Longitudinal Data

Exercise 4

Finishing up on stationary models - due Wed., Oct. 1

1. (This is just a rehash of class to make sure you can do the algebra
   yourselves)

Consider the following models with a single iv (so always has y_t =
bx_t plus other stuff)

a. Simple static model, iid errors
b. Same, but ar1 errors
c. Same, but MA1 errors
d. LDV (y_t=bx_t + py_{t-1} + iid error)
e. d with AR1
f. d with MA1 error
g. ADL model (y_t = bx_t + dx_{t-1}+ py_{t-1}+iid error)
h. Error correction model

Write each using lag operators
Solve each (that is get y in terms of x's and errors, no lagged y's)
Show the interrelationship amongst the various models, which are
subsets of which, etc.

2. We can write a model with different speeds of adjusment as:

y_t = b\frac{1}{1-pL}x_t + d\frac{1}{1-rL}z_t + \nu_t where \nu is
iid.

Rewrite this in more standard form as an ADL model (with maybe more
than one lag)

Now make the errors AR1 - redo the rewriting 

What would happen if we had three iv's with different speeds of
adjustment (iid errors); four?

3. Use simar1errorldv (the simulation program on the web) to
   experiment with what happens if you do OLS with a lagged dependent
   and serially correlated errors? Try several situations and see when
   the problem is severe, when not.

4. Using either british or us data, model approval (or something else
   if you prefer). What is the error process? What lags of the iv's
   belong in the spec? What model do you like? Interpret the
   model. (Use more than one iv.) What is the impulse response function?