Stephane

I'm trying to wrap my head around small and big o notations in the context of asymptotics for estimators. For the sake of clarity, pick for example this model:

Y = XB + u.

Let b be the OLS estimator of B (i.e., b := (X'X)^-1 X'Y). Under certain conditions, we can show:

plim(b-B) = 0 and sqrt(N)(b-B) converges to a normal distribution centered at 0.

QUESTIONS (read '_p' as an index):

1. My understanding of the o_p(.) notation is that we could also write the first statement above as b-B = o_p(1). Is this correct?

2. What is the convergence rate of the OLS estimator?

3. How would you tie any of this to the big o notation O_p?

Thanks in advance!

Most of my economics curriculum (PhD student) has focused on discrete time economic models and, hence, discrete time dynamic programming problems. I was wondering if anyone had good textbook-like references for continuous time models in economics? I am interested in continuous time DSGE models, to be specific.

What I am looking for is some kind of hands-on approach with relevant examples. If I need to cross the t's and dot the i's later, this background will make it easier anyway.

In other words, for my purposes, a book that only goes through abstract theorems and proofs would be a huge waste of time because:

1. I wouldn't know how the results are used because I lack the background;

2. In economics, we always solve the same kinds of problems, so only a handful of the tricks in the whole book are going to be useful anyway.

Any help is appreciated. Thanks.

Suppose we have a random variable, s, following a two states discrete time first order Markov Chain. Call these states A and B.

I'd like to know WHY, if P(A) is the unconditional expectation of state A, then 1/A is the average duration of this state. Thanks!

What if you could be crazy? What if you could simply be sincere and true to yourself from the very first second and could just dive without holding anything back?

It is a very bad plan in practice because not everyone wants something serious and there is a clear incentive to lie...

Is there any place for a man to be passionate and romantic then? Apart from months later in a well ordered manner, I mean...

I am curious because I might enroll in the program, but my background specific to finance is limited. If it helps, my background is centered around econometrics, mostly.