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Project description
I only want assignment 3 to be done.
Unfortunately, there is a misprint in 3a: In the final line of this assignment, the formula that you are to conclude with should not have an x but a y in it. That is, it should be (y-mu)^2 and not (x-mu)^2 in the exponent
I only want assignment 3 to be done.
Unfortunately, there is a misprint in 3a: In the final line of this assignment, the formula that you are to conclude with should not have an x but a y in it. That is, it should be (y-mu)^2 and not (x-mu)^2 in the exponent
1
Term paper
:
GRA 60
393
Multivariate Statistics with Econometrics
Examination start date:
1
4
Nov
,
201
3
09
:
00
Total no. of pages:
12
excl
. a
ttachments
Examination end date:
0
2
Dec
,
201
3
12
:
00
No. of a
ttachments:
4
, with file names
specified on the
next
page
Counts
4
0 % of GRA 60
3
9
The weighting
of the
exam
problems
is
specified on the next page.
Responsible department:
Economics
F
ORMAL REQUIREMENTS
–
READ THIS CAREFULLY
The examination
must
be solved
individually or in groups of up to three
(3)
students. Collaboration between
groups
(
on the preparation of the
exam paper)
is regarded as cheating or attempting to cheat and is covered under
“Regulations relating to Admissions, Studies and Examinations”. All students
are responsible
to
familiari
se
themselves with these rules and regulations.
Group submission requires exam registration in identical exam code
and at the same exam location.
This
means that students taking this exam for the first time
cannot
be on a group together with the students taking the
exam as a re
–
take
(as they are taking
the exam with exam code GRA6039
1
)
The exam paper
has a page
–
limitation that is described on the next page, and
must be adequately stapled, or
bound, and submitted in
three (3)
copies. Please
refrain from using plastic covers, or similar binders.
The front page must contain the following information:
•
Student ID number
(7 digits
placed in the
top right corner
. The students’ names
must not
be written on
the front page.)
•
Examination code, course
name and subject title
•
Date of submission and deadline
•
Examination location
•
Marked “Confidential”, if applicable
G
uidelines for layout:
•
Type
–
written on A4 size paper with 5 cm. left margin, 2 cm right margin, 2 cm. at the top and bottom
of
the page
•
Font
Times New Roman
in size 12, and line spacing of 1½. (Approx
.
300
–
350 words per page)
.
All
pages must be numbered
.
Submission:
The
exam
paper must be
submitted
within the deadline at the candidate’s examination location.
O
nly students at BI Nettstudier and
BI Bank og
Forsikring
may submit their papers
by postal mail
to their
examination location. This also applies for candidates from our Bachelor of Management programmes, Master of
Management programmes and customized progr
ammes.
Y
our exam
paper must be sent as “Express
–
Over night cash”.
Minimum dimension
required
: 23x13x1 cm.
From abroad DHL, TNT etc must be used. The shipment must be registered at the distributor within the deadline
of handing in the paper.
For exact postal address to your examination location, see
www.bi.edu
.
Postal ad
d
ress for examination location
s
BI Oslo, BI Nettstudier
and
BI
Bank og Forsikring is:
Handelshøyskolen BI
i
Oslo, Eksamenskontoret, 0442 OSLO
,
Norway.
N
B!
The deadline is absolute. Late
exam
papers will not be graded
.
Please remember to fill
in
the Student Declaration.
Good luck!
HOME EXAM IN GRA6039
MULTIVARIATE STATISTICS WITH ECONOMETRICS
FALL 2013
STEFFEN GR�NNEBERG
The exam is divided into two parts, and consists of in all four problems. The �rst
part, comprising two problems, is entirely practical and concerns applied statistics.
The second part, also comprising two problems, is entirely theoretical.
Part I of the exam contains 85 % of the total points on the exam, and part II
therefore contains the remaining 15 %. In each problem, each sub-problem carry
equal marks.
The page limit for the
rst and second
problem is
6 type-written pages
. You
must solve these problems using Stata, and you must include the source code for
your complete analysis. The Stata-code is to be included in an appendix which does
not have a page limit.
