Author: Zachary Bartsch

Borrowing, Beef, and Break-even

Zachary Bartsch2 Comments

Interest rates communicate the value of resources over time. For example, if you take out a loan, then the interest rate tells you how much you must to pay in order to keep that money over the life of the loan. The interest rate also reflects how much the lender will be compensated in exchange for parting with their funds. On the consumer side, the interest rate reflects the price that the borrower is willing to pay in order to avoid delaying a purchase.

When a business borrows, the interest rate reflects the minimal amount of value that they would need to create in order to make an accounting profit. For example, if a business borrows $100 for one year at an interest rate of 5%, then they need to earn $105 by the time that they repay the loan in order to break even with zero profit. The business would need to earn more than 5% in order to earn a profit on their borrowing and investment venture.

The longer the business takes to repay their loan, the more interest that accrues. And, the higher the interest rate, the more they need to earn in order to repay their loan.

This logic applies to all production because all production takes time. If production takes very little time, then the impact of the interest cost is miniscule. But, if production takes longer, then interest rates become increasingly relevant. These kinds of products include trees, cheese, wine, livestock, etc. Anything that ages, ferments, or has a lengthy production process will be more sensitive to the cost of borrowing.

How?

The growth pattern for most (all?) goods looks similar. Below-left is a growth chart for dairy cows . Notice that calves grow quickly at first, and their growth slows over time. For the sake of argument, let’s say that the change in value of a cow mimics the change in weight (Yes, I know that dairy and beef cows are different, but the principle is the same).  Below-right is the monthly percent change. Even at an age of 25 months a cow is still growing in value at 2.4% per month or 33% per year.

Of course, there is a risk that some cows don’t survive to slaughter, lowering the expected growth rate. Since most cattle are slaughtered between 18 and 24 months of age, their growth rate at the time of slaughter is 4.4%-2.7% per month. As the interest rate at which farmers borrow rises, the optimal age at slaughter falls. Otherwise, the spread between the growth rate and the interest rate could go negative. Even so, what an investment! If you can borrow at, say, 8% per year, then you’ll make money hand-over-fist on the spread.

Except… Cows cost money to raise, and most of that cost is feed. According to the production indicators and estimated returns published by the USDA, the cost of feed in February of 2023 was $158.11 per hundred pounds of beef. The selling price of beef was $161.07. That leaves $2.96 or a profit of 1.87% earned over the course of 1.5-1.75 years. That investment is starting to look a lot less good, especially since it doesn’t include the cost of maintaining facilities, insurance, etc. It’s no wonder that farmers and ranchers are serious about their subsidies. Clearly, with such tight margins, farmers and ranchers are going to look good and hard at the interest rates that they pay on their debt. And, they do have debt.

However, the recent increase in beef prices is not caused by higher interest rates.

That 1.87% profit margin is at prices and costs from February 2023. Since 2020, the price of cattle feed ingredients (grain, bean, and oil) peaked in the summer of 2022 and are still substantially more expensive than pre-Covid (see below). That means that cows getting slaughtered right now were raised on more expensive feed. This February 2024, the cost of feed per 100lb. of cattle was $191.80. But the cattle selling price was only $180.75. That’s a $11.05 loss for cattle raising. Wholesale prices of cattle might be up recently, but the cost of feed is up by more. It’s not the cattle farmers who are benefiting from the high beef prices. In fact, they’re getting squeezed hard.

There is good news. The cost of feed ingredients has been falling recently, which means that beef farmers should begin to see some relief if the recent trend continues. For Consumers, the price of beef is already down from its 2023 peak.

The Money Value of Time

Zachary Bartsch1 Comment

Economists rightly make a big deal out of specialization and trade. They proceed to go one step further and say that it’s better to pay someone else to perform some service, even if you can perform it yourself. One the assumptions underlying this advice is that time and money are both fungible and convertible.

How are economists right and wrong about the convertibility of time and money? In one sense, we can change how much we work and change how much income we have. That seems plain. But it also requires some start-up costs to have an easy go-to means of earning more income. For example, Uber drivers are registered with Uber already.  Joe from the street can’t start driving tomorrow without substantial preparation.

If economists are wrong about the convertibility of earned time and earned money, then they still have standing. We all have an endowment of time, if not money. But there are plenty of goods that have a money price and a time price that have an inverse relationship.  The advantage of having a time budget is that you can offset some of the money price of goods with time such that more of the money budget can be spent otherwise.

For example, I had to buy a new golf cart battery. One option was to spend $2,400 for a guy to come replace my old battery for me. The other option was for me to spend $1,500 and one evening to do it myself. Given that I typically do chores in the evening anyway, the time-cost to me didn’t feel all that imposing.

