3 Economic Lessons in 1 Classroom Activity

I teach one hour-forty minute classes on Tuesdays and Thursdays. And I allot only sixty minutes for exams. While student enjoy having the unexpected spare time after an exam, that’s a lot of learning time to miss. Therefore, after my midterms, we do an in-class activity that is a low-stakes, competitive game (and, entirely voluntary).

I call this game “The Extent of the Market” and it has three lessons. Here’s how the game works:

I have a paper handout, a big bag of variety candy, and a URL.  The handout is pictured below-left and lists the types of candy. Each student rates their preference with zero being the least preferred candy. Whether they keep their preferences a secret is up to them. Next, I distribute two pieces of candy to each of them. Importantly, their candy endowment is random and they don’t get to choose or trade (yet). Finally, the URL takes them to a Google sheet pictured below-right where they can choose an id and enter there ‘value score’ under Round 0 by summing the candy ratings of their endowment.

Round 1 is where they get to make choices. I tell students that their goal is to maximize their score and that there is a prize at the end. They are now permitted to trade with anyone at their table or in their row. It doesn’t take long since their candy preferences compose of only the short list, their endowments are small, and the group of potential trade partners is small. When trading is finished, they enter there new scores under round 1.

Lesson #1: Voluntary trade makes people better off.

For each transaction that occurred, someone’s score increased. And in most cases two people’s scores increased. Not everyone will have traded and not everyone will have a higher score. But no one will have a lower score, given the rules and objective of the game. Importantly, the total amount and variety of candy in the little classroom economy hasn’t changed. But the sum of the values in Round 1 increased from Round 0. Trade helps allocate resources where they provide the most value, even if the total amount of physical stuff remains fixed. If it’s a microeconomics class, then this is where you mention Pareto improvements.

Round 2 follows the same process, but this time they may trade with anyone in their quadrant or section of the room. After trading concludes, they enter their scores at the URL under round 2.

Lesson #2: More potential trade partners increases the potential gains from trade.

Again, the variety and total amount of candy in the room remains constant. The only thing that increased was the size of the group of people with whom students could trade. And, they again earn higher scores or, at least, scores that are no lower. People have diverse resources and diverse preferences, and the more of them that you can trade with, the more opportunities to find complementary gains. Clearly, this means that increasing the size of the pool of trading partners is beneficial. One among the many reasons that the USA has had great economic success is that we are a large country geographically with diverse resources and a population of diverse preferences. This means that we have a large common market with many opportunities for mutually beneficial trade. The bigger that we make that common market, the better. Clearly, the implications run afoul of buy-local and protectionist inclinations.

Round 3 proceeds identically with students able to trade with anyone in the room and they enter their scores. At this time the game is finished. It’s important to identify the cumulative class scores across time and to reemphasize lessons #1 & #2. Often, the cumulative value-score will have doubled from Round 0, despite the fixed recourses, making no one worse off. If trading with a row, and then a section, and then the whole class results in gains, then there is an analogy to be drawn to a state, country, and the globe.

Lesson #3: Trade changes the distribution of resources.

Despite an initial distribution of resources, voluntary trade changed that distribution. While no one is worse off and plenty of students are better off, measured inequality may have been affected. Regardless, once a voluntary trade occurs, the distribution of candy and of scores changes. This has implications for redistributive policies. If income or wealth is redistributed in order to achieve some ideal distribution, then the ability to freely trade alters that distribution. The only way to achieve it again would be for another intervention to change the candy distribution by force or threat thereof.  Consider that sports superstar Lebron James became rich by playing basketball for people who like to watch him. If we redistribute his income, and then permit him the freedom to voluntarily play basketball again, then the income distribution will change as he again trades and increases his income.  Similarly, giving money to a low marginal product worker can provide some short-term relief. But, if the worker resumes their prior behavior and productivity, then the same determinants and resulting income persist.

