Post by: UBS on September 16, 2014, 01:26:23 am
gdp2000i : the level of GDP in country i in the year 2000 ('000 USD)
openi : openness, the sum of imports and exports as a proportion of GDP, average (2000 - 2010)
consi : private consumption expenditure as a proportion of GDP, average (2000 - 2010)
govti : government expenditure as a proportion of GDP, average (2000 - 2010)
investi : investment expenditure as a proportion of GDP, average (2000 - 2010)
The dependent variable is growth, the average annual percentage
growth rate in per capita GDP for each country during the years 2000 - 2010.
So, my question is, if the coefficient of Open is 0.9594 - interpreting this would it be:
'a 1 unit increase in the proportion of the sum of imports and exports over GDP, average (2000 – 2010), predicts an increase of 0.9594% in the average annual percentage growth rate in per capita GDP for each country during the years 2000 – 2010 holding the level of GDP in country i in the year 2000, private consumption expenditure as a proportion of GDP, average (2000 - 2010), government expenditure as a proportion of GDP, average (2000 - 2010) and investment expenditure as a proportion of GDP, average (2000 - 2010) fixed.'
I'm not sure whether it's be 0.9594% or 95.94%...or neither?
Post by: Reckoner on September 16, 2014, 09:34:58 am
From the look of the regression, you have no logged variables, so the percent increase doesn't apply, so we're looking at the percentage point increase. However, I don't know the exact units of the dependent variable. In eViews, was a growth rate of 3% entered as "3", or "0.03"? If it were 3% then it would be "....increase by 0.9594 percentage points", while if it were 0.03 then it would be "... increase by 95.94 percentage points". I expect it would be the first one though.
Also, what units were the "openness" variable in? If they have units, best to say what they are rather than just "a 1 unit increase".
Also try to chuck the words "on average" somewhere in there.
Post by: donkson on September 16, 2014, 10:49:56 am
Post by: kinslayer on September 16, 2014, 11:04:17 am
If the coefficient of openi is 0.9594, then an increase in openi of one unit does indeed (edited) correspond to a predicted increase in growthi of 0.9594 percentage points, holding all of the other explanatory variables in the model constant.
also you can just say holding all else constant rather than typing out every variable.
You need to be careful with this language though, since you can only control for the variables you have included in your model. Everything else is in the error term and you can't hold that constant.
edited
Post by: Auran on September 16, 2014, 05:51:53 pm
Post by: UBS on September 16, 2014, 06:23:22 pm
On a side note, for those doing this assignment, did anyone get the suppose growth rate of ~25 for question 3 in the table format? Was that supposed to be an example since the value I got was a lot lower than that
You mean the intercept term? Yeah I think that's random, I got something ~6 for the full sample
btw Auran, what sort of things did you talk about in question 4b: 'In its simplest version, the convergence hypothesis implies that poorer countries will eventually catch up to richer countries because of their faster growth rates, and hence that global poverty will disappear of its own accord. Are your results consistent with this implication?'
Post by: Auran on September 16, 2014, 06:56:07 pm
btw Auran, what sort of things did you talk about in question 4b: 'In its simplest version, the convergence hypothesis implies that poorer countries will eventually catch up to richer countries because of their faster growth rates, and hence that global poverty will disappear of its own accord. Are your results consistent with this implication?'
I simply stated that the results were not consistent with the convergence hypothesis and made some comments about the intercept.
Post by: kinslayer on September 16, 2014, 10:06:30 pm
My thinking is that once you restrict your sample, if you wish to keep the simple random sample assumption (which we need for OLS) then your PRF must be in a different population, so I'm not sure how you can draw conclusions from one regression to the other. Besides, the basic convergence hypothesis says that poorer countries grow more quickly. If you look only at the poorest countries, does it really matter whether the coefficient on gdp2000 affects growth?
I emailed my tutor, dunno if she will want to answer though lol.
BTW, I messed up my earlier post, sorry about that. Edited it
Post by: Reckoner on September 16, 2014, 10:18:40 pm
Post by: kinslayer on September 16, 2014, 10:20:29 pm
Post by: Reckoner on September 16, 2014, 10:45:56 pm
Have fun!
With econometrics, there's no other way! He says after giving up on his own econometrics assignment for the night because of loss of interest
Not too sure on 4b either, although I suspect you just need to be more general in your interpretation of the convergence hypothesis. That is, does it seem that countries with lower GDPs grow faster than those with higher GDPs (as opposed to "poor" vs "rich" countries) and see if this holds for richer countries, and see if it holds for poorer countries. But to do any testing on this, I suspect you'd need to run cross equation restrictions, which would involve some sort of systems of equations modelling (or perhaps a dummy variable? idk). Covered in ETC3410, but I can't go any deeper at this stage (Only just started the topic and I'm 2 lectures behind...)
Post by: Sam_95 on September 17, 2014, 12:35:20 am
mean of growth for a country with these statistics, and Önd a 95% prediction interval.
