Final Exam Part I

Data-Based Economics

Author

Year 2024-2025

Final Exam - Part 1

This part is meant to last about one hour. It must be sent as a Nuvolos assignment by 12pm. Don’t worry if it is not finished.

You are free to use any online resource.

It is however strictly forbidden to communicate with other students.

In answering the questions below, don’t hesitate to comment abundantly your code, to reflect on what you are doing and take initiatives when you deem it relevant.

Happy coding ! 💪

Simple Plots

Question 1: Modify the code below so as to add a grid, a legend (line 1: “f1(x)”, line 2: “f2(x)”), an x-axis label (“x”), a y-axis label (“f(x)”) and a title (“Functions”). 

from matplotlib import pyplot as plt
x = [e for e in range(10)]
y1 = [4*(e/10)*(1-e/10) for e in x]
y2 = [1-(e/10)*(1-e/10) for e in x]
plt.plot(x,y1)
plt.plot(x,y2)

# add some lines here

plt.show()

The Feldstein-Horioka Puzzle

In a famous paper, Domestic saving and international capital flows (Economic Journal, 1980), Martin Feldstein and Charles Horioka, exposed the following puzzle:

  • if international flows of capital were frictionless, capital allocations should be determined by productivity differentials
  • as a result, fluctuations in investment in a given country should be primarly explained by capital flows, not domestic savings
  • yet, the data shows a strong correlation between domestic saving and domestic investment

In the original paper, the following regression was run for each country:

\[\frac{I_t}{Y_t} = \alpha + \beta \frac{S_t}{Y_t} + \epsilon_t\]

where \(I_t\) is investment, \(Y_t\) is gdp, \(S_t\) is total savings (which can be computed from consumption \(C_t\) as \(Y_t-C_t\)).

Your goal is to estimate this relationship for the USA.

Question 2: Which value of \(\beta\) (high \(\beta\) or low \(\beta\)) is associated to a high mobility of capital . Explain.

The following code downloads aggregates from the national accounts using dbnomics.

import dbnomics
df_ = dbnomics.fetch_series([
    "OECD/QNA/USA.P5.LNBQRSA.Q", # investment
    "OECD/QNA/USA.B1_GS1.LNBQRSA.Q", # GDP
    "OECD/QNA/USA.P3.LNBQRSA.Q" # consumption
]);
df_.head()
# keep only the relevant part
df_ = df_[["Subject","period","value"]]
df_.head()
df = df_.pivot_table(index="period", columns="Subject", values='value').reset_index()
df.head()

Question 3: Describe the database

df.describe()

Question 4: Remove all lines containing NaN values. What is the timespan of the database?

Question 5: Rename the columns of table df so that they become [“Consumption”, “Investment”, “GDP”]

Question 6: Create a new column Savings equal to production minus investment.

Question 7: Plot the evolution over time of all time series.

Question 8: Compute and add to the database the two new variables: I_Y for \(\frac{I_t}{Y_t}\) and S_Y for \(\frac{S_t}{Y_t}\).

Question 9: Make a scatterplot of \(I_Y\) againts \(S_Y\).

Question 10: Run the feldstein-horioka regression using statsmodels or linearmodels as you prefer. Intepret the results.

Bonus 1 (intermediate): Run the same regression for different countries and compare the results.

Bonus 2 (harder): Run the same regression for different subperiods: 1970-1979, 1980-1989, 1990-1999, 2000-2009, 2010-2019 and 2020-2023. What happens to the coefficients?

Screen Time and Autism

A series of studies have found that the amount TV watching by early children is positively correlated to their probability to develop some autism spectrum disorder.

One of these studies, carried out in several US counties has regressed autism rates on the average amount of early screen-time exposure in these counties, instrumenting TV watching with the average precipitation level (amount of rain).

Question 11: How could this work? Explain and comment (briefly)

Prompt Engineering

Warning: This exercise does not yield any point 😎.

Go to https://gandalf.lakera.ai/ and try to break the password.

Report below the highest stage you managed to solve with the corresponding password and prompt.