It’s a fund game and students enjoy it. There are some important limitations. #1: There is no production in this game nor incentives for production. This is a feature for the fixed resources aspect of the game. But this is a bug insofar as students think about US jobs vs international jobs. I can assert that the supply side works similarly to the demand side, but students see it less clearly (it helps to draw these parallels throughout the semester). #2: While there is a maximum possible score in the game, the value created in reality is unbounded. There is no highest possible score IRL. #3: There are no feedback dynamics. Taxes associated with income redistribution cause workers to require higher pay, worsening pre-tax inequality. People respond to incentives, and the tax/subsidy component that determined the initial distribution of candy is absent.

It’s a fun game. If you try it, then please let me know how it goes or leave suggestions in the comments.


*By default, Google Sheets anonymizes users. You could have them sign in or use an institutional cloud drive to remove problems that might be associated anonymity.

**If your student can’t handle choosing their own id, then you can just list your students.

***Ideally, each increased trade-group is a superset of the prior round’s potential trading partners.

****You can do more than 3 rounds, but the principle doesn’t change

*****More trade will occur with more students, a greater variety of possible candies, and with more candies endowed per person. You can alter these as needed depending on the classroom limitations.

Covid Death Structural Breaks

xtbreak (STATA)

I found a new time series and panel data tool that I want to share. What does it do? It’s called xtbreak and it finds what are known as ‘structural breaks’ in the data. What does that mean? It means that the determinants of a dependent variable matter differently at different periods of time. In statistics we’d say that the regression coefficients are different during different periods of time. To elaborate, I’ll walk through the same example that the authors of the command use.

You can download the time series data from here: https://github.com/JanDitzen/xtbreak/blob/main/data/US.dta

The data contains weekly US covid cases and deaths for 2020-2021. Here’s what it looks like:

So, what’s the data generating process? It stands to reason that the number of deaths is related to the number of cases one week prior. So, we can adopt the following model:

That seems reasonable. However, we suspect that δ is not the same across the entire sample period. Why not? Medical professionals learned how to better treat covid, and the public changed their behavior so that different types of people contracted covid. Further, once they contracted it, the public’s criteria for visiting the doctor changed. So, while the lagged number of cases is a reasonable determinant of deaths across the entire sample, we would expect it to predict a different number deaths at different times. In the model above, we are saying that δ changes over time and maybe at discrete points.

First, xtbreak allows us to test whether there are any structural breaks. Specifically, it can test whether there are S breaks rather than S-1 breaks. If the test statistic is greater than the critical statistics, then we can conclude that there are some number of breaks. Note that there being 5 breaks given that there are 4 depends on there also be at least 4 breaks. And since we can’t say that there are certainly 4 breaks rather than 3, it would be inappropriate to say that there are 4 or 5 breaks.

Great, so if there are three structural breaks, then when do they occur? xbtreak can answer that too (below). The three structural breaks are noted as the 20th  week of 2020, the 51st week of 2020, and the 11th week of 2021. Conveniently, there is also a confidence interval. Note that the confidence intervals for 2020w11 and 2021w11 breaks are nice and precise with a 1-week confidence interval. The 2nd break, however, has a big 30-week confidence interval (nearly 7 months). So, while we suspect that there is a 3rd  structural break, we don’t know as precisely where it is.

Regardless, if there are three structural breaks, then that means that there are four time periods with different relationships between lagged covid cases and covid deaths. We can create a scatter plot of the raw data and run a regression to see the different slopes. Below we can see the different slopes that describe the impact of lagged covid cases on deaths. Sensibly, covid cases resulted in more deaths earlier during the pandemic. As time passed, the proportion of cases which resulted in death declined (as seen in the falling slope of the dots). It’s no wonder that people were freaking out at the start of the pandemic.

What’s nice about this method for finding breaks is that it is statistically determined. Of course, it’s important to have a theoretical motivation for why any breaks would occur in the first place. This method is more rigorous than eye-balling the data and provides opportunities to hypothesis test the number of breaks and their location. If you read the documentation, then there are other tests, such as breaks in the constant, that are also possible.