This appendix must not include anything other than
the Stata source code.
The exam has four attachments relating to the data that is to be analyzed in the
rst part of the exam, with �le names as follows.
US
macro
data.dta”
Assignment1
data
source
links.pdf”
All
data
generation
steps.zip”
Lothian
Taylor
96.dta”
Detailed descriptions of these �les are given in the exam text.
There is no page limit for
the second part of the exam
(i.e. the third and fourth
problem), which concerns theory. For part II of the exam, you may choose freely
whether you write your solution in a word processor or by hand. If you write the
solution by hand, do be careful to write as clearly as possible. Obscure passages
will simply be ignored.
You will be severely penalized for breaking these rules.
While the home exam is a group project, it is strictly forbidden to collaborate
between groups. Groups that collaborate with other groups not only face the dire
consequences of being caught as a cheater, they are watering out their own grade:
The grade limits depend in part on the overall performance of all the groups, so
sharing your hard earned answers decreases the likelihood of getting the best grade
that you can.
Term paper
:
GRA 60
393
Multivariate Statistics with Econometrics
Examination start date:
1
4
Nov
,
201
3
09
:
00
Total no. of pages:
12
excl
. a
ttachments
Examination end date:
0
2
Dec
,
201
3
12
:
00
No. of a
ttachments:
4
, with file names
specified on the
next
page
Counts
4
0 % of GRA 60
3
9
The weighting
of the
exam
problems
is
specified on the next page.
Responsible department:
Economics
F
ORMAL REQUIREMENTS
–
READ THIS CAREFULLY
The examination
must
be solved
individually or in groups of up to three
(3)
students. Collaboration between
groups
(
on the preparation of the
exam paper)
is regarded as cheating or attempting to cheat and is covered under
“Regulations relating to Admissions, Studies and Examinations”. All students
are responsible
to
familiari
se
themselves with these rules and regulations.
Group submission requires exam registration in identical exam code
and at the same exam location.
This
means that students taking this exam for the first time
cannot
be on a group together with the students taking the
exam as a re
–
take
(as they are taking
the exam with exam code GRA6039
1
)
The exam paper
has a page
–
limitation that is described on the next page, and
must be adequately stapled, or
bound, and submitted in
three (3)
copies. Please
refrain from using plastic covers, or similar binders.
The front page must contain the following information:
•
Student ID number
(7 digits
placed in the
top right corner
. The students’ names
must not
be written on
the front page.)
•
Examination code, course
name and subject title
•
Date of submission and deadline
•
Examination location
•
Marked “Confidential”, if applicable
G
uidelines for layout:
•
Type
–
written on A4 size paper with 5 cm. left margin, 2 cm right margin, 2 cm. at the top and bottom
of
the page
•
Font
Times New Roman
in size 12, and line spacing of 1½. (Approx
.
300
–
350 words per page)
.
All
pages must be numbered
.
Submission:
The
exam
paper must be
submitted
within the deadline at the candidate’s examination location.
O
nly students at BI Nettstudier and
BI Bank og
Forsikring
may submit their papers
by postal mail
to their
examination location. This also applies for candidates from our Bachelor of Management programmes, Master of
Management programmes and customized progr
ammes.
Y
our exam
paper must be sent as “Express
–
Over night cash”.
Minimum dimension
required
: 23x13x1 cm.
From abroad DHL, TNT etc must be used. The shipment must be registered at the distributor within the deadline
of handing in the paper.
For exact postal address to your examination location, see
www.bi.edu
.
Postal ad
d
ress for examination location
s
BI Oslo, BI Nettstudier
and
BI
Bank og Forsikring is:
Handelshøyskolen BI
i
Oslo, Eksamenskontoret, 0442 OSLO
,
Norway.
N
B!
The deadline is absolute. Late
exam
papers will not be graded
.
Please remember to fill
in
the Student Declaration.
Good luck!
HOME EXAM IN GRA6039
MULTIVARIATE STATISTICS WITH ECONOMETRICS
FALL 2013
STEFFEN GR�NNEBERG
The exam is divided into two parts, and consists of in all four problems. The �rst
part, comprising two problems, is entirely practical and concerns applied statistics.