The Full Sample, Richer countries, or Poorer Countries regression
Post by: kinslayer on September 17, 2014, 12:49:53 pm
what equation did you guys use for 5a? Using the appropriate regression from question 4, calculate the estimated conditional
mean of growth for a country with these statistics, and Önd a 95% prediction interval.
The Full Sample, Richer countries, or Poorer Countries regression
For the prediction interval you respecify the regression to give the prediction as the constant, then use the standard error and two-sided critical value to get the prediction interval. It's the same thing as we did in tutorial 5,6 etc. I think it's in the lecture notes as well.
What t-statistics did you guys get for the gdp2000 variable?
I found that it wasn't significant for the poorer countries, but it was significant in the full sample and for richer countries. I think I was supposed to find the opposite :S (convergence holds for poorer countries but not rich).
Post by: Auran on September 17, 2014, 02:14:29 pm
I found that it wasn't significant for the poorer countries, but it was significant in the full sample and for richer countries. I think I was supposed to find the opposite :S (convergence holds for poorer countries but not rich).
I got that it wasn't significant in all the 3 test. What test did you use? Two-tailed? One-tailed?
Post by: kinslayer on September 17, 2014, 02:15:49 pm
I got that it wasn't significant in all the 3 test. What test did you use? Two-tailed? One-tailed?
One tailed, with
Post by: Auran on September 17, 2014, 03:22:38 pm
One tailed, withand
I used one tailed with [/tex]H_1 : \beta_1 > 0[/tex] instead. Wasn't we suppose to find whether it increases growth, which we would test for by if [\tex]\beta_1 > 0[/tex]? Or I do it wrong?
Post by: kinslayer on September 17, 2014, 04:08:11 pm
Post by: Auran on September 17, 2014, 05:13:49 pm
the convergence hypothesis is about whether or not richer countries grow slower, so it would be <0 (richer countries grow more slowly).
Okay I understand now. In that case doesn't it change according to the assumption? <0 for rich countries, >0 for both full sample and poorer countries (since full sample also contains poorer countries and that poorer countries grow more quickly). Or is it just <0 for all?
Post by: Sam_95 on September 17, 2014, 05:45:38 pm
For the prediction interval you respecify the regression to give the prediction as the constant, then use the standard error and two-sided critical value to get the prediction interval. It's the same thing as we did in tutorial 5,6 etc. I think it's in the lecture notes as well.
Hang on, I'm talking about the first part of Q5a. I'm guessing you'd have to put in the values of 'Australia's statistic's' that are given into a regression and find the average growth. But which regression from Q4. do you put the values into? It's asking 'Using the appropriate regression from question 4' I'm guessing the richer countries reg?
What t-statistics did you guys get for the gdp2000 variable?
I found that it wasn't significant for the poorer countries, but it was significant in the full sample and for richer countries. I think I was supposed to find the opposite :S (convergence holds for poorer countries but not rich).
Yeah, I got that too
Post by: kinslayer on September 17, 2014, 07:38:20 pm
Hang on, I'm talking about the first part of Q5a. I'm guessing you'd have to put in the values of 'Australia's statistic's' that are given into a regression and find the average growth. But which regression from Q4. do you put the values into? It's asking 'Using the appropriate regression from question 4' I'm guessing the richer countries reg?
Oh yeah, you use the one with the gdp2000>5 filter
Post by: Sam_95 on September 17, 2014, 07:51:14 pm
Post by: UBS on September 17, 2014, 08:15:28 pm
Growth
C
GDP2000-34.07196
OPEN-0.412005
CONS-0.648852
GOVT-0.061441
INVEST-0.297386
then 95% Prediction interval = [C – 1.987*std. error of C, C+ 1.987*std. error of C]
and for 5b) just change OPEN-0.312005 leave everything else the same?
Q5c) got me confused. I know you're meant to find the difference between the 2 regressions in a & b ...but
Post by: kinslayer on September 17, 2014, 11:48:34 pm
Post by: UBS on September 18, 2014, 12:14:53 am
You need a standard error to calculate a confidence interval. You can get that by multiplying OPEN by 10 in the regression
So would that be growth c 10(gdp2000-34.07196) open-0.312005 cons-0.648852 govt-0.061441 invest-0.297386;
with the standard error being the number in the Std. Error column & Open row?
Farrr out, soooo confused with the last one >:(
Post by: kinslayer on September 18, 2014, 09:12:36 am
Post by: UBS on September 18, 2014, 01:26:04 pm
Post by: twatter on October 08, 2014, 11:04:40 pm
ex_ret c sp100 sp200 sp300 small reit
But when I try to estimate it, I get the error 'Near singular matrix error. Regressors may be perfectly colinnear.'
What am I doing wrong?
Post by: kinslayer on October 08, 2014, 11:09:09 pm
In Assignment 2, for Q1c. it's asking to estimate a single regression, which I think is :
ex_ret c sp100 sp200 sp300 small reit
But when I try to estimate it, I get the error 'Near singular matrix error. Regressors may be perfectly colinnear.'
What am I doing wrong?
lecturer said leave out sp100
there's linear dependence b/w the dummy variables if you leave it in
Post by: twatter on October 08, 2014, 11:34:55 pm
But if you drop sp100, how do you find out the mean excess return for sp100?