See this ppt by the authors for more: https://www.stata.com/meeting/germany21/slides/Germany21_Ditzen.pdf

See this Stata Journal article for more still: https://repec.cal.bham.ac.uk/pdf/21-14.pdf

A Measure of Dissimilarity

I recently learned about an interesting statistic for social scientists. It’s called the “Dissimilarity Index”. It allows you to compare the categorical distribution of two sets.

Many of us already know how to compare two distributions that have only 2 possible values. It’s easy because if you know the proportion of a group who are in category 1, then you know that 1-p will be in category 2. We can conveniently denote these with values of zero and one, and then conduct standard t-tests or z-tests to discover whether they are statistically different. But what about distributions across more than two possible categories?

Continue reading

How ChatGPT works from geography and Stephen Wolfram

By now, everyone should consider using ChatGPT and be familiar with how it works. I’m going to highlight resources for that.

My paper about how ChatGPT generates academic citations should be useful to academics as a way to quickly grasp the strengths and weakness of ChatGPT. ChatGPT often works well, but sometimes fails. It’s important to anticipate how it fails. Our paper is so short and simple that your undergraduates could read it before using ChatGPT for their writing assignments.

A paper that does this in a different domain is “GPT4GEO: How a Language Model Sees the World’s Geography” (Again, consider showing it to your undergrads because of the neat pictures, but probably walk through it together in class instead of assigning it as reading.) They describe their project: “To characterise what GPT-4 knows about the world, we devise a set of progressively more challenging experiments… “

For example, they asked ChatGPT about the populations of countries and found that: “For populations, GPT-4 performs relatively well with a mean relative error (MRE) of 3.61%. However, significantly higher errors [occur] … for less populated countries.”

ChatGPT will often say SOMETHING, if prompted correctly. It is often, at least slightly, wrong. This graph shows that most estimates of national populations were not correct and the performance was worse on countries that are less well-known. That’s exactly what we found in our paper on citations. We found that very famous books are often cited correctly, because ChatGPT is mimicking other documents that correctly cite those books. However, if there are not many documents to train on, then ChatGPT will make things up.

I love this figure from the geography paper showing how ChatGPT estimates the elevations of mountains. This visual should be all over Twitter.

There are 3 lines because they did the prompt three times. ChatGPT threw out three different wrong mountains. Is that kind of work good enough for your tasks? Often it is. The shaded area in the graph is the actual topography of the earth in those places. ChatGPT “knows” that this area of the world is a mountain. But it will just put out incorrect estimates of the exact elevation, instead of stating that it does not know the exact elevation of those areas of the world.

Another free (long, advanced) resource with great pictures is Stephen Wolfram’s 2023 blog article “What Is ChatGPT Doing … and Why Does It Work?” (YouTube version)

The first thing to explain is that what ChatGPT is always fundamentally trying to do is to produce a “reasonable continuation” of whatever text it’s got so far, where by “reasonable” we mean “what one might expect someone to write after seeing what people have written on billions of webpages, etc.

If you feel like you already are proficient with using ChatGPT, then I would recommend Wolfram’s blog because you will learn a lot about math and computers.

Scott wrote “Generative AI Nano-Tutorial” here, which has the advantage of being much shorter than Wolfram’s blog.

EDIT: New 2023 overview paper (link from Lenny): “A Survey of Large Language Models

Government Purchases and How Markets Avoid Messes

The government is unique among economic institutions insofar as it can use coercion legally. But not all activities are coercive. Clearly, taxation is overwhelmingly coercive. Some people say that they are happy to pay taxes, but the voluntary gifts to the US Treasury are itsy-bitsy (just over $1m for FY 2023). Most regulations also include the threat of fines or jail time for non-compliance.

