at the beginning of adulthood. Specifically, our estimates
decompose the population into four types according to the realization of
the shock. In the beginning of adulthood, the differences in the present
value of earnings among these four types are large. If the majority of the
population is normalized to one, the other three groups show present
values for earnings that are 1.63, 4.66 and a whopping 74.93 (this latter
group is very small in size) times bigger. Moreover, these characteristics
persist over generations. Households at retirement have expected values
for their progenie of 1.00, 2.47, 27.92 and 46.56 respectively. 

With very different methods, Keane and Wolpin (1997) points to the fact
that differences in the fate of people are determined very early in life.
Essentially they find that, utility-wise, cross sectional differences are
accounted for mostly (90%) by features already present in agents by age 16
rather than in the actual shocks that the agents receive after age 16.
Knowles (2001) argues that the explicit consideration of fertility choice
and its associated implication of a negative relation between fertility
and parental education, changes the implications of models where agents
smooth consumption by holding assets when facing uninsurable shocks. In
particular, wealth dispersion is greatly increased. 

These findings point out something quite important that most differences
in economic performance do not occur in the strict realm of the labor
market. On the contrary, they have occurred by the time people enter the
labor market. 

Inspired by these findings, part of my research is now devoted to the
understanding of how the family shapes the economic performance of
individuals and of their progenie. This requires the construction of
models that explicitly take into account that households and individuals
are very different entities (going against the old tradition in economics
that treats households as the basic economic unit). These models owe a lot
to the work of Gary Becker who brought the family to the realm of
economics.   

These structures have still to be embedded in models of the macroeconomy
that display aggregate characteristics that can be mapped back to
aggregate data in order to discipline the research. The discipline comes
partly due to the quantitative restrictions imposed by macroeconomic
aggregates, and partly from the general equilibrium restrictions that the
model imposes (things like the number of males of type x married to
females of type y, is equal to the number of type y females married to
type x males). The key paper in bringing the family to macroeconomics is
Aiyagari, Greenwood and Guner (2000).

The basic structure of aggregate models with families 

Let me summarily describe how these models operate. Agents differ
typically in age, sex, and other economically relevant characteristics
such as education or skill. Agents, upon becoming adults, bump into each
other and choose whether to form a household, and/or, in the case of
females choose whether to try to have a child. Their decisions depend on
who they bump into, their general characteristics (age, marital status,
education, skills) and perhaps something that is not shared by others, a
personal assessment, love in one word. The decisions depend not only on
who they bump, but also on what else is out there, this is on what agents
expect to happen in the future. Forming a household provides some
advantages beyond the pure joy of being together: there are increasing
returns to consumption, opportunities to share income risks, and to take
advantage of division of labor between home and market activities, as well
as the possibility of jointly raise children over whom they have altruist
feelings. Besides the decisions of the agents regarding family formation,
there are typically some form of consumption/savings decision either in
the form of financial assets or in the form of educational investment in
the children.

Other questions that are currently addressed

There are some recent social changes that we are addressing that require
models with explicit household formation. They include the actual decrease
in married couples that has occurred in the U.S. in the last 25 years and
that can be accounted for by the increase of both absolute and relative
female wages (Regalia and Ríos-Rull 2001). A similar issue that is
currently under study is the formidable increase in female (and not so
much male) college attendance that has occurred in the last 25 years. To
understand it we have to start understanding why it was that men used to
go more to college than women. This is not so clear. In recent work
(Ríos-Rull and Sanchez 2001) we found that it is not because of parental
preference or of cheaper costs of attendance for males, rather it seems
that by attending college males acquire a lot more than just higher wages,
they became better parents (in the sense that they are more able to
educate their children). A student of mine, Nishiyama (2001) tackles some
properties of the wealth distribution and of precautionary savings using
models where parents and children coexist and where the parents altruistic
feelings generate both bequests and inter--vivos transfers. In this way he
can measure to what extend parents have altruistic feelings over their
children (note that the two workhorses in macroeconomics the infinitely
lived dynastic model and the overlapping generations model assume either
that parents care about their children as much as they care about
themselves or not at all). He finds that parents care about their children
about half as about themselves. In another work (Cubeddu and Ríos-Rull
1998) we explore how divorce operates in pretty much the same way as an
uninsurable earnings shock, and a very large one at that. Another student
of mine, (Bethencourt 2002) is exploring the changes in living
arrangements between adult households and there elderly mothers.  

