ECMT3120: Assignment 2
Yiran Xie
Due Date: August 23 (Before the Lecture)
Please prepare your answers in a separate document in pdf format. Please organize your home-
work answers in the order in which they are asked on this assignment. You may handwrite your
solutions, but please make sure that it is legible. Always include your computer code for numerical
exercises and indicate which computing software you are using. Always provide explanations and
justifications to your answers. You should submit two files – one PDF with your answers to the
practice questions and your software output, and the code (i.e., the do-file).
Question 1
Consider the simplified classical normal linear regression problem written in matrix notation:
y = Xβ + u, u ∼ N(0,σ2In), β ∈ RK , σ > 0,
where y is an n-vector of endogenous variables, and X is a n× k matrix of regressors. Under what
condition(s) is the parameter β point-identified in this model? Explain your answer.
Question 2
This question concerns the error-variables model discussed in the lecture notes on identification.
Recall that
• The observed data consist of two variables X1 and X2.
• Let X ′′1 and X ′′2 denote the measurement errors.
1
• The two-variate model we have is
X1 = X
′
1 +X
′′
1 , X2 = X
′
2 +X
′′
2
where the object of interest is the true slope in the regression of X ′1 on X ′2, which we denote
by β.
Assume that (i) cov(X ′′1 , X ′′2 ) = 0, (ii) cov(X ′1, X ′2) > 0, and (iii) cov(X ′′i , X
′
j) = 0, for i, j = 1, 2.
Derive the identified set for β.
Question 3
This question is a numerical replication exercise with data from the World Values Survey and
Arab Barometer. You can use any computing software you wish. The data is in Excel format
and can be found on the Unit’s Canvas page under Data. In it are 2013 and 2016 survey weights,
and ordinal data on confidence levels in the following Lebanese public institutions: government,
courts, parliament, and police force. (Note that variable weight – the survey weights – is a numeric
variable aiming at adjusting some sociodemographic characteristics in the sample population to the
distribution of the target population. It has been computed using the marginal distribution of Age,
Sex, Education and Region. You should take the survey weight into account when you generate
the CDFs.)
1. Estimate the nonresponse probabilities for each of these ordinal variables, and tabulate your
results.
2. For each of these ordinal variables, compute the worst-case bounds on their CDFs, and plot
them in a single figure.
3. For which variables do you find evidence for a first-order stochastic dominance relationship
across 2013 and 2016. Explain.