But once the government has the money in their coffers, there is plenty that they can do consensually. Once they have the resources, they are often just another potential transactor in the markets for goods and services. While the government can transact as well as anyone else, there is a fundamental theoretical difference for how we should interpret those transactions. Specifically, there is a principal-agent problem such that we can’t quite identify the welfare that is enjoyed by consumers when the government makes purchases. We really have very little idea.

Garett Jones uses the analogy of the government confiscating potatoes. The worst use would be for the government to throw the valuable resources into the river. Those resources help no one. Improved welfare would be yielded if the government just transferred those potatoes back to people. Sure, there’s the transaction cost of administration, but people get their potatoes back. Finally, the great hope is that the government takes the potatoes and makes tasty potato fritas such that they return to the public something more valuable than they took. These might be things that fall into the public goods category or solving collective action problems generally.

The above examples illustrates that how the government spends matters a lot for the welfare implications of the newly purchased government resources. But, we need to recall that there is an entire private segment of the market that is affected by the government transactions.

Short-Run Analysis

In a competitive market, firms face increasing marginal costs and make decisions about their levels of output. When the government makes purchases, it’s simply acting as another demander. How does the entry of a larger demander affect everyone else in the market? See the below GIF.

Continue reading

Teaching Taxes w/GIFs

Last time the gifs were simply about price & quantity and welfare. I’m sharing some more GIFs, this time in regard to welfare and taxes.

First, see the below gif. It shows us that both consumer surplus (blue area) and producer surplus (red area) always rise if there is a demand increase (assuming the law of supply and law of demand).

Next, let’s consider a basic tax. We can represent it as the difference between what the demander pays and what the supplier receives. The bigger the tax, the bigger the difference between the two.

Now let’s combine the tow ideas: If taxes rise, then the quantity transacted falls, price paid rises, price received falls, and both consumer and producer surplus fall. Not only that, since there is an inverse relationship between the tax rate and the quantity transacted, it may be that increasing the tax rate more *reduces* revenue. The idea that there is a tax revenue maximizing tax rate is illustrated below right and is known as the Laffer curve.

Continue reading

Teaching Resource: List of Econ Podcasts for Spring 2024

In addition to all the usual items for a principles of macroeconomics class, I’m asking my students to listen to one podcast episode this semester. They have to write a short summary on a discussion board for credit.

It took me a bit of time to collect this list of links. I also give them some discretion to find their own episode, but I’m not posting my rules on that point here. This list is something you can copy, paste, and modify. The point is to have all the web links in one place so that students can just click around. There have been many great podcasts over past 2 decades, but I list relatively new content so that we get a bit of “current events” thrown in. So, even if you’ve assigned podcasts before, this new list might be helpful.

Re-release: Claudia Goldin on the Economics of Inequality
Conversations with Tyler
https://cowenconvos.libsyn.com/re-release-claudia-goldin-on-the-economics-of-inequality
https://podcasts.apple.com/us/podcast/re-release-claudia-goldin-on-the-economics-of-inequality/id983795625?i=1000630726259

Reid Hoffman on the Possibilities of AI
Conversations with Tyler
https://cowenconvos.libsyn.com/reid-hoffman-0
https://podcasts.apple.com/us/podcast/reid-hoffman-on-the-possibilities-of-ai/id983795625?i=1000618616078

Simon Johnson on Banking, Technology, and Prosperity
Conversations with Tyler
https://cowenconvos.libsyn.com/simon-johnson
https://podcasts.apple.com/us/podcast/simon-johnson-on-banking-technology-and-prosperity/id983795625?i=1000613373427

Tom Holland on History, Christianity, and the Value of the Countryside
Conversations with Tyler
https://podcasts.apple.com/us/podcast/tom-holland-on-history-christianity-and-the/id983795625?i=1000605361914
https://cowenconvos.libsyn.com/tom-holland

Brad DeLong on Intellectual and Technical Progress
Conversations with Tyler
https://cowenconvos.libsyn.com/brad-delong
https://podcasts.apple.com/us/podcast/brad-delong-on-intellectual-and-technical-progress/id983795625?i=1000601069514