Other questions that I would like to address

The interrelation of quantitatively theoretical economic models (models
with explicit utility maximization and with the equilibrium requirement of
compatibility between agents decisions that can be explicitly solved and
compared with data) with demographics is likely to go forward and be used
to address more issues. Central among them is, I think, the issue of
differential mortality. Life expectancy differs a lot among groups of
people, for example, women live more than men (a feature that could
perhaps be imputed to better engineering). But more interesting to
economists is that married men, and educated men live longer that their
single and uneducated counterparts. To understand why is very important:
imagine it is that education or income is it that allows people to access
better care, or at least to be informed about healthier life styles, then
perhaps well intentioned governments may want to subsidize education or
health care or even redistribute income in order to increase life
expectancy. If, however, the characteristics that makes people be
educated and have high income also make them live longer (such as a higher
valuation of the future) then the ability of governments to affect life
expectancy is much more limited and redistributive policies and policies
that subsidize education and health care lose a lot of their appeal.   

New technical challenges that have appeared

Models of the family present numerous challenges that have to be
addressed. I will now discuss some of those challenges. 

First and foremost, the household does not have preferences, the
individuals do. Somehow, we have to aggregate from the individuals to the
household in order to attain an operational decision rule. One way to do
this is to formulate the problem in a such a way that both adult household
members agree over the allocations of resources. This is not always easy
since they may have different time horizons or because the household may
break up. Another way to deal with this is to find the allocation that
solves a weighted average of the utilities or even (better) to assume a
bargaining process between the household members that yield a specific
allocations. 

Second, the use of models with families brings to the forefront of
quantitative economic theory a set of functional forms and parameters that
are new and that cannot be clearly related to other work that we do.
Things like the human capital acquisition and evolution, the
characteristics of affection between people, the mapping between intent
and success of having children and so on and so forth. The old way of
mapping models to data in macroeconomics by mere parameter picking shows
its shortcomings very clearly now. Therefore, calibrating models with
families can only be done as part of an explicit estimation process
(something that is also behind other work in macroeconomics, although
perhaps not so clearly). An obvious way of calibrating these models is
then by specifying a list of statistics that the model has to match, and
choosing the parameters that do that in the best possible way. This
process is also known as exactly identified method of moments, and it is
certainly not the only way to do it, but it has the very nice implication
of cleanly separating what the model is restricted to do and what the
model can tell us. Using a more general version of GMM estimators has the
disadvantage that there is a lack of clear separation between what the
model can be used for and what is imposed in the model. 

Third, related to the previous point, there is now a new set of statistics
that can be used as calibration targets, or more generally, to compare
model and data. Of course, we still use the same aggregate statistics that
allow us to relate to the whole economy and that impose a tremendous
amount of discipline such as consumption to output ratio, wealth to output
ratio and others. Understanding inequality implies understanding the
cross-sectional distribution of wages, hours worked, consumption,
education and wealth. But now, these statistics can be looked at in a new
light. The data for those variables is collected sometimes at household
level and sometimes at person level. Models that explicitly incorporate
families allow us to look simultaneously at the joint distribution of all
those statistics. This is particularly important because hours and wages
of spouses are now part of the information set of the same household.

The role of new computational tools

In the discussion of the last few paragraphs, I have emphasized the
calibration process as a formal process of restricting the model by
imposing that some of its statistics have certain desired values
(typically their data counterparts). Implementing this is only possible if
we are able to compute the equilibrium of the models that we use and its
statistics very cheaply. Until very recently, computing the equilibrium of
a simple economy was a feat. Now the complications arise from two
different angles: we want to compute equilibria of complicated economies
(economies with many agents that differ in various dimensions) and we want
to compute equilibria many times so we can choose the right
parameterizations. 

