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ECON0055 Take Home Exam
Name: …………………………………….. Student nr: ……………………
This is the Take Home Exam, the submission deadline is Monday January 26th at 09h00 am.
Technical Question
Choose one of the technical questions below and use the subsequent answer-form to answer the
sub-questions of that question.
Technical Questions
1. Core-periphery networks
Consider a research community, of 250 agents, that has the structure of a core-periphery
network.
a: Take from the practicals, or create yourself, a random network model that produces core periphery networks and briefly describe how your type of networks compare to those in the
module-literature of core-periphery networks.
b: Now suppose we assign a default ‘relevance’ rj = 1 to every researcher j and we want to
calculate a weight hj assigned to that researcher based on i) their default relevance and ii) how
they are connected within the network, by an equation
h = B[A] . r , where the matrix B[A] is a
function of the adjacency matrix A of the network. Choose a B[A] and comment on why you made
that choice.
c: Explore the outcomes of the model
h = B[A] . r for core-periphery networks A that you
generated from the random network model.
2. Citation cliques
Consider a citation network with an adjacency matrix A where Aij = 1 if there is a link i j
indicating paper j has cited paper i, and Aij is 0 otherwise. A clique of papers i, j, k, are formed
by papers for which both paper i as well as paper j are cited by paper k, and paper j is also
citing i. The paper i is the root of the clique.
a: Draw the network of papers i, j, k.
b: Suppose we calculate the list T with elements Ti = ∑n
j,k=1 Aij Ajk Aik, or Ti = A2 . AT
ii. Explain in
words how this list counts the number of cliques of that each paper is at the root of.
c: What does the trace Tr A2 . AT represent Explore the distribution of cliques in an ER citation
network with at least 100 nodes, compare it to a citation-distribution in the same network, and
draw a conclusion from your exploration on whether the “clique-score” is a interesting measure
for the impact of a paper.
3. Puzzle networks
Consider a a collection of 150 research-puzzles that has the structure of an Erdos-Rényi network
with local vs global link-probabilities. We saw a model ER4[n, b, pclose, pdistant] for such a
network in the practicals.
a: If n = 150, pclose = 0.2, and pdistant = 0. Explore, by simulations, what is the effect of the value of
the parameter 0 < b < 25 on the spectrum of eigenvalues of the adjacency matrix of this network
b: If the network-weighted, relative, relevance of puzzles
h is given in terms of the ‘raw’ relative
relevance r is given by h
= + ζ A + ζ
2
2
A2
r , explain why it is fair to say
h only takes into account
1-step and 2-step connections
c: For sufficiently small ζ < ζc we can take into account infinitely long paths and get
h = ( – ζ A)
-1 r . Use a sample of such ER4 networks, for various values of b, explore the
connection between ζc and b and comment on the effect of b and its connection to ζc when
interpreting the possibilities to assign a ‘paradigm’ to the puzzle network if they assume the
weight of connections ζ → ζc.
Technical Question Answers
Question chosen : …
a: Use the box below to provide your answer.
Comment:
b: Use the box below to provide your answer.
Comment:
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ECON0055 Exam 25-26.nb 3
c: Use the box below to provide your answer.
Answer:
Essay Question
Choose any one of the following 3 Essay questions and:
Write an essay that answers the question,
make use of at least 2 sources taken from published academic literature (papers, working papers or books),
and ensure the essay does not exceed 750 words in length.
Essay Questions
1. Paradigms and Patents
Patents also can ‘cite’ each other, because a patent-application usually needs to make clear
how the new patent would be distinct from patents awarded to similar or related inventions /
innovations. Suppose we have a network of patens and patent-applications for technologies
related to a production process Q. Could we talk about a “production-paradigm” using the
connection we discussed in the course between (citation) networks and paradigms
2. AI and capital depreciation
AI technology has existed in some form for a few years now, but has only in the last 3 years
gained general attention after the development of LLMs. “Training” a new AI comes at very
significant cost and agents deciding on investment- or adoption-choices will likely base their
decisions on beliefs about AI. Discuss what you think the role of such beliefs are for the current
debate on whether or not, or how, to deploy AI, or for a technological change, of your own
choice, in the past, and what role the “cost of information” might play in the formation of such
beliefs.
3. A divorce of Sciences
In class we discussed the case of diverging notions of “normal science” between Astronomy and
Astrology in the 17th century. Discuss this, or a different example of your own choice, in terms
of a divergence of the characteristics of ‘normal science’ when it comes to concepts or tools
being deemed ‘normal’, and form an opinion whether there are economic incentives that might
explain why such separations arise.
Answer Essay Question
Write a short essay outlining i) what is the topic of your individual research project, ii) which are
the arguments for the relevance / interest in this topic, iii) what type of paper is it going to be, iv)
how do you view the feasibility of your project, and v) list and cite at least 3 published sources you
have used in writing this outline. Word-limit: 500 words.
Question chosen : … Word count: … … … … … …
Write the essay and add the pages of your essay as pdf-file following this page!
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