Mark Carney on Central Banking and Shared Values
Conversations with Tyler
https://cowenconvos.libsyn.com/mark-carney
https://podcasts.apple.com/us/podcast/mark-carney-on-central-banking-and-shared-values/id983795625?i=1000523160780

EconTalk Episodes
Tyler Cowen on the GOAT of Economics
https://simplecast.econtalk.org/episodes/tyler-cowen-on-the-goat-of-economics

Jennifer Burns on Milton Friedman
https://simplecast.econtalk.org/episodes/jennifer-burns-on-milton-friedman

Michael Munger on How Adam Smith Solved the Trolley Problem
https://simplecast.econtalk.org/episodes/michael-munger-on-how-adam-smith-solved-the-trolley-problem

Daron Acemoglu on Innovation and Shared Prosperity
https://simplecast.econtalk.org/episodes/daron-acemoglu-on-innovation-and-shared-prosperity

Michael Munger on Industrial Policy
https://simplecast.econtalk.org/episodes/michael-munger-on-industrial-policy

Macro Musings Episodes
Tyler Cowen on the Greatest Economist of All Time and Other Macro Awards
https://macromusings.libsyn.com/tyler-cowen-on-the-greatest-economist-of-all-time-and-other-macro-awards

Nicolas Cachanosky on Dollarization in Argentina
https://macromusings.libsyn.com/nicolas-cachanosky-on-dollarization-in-argentina

Charlie Evans on the Past, Present, and Future of U.S. Monetary Policy
https://macromusings.libsyn.com/charles-evans-on-the-past-present-and-future-of-us-monetary-policy

Shruti Rajagopalan started a new podcast called Ideas of India. 
https://www.mercatus.org/ideasofindia

Or you can listen to Shruti here: https://www.mercatus.org/hayekprogram/hayek-program-podcast/peter-boettke-austrian-economics-and-knowledge-problem-pt-1

Women in Economics Podcast from the St. Louis Fed
Women in Economics: Isabel Schnabel
https://www.stlouisfed.org/timely-topics/women-in-economics/isabel-schnabel

Women in Economics: Heidi Hartmann
https://www.stlouisfed.org/timely-topics/women-in-economics/heidi-hartmann

Women in Economics: Stephanie Aaronson
https://www.stlouisfed.org/timely-topics/women-in-economics/stephanie-aaronson

Women in Economics: Christina Romer, Janice Eberly and Shelly Lundberg
https://www.stlouisfed.org/timely-topics/women-in-economics/romer-eberly-lundberg

Supply & Demand, With gifs

I’ve discussed the ways to teach supply and demand in the past. Regardless, almost all principles of economics classes require a book. But even digital books are often just intangible versions of the hard copy. Supply and demand are illustrated as static pictures, using arrows and labels to do the leg-work of introducing exogenous changes. There’s often a text block with further explanation, but it lacks the kind of multi-sensory explanation that one gets while in a class.

In a class, the instructor can gesticulate and vary their speech explain the model, all while drawing a graph. That’s fundamentally different from reading a book. Studying a book requires the student to repeatedly glance between the words and the graph and to identify the appropriate part of the graph that is relevant to the explanation. For new or confused students, connected the words to one of many parts of a graph is the point of failure.

This is part of why the Marginal Revolution University videos do well. They’re well produced, with context and audio-overlaid video of graphs. It’s pretty close to the in-person experience sans the ability to ask questions, but includes the additional ability to rewind, repeat, adjust the speed, display captions, and share.

Continue reading

3 Great Habits from 3 Great Economists

Jumping right in:

Acknowledge Biases

Have you ever tried to do something objectively. It’s impossible. We might try, but how do we know when we’ve failed to compensate for a bias or when we’ve over compensated. Russ Roberts taught me 1) all people have biases, 2) all analysis is by people, & 3) analysis should be interpreted conditional on the bias – not discarded because of it.