The second part, also comprising two problems, is entirely theoretical.
Part I of the exam contains 85 % of the total points on the exam, and part II
therefore contains the remaining 15 %. In each problem, each sub-problem carry
equal marks.
The page limit for the
rst and second
problem is
6 type-written pages
. You
must solve these problems using Stata, and you must include the source code for
your complete analysis. The Stata-code is to be included in an appendix which does
not have a page limit.
This appendix must not include anything other than
the Stata source code.
The exam has four attachments relating to the data that is to be analyzed in the
rst part of the exam, with �le names as follows.
US
macro
data.dta”
Assignment1
data
source
links.pdf”
All
data
generation
steps.zip”
Lothian
Taylor
96.dta”
Detailed descriptions of these �les are given in the exam text.
There is no page limit for
the second part of the exam
(i.e. the third and fourth
problem), which concerns theory. For part II of the exam, you may choose freely
whether you write your solution in a word processor or by hand. If you write the
solution by hand, do be careful to write as clearly as possible. Obscure passages
will simply be ignored.
You will be severely penalized for breaking these rules.
While the home exam is a group project, it is strictly forbidden to collaborate
between groups. Groups that collaborate with other groups not only face the dire
consequences of being caught as a cheater, they are watering out their own grade:
The grade limits depend in part on the overall performance of all the groups, so
sharing your hard earned answers decreases the likelihood of getting the best grade
that you can.
I hope that while working through these problems, you will �nd them interesting,
and end up learning much from them. Good luck on the exam!
PART I: Applied statistics
(2 assignments, counting 85 % in total)
Assignment 1.
(Counts 42.5 %)
In Lecture 6, we followed Stock & Watson’s discussion in their Chapter 14 of Intro-
duction to Econometrics” through modeling the in ation rate using an ADL-model
using lagged values of the in ation rate and the unemployment rate. The motivation
for including the unemployment rate was the Phillips curve. However, much more
2
�
�
�
�
HOME EXAM { GRA6039, FALL 2013 3
data { which may be highly relevant for forecasting in ation { is available in pro-
prietary and even open databases online. Can we improve our forecast capabilities
through including many more covariates?
The research paper Di�usion indexes” by Stock & Watson (1998) suggests a
methodology for incorporating many, many covariates in an ADL-model by using
some of the principal components of a large set of potentially relevant covariates.
They provide a mathematical framework that justi�es this use under fairly general
conditions, even quite far away from the IID setting we worked with when we
studied PCA during the fourth part of our course. The basic PCA idea is very
general: identify rotations of a data-matrix so that their columns have zero empirical
covariance and sort the rotated data columns according to their empirical variance.
While we followed Johnson & Wichern in interpreting this statistical tool when the
data-generating mechanism has no time-dependence, it is also often valid when the
data-generating process is allowed to have time-dependence.
The paper can be read at
and end up learning much from them. Good luck on the exam!
PART I: Applied statistics
(2 assignments, counting 85 % in total)
Assignment 1.
(Counts 42.5 %)
In Lecture 6, we followed Stock & Watson’s discussion in their Chapter 14 of Intro-
duction to Econometrics” through modeling the in ation rate using an ADL-model
using lagged values of the in ation rate and the unemployment rate. The motivation
for including the unemployment rate was the Phillips curve. However, much more
2
�
�
�
�
HOME EXAM { GRA6039, FALL 2013 3
data { which may be highly relevant for forecasting in ation { is available in pro-
prietary and even open databases online. Can we improve our forecast capabilities
through including many more covariates?
The research paper Di�usion indexes” by Stock & Watson (1998) suggests a
methodology for incorporating many, many covariates in an ADL-model by using
some of the principal components of a large set of potentially relevant covariates.
They provide a mathematical framework that justi�es this use under fairly general
conditions, even quite far away from the IID setting we worked with when we
studied PCA during the fourth part of our course. The basic PCA idea is very
general: identify rotations of a data-matrix so that their columns have zero empirical
covariance and sort the rotated data columns according to their empirical variance.
