ARE/ECN 115A

Fall 2025

Problem Set 1. Exploring Development Indicators and Service Exports in GDP

DUE: OCTOBER 14 BY 11:59 PM PST

1-hour grace period to submit with 25% penalty. After that, submissions will not be accepted.

PLEASE READ THE FOLLOWING INSTRUCTIONS:

In this problem set, you will become familiar with publicly available data on development indicators, practice graphing in Excel, and reinforce your understanding of concepts from the first two weeks of class. You may work individually or in groups ofa maximum size of 3. If you have any questions about this problem set, contact the TAs or the professor.

1.   By writing your name above and submitting this Problem Set, you agree to adhere to the Copyright statement and the Code of Academic Conduct highlighted in the course Syllabus.

2.   The use of AI is NOT permitted on this problem set.

3.   Download this PDF file to your computer and open it using Acrobat Reader (the free version of the software). Trying to fill it in through your internet browser or with another software may cause some features of this document not to work.

4.   You will make extensive use of Excel in this Problem Set. If you do not have Excel installed on your computer, please refer to Canvas’s “Additional UC Davis Resources for Students” page (under Modules/Module 0 Syllabus & Student Resources).

5.   You can work individually or in groups of up to 3 members. You can use the Discussion board page on Canvas to find group members.

6.   Your group will turn in a single PDF of the problem set on Gradescope. Go to the Canvas course site, click Gradescope on the left panel, and it will automatically lead you to the Gradescope page. You should be able to see the Problem Set 1 for this course on your dashboard. When you are ready to submit, click the Problem Set 1 > Submit PDF > Select PDF > locate the file > Upload PDF > Submit. To select group members, you can use “view or edit group” on the right of the page and then add your group members by name or email. If you need to, select the Resubmit button below your submission in the bottom right corner of your screen. Your instructor or TA will only see your most recent submission when they grade the assignment.

7.   Indicate the members in your group on this PDF and Gradescope at the time of submission. When you upload the assignment, you must identify all group members on Gradescope. Otherwise, only the individual who uploads the assignment will receive credit. You must also write all your group members’ names and ID numbers on this pdf. A 5 point penalty will be applied per name not indicated on the pdf submission or on Gradescope.

8.   Type your responses in the designated boxes. DO NOT change the size of the boxes. We have given twice the space that we used in the answer key for you to type your answers.

9.   To insert the graphs: (1) save the graph in Excel (Right Click -> Save as Picture) as a .jpeg, .png, or .gif file; (2) Click the “insert image” icon in the respective box in the PDF and select the file saved in the previous step. To receive full credit, ALL graphs must include a title, trendline (if requested), axes titles, and legends when applicable. Make sure to use visible colors; specifically, the color of the trend line should differ from the data points. Do not delete or remove the outliers; plot all the data points. The graphs on the PDF and the Excel file should match; otherwise, all points from the graphs will be set to 0.

10. Each student must submit an Excel file on Canvas. Note that the Excel file can be the same for students in the same group. Your individual Excel submission is worth 5 points. Your Excel file must have 4 separate tabs labeled as follows: "Question 1", "Question 2", "Question 3 - US",  and "Question 3 - Brazil".  Your Excel file must show all your plotting and calculations.

Question 1: Development is multidimensional.

As we argued in class, income per capita is a good yardstick of development if it is strongly correlated with important indicators that directly measure well-being, such as education, and health. In this problem, you will empirically explore the strength of the relationships between income per capita, health, and education using data from the World Bank.  Go  to  the  World  Bank  database  of development  indicators  and  download  the  three variables listed below for ALL countries for the year 2022. See section slides if you don’t remember how to navigate the World Bank database website.

•    GDP per capita (constant 2015 US$)

•    School enrollment, primary (% gross)

•    Prevalence of undernourishment (% of population)

(HINT: Make sure you do not download data points for regions like “Small states”, “World”, “East Asia Pacific”, etc.)

A.  Report the values for the following countries and indicators.

B.   Generate two scatter plots with trendlines:

1)   Primary school enrollment against GDP per capita using the LINEAR trendline. Title this plot “Figure 1: Primary School Enrollment vs GDP per capita for 2022.”

2)   Prevalence  of undernourishment  (% of population) against GDP per capita using the

LOGARITHMIC trendline. Title this plot “Figure 2: Prevalence of undernourishment (% of population) vs GDP per capita for 2022.”

