Hi everyone,
Another question. When we correspond their quarterly coding for dummy
variables (i.e., Treaty of Paris in 73:1), do we code for every month in that
quarter (January-March) or do we research each event and code just for the
months that it occurred in? Example: Treaty of Paris occurred January 1973,
but they code for the entire quarter, do we code for 73:1 or January 1973 only?
I tentatively assume that we are to follow the authors' coding for the quarter,
but since our data is monthly I do not know how much we are allowed to diverge
from the authors' method in replicating the results.
Sincerely,
Sean
Hi everyone,
Another question. When we correspond their quarterly coding for dummy
variables (i.e., Treaty of Paris in 73:1), do we code for every month in that
quarter (January-March) or do we research each event and code just for the
months that it occurred in? Example: Treaty of Paris occurred January 1973,
but they code for the entire quarter, do we code for 73:1 or January 1973 only?
I tentatively assume that we are to follow the authors' coding for the quarter,
but since our data is monthly I do not know how much we are allowed to diverge
from the authors' method in replicating the results.
Sincerely,
Sean
Hey everyone,
Nick and I are very confused about positive and negative dummy
variables. We were under the impression that dummy variables were
things you just stuck in a 1 for when something was happening and a 0
when it wasn't, and it was just a simple binary indicator with no
judgements about whether something was a positive or negative effect
until AFTER the regression was run. However the article codes events
perceived to be negative as -1, and positive things as +1 or even +2.
Does this mean that we create a dummy with a -1 during the months that
the supposed "negative event" was happening? Or just do a standard
dummy variable and expect a negative sign at the end?
Hope everyone's getting around in the snow alright (doing ok, Jas??)
Zoe & Nick
Jason,
> but i thought the sample variance was the difference between the Y's
> and the mean Y's, and the error term is the difference between the Y
> hats and the Y's.
(Y - mean Y)^2 may or may not be the sample variance. It depends on
whether you have a sample or the population. Say you have a sample,
then \Sum(Y-\bar{Y})^2 is the sample variance. But that is not
directly related to the variance around beta. Whenever you calculate
variance you ask "variance around what estimate of central tendency?".
The mean is the most common estimate of central tendency so we usually
assume we want to know the variance around the mean. But we could
just as well calculate the variance around the median.
When uncertainty around beta is of interest, we are interested in the
variance around our estimate of beta. And for this Y-\hat{Y} is
obviously of interest because \hat{Y} is a function of beta. If we
have an intercept (as we almost always do), we already have
information about the mean of Y in our \hat{Y}. Linear regression can
be thought of as an estimate of the mean---an estimate which varies,
unlike the basic mean, with values of X. Because the OLS estimate
varies with the values of X, OLS provides an estimate of the
conditional mean: the mean of Y, given values of X. In the lingo, OLS
is a M-estimator (where M can be thought to denote "mean"). And
obviously, the mean is also an M-estimator.
> i thought variance was around the mean, not the predicted values...
When we calculate the variance around the mean, our predicted value of
each value of Y is simply the mean.
Jas.
Jason Lakin writes:
> well, it is probably me who does not understand. but i thought the sample
> variance was the difference between the Y's and the mean Y's, and the error
> term is the difference between the Y hats and the Y's. So how does summing
> up the error terms give you the sample variance? i understand we don't have
> the population variance, but i don't understand why the error term is
> equivalent to the sample variance. i thought variance was around the mean,
> not the predicted values...
>
> j
> ----- Original Message -----
> From: "Jasjeet Singh Sekhon" <jasjeet_sekhon(a)harvard.edu>
> To: "Jason Morris Lakin" <jlakin(a)fas.harvard.edu>
> Sent: Saturday, December 06, 2003 2:33 PM
> Subject: RE: pop variance
>
>
> >
> > Jason Morris Lakin writes:
> > > hey jas. one more quick question about stats, and one other
> question...why do
> > > we use the error term to estimate pop variance for beta, and not the
> sample
> > > variance?
> >
> > I'm not sure I understand. The error is the sample variance (if based
> > on \hat{\epsilon}) or the population variance (if it is just
> > \epsilon). We cannot use the pop variance because we don't know it.
> > (we would use it if we knew it). Just like in sampling, if we knew
> > the pop variance (sigma) we would use that instead of \hat{\sigma}.
