Big unsolved problems
  - intertemporal pricing: equity premium, peso
  problem (forward exchange rate)
  
 - insurance: consumption correlation; insurance
  pooling/adverse selection mechanism design
  problem
  
 - wealth and poverty over time and in cross-section
  
 - the demographic transition
  
 - intermediaries and specialization
  
 - losses from rent-seeking
  
 - "bubbles"
 
Smaller but significant issues
  - x-inefficiency in monopoly
  
 - tradeoff between numbers, observability and
  patience in repeated games
 
General advice on writing a good thesis
There are many answers to the question of
what might constitute a good dissertation.
This is an effort to provide one answer to
that question. Part of writing a dissertation
is learning the skills required to be a practising
economist. Nowadays economists write scientific
papers and not books, and they often collaborate
with other researchers in conducting scientific
research. So a good thesis can constitute
2-3 essays, each written in the form of a
paper that might be submitted to a journal.
Collaborative essays with other students
are especially good.
A good essay would have three parts: a stylized
fact or facts to be explained; a theoretical
model to explain the facts and a determination
of how well the model succeeds in explaining
the facts.
  - The literature on the stylized fact or empirical
  puzzle should be reviewed and ideally, data
  should be analyzed to verify the fact. As
  a rule, stylized facts vary in how puzzling
  they are. The more puzzling the fact, and
  the more satisfying the answer, the better
  the paper.
  
 - The adequacy of existing explanations of
  the fact should be discussed. What new
  insight
  do you have to contribute to the analysis?
  You may have either a new idea, or wish
  to
  provide a carefully worked out model of
  an
  idea that has been discussed informally.
  Focus on those features of the economy
  that
  are of greatest relevance to the facts
  you
  wish to explain. Do not add elements to
  the
  model merely because they exist in real
  life:
  the goal is to explain the facts as simply
  as possible. If you wish to depart from
  the
  hypothesis of rationality, proceed with
  care.
  Although weakening of rationality may be
  useful, try to avoid arguing that economic
  actors behave in capricious or foolish
  ways,
  or designing modes of behavior that conflict
  with the basic fact that most people behave
  relatively sensibly in making day to day
  decisions. Assuming that a small part of
  the population is not rational, or that
  individuals
  are only approximately rational is plausible,
  provided that this assumption plays some
  real role in the analysis.
  
 - There are several methods that you can use
  to derive conclusions from your model. A
  theoretical analysis will typically focus
  on important special cases and prove theorems
  concerning the working of the model. A simulation
  analysis can generate summary statistics
  for comparison with data. Econometric analysis
  can provide useful summaries of the data.
  Generally some combination of methods is
  used. When econometric analysis is used attention
  should be focused on the economic (as opposed
  to statistical) significance of the parameters,
  and whether the model does a good job of
  fitting the data along economically relevant
  dimensions (warning: statistical goodness
  of fit statistics rarely provide a useful
  answer to this question).