Note: Set max for horizontal axis at 80,000 & label Axes appropriately.

Figure 1.

Figure 2

C.   Comment on the trendline for the correlation between primary enrollment and GDP per capita (i.e. is the trend positive, negative or zero)? What does this correlation imply about the relationship between the two variables?

D.  Comment on the trendline for the correlation between the prevalence of under-nourishment and GDP per capita. Although this graph only depicts correlation (and not causality), what do you think about the direction of causality? i.e., do you think that increases in GDP cause changes in under-nourishment or vice versa?  Provide a BRIEF discussion in the box below. Your discussion should identify one potential mechanism that explains the causal relationship.

Question 2: Human Development Index (HDI)

The HDI was modeled after Sen’s notion of development. According to the UNDP, “the HDI was created to emphasize that people and their capabilities should be the ultimate criteria for assessing the development of a country, not economic growth alone. The HDI is a summary measure of average achievement in key dimensions of human development: a long and healthy life, knowledge, and decent living standards. The HDI is the geometric mean of normalized indices for each of the three dimensions.” In this problem, we will practice computing the HDI, plotting HDI and its components over time, and interpreting our results for one country of your choice.

Go to Canvas Files/Problem Sets/Problem Set 1. The Excel file PS1_HDI_Data contains time series data on the four HDI components listed below from 1990-2023 for Brazil. The four components are:

I.      LE: Life Expectancy at birth. This variable is defined as the average number of years a newborn is expected to live if mortality patterns at birth remain constant.

II.      EYS: Expected years of Schooling. This variable is forward looking and provides an indication about the years of schooling that the current school-age population will complete. It is defined as the number of years of schooling a child of school entrance age (6 years old) can expect to complete if prevailing patterns of age-specific enrolment rates persist throughout the child’s schooling life.

III.      MYS:  Mean  years  of  Schooling  (MYS).  This  variable  is  defined  as  the  average  years  of schooling completed by adults in the population who are ages 25 and over. This indicator reflects the average level of education of the current working age (and elderly) population.

IV.      GNI PC: GNI per capita. This variable is defined as Gross National Income per capita. It is similar to Gross National Product as discussed in class.

A.  Plot a time series graph that includes both EYS and MYS over the period 1990 – 2023. Title your graph “Figure 3: EYS and MYS of Brazil, 1990-2023”

Figure 3

Now let’s use Figure 3 to interpret the evolution of education in Brazil over the past 30 years.

B.   Comment on the relationship between EYS and MYS. Ex: Which one is bigger? What factors might explain this? Please provide at least one possible reason that would explain this relationship. (You don’t have to do research on Brazil but the explanation must be consistent with the figure).

C.  Now let’s turn to the sub-indices and the overall HDI. In your Excel spreadsheet, calculate the value of each of the sub- indices and the HDI in each year. Generate a time-series graph that includes four curves, one for each of the three component indices: I(LE), I(E), I(GNI) and one for the overall HDI over the period 1990 – 2023. Title this plot “Figure 4: Brazil HDI over time”. Shade I(HDI) red and increase I(HDI)’s width to 3pt so that it stands out from the components.

D. Analysis.

A.  Comment on the trend of HDI for Brazil over the 1990 - 2023 period. Which component index (or indices) seem to be the most critical drivers of change in the overall HDI over this period?

B.   There is a negative shock visible in one of the indices. What index is it? When did it happen? What might explain it?

Question 3: Education Services and GDP

Services are a major and growing component of GDP as economies develop. Among these, education services play a significant role, not only domestically but also as part of international trade. In fact, education services are an important element of many countries’ net exports.

This question asks you to examine the net exports of educational services for the United States and Brazil. To do so, you will need to download official data from government sources for both countries. This may be a frustrating exercise, but that is how research is done!! We have provided step-by-step "Data Guides" download that data into Excel on Canvas under Files/Problem Sets/Problem Set 1.

A.  Plot a time series graph of education exports, education imports and net education exports for the US.

B.  Plot a time series graph of education exports, education imports and net education exports for BRAZIL.

Figure 6

C.  Interpret the figures:

i.      Which country is a net exporter of education services?  Which is a net importer?

ii.      What was the impact of the pandemic?

D.  Discuss: The Trump administration is considering significantly reducing visas for higher education for international students to study in the US.  Based on the figures you created above, how would this policy affect GDP in the US?  And in Brazil?