> >
> > > non-stat question: meant to ask you the other day...do you have any
> thoughts
> > > about whether i am better off taking 2nd semester micro now or the
> comparative
> > > field seminar
> >
> > You should take the 2nd semester micro. Given your background, you'll
> > learn a lot more. And it is important to learn that stuff as early as
> > possible.
> >
> > > this would mean taking the field seminar during my generals semester
> >
> > That shouldn't be a problem. Generals are easy.
> >
> > Jas.
> >
> >
> > Jason Morris Lakin writes:
> > > hey jas. one more quick question about stats, and one other
> question...why do
> > > we use the error term to estimate pop variance for beta, and not the
> sample
> > > variance?
> > >
> > > non-stat question: meant to ask you the other day...do you have any
> thoughts
> > > about whether i am better off taking 2nd semester micro now or the
> comparative
> > > field seminar. my gut was that i needed to take the seminar now, but
> the more i
> > > think about it, the more i think i can take it next year. i can't take
> both with
> > > 2000 and german--- too much work, and i have some other stuff going on.
> i was
> > > going to put off econ bc it's less "important" for poli sci, but i
> would rather
> > > take it now and get it over with. this would mean taking the field
> seminar
> > > during my generals semester...otherwise, it would mean probably putting
> off game
> > > theory for at least a year, maybe two. thoughts?
> > >
> > > cheers,
> > > jason
> > >
> > >
> > >
> > > Quoting Jasjeet Singh Sekhon <jasjeet_sekhon(a)harvard.edu>:
> > >
> > > >
> > > >
> > > > Hi Jason,
> > > >
> > > > > hi jas. how are you?
> > > >
> > > > I'm hanging in there. Thanks for asking. Hows end of term stuff
> > > > treating you?
> > > >
> > > > > is the following true: the implicit assumption of the regression
> is that
> > > > it
> > > > > doesn't matter what the level is, because we assume that the effect
> of a
> > > > > particular variable is consistent across different configurations
> of the
> > > > other
> > > > > variables
> > > >
> > > > In OLS, yes. (and this answers your previous question)
> > > >
> > > > > (homoskedasticity).
> > > >
> > > > This term is usually applied to the error variance and not the
> > > > homogeneity of the effect. But OLS **IS** making the assumption you
> > > > state that the effect of a particular variable is constant across
> > > > different levels of the that (and other) variable.
> > > >
> > > > > actually, it doesn't do it in this
> > > > g> discrete way, but rather uses calculus to estimate much smaller
> intervals.
> > > > The
> > > > > point is, the B that it spits out for democracy is ultimately some
> kind of
> > > >
> > > > > average of all of the B's from each of these small lines----under
> the
> > > > > assumption that there is no systematic variation as you move up the
> income
> > > >
> > > > > scale (again, homoskedasticity).
> > > >
> > > > You are correct. But your use of the terms homoscedasticity and
> > > > heteroscedasticity doesn't follow convention because the terms refer
> > > > to the error variance and not the constancy (or lack there of) of the
> > > > effect. Of course one way to get a heteroscedastic error is to have
> > > > the situation in which the effect of income on Y is different at
> > > > higher levels than lower (which would imply that your error variance
> > > > would vary between observations with lower or higher variance IF you
> > > > estimated a model which assumed a constant effect).
> > > >
> > > > > if you don't do this, then a U-
> > > > > curve type relationship (democ is bad for growth at low income
> levels, good
> > > > for
> > > > > growth at high income levels) could end up looking like no effect.
> > > >
> > > > Correct.
> > > >
> > > > > 2) in line with this, is it correct to say that a regression gives
> us no
> > > > > information about the interactions between independent vars (say
> dem/repub
> > > > and
> > > > > inflation when we regress approval on them) unless we include an
> > > > interaction
> > > > > term?
> > > >
> > > > Correct.
> > > >
> > > > Cheers,
> > > > Jas.
> > > >
> > > >
> > > > Jason Morris Lakin writes:
> > > > >
> > > > > hi jas. how are you?
> > > > >
> > > > >
> > > > > 1)so i have a basic question about regression...when you do a
> multiple
> > > > > regression, the idea is that you are trying to assess the impact
> of
> > > > particular
> > > > > variables "holding others constant." which begs the question,
> constant at
> > > > what
> > > > > level?