We all know that there have been enormous improvements in hardware and
some in software to do the required calculations. Recently, the power of
supercomputers has started to trickle down to the average economist in the
form of parallel processing via cheap Beowulf clusters. Here at Penn we
just have acquired two of these clusters with a total of 15 processors
that we expect will allow us to improve our ability to deal with
increasingly more sophisticated models and more stringent estimation
procedures. Ellen McGrattan in the Minneapolis Fed was the first one to
have one of these machines, and her generous support to help others learn
has made their use a lot easier. Parallel processing is particularly
appropriate for problems that are intensive in things like value function
iteration (and other iterative methods to solve dynamic programming
problems), that is, problems where calculations need not be simultaneous.
This is exactly the type of problem that is pervasive in quantitative
economic theory.  

Selected references to the papers mentioned are available in the web     
version of this newsletter at http://www.EconomicDynamics.org/

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EconomicDynamics Interviews Mehmet Yorukoglu on Economic Revolutions

Mehmet Yorukoglu is Assistant Professor of Economics and of Social
Sciences at the University of Chicago. His fields of interests are
technology innovations, fluctuations and investment.

EconomicDynamics: In "Engines of Liberation", you argue with Jeremy
Greenwood and Ananth Seshadri that the increase in female labor market
participation is due to the introduction of significant technology
improvements in the household sector. Would you therefore say that the
various movements fighting to liberate women were not a factor in their
access to the labor market? 

Mehmet Yorukoglu: There is an underappreciated relationship between social
norms and economic (usually technological) constraints. Individuals and
societies may have tastes over social norms and they can certainly develop
these tastes. Therefore, one must recognize that social norms have to be
in the utility function but it is always subject to economic and
technological constraints. Social ideals and movements are like seeds
which need appropriate environment for their cultivation. This environment
is usually determined by technology. To me, arguing that social norms
solely determine social equilibrium is a bit like arguing that automobiles
are invented because suddenly people developed a taste for faster travel.

Take democracy for instance. That ideal was around at least since Ancient
Greeks. The city-state of ancient Athens was a direct democracy between
500 BC and 320 BC. Although only around 15% of the population was eligible
to vote, important public affairs were decided according to citizens'
votes. But democracy then was so time consuming and slow that voting about
one issue usually took a day before thousands of people filling large
amphitheaters voted. This of course proved to be a disadvantage for Athens
when some fast decision were necessary for a vital issue. Some historians
argue that this inability of Athens in fast action prepared its end. It
took millenniums for a successful application of democracy to prevail.
Social ideals usually remain as utopias until economics and technology
favor their successful application. The same arguments can be made for
prohibition of slavery, and other social changes.

In "Engines of Liberation", we argue that before the technological
improvements in the household sector, the economic environment was in an
equilibrium where women specialized in household production and men
specialized in market work. This specialization had social outcomes far  
beyond itself (allocation of power and decision making in the house and in
the market). This equilibrium continued until technological improvements 
in the household sector freed up female labor allowing it to participate
in the market production. Actually, there is some evidence that during
that period public opinion about female work did not change significantly.
For instance, after reviewing public opinion poll evidence, Oppenheimer
(1970) concludes "it seems unlikely that we can attribute much of the
enormous postwar increases in married women's labor force participation to
a change in attitudes about the propriety of their working." 

Therefore, I think although social movements definitely catalyzed the
increase in female labor force participation, the engine that removed the
bottleneck still resides on the technology side.

ED: In "1974", you argue with Jeremy Greenwood that the introduction of a
new technology leads to a sudden increase in a stock prices, followed by 
higher growth rates. Are you still convinced by your model and story
seeing the recent developments in stock prices, in particular for the IT
sector? 

