Surely makes you lose your mind

This intriguing problem has come up in Macro.

We're analysing dynamic systems (on a very, very basic level) and working out when they are "determinate" and/or "stable". Before anyone brings in the heavy artillery, I should say we haven't used any actual differential equation theory. We've been told this: if \epsilon represents a stochastic exogenous shock (with mean zero), and the system is

 \left[ \begin{array}{c} y_{t} \\ \pi_{t} \end{array} \right] = A \left[ \begin{array}{c} y_{t+1} \\ \pi_{t+1} \end{array} \right] + \left[ \begin{array}{c} \epsilon_{y,t} \\ \epsilon_{\pi,t} \end{array} \right]

then the system is "determinate" if and only if both the eigenvalues of the matrix A are inside the unit circle. "Determinate" seems to mean having a unique solution (economists are pussies), and is taken to be synonymous with "stable" (lazy pussies, at that).

On occasion we work with a model where the form of the matrix is simply heinous, and calculating the eigenvalues becomes difficult. In case of this, clever textbook writers have come up with conditions which imply that both eigenvalues will be inside the unit circle. However, they don't always state the assumptions necessary for the implication to hold.

The problem with the current Macro assignment is that a question was designed using some of these clever stability conditions, but that those particular conditions rely on unwritten assumptions which the assignment question violates, with the result that the system of the assignment is actually not stable at all.

The matrix of the system has the form:

A = \left[ \begin{array}{cc} 1-\frac{\phi_{y}}{\sigma} & \frac{1-\phi_{\pi}}{\sigma} \\
\kappa(1-\frac{\phi_{y}}{\sigma}) & \beta - \frac{\kappa}{\sigma}(\phi_{\pi}-1) \end{array} \right]

The conditions which supposedly imply eigenvalues inside the unit circle (Gali 2008, pg 79) are:

\kappa (\phi_{\pi}-1) + (1-\beta)\phi_{y} > 0

\kappa (\phi_{\pi}-1) + (1+\beta)\phi_{y} < 2\sigma(1+\beta)

These conditions fail when \sigma=\beta=\kappa=1 (EDIT: and \phi_{y}=0). Why? What are the unwritten assumptions under which the conditions can be derived, and which of the parameter values are violating them?

Stir crazy, Lord

Tonight I managed to create that rare thing, a meal that was enjoyable in both the cooking and the eating. Italian vege pasta alongside porterhouse steak, followed by rice pudding. The pasta, to my surprise, turned out full of flavour, of a good consistency and quite able to stand on its own two feet. I could easily have omitted the steak to make it a two-dish vegetarian meal.

The close concentration of culinary creativity helped to get rid of some of my fourth-week blues. (Sitting in lectures for five hours is just not my idea of a good day.) Here are some 33% observations:

• Macro: Why put so much effort into deriving the model, then spit out the key results with no derivation?
• Metrics: Sigh... I wish I'd done more stats.
• Growth: Is this paper going slow, or am I missing something?
• Micro: OMG, I love Micro.

This week I have only one assignment to do. Maybe I'll get some reading done? Don't laugh!

Outriding fences

Our neighbours at the bach are letting us use their wireless. Isn't that sweet of them?

Signal is best by the kitchen window.

Already standing on the ground

Surely there are better things I could be doing with my life than waiting, on average for ten whole minutes per session, for Westpac online banking to load up. Before you tell me it's my connection, Kiwibank online banking takes less than a minute.

(In fact, Westpac takes so long that Kiwibank now times me out before Westpac is halfway in. This makes it rather tricky to bank in both places simultaneously.)

My connection, however, is becoming a real problem now that I spend half my waking hours in a place with no personal internet access, and the other half in a place with only dialup. When am I supposed to download updates, buy music, upload photos and do all the other things I usually do at university?

Use his back or use his brains

If there is a French Green party, is it called Chartreuse?

My program never did terminate - I had to abort it. It only got this far in the first hour:

I'd been looking for output something like this, but with tighter convergence as a result of many more points:

It looks like I was getting there, but it probably would have taken four hours or so all up. Possibly something less bulky than EViews could do it in a sensible amount of time, but probably not with such syntactical ease.

Don't you draw the Queen of Diamonds

Assignment 1 is nearly all done. I need to look up a few more definitions in the textbook (sequential rationality, rationalizable) and a bit of notation, and I also need to work out if it's possible to put a circle around a number in LaTeX. At the moment I'm making do with $\mathring{number}$, which isn't as clear visually as I'd like. All things considered I'll probably have the assignment finished by lunchtime tomorrow, meaning I'll have no further excuse for not doing that other assignment (a 1500-word essay, srsly) which is also due next week.

The bright lights have faded too soon

On Wednesday I proofread the essay, on Thursday I gave it to my sister to shorten my more Hardyesque sentences (Thomas, not Godfrey), and on Friday I made the corrections and handed it in. Charles had his door open as I went past, so we had a nice chat about things in general. He was there in my first year of sociology, and there he was again in my last. He'll most likely be the one to mark this final essay.

The CTU never did get back to me with corrections of their own. I'll send them a final copy when I get my grade back.