> > > > >
> > > > > is the following true: the implicit assumption of the regression
> is that
> > > > it
> > > > > doesn't matter what the level is, because we assume that the
> effect of a
> > > >
> > > > > particular variable is consistent across different configurations
> of the
> > > > other
> > > > > variables (homoskedasticity).
> > > > >
> > > > > example: let's say we want to test the effect of democracy on
> economic
> > > > growth,
> > > > > holding "constant" level of GDP per capita. let us further assume
> (for
> > > > the
> > > > > sake of argument) that we actually have real variance in
> democracies and
> > > >
> > > > > GDP/capita (which has not been true). the regression does the
> following,
> > > > with
> > > > > these variables entered in: it says, at $10,000 of income, what is
> the
> > > > effect
> > > > > of democracy on growth (it fits a line between less democracy and
> more
> > > > > democracy at this income level); at $20,000, what is this effect
> (fits
> > > > another
> > > > > line), at $30,000, it does the same thing. actually, it doesn't
> do it in
> > > > this
> > > > > discrete way, but rather uses calculus to estimate much smaller
> intervals.
> > > > The
> > > > > point is, the B that it spits out for democracy is ultimately some
> kind of
> > > >
> > > > > average of all of the B's from each of these small lines----under
> the
> > > > > assumption that there is no systematic variation as you move up
> the income
> > > >
> > > > > scale (again, homoskedasticity). if there is a change in effect
> as you
> > > > move up
> > > > > the income scale (heteroskedasticity), the B's are biased
> downwards for
> > > > higher
> > > > > incomes.
> > > > >
> > > > > if you wanted to know if there was a relationship of this type
> (democracy
> > > >
> > > > > affects growth more/less at higher/lower income levels), you could
> use an
> > > >
> > > > > interaction term of democracy/income level. if you don't do this,
> then a
> > > > U-
> > > > > curve type relationship (democ is bad for growth at low income
> levels,
> > > > good for
> > > > > growth at high income levels) could end up looking like no effect.
> > > > >
> > > > > 2) in line with this, is it correct to say that a regression gives
> us no
> > > >
> > > > > information about the interactions between independent vars (say
> dem/repub
> > > > and
> > > > > inflation when we regress approval on them) unless we include an
> > > > interaction
> > > > > term?
> > > > >
> > > > > thanks a million
> > > > > jason
> > > > >
> > > >
> > >
> > >
> > >
> > >
>
Class -
After speaking to Professor Sekhon about his expectations for the second
problem, I realize that I need to clarify what we are seeking and
contradict what I said in section.
The purpose of this problem is to make you replicate the analysis
summarized in the Table Five I showed you in section. That means you
must do everything they did, i.e. include the various controls for
Vietnam, Watergate, etc. (as explained in a footnote referenced in the
table.) You must do this in order to know whether your data and
analysis are consistent with the earlier result.
I'm sorry for any confusion,
Jacob
Hello All,
Section tomorrow (and for the foreseeable future unless noted
otherwise) will be unified. So everyone should come at the earlier
time.
Also, please let Jacob know tomorrow during section if you prefer
section next week to be on Tuesday or Wednesday. I think I detected
some hesitation about Tuesday. It doesn't matter to us because Jacob
is in town on Wed. We were just worried from past experience that
classes on the Wed before thanksgiving are often sparsely attended.
Cheers,
JS.
Does anybody know if this week's sections will be split again, or are we
on the combined schedule for good?
Kai-Hua
--
~-~-~-~-~-~-~-~-~-~-~-~-
Kai-Hua Yu
364 Currier Mail Center
Cambridge, MA 02138
(617) 493-6916
Currier House, Gilbert 416
Hello All,
Homework #7 has been posted on the course website. It consists of
three questions. Questions 1 and 2 are due Dec 11 and question 3 is
due at the beginning of section Dec 17. So there are actually two
homework assignments in one (that's why the total for this homework is
200 points). Question 3 is rather open ended so it is in your
interest to start it early and ask questions often.
The main section of the final will be very similar to questions #2 and
#3. The final will, however, also include some math questions.
This is the last homework assignment of the year.
At this point in the course, even more so than in the beginning, it is
very important to stay on top of the readings including the Wonnacott,
Freedman, Achen and Dalgaard books.
Hint: reading up on interactions may be helpful. See page 439 of
Wonnacott and Wonnacott ("Different Slopes as Well as Intercepts").
Cheers,
JS.