MY: In "1974", IT revolution is modeled in the following way. Until the
date of technological breakthrough the economy is assumed to be on a
balanced growth path where individuals solve their problems assuming that
the economy will be on this path forever. But suddenly, and unexpectedly,
the technological breakthrough occurs creating a change in individuals'
expectations. They suddenly become aware of the technological breakthrough
and they have perfect foresight about the future of the economy from then
on. Therefore, at the date of breakthrough the stock value of firms jump
up and converges to a higher balanced growth path. This setup of
expectations is not realistic in at least two ways. First, in reality,
both technological improvements and people's understanding and
expectations about these improvements change only gradually. Second,
people do not have perfect foresight about the future of a new technology.

Also diffusion of a new product can create cycles in economic activity and
in the value of the firms producing the new product. In a study with
Jeremy Greenwood titled "From Model T to Great Depression:
Automobilization and Suburbanization of US", we model the diffusion of
automobiles and the suburbanization wave in US during the first part of
the 20th century. After Henry Ford's genius application of assembly lines
to automobile production (Model T), the US experienced an era of fast
diffusion of automobiles across households. By 1929, more than 30 million
cars had already been produced, more than half of households in US had at
least one car--a figure which would not increase much until the end of the
WWII. We show that diffusion of new goods can create cycles in output and
values of new good producing firms. The faster is the diffusion of the new
good, the larger can be the cycles. Therefore, one can suspect that fast
diffusion of IT related products can also lead to similar cycles in output
and stock value. The automobile diffusion data also shows that the
producers of a new product can make big expectational mistakes since
forecasting future technological progress and demand for a new product is
a hard task. The data shows that the large automobile producers like Ford
and GM made very large investments just before the depression. Now, they
couldn't forecast the depression, no big deal, nobody did. But it seems
like by the end 1929 demand for automobiles entered into a temporary
saturation point separate from the depression itself. Because of the fast
diffusion of cars, before the early adopters wanted to replace their cars,
most of the households who were willing to buy one at a reasonable price
already bought one. Similar expectational mistakes on the firms' side are
also possible for IT related new products.

Additionally, I think one important point which was not realized early on
is that IT improvements increase consumer surplus more than they increase
firms' profits. With cheaper information available to consumers,
competition among firms become fiercer, driving down profits. Increasing
variety of products in the market, and increased customization of products
to individual consumers improve their utility without benefiting firms'
bottom lines much.

ED: One recurring result in your research is that faster growth leads to a
more unequal distribution of income or assets. Yet, the literature is not
so clear cut. What distinguishes your models form the rest in this
respect? 

MY: In "1974", faster technological progress increases income inequality   
because skilled individuals facilitate the adoption of the new
technologies. When new technologies really bring breakthroughs, meaning
that they are very different from the existing ones, there is much more to
learn about them and the demand for skilled individuals and the premium
that they enjoy increases. This argument is, in general, true for all
technological breakthroughs. There is nothing specific to the nature of IT
in it. 

However, I think the new economy, driven by IT, has strong inequality
creating mechanisms far beyond what the technological breakthrough model
presented in "1974" provides. The new economy is becoming more and more 
information based. One can categorize the goods in the market according to
their information intensity. With information becoming cheaper,
information intensity of the goods increase. One thing that is key for
information is that once it is produced it can be reused at an
insignificantly small marginal cost. This makes the markets for
information intensive goods very concentrated with only few producers.
This is a very strong inequality creating mechanism. As the goods get more
information intensive, very productive top few producers capture the whole
market. Asymptotically, as the good becomes totally an information good, a
small difference in human capital (productivity) of producers creates an
infinite amount of difference in their output. Broader implications of
such an economy are studied in "The New Economy: Some Macroeconomic
Implications of An Information Age" which is joint work with Thomas F.
Cooley. 

Selected references to the papers mentioned are available in the web    
version of this newsletter at http://www.EconomicDynamics.org/newsletter/.

