Alright I'm at my wits end here. 24 hours into it and I'm still coming up with no plausible solution. I must have lost a whole bunch of hair during the process. Desperate times call for desperate measures, so whoever can help me with the first question within the next 8 hours gets a free $5.99 GOG (or 2 GOGs on offer). Sorry wish I could offer more but my part-time allowance is currently on hold until the holidays.

I have completed question 1a, but question 1b escapes me. 1c and 1d look doable, but I'm so bloody annoyed, tired and fed up with this assignment that I am done with this for the night. I need sleep. The rest of the assignment is also doable. It's just this <insert series of crude adjectives> question that bugs the hell out of me, because apparently people I know who are assigned this week's assignment aren't too sure how to do it too.

PS I'd appreciate if you could provide me with an explanation too. No point in asking if I don't know what's going on :P

-edit- Btw I'll just provide the various methods I took to try and solve it.

Firstly I tried modifying the equation so that lambda = B/(1-B). Tried working on this angle for a while, to no avail.

Secondly, I tried using the derivative for LS to work out a solution. Also failed.

Was I on the right track? Or completely off?

I take it you have some idea what alpha ought to be, otherwise, when you do the substitutions that you've been provided there's no way that you can arrive at one specific beta value.

Personally, this isn't quite my cup of tea, I'm much happier with physics or some other use of math.

EDIT: If you take the derivative there, it would get rid of the alpha.

EDIT2: looking at what you were given, it appears to me that there's a possibility of defining the variables at a constant value such that the domain covers things which are undefined. It's a bit early in the morning here, but I think that's probably going to help.

But, this isn't quite my field, so I could be wrong.

Yea you can get rid of the alpha. Problem isn't in the alpha, it's in trying to prove that (correct me if I'm wrong) Var(beta) = 0 as n tends to infinity, if the modulus of dependent variables' coefficients < 1. And that's the problem. I cannot make the connection, not mathematically nor intuitively. It's killing me, literally. I think I have more caffeine in my blood now than I ever did for the last few semesters.

I know what you mean about math. I am happy with all my other econs modules because they're really no-brainers. Just differentiate here and there, find some connection, make a few assumptions, presto! You get an answer.

With regressions, I always seem to come to a dead end. I worked harder on this one module alone compared to the combined effort of 2 other economics modules (International Trade and Environmental), and I still botched up my mid-terms.

Unless I'm mistaken, the reason why it's indefinite is that the LS estimator over estimates the coefficient it represents for portions of the estimated range. If you use the entire range, assuming it's accurate, the beta should correspond to the necessary coefficient. However, if you're only using a portion of that domain, you don't have any assurance that the beta won't be off.

That's conceptually, it's still a bit too early for this, especially given that I'm in humanities mode right now, but I think that should at least give you some hint about how to go about this.

Hmm no that's not it but thanks anyway =)

It's not that it's indefinite, it's that it's inconsistent i.e. variance does not converge over a large sample. The difficulty in this question is created by that stupid additional Ct on the right hand side of the equation when you substitute Yt = Ct + It.

Anyway I *think* I may have the answer, that is if I didn't make any erroneous assumptions in my workings. I'm supposed to be completing the workings right now, but I need to finish bidding for some stuff on eBay first =p

Still looking for help. I haven't slept in over 30 hours, and I have to go to school in a few more hours. This is Sparta.

I will throw in 2 more games on offer, making a total value of $10 worth of games, if anyone can help me solve 1b, 1c and 1d.

I'm not familiar with any of the economic jargon on display so my M.Sc. in maths is pretty much useless here, but what the heck:

It looks like an instrumental variable problem. I didn't take much statistics, but as I recall, an instramental variable is one that is correlated with the independent variable but not with the error term.

I think the key in b) may turn out to be the alpha term. If you solve for beta and write out the expression for an ordinary least squares, you seem to get an expression that approaches something involving alpha in the limit, which I think would show that the estimator is inconsistent.

c) and d) I have no real clue about. I don't know what the heck iid(0, delta_v^2) is supposed to be, or what a l(1) unit root process is.

Thanks for the help anyway bros. I discussed the answer with my friend yesterday before handing in my script, and we think you have to write out the LS formula for B-hat first (B-hat is the estimator), then apply probability limits to the numerator and denominator of the sum of squared values there to convert them to variances, and finally show that if values r stationary, variances are not relative to time and will therefore remain constant, so B-hat will not equate to B. Something like that.

But anyway thanks again for trying :-)