Solution Set 6
Econometrics
Spring 2014
Dr. Ani Dasgupta
1. (a) Attached is the log le containing the two regressions, both of which show that apart
from price, all other variables appear with the right coecients (positive) though
not all are signicant. W

Solution Set 7
Econometrics
Spring 2014
Dr. Ani Dasgupta
1. We are given
X(X X)1 X = X(X X)1 X
Premultiply by (X 1 X)1 (X 1 ) to obtain
(X X)1 X = (X 1 X)1 X
Premultiplying by 1 y to get
(X X)1 X y = X 1 X)1 (X 1 y)
.
2. A Breusch-Pagan test is appropriat

Problem Set 5
Econometrics
Spring 2014
Dr. Ani Dasgupta
Note: Submit solutions for 1-6, and for 7 if you are interested in that extra-credit problem.
1. (a) Give an example to show that xn d x, yn d y, does not always imply xn + yn d
x + y (here xn , yn ,

Solution Set 5
Econometrics
Spring 2014
Dr. Ani Dasgupta
1. (a) Let xn be 1 if a certain fair coin toss results in head (0 otherwise) and let yn be 1
if the same fair coin toss results in a tail (0 otherwise). Let x = y = xn . Then,
all these random varia

Topic 7 : Nonlinear Models
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Spring 2014. Please

Topic 10: Systems of Equations
Dr. Ani Dasgupta
Mass. Maritime Academy and Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Spring 2015. Please do not circulate without permission.
1
1.1
SUR (or SURE)
Th

EC508 Problem 5 Solution
gen ry=gdp*100/gdpp
gen mp=impp/gdpp
tsset time
reg imp ry mp time
Source |
SS
df
MS
Number of obs =
57
-+-F( 3, 53) = 1535.44
Model | 67578.109 3 22526.0363
Prob > F = 0.0000
Residual | 777.546915 53 14.6706965
R-squared = 0.9886

Topic 9: Limited Dependent Variables
Dr. Ani Dasgupta
Mass. Maritime Academy and Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Spring 2015. Please do not circulate without permission.
1
Logit/Probit M

Topic 1 : Linear Algebra for Econometrics
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Sprin

Topic 8: GLS, Heteroskedasticity and Autocorrelation
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
Univer

Topic 6: Endogeneity and Instrumental Variables
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University,

Topic 6: Endogeneity and Instrumental Variables
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University,

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NLS and GMM in STATA
Dr. Ani Dasgupta
Department of Economics
MMA and Boston University
1
NLS
To estimate a nonlinear least squares model, the command one issues is of the form
nl (y = expression)
where expression is the conditional expectation of y|x. Th

ML ESTIMATION IN STATA
Dr. Ani Dasgupta
MMA and BU
1
Introduction
Maximum Likelihood estimation in STATA requires 2 parts:
1. Writing a likelihood evaluator program (say mylike)
2. Issuing ML command(s)
We will conne ourselves to those setups where the li

Topic 1 : Linear Algebra for Econometrics
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Sprin

Topic 0: An Exhortation to Econometrics
Dr. Ani Dasgupta
International Business Department
Mass. Maritime Academy
and
Department of Economics
Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Spring 2014.

EC508 Solution to Problem Set 2
1. Two-tail test. 28 degrees of freedom.
Critical value of t-statistic = 2.048 at the 95 percent confidence level
Computed t (for zero null hypothesis) on intercept (1.92) < 2.048
We cannot reject the null-hypothesis that t

EC508 Problem Set 3 Solution
Do file
gen le=ln(earnwke/uhourse)
gen sch=0 if grade92 = 31
replace sch=2.5 if grade92 = 32
replace sch=5.5 if grade92 = 33
replace sch=7.5 if grade92 = 34
replace sch=9 if grade92 = 35
replace sch=10 if grade92 = 36
replace

Solution to Problem Set 4
1. The appropriate F-statistic is already printed by Stata.
F( 3, 1277) = 181.52
The critical value of F at the 5 percent significance level is 2.61
The null hypothesis can be rejected (with 95 percent confidence that a type I er

Topic 3 : The Classical Linear Model
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Spring 201

Topic 0: An Exhortation to Econometrics
Dr. Ani Dasgupta
International Business Department
Mass. Maritime Academy
and
Department of Economics
Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, Spring 2015.

Topic 5 : A Small Dose of Large Sample Theory
Dr. Ani Dasgupta
Department of International Business, Mass. Maritime Academy
and
Department of Economics, Boston University
Draft lecture notes for a graduate econometrics course oered at Boston
University, S

Problem Set 6
Econometrics
Spring 2014
Dr. Ani Dasgupta
Note: This is a practice PSet; you do NOT have to submit solutions.
1. Several years ago a few students of mine wanted to study the demand for baseball games
and to examine whether the owners are cha

A Smorgasbord of Problems
Econometrics
Spring 2014
Dr. Ani Dasgupta
Model Building, CLM, Large Samples
1. In class I mentioned that every year I have plotted the takehome scores against the
midterm scores, I have observed the same pattern about the regres

Writing Tips for Ph. D. Students
John H. Cochrane1,2
Graduate School of Business
University of Chicago
5807 S. Woodlawn
Chicago IL 60637.
773 702 3059.
john.cochrane@gsb.uchicago.edu
http:/gsbwww.uchicago.edu/fac/john.cochrane/research/Papers/
June 8, 200