Further, if I free up some time, then what happens to it? I can leisure. That’s what economists call any time spent that isn’t working. But after that leisure, it’s gone. There some saving your time for later in the form of bringing other chores earlier in time. But there’s certainly no allowing your time to earn compound interest. That’s where the advantage of self-service really shines IMO. I can give up $900 and enjoy one evening of leisure. Or, I can given up an evening of leisure, put the savings into an investment account, and then reap double the evening’s worth seven years later. Then I’ll have two nights of leisure rather than one. To me, that’s the biggest difference between time and money. I can earn interest on my money in a way that I can’t earn interest on my time.

How This Economist Cares for a Baby

Zachary Bartsch2 Comments

I have four children, and all them were or are babies. As an economist, I know that becoming more productive includes contributions to labor, capital, and technology. Caring for and pacifying babies is no different. Here are some of my methods for pacifying and employing babies who are 4-18 months old.

Own a pacifier. You don’t need to use it or even force it into your baby’s mouth. But just have it around. Paul Romer said that we learn and innovate by interacting with capital. So, let’s get the capital.

Employ your baby’s labor. Children as small as 2 or 3 can go get the eggs from the hen house. But what about a smaller baby? Of course we need to stimulate, feed, water, change, and rest the baby. But sometimes, you just need them to be quiet. What to do? Babies respond to Pavlovian stimulus at a very early age. If they’re crying or even just somewhat bored, then place the pacifier in their hand and say, in a very low but normal voice, ‘pacifier’. Babies will instinctively put the pacifier in their mouth. If you have it clipped on, then eventually, they’ll be able to find it when they need it. Developing physical human capital takes work experience and time. I always insist that my older children place the pacifier in the baby’s hand rather than the baby’s mouth. Greater human capital will yield productivity gains.

There came a point when my baby would awaken at night. I wouldn’t even get out of bed. I’d just calmly, and dispassionately say ‘pacifier’. And our baby would pop the pacifier in their own mouth. Employ your baby’s labor. Innovation happens when you interact with capital.

In the same vein, I’d balance the baby bottle on my child’s front side, and place their hands on it. Next thing I knew, my baby was holding their own bottle earlier than the internet said that I should expect them to. Those little hands aren’t useless. They’re low marginal product labor just waiting to be employed. Given that home production is a team effort and labors have interaction effects, that small marginal product for the baby frees your labor to have a larger marginal product for the household. Take advantage of interaction effects, specialization, and comparative advantage.

How do you produce sleep in a baby? Let’s examine the production function. It typically includes: warmth, a clean diaper, darkness, a full belly, maybe some motion, and a lack of disruptive noise. Once the baby is asleep, you really only need the warmth, darkness, and peaceful noise. Leverage your capital to make yourself more productive. Capital may not be able to replace you in helping your baby fall asleep. But it can replace you to help keep them asleep. Repurpose your current stock of capital. If only there was a warm, dark, white noise chamber in your house already. There is. It’s called a bathroom. Get your infant to fall asleep, then put them in the dark bathroom with the fan on. Now you can grade your papers, clean the house, or write your articles.

Addendum on diaper changing:

When it comes to changing a diaper, you should act like you have a low discount rate. That is, you should bear the cost of preparing a changing space so that your future self is thankful. This means preparing the changing pad, opening the new diaper, unfolding the wipes, preparing for diaper disposal, and preparing any new clothes. This makes the diaper changing process much easier and mitigates stochastic costs like leaks, mid-change accidents, etc. Further, your MPL is lower when you have to mind a baby who’s on an elevated surface. Employ your labor when it’s more productive – before you lay them down.

Do you have a baby who fights or cries during diaper changes? Take a hint from the Fed and engage in forward guidance. Did you know that if you blow in a baby’s face, that they instinctively close their eyes and mouth and stop flailing? Early on this can act as a reset and interrupt crying. As a baby gets older, they’ll learn to anticipate the blown air. But only if you build your reputation.

When my 12 month old would start to fight, I’d audibly inhale. My baby would immediately stop fighting and clothes her eyes and mouth, and stop flailing in preparation of me blowing in her face. That’s called forward guidance. Building a reputation of action means that signaling action is often just as good as the act itself. But be careful, if you always blow in their face, they grow accustomed to it due to expectations augmented responses. So, I introduce stochastic bluffs wherein I audibly inhale, but then neglect to blow in their face. Stimulus only works repeatedly if you can violate their expectations.

Stay tuned for more economist parenting tips.

Wanna Teach Economics?

Zachary Bartsch1 Comment

At Ave Maria University, we have an open economics faculty position. Indeed, it’s late in the job market and we haven’t settled a match. That’s what accounts for my late post. I interviewed someone today when I otherwise would have been grading. So, I spent my evening writing feedback on papers (pleading for greater concision).

We are a small department at a Catholic liberal arts school. When staffed, we employ 3 full time Econ faculty plus 1 or 2 adjuncts. We’re primarily a teaching university, teaching 3-class loads each semester. The students are great people. They have better moral fiber than I did at their age and the Econ majors tend to be smarter and more capable than I was at their age.