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Society for Economic Dynamics: Letter from the President

Dear SED Members and Friends:

It is once again time for my annual invitation to continue your support of
the Society for Economic Dynamics by paying the annual membership dues,
submitting your research and subscribing to the Review of Economic
Dynamics, and participating in our annual conference. This year the
Society has continued its extraordinary growth. Our membership is at an
all-time high and participation in our annual conference set new records.

This past year our conference was held in Stockholm Sweden at the
Stockholm School of Economics. It was a spectacular success. David Domeij
and Martin Floden of the Stockholm School of Economics were the organizers
and Ellen McGrattan was the program chair. It was our most successful
conference yet in every dimension. The local arrangements, including the
weather, were wonderful and the conference program was impressive.

The 2002 conference will be held on June 28-30th in New York City. The
meetings will be held at the Stern School of Business at New York
University. Our planning for this conference was set back by the tragic 
events of September 11th, but we are now well along and New York City is
returning to normal and is as exciting as ever. You can look forward to
an interesting conference and a fun stay in the city. June is a great time
to visit New York. Narayana Kocherlakota of the University of Minnesota
and Fabrizio Perri of New York University are organizing the program. The
plenary speakers will be Orazio Attanasio, Lee Ohanian, and Wolfgang
Pesendorfer. The call for papers is at http://www.minneapolisfed.org/sed/.
Plan on participating - you won't want to miss it.

This year for the first time the SED sponsored another small research
conference jointly with the C.V. Starr Center at New York University. The
topic of the conference was "Macroeconomic Perspectives on Families and
Inequality." It was organized jointly by Raquel Fernandez, Jeremy
Greenwood, and Víctor Ríos-Rull. We heard nine papers over one and a half
days and these will appear in the spring of 2002 as a special issue of the
Review of Economic Dynamics. The conference was so successful that we
will have another next year at about the same time. Sydney Ludvigson,
Ellen McGrattan, and John Heaton are organizing it. The call for papers is
on the SED web site and enclosed with this newsletter.

Please join again in support of the Society for Economic Dynamics.
Information about how to pay your 2002 dues and your subscription to RED
are available on the SED website at http://www.EconomicDynamics.org/

I look forward to seeing you in June in New York.

Sincerely,

Thomas F. Cooley, President
Society for Economic Dynamics

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Society for Economic Dynamics: Call for Papers, 2002 Meetings

The 2002 meetings of the Society for Economic Dynamics will be held June
28-June 30, 2002, on the campus of New York University. The program
co-chairs are Narayana Kocherlakota and Fabrizio Perri. The plenary
speakers for the conference are Orazio Attanasio, Lee Ohanian, and
Wolfgang Pesendorfer. 

The Society for Economic Dynamics solicits applications in all areas of
dynamic economics to be presented at this conference. Members and
non-members are invited to participate. The deadline for submissions is
February 1, 2002. Please use our standardized form available at
http://www.minneapolisfed.org/sed to submit an abstract, and include the
name, affiliation, address, and e-mail address of the author interested in
presenting the paper. This form is required for all applicants.
Submission of the paper is optional and should be done by submitting a URL
via the standardized form or by mailing a hardcopy to: SED Conference,
ATTN: Narayana Kocherlakota, Department of Economics, University of
Minnesota, 1035 Heller Hall, 271 19th Avenue South, Minneapolis, MN 55455.
Fax transmissions will not be considered.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Society for Economic Dynamics: Call for Papers, 2002 CV Starr/RED
Conference on Finance and the Macroeconomy

On October 11-12, 2002, the C.V. Starr Center of New York University and
the Society for Economic Dynamics will host the second annual CV Starr/RED
conference. This year's topic is on Finance and the Macroeconomy. A
combination of invited and submitted papers will be chosen for the
program. Selected papers will be considered for publication in a special
issue of the Review of Economic Dynamics. The program will be devoted to
state-of-the-art research in the nexus between finance and macroeconomics.
Any high quality research in this area will be considered for inclusion on
the program. Examples of suitable topics include but are not limited to: 

