Thanks again to Trond V., who discovered yet another false statement in Stock and Watson.

On page 257 they write that the estimated variance of B1 divided by the true value of B1 will converge to -1

This is of course not correct. Since the numerator will converge towards the true value (which is the denominator), this will converge towards 1 and not -1. 

Many requested this, and here it is. 

[Link]

Update:

After several verbal threats to the scanner, sledgehammer acquired and attempts made, the effort finally paid off. 

Solution proposals are up (you find them under the "Seminars"-tab)

H.

Edit: Since some find them hard to find, here are direct links. 

Solutions to seminar problems V13 (last year)

Solutions to seminar problems V14 (this year)

Hi all.

I've had quite a few requests for the solutions to the seminar problems from those who didn't attend the seminars. 

I am trying to sort this out. However, the scanner didn't want to co-operate with me today, so I'm so far unsuccessful in scanning my notes. 

It will be my hand-written notes you will receive if/when I manage to scan them. Will do another attempt on Monday. 

Again - If you have specific questions in Stock and Watson you need help with, I will try my best to give you a brief solution by email. However, note that I also have exams. 

Best of luck on your exam.

Herman

The data set for seminar 10 is only available in Excel format on the companion website of Stock and Watson. The data file in Stata format can be downloaded from the course website. Type "tsset time" in Stata such that you can use time series commands.  

The file with exercises that are discussed during the seminars is updated and now includes the exercise set for seminar 10. During seminar 10 we will discuss the following regular exercises: 14.2 a-c & e; 14.3; 14.4 and the following empirical exercises: E14.1; E14.2; E14.5 a-b.

The set of exercises that will be discussed during seminar 9 is changed. The following exercises will be discussed: 13.3, 13.5, 13.7, 13.8 and E13.1. The exercises for seminar 10 will be announced in the coming week.

My pardons for not getting through everything at the seminar today. However, to make up for it, I made a note on the solutions to the last parts. You can enjoy reading it in your weekend.

Herman.

You are asked to do a number of statistical analyses using the data provided in the regression table. However, they do not report the number of observations and as we know this could affect the critical values.

We carry on imagining n is "sufficiently large" for the t-distribution to converge to the standard normal. So when doing two-sided tests or constructing confidence intervals at a 5% significance level, use t_c = 1.96

Since the data collected is on houses sold in a particular neighborhood over the past year, this could be quite inaccurate actually. A more likely number of observations lies way lower than convergance, but then again your guess is as good as mine. 

Herman

Some of you have asked me if there exists more challenging exercises. Yes, it does. The seminar exercises from V13 have been posted (Under Seminars) and their solutions have been posted under Seminars: notes and do-files.

I do not however guarantee that the solutions are 100% complete or correct, but they should be fairly so.

Popsicle to anyone who finds a mistake. 

Note: These are meant to be helpful for your own self-study with the course. They should provide insight into some topics we have discussed in the seminars. They are not at all a replacement, but an extra challenge if you feel comfortable with the seminar exercises. 

In the regressions given in the theoretical exercises we are using the standard error of the regression (SER), while Stata provides us root mean squared error (rMSE). To clarifly the relationship:

rMSE= sqrt(MSE)=sqrt(SER).

To provide rMSE you take sqrt(MSR) which you find in Your regression output. MSR is the mean squared residuals, which is SSR/degrees of fredom (df).

Note: Stata uses e for error (not explained as in the book) thus you can think of MSE as MSR, mean squared residuals.

This also means that:

SS model = ESS in textbook, explained sum of squares
 

Hope this clarifies any confusion between the language in the book and stata's language. Let me know if there are other sources of confusion.

Siv-Elisabeth

Will talk about "the i.i.d. modelling concept". We will also discuss modelling assumptions about the joint distribution of the variables, and the alternative to "only" make assumptions about the conditonal pdf.  Hopefully, there will be time for data analyses from Hong Kong and Norway.

R

For seminar 3:

On the TOP of page 251 in Stock and Watson (exercise 6.10c) some essential parts have dropped out when they printed the book. The complete sentence should read as follows:

Thus, if you are interested in Beta1, it is best to leave X2 out of the regression if it is correlated with X1.

Where the bolded parts are missing from the book. Hope this makes you able to prepare well for the seminars this week. Good luck.

Herman.

I have annotated two errors, in slide 10 and 13, so hopefully consequences are not too large. Thanks for pointing it out!

R

Are about inference in the multivariate regression model. In lecture 9 the focus is on the t-test-type-tests. In lecture 10 the F-test enters the stage!

(Slide to Lect 10 will be posted separately)

R

Someone in the thursday seminar group questioned the approach in the last part of 2.24 d where I (in the expression inside the square root)  move (1/sigma^2) from the denominator to inside the summation in the nominator.

There are two steps:

1) Apply the rule of complex fractions (norsk: brudden br?k) on the expression inside the square root.  (a/b)/(c/d)=(ad/bc). Here a=sum(Y_i^2) b=sigma^2 c=(n-1) and d=1. Alternatively: multiply with 1/sigma^2 in both the nominator and the denominator

Thus: sqrt((sum(Y_i^2)/(sigma^2*(n-1))=sqrt((sum(Y_i^2)/sigma^2)/(n-1))

2. Apply the rule of a sum with a constant first: csum(x)=sum(cx) so I can put sigma inside the summation.

sqrt((sum(Y_i^2/sigma^2))/(n-1))

Hi all.

Herman nicely pointed out to me that I have made a mistake in the solution guideline for seminar 1. I was sloppy With where the number 2 was put writing that 1/n+1/n=1/2n when I of course ment 2/n. This carried through in the remainder of the solution and causing an illegal cancellation later.

I have corrected the mistake and uploaded the New solution, but if you understood the explanation here you may aswell simply correct it in your notes if you have already printed it.

I am sorry for any inconvenience.

Siv-Elisabeth

Busy econemetric week for everyone I guess. Lecture 8 (Mult. reg II) is already tomorrow.  See you there!

R

Unfortunately I was unable to finish up exercise 3.20 and didn't have time for 3.21 in the seminar on Monday. I have thus made a note on these two exercises. If you have any questions or find any errors in my solution contact me on s.e.skjelbred(@)econ.uio.no. Also feel free to contact me about comments on how I do the seminars for example the speed at which I go through the exercises.

Siv-Elisabeth

Will at least comment on the two last DIY exercises (Seminar 1 problem set).

Then 5 minutes to check, by simulation that Type-I error is actually 5 % if  we choose 5 % signficance level and the assumption of the simple regression model holds (for "t-test").

Then start talking about the mutiple regression model (slide set 7)

RNy

.

Linn Bredesen email:   linnbredesen@gmail.com

Kristine Wika Haraldsen email: kristiwh@student.sv.uio.no

To clarify any confusions prior to the seminars, I would like to inform that in eq. (3.29) in Stock and Watson (Third edition) pp.130 which we use for Q3.21 there is a minor misprint.

In the very last part of the expression, the subscript on the Y-bar should be a w and not m.

Hope this makes you able to solve also the last questions for the seminars next week.

Sincerely,

Herman

It will come as no supprise, I guess, that I will try to get through both talks (slide set 5 and slide set 6) today, so as to hang on to the schedule.

Will nevetheless start by Monte Carlo simulating some of the properties of our LS-based estimators and test.

R