The university is located in Ave Maria, Florida which is a small town near Naples, the very wealthy destination of snowbirds and retirees. Most faculty live near the university, send their kids to the nearby private school, and attend the same masses. There is a lot of community here.

We’re happy to take economists of almost any specialization. A focus on micro or stats or data analysis would be a plus. The link to apply is below. I’d be thrilled to learn that this is how we met.

https://workforcenow.adp.com/mascsr/default/mdf/recruitment/recruitment.html?cid=70cb71c1-96f8-4956-8cce-ce625b0b2943&ccId=19000101_000001&type=JS&lang=en_US&jobId=466997

Covid Death Structural Breaks

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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

Arbitrary Framing & Economic Reality

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Subjectivism is popular at many universities. I am not talking about the economics kind in which people have a diversity of preferences. I’m talking about the subjectivism that permits different and conflicting assertions of truth to be simultaneously correct. This is where the ‘my truth’ language enters. Having a diversity of feelings is one thing – and unavoidable. Having different practical claims about the material world is another. Many universities have embraced Descartes’s unreliability of the senses writ large. The result is that people of seeming plentiful intellectual capacity dogmatize themselves into speaking such that nothing is considered a default. Nothing “is normal”, there is only “normal for someone”.

It’s a perfectly defensible model of the world. And, as we know, models are applicable only insofar as they’re useful. The subjectivist model is great at describing the diversity of preferences and priorities. The model is bad for math and achieving material ends. Further, it can serve to hinder our understanding of worldly or social phenomena.

Here’s an example.

Consider people who don’t speak the same language. They may or may not have some other compensatory skill. For Mandarin speakers, we can rightfully say that they can’t speak or communicate as effectively with the English-speaking majority of people in the US. We can also say the converse: The English-speaking majority can’t speak Mandarin or communicate as effectively with the Mandarin-speaking minority. There’s a certain symmetrical beauty to being able to interpret reality both ways. It exercises our cerebral cortex.

However, modeling the descriptive statements as intrinsically equivalent harms our ability to sensibly understand and analyze the circumstances. Specifically, we need to talk about opportunity costs.

Consider an urban storeowner in America who speaks only Mandarin. Consider also an only-English-speaking customer who has a question about an item for sale. We can perform the same symmetrical analysis as above saying that they both speak different languages. Importantly, however, they face substantially different opportunity costs in two ways.

First, the English-speaking customer has low-cost alternatives. The language barrier need not be insurmountable. If the transaction cost of more difficult communication is adequate, then the English-speaking customer can go elsewhere relatively easily and purchase from the English-speaking storeowner down the block. They have plenty of low-cost opportunities for gains from trade. Clearly, there is nothing intrinsically advantageous about speaking English. What’s advantageous is speaking the more popular language.

By having access to the larger market, the English speaker has access to greater specialization and to more buyers and sellers. If the language difference is the only difference between two people, then the one who speaks the majority language has an economic advantage. I mean ‘economic’ in both the pecuniary and non-pecuniary sense. Speaking the majority language has the consequence of greater income. But that comes from the very real differences in costs and benefits associated with trade. If the exact same person spoke only a minority language, then their income would be lower along with their lesser access to trading partners. Therefore, while it is symmetrically true that the English speaker can’t speak Mandarin and that the Mandarin speaker can’t speak English, it is not true that they face the same opportunity costs.

Second, and probably more trivially, it may be that most English speakers never have occasion to interact with any Mandarin-only speakers. Whereas Mandarin speakers in the US have constant potential interactions with English speakers. It would therefore belie the costs and benefits to simply say that they symmetrically can’t speak the same language. Indeed, many English-speakers have no motivation nor awareness of potential Mandarin-speaking trade partners. At the same time, in the US, Mandarin speakers would very much have an awareness and occasion to interact with English speakers. While it is true that they don’t speak the same language, they differ by their access to potential trade partners who speak a different language. It wouldn’t reflect the incentives to say that the English speaker is less able to communicate with Mandarin speakers when they largely lack even the awareness of the minority language.

Conclusion

An analysis of English and Mandarin speakers in the US is not a symmetrical analysis. It doesn’t matter whether we frame English speakers has having a lower opportunity cost to trading with Mandarin speakers, or whether we frame Mandarin-speakers as having a higher opportunity cost to trading with English speakers. The economic truth is that the opportunity costs differ, no matter how we might try to equivocate about what normal is. Obviously, the above analysis isn’t specific to Mandarin and English, nor to language necessarily. While framing a circumstance with a default is an arbitrary modelling decision, asserting that two alternatives means or practices have the same opportunity cost or the same productive capacity is indefensible and often doesn’t reflect the underlying economic reality.

A Measure of Dissimilarity

Zachary Bartsch1 Comment

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?

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Government Purchases and How Markets Avoid Messes

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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.

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Teaching Taxes w/GIFs

Zachary Bartsch2 Comments

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.

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Supply & Demand, With gifs

Zachary Bartsch8 Comments

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.

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