- Heterogeneity: The impact of heterogeneity on asset prices. This could
include but is not limited to investigations of differential financial
market participation, the role of the wealth distribution in understanding
savings and securities prices, the effects of preference heterogeneity,
and the importance of human capital in understanding financial markets.
- Institutional and Demographic Developments: Investigations of
institutional or demographic changes that affect aggregate real activity
and financial markets. Examples include social security reform, pension
reform, changes in regulations of asset markets, changes in demographic
characteristics of the population, changes in taxation, and changes in the
costs of transacting.
- Asset Pricing and the Macroeconomy: Empirical and theoretical
investigations of the macroeconomic sources of systematic risk underlying
asset returns, in both a cross-sectional and a time-series setting;
macroeconomic explanations for conditional volatility and predictability
of equity index returns; implications of time-varying discount rates for
real macroeconomic variables. 

Submissions will be reviewed by a selection committee consisting of John
Heaton (University of Chicago), Sydney Ludvigson (New York University) and
Ellen McGrattan (Federal Reserve Bank of Minneapolis). Papers received
will be considered submissions to both the conference and the special
issue. Papers selected for the conference will be refereed and must meet
the high academic standards of the Review. As such, they are to constitute
original and unique research that will not published in similar form
elsewhere. The program committee will edit the special issue.

The deadline for submissions is April 8, 2002. Only authors of accepted
papers will be notified. This will be done by April 30, 2002. Please email
a PDF file for your paper--or a detailed proposal--to [log in to unmask]

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Review: Kotlikoff's Essays on Saving, Bequests, Altruism, and Life-Cycle
Planning 

Laurence J. Kotlikoff is now well known for his work on intergenerational
issues. 14 of his essays, 5 not previously published, on this general
topic have been reunited in a book that offers the various facets of his
work. Three fields are covered. First, 3 essays on savings and bequests
documents that the life-cycle theory is capable of explaining the secular
decline in the U.S. savings rate with the massive redistribution between
generations introduced after WWII in which older people receive annuities
that reduce incentives to save. This increased wealth inequality and
reduced the wealth equalizing effect of unintentional bequests.
 
The next five essays tackle voluntary bequests. Kotlikoff and coauthors
show that intergenerational altruism is largely absent from the data:
the distribution of average within-cohort consumption changes depends on
that of average within-cohort resource changes, the same applying within
extended families, and families with transfers have only small and
insignificant voluntary transfers compared to the forced ones. Barro's
Ricardian Equivalence then looses credence not only empirically, but
theoretically as well as two essays show: strategic transfer behavior
between parents and children are altered by exogenous redistribution, and
asymmetric information prevents parents from enforcing efficient effort of
their children.

The last 6 essays pertain to life-cycle planning, already the subject of a
recent book by Kotlikoff.  Here, some the new book present some older
evidence that households do not optimize intertemporally, namely that
consumption does not only depend on new information, household
over-discount future earnings, both in experiments and in empirical data,
households are largely financially illiterate and often poorly advised.
Then a financial planning tool is introduced and used to show how people
close to retirement are under-saving, except for low-income households who
can rely on social security.

Any student of life-cycle behavior and savings should have this collection
of essays on his/her bookshelf. It provides several challenges to current
modelling of intertemporal household behavior that should keep researchers
(and practitioners) busy for quite a while.

"Essays on Saving, Bequests, Altruism, and Life-Cycle Planning" is
published at MIT Press.
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Impressum 

The EconomicDynamics Newsletter is a free supplement to the Review of
Economic Dynamics. It is distributed through the EconomicDynamics mailing
list and archived at http://www.EconomicDynamics.org/newsletter.htm. The
responsible editors are Christian Zimmermann (RED associate editor),
[log in to unmask] and Gary Hansen (RED coordinating editor),
[log in to unmask] 

The EconomicDynamics Newsletter is published twice a year in April and
November. 

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