Post by: kinslayer on October 08, 2014, 11:39:36 pm
ohh yup, makes sense.
But if you drop sp100, how do you find out the mean excess return for sp100?
Sorry, I haven't actually started the assignment yet. For Q1c you do use sp100, just take out the intercept so that each of the coefficients represents the mean.
Later in the assignment there are regressions where you need constant term in there. You leave out sp100 for those ones.
Post by: twatter on October 08, 2014, 11:43:46 pm
Post by: Sam_95 on October 09, 2014, 12:40:22 am
For 1d. did you guys just use the same regression as you did in 1c. and then do the wald test for the hypothesis test?
Post by: Sam_95 on October 09, 2014, 08:28:32 pm
Later in the assignment there are regressions where you need constant term in there. You leave out sp100 for those ones.
would that be for Question 2, cause I'm getting that error too, unless I drop a regressor
Post by: kinslayer on October 09, 2014, 10:51:42 pm
would that be for Question 2, cause I'm getting that error too, unless I drop a regressor
Ya you can't include all the dummy variables and the constant. Still haven't started it, but lecturer (and my tutor) told me to drop sp100 for Q2 onwards
Post by: UBS on October 13, 2014, 07:41:52 pm
Is it asking whether the coefficient of Sp100 (B1) in Q1 differs significantly to B1 in Q2? If so, how do go about finding that?
Post by: twatter on October 13, 2014, 09:42:52 pm
In Q2b. What does it mean when it asks 'Use this interval to test whether B1 differs significantly from one'?
Is it asking whether the coefficient of Sp100 (B1) in Q1 differs significantly to B1 in Q2? If so, how do go about finding that?
yeah confused about that question myself, terribly worded
----
with 2c. it's asking to compute a 95% PI, with risk of 4% - but for small companies fund
I think you'd change the equation (tr_err - 0.4)...but what's the other step in order to make sure you get answers for a small companies fund?
Post by: Reckoner on October 13, 2014, 10:00:13 pm
In Q2b. What does it mean when it asks 'Use this interval to test whether B1 differs significantly from one'?I interpreted it as you're effectively testing the null that B1=1, and using the interval to do so.
Is it asking whether the coefficient of Sp100 (B1) in Q1 differs significantly to B1 in Q2? If so, how do go about finding that?
with 2c. it's asking to compute a 95% PI, with risk of 4% - but for small companies fund
I think you'd change the equation (tr_err - 0.4)...but what's the other step in order to make sure you get answers for a small companies fund?
Remember, think of the intercept as a point prediction for the return when all of the regressors are equal to 0. So we need to transform certain variables so that the intercept tell us the point prediction when the transformed variabels are equal to 0. So if the model is Wage = B0 + B1age + B2education; the intercept would give a point prediction for a when education=0 and age=0.
So if we want to do a point prediction for when age = 40, we do the transformation age'=age-40. As such when we estimate Wage = B0 + B1age' + B2education, the intercept will give us the point prediction for when age'=0 and education = 0.
Note that when
age'=0
age-40=0
age=40
So the point prediction for age' being 0 is really a point prediction for age being equal to 40.
See if you can use this template to help with figuring out what to do for your questions (ie change the variables names). (hint: what value of the variable small do we want to make a prediction for?)
Hopefully this helps you get to the answer, if you're still confused maybe I'll be less vague if you ask again :P (or someone a bit nicer will answer for you :P)
Edit, changed variable names in example
Post by: twatter on October 13, 2014, 10:41:41 pm
Post by: kinslayer on October 14, 2014, 01:04:37 pm
So if the confidence interval you found for β1 contains 1, then...
Post by: Sam_95 on October 14, 2014, 05:24:50 pm
And to construct the 95% PI, just look at the coeff. & std.error of (TR_ERR-0.4)/2?
Post by: UBS on October 14, 2014, 09:05:07 pm
gaah, so stuck on Q2d. I know we did marginal effect in tutes last week, but we only looked at quadratic & log regressions...not the basic regression.
Post by: twatter on October 15, 2014, 05:19:15 pm
Someone pleasee help!!
Post by: twatter on October 16, 2014, 12:04:05 am
Post by: kinslayer on October 16, 2014, 07:59:40 pm
I dunno what to put for 4.d). for i) I have something about how the effect is linear in the first case but in the second case it's logarithmic, i.e. increasing risk will increase returns but relative to the return you already have.. for ii) I'm not sure... the intervals overlap, and I got that the second one was slightly narrower, giving a 'better' prediction? for iii) no idea. We can't use R^2, not sure whether just using Schwarz criterion is okay.
Post by: Sam_95 on October 16, 2014, 08:21:41 pm
And seriously guys...is it TR_ERR-0.4 or TR_ERR- 4 for Q2c. That's doing my head in!
Post by: kinslayer on October 17, 2014, 12:58:03 am
Post by: UBS on November 12, 2014, 02:02:01 pm
The lecturer put up some past exams a few weeks ago..but then took them all down for some reason, I downloaded them thankfully.