Problem set 3

Due by 11:59 PM on Saturday, September 21, 2019

Submit this as a PDF on iCollege. You can use whatever you want to make your drawings, including Gravit Designer, Adobe Illustrator, Excel, PowerPoint, Microsoft Paint, or photographed/scanned pen and paper.

Cite your sources and show your work.


Consider the society you live in, or another society with which you are familiar.

  1. To make society fairer (according to the substantive judgement of fairness), would you want greater equality of income, happiness, or freedom? Why? Would there be a trade-off between these aspects? (≈30 words)
  2. Are there other things that should be more equal to achieve greater substantive fairness in this society? (≈30 words)
  3. How fair is this society, according to the procedural judgement of fairness? (≈30 words)
  4. Suppose that, behind a Rawlsian veil of ignorance, you could choose to live in a society in which one (but only one) of the three procedural standards for fairness (voluntary exchange of property, equality of opportunity, and deservingness) would be the guiding principle for how institutions are organized. Which procedural standard would you choose, and why? (≈50 words)


  1. Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land.

    Farmer 2
    1 cow 2+ cows
    Farmer 1 1 cow 8, 8 2, 10
    2+ cows 10, 2 4, 4
    1. What category of game is this?
    2. What is/are the Nash equilibrium/equilibria?
    3. What is/are the Pareto efficient outcome(s) in this game?
  2. The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in this new payoff matrix:

    Farmer 2
    1 cow 2+ cows
    Farmer 1 1 cow 15, 15 2, 10
    2+ cows 10, 2 4, 4
    1. What category of game is this?
    2. What is/are the Nash equilibrium/equilibria?
    3. What is/are the Pareto efficient outcome(s) in this game?
  3. How is Pareto efficiency different from fairness? (≈30 words)


You’re in for some exciting times! You get to do some actual econometric analysis and measure the effect of a real world policy using a fundamental causal inference method: differences-in-differences (DiD). With DiD, you compare the difference between two groups (treatment and control) before and after an intervention took place. With this difference, you can actually tell a causal story about an intervention, rather than just talking about correlations.

Go to chapter 3 in CORE’s new Doing Economics book and walk through the empirical project there, measuring the effect of Berkeley’s 2014 sugar-sweetened beverage tax.

Download this file to get all the data you need. In CORE’s instructions it says to go to Berkely’s project-specific website to get the data, but you don’t need to—I’ve collected it all here in one Excel file:

CORE provides step-by-step instructions for how to do this all in Excel.If you’re feeling super adventurous, you can follow the instructions in R, but don’t worry about that.

Make sure you click on the + sign in the green “Excel Walk-Through” sections to see these instructions:

When questions ask about statistical significance, look in the original article for *, **, †, and ‡ signs (and look in the figure footnotes to see what ranges of p-values they indicate (like ‡ means \(p < 0.05\))). You don’t need to calculate the p-values on your own (and you can’t really in Excel anyway). If you haven’t taken stats yet, or you can’t remember what p-values mean, look at the super fast bullet-point crash course in statistical significance at the bottom of this page.

Importantly, CORE provides the answers for you (\(•◡•)/) so you can check your own findings. The important part of this assignment is figuring out the process for making PivotTables + understanding the intuition behind DiD as a method of analyzing the effectiveness of a policy.

It’ll be really tempting to copy/paste their answers into your assignment. Don’t do that—answer the questions in your own words.

Answer the questions below (these are in the Doing Economics chapter, but tend to get buried in the explanatory text). I’ve added some additional hints below, too.

The treatment group

  1. Do this. (But don’t just copy/paste the answer from CORE. It’ll be tempting, but don’t do it!)
  2. Make these frequency tables.
  3. Do this. The trickiest part here is filtering the data correctly. In the original paper, the authors included products that existed in a store across all three time periods. For instance, if one store dropped a product in 2016, the product for that store is not included—but it can be included for other stores if they still sold it in 2016. Use the COUNTIFS() function in Excel (as shown in Doing Economics Excel Walk-Through 3.2; a value of 3 means the product was in the store for all 3 cycles; if it’s 2 or 1, it was missing in one or more cycles. You’ll have a formula that looks something like this: =COUNTIFS(A:A, A2, L:L, L2)). Also, remember to exclude supplementary drinks.
  4. Calculate differences in average price per ounce and make the graph.
  5. Try to answer this, but you don’t need to calculate any of the p-values—look at the original paper for stars and confidence intervals. Low p-values (under 0.05, or 5%) indicate statistical significance.

The control group

  1. Do this. (Again, for this and all these others, don’t copy/paste the answer from CORE!)
  2. Make the table and plot.
  3. Answer this. Again, you don’t need to calculate any of the p-values here, but you do need to discuss what they mean.
  4. Answer this.
  5. Answer this.
  6. Speculate about this.

Statistical significance crash course