Exercise on  time series cross section data

Continuous

1. Use the garrett data from last week. Drop the lagged depedent
   variable from the specification. What do the results look like. 

2. Now correct for first order serial correlation. Compare the results
   with 1.

3. Put the lagged dependent variable back in. Do a test for remaining
   serial correlation. What does it tell you.

4. Compare the results with a lagged dependent variable with the
   results in 2.


Continuous interpretation

Here are the stationary models I can think of. You will work with more
than one IV, but for interpretation discuss only one iv of interest. I
have given them names, but these are non-standard and may not appear
in texts.  ERRORS ARE IID UNLESS NOTED, PLEASE  ADD CONSTANTS

OLS y_t=bx_t
AR1 y_t=bx_t, errors ar1 (\epsilon_t = \rho \epsilon_{t-1}+\nu_t)
Finite Distributed Lag  y_t = b1 x_t + b2 x_{t-1}
Lagged DV y_t = b x_t + \phi y_{t-1)
Autoregressive distributed lag DL y_t = b1 x_t + b2 x_{t-2}  + \phi y_{t-1) 
Error correction  \Delta y_t = \Delta x_t - \phi(y_{t-1_ - \gamma x_{t-1})

1. Estimate each model using the Garrett data/

2. Which models are nested inside bigger models? For those that are
   nested, test the smaller against the bigger model. (If you cannot
   do the actual tests, look at the coefs and see whether you think
   the constraint (the smaller model) makes sense).

3. For each model, plot an impulse response function for one x - that
   is, generate enough data points so that the model is in steady
   state, then shock x by one unit for one time period and plot the
   behavior of y.

3a. Use your words to describe each of the plots.

4. Do the same thing but for a unit response function, that is shock x
   by one unit and keep it at the new level until a new equilibrium is
   reached.

5.  Use your words to describe each of the plots.


Binary


I. Use orum.dta. The stata codebook command will give you something
   about the variables, read any of the Oneal and Russett pieces (eg
   the word document onealrussettforking.doc which is more or less
   what came out in JPR, 2001)

1, Run a simple logit on disputes (0 1 if a MID) on trade, contiguity,
allies and the other usual suspects.

2. What happens if you huberize on dyadid (so assume all obs in a dyad
   are interdependent)?

3. What happens if you drop second years of disputes ( add if
   ongodisp!=1 to your logit command)?

4. What happens if you do this an put in py and the three pys* spline
   variables?


II. Use the przeworski data. Codebook is in dataset, but I assume you
   have learned Democracy and Development by heart anwyay.

1. Run a logit (adam uses probit, but no matter) on democ (vs autoc)
   on some iv's you like.

2. Now rerun the same thing twice, once conditioning on prior autoc,
   once on prior democ. 

3. Rerun two, but in interactive form (logit democ ivs L.democ
   L.democ*ivs)

4. Compare 2 and 3; compare either to 1. What did you learn?