While we followed Johnson & Wichern in interpreting this statistical tool when the
data-generating mechanism has no time-dependence, it is also often valid when the
data-generating process is allowed to have time-dependence.
The paper can be read at
http://www.nber.org/papers/w6702.pdf
. This is an
important paper, and the technical version of the paper together with the actual
published paper has a massive 2 000 citations according to Google Scholar. Note
that you need not read the (quite advanced) technical details of this paper in order
to answer this exam.
We will in this assignment study a small-scale replica of a part of their paper’s
empirical example by assessing if using principal components to forecast in ation
yields improvements compared to the forecast capabilities of an AR-model and a
na
�ve ADL-model.
Note that the ideas contained in Stock & Watson’s paper are part of a much larger
framework in modern econometrics, which includes so-called dynamic factor models,
which are based on the factor models we studied in our treatment of Exploratory
Factor Analysis. However, our perspective will here be based exclusively on the
PCA idea.
The exam’s appendix describes the data-set which we will use as the basis for
our experiment. Note that you are not asked to test the structural stability or test
for unit roots in this assignment.
(A) Run a PCA analysis on all variables, except for the in ation variable (and,
of course, the time-variable).
Stata hint:
Because there are so many variables, it may be easier to
read the PCA output after requesting that only loadings whose absolute
values exceed a pre-speci�ed number are printed. For example,
pca d*,
blanks(0.25)
will only print loadings with an absolute value exceeding
(the arbitrarily chosen) 0
:
25, and where
d*
is a short-hand for all variables
with names starting with d”.
(B) We will here compare the performance of the following three types of models.
I) An AR-model for the in ation measure.
II) An ADL-model using autoregressive terms of the in ation measure
and lags of principal components as covariates.
III) An ADL-model where autoregressive terms of the in ation measure
and lags of all other variables (excluding the time-variable) are covari-
ates. All covariates, except lags of the in ation measure, are to be
included with the same number of lags.
For all three models, you must choose the appropriate number of lags of
the in ation measure to include.
For model II you must choose the number of principal components to
include and the number of lags to include for the selected principal compo-
nents. You may assume that the AIC/BIC methodology is valid as a model
selection tool also in model II (even though, as explained in the paper,
important paper, and the technical version of the paper together with the actual
published paper has a massive 2 000 citations according to Google Scholar. Note
that you need not read the (quite advanced) technical details of this paper in order
to answer this exam.
We will in this assignment study a small-scale replica of a part of their paper’s
empirical example by assessing if using principal components to forecast in ation
yields improvements compared to the forecast capabilities of an AR-model and a
na
�ve ADL-model.
Note that the ideas contained in Stock & Watson’s paper are part of a much larger
framework in modern econometrics, which includes so-called dynamic factor models,
which are based on the factor models we studied in our treatment of Exploratory
Factor Analysis. However, our perspective will here be based exclusively on the
PCA idea.
The exam’s appendix describes the data-set which we will use as the basis for
our experiment. Note that you are not asked to test the structural stability or test
for unit roots in this assignment.
(A) Run a PCA analysis on all variables, except for the in ation variable (and,
of course, the time-variable).
Stata hint:
Because there are so many variables, it may be easier to
read the PCA output after requesting that only loadings whose absolute
values exceed a pre-speci�ed number are printed. For example,
pca d*,
blanks(0.25)
will only print loadings with an absolute value exceeding
(the arbitrarily chosen) 0
:
25, and where
d*
is a short-hand for all variables
with names starting with d”.
(B) We will here compare the performance of the following three types of models.
I) An AR-model for the in ation measure.
II) An ADL-model using autoregressive terms of the in ation measure
and lags of principal components as covariates.
III) An ADL-model where autoregressive terms of the in ation measure
and lags of all other variables (excluding the time-variable) are covari-
ates. All covariates, except lags of the in ation measure, are to be
included with the same number of lags.
For all three models, you must choose the appropriate number of lags of
the in ation measure to include.
For model II you must choose the number of principal components to
include and the number of lags to include for the selected principal compo-
nents. You may assume that the AIC/BIC methodology is valid as a model
selection tool also in model II (even though, as explained in the paper,