The only people who don’t have biases are persons without values – which is no one. We all have apriori beliefs that color the way that we understand the world. Recognizing that is the first step. The second step is to evaluate your own possible biases or the bias of someone’s work. They may have blind spots or points of overemphasis. And that’s OK. One of the best ways to detect and correct these is to expose your ideas and work to a variety of people. It’s great to talk to new people and to have friends who are different from you. They help you see what you can’t.

Finally, because biases are something that everyone has, they are not a good cause to dismiss a claim or evidence. Unless you’re engaged in political combat, your role is usually not to defeat an opponent. Rather, we like to believe true things about the world. Let’s get truer beliefs by peering through the veil of bias to see what’s on the other side. For example, everyone who’s ever read Robert Higgs can tell that he’s biased. He wants the government to do much less and he’s proud of it. That doesn’t mesh well with many readers. But it’d be intellectually lazy to dismiss Higgs’ claims on these grounds. Higgs’ math and statistics work no differently than his ideological opponents. It’s important for us to filter which claims are a reflection of an author’s values, and the claims that are a reflection of the author’s work. If we focus on the latter, then you’ll learn more true things.

Know Multiple Models

In economics, we love our models.  A model is just a fancy word which means ‘argument’. That’s what a mathematical model is. It’s just an argument that asserts which variables matter and how. Models help us to make sense of the world. However, different models are applicable in different contexts. The reason that we have multiple models rather than just one big one is because they act as short-cuts when we encounter different circumstances. Understanding the world with these models requires recognizing context clues so that you apply the correct model.

Models often conflict with one another or imply different things for their variables. This helps us to 1) understand the world more clearly, and 2) helps us to discriminate between which model is applicable to the circumstances. David Andolfatto likes to be clear about his models and wants other people to do the same. It helps different people cut past the baggage that they bring to the table and communicate more effectively.

For example, power dynamics are a real thing and matter a lot in personal relationships. I definitely have some power over my children, my spouse, and my students. They are different kinds of power with different means and bounds, but it’s pretty clear that I have some power and that we’re not equal in deed. Another model is the competitive market model that is governed by property rights and consensual transactions. If I try to exert some power in this latter circumstance, then I may end up not trading with anyone and forgoing gains from trade. It’s not that the two models are at odds. It’s that they are theories for different circumstances. It’s our job to discriminate between the circumstances and between the models. Doing so helps us to understand both the world one another better.

Continue reading

Update on Game Theory Teaching

I wrote at the end of the summer about some changes that I would make to my Game Theory course. You can go back and read the post. Here, I’m going to evaluate the effectiveness of the changes.

First, some history.

I’ve taught GT a total of 5 time. Below are my average student course evaluations for “I would recommend this class to others” and “I would consider this instructor excellent”. Although the general trend has been improvement, improving ratings and the course along the way, some more context would be helpful. In 2019, my expectations for math were too high. Shame on me. It was also my first time teaching GT, so I had a shaky start. In 2020, I smoothed out a lot of the wrinkles, but I hadn’t yet made it a great class. 

In 2021, I had a stellar crop of students. There was not a single student who failed to learn. The class dynamic was perfect and I administered the course even more smoothly. They were comfortable with one another, and we applied the ideas openly. In 2022, things went south. There were too many students enrolled in the section, too many students who weren’t prepared for the course, and too many students who skated by without learning the content. Finally, in 2023, the year of my changes, I had a small class with a nice symmetrical set of student abilities.  

Historically, I would often advertise this class, but after the disappointing 2022 performance, and given that I knew that I would be making changes, I didn’t advertise for the 2023 section. That part worked out perfectly. Clearly, there is a lot of random stuff that happens that I can’t control. But, my job is to get students to learn, help the capable students to excel, and to not make students *too* miserable in the process – no matter who is sitting in front of me.

Continue reading