Hyperinflationary Efficiency?

I’m advising a senior thesis for a student who is examining the strength of Purchasing Power Parity in hyper-inflationary countries. Beautifully, the results are consistent with another author* who uses a more sophisticated method.

For those who don’t know, absolute purchasing power parity (PPP) depends on arbitrage among traders to cause a unit of currency to have the same ability to acquire goods in two different countries. If after converting your currency you can afford more stuff in foreign country, then there is a profit opportunity to purchase there and even to re-sell it in your home country.

Essentially, when you make that decision, you are reducing demand for the good in your home country and increasing demand in the foreign country (re-selling affects the domestic supply too). Eventually, the changes in demand cause the prices to converge and the arbitrage opportunities disappear. At this point the two currencies are said to have purchasing power parity – it doesn’t matter where you purchase the good.

So does PPP hold? One way that economists measure the strength of PPP is by measuring the time that it takes for a typical purchasing power difference to be arbitraged away by 50% – its ‘half-life’.  The more time that is required, the less efficient the markets are said to be.

The ex-ante question is: Is PPP be stronger or weaker during hyperinflationary periods?

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Singing IPUMS Praises

This is a late post, but I just want to sing the praises of IPUMS.

I first encountered IPUMs data in Sacerdote’s paper on intergenerational human capital transfers in which he showed literacy rates by birth cohort throughout the 19th century (figure 4 is downright beautiful). I’ve since dug-in myself concerning school attendance and human capital.

In the papers that students write in our econ elective classes, it’s not unusual for them to contain FRED data. Given that we don’t teach time-series, the papers are usually empirically weak. But this semester in my Wester Economic History course, I’ve encouraged student to utilize IPUMS. There are 4 students who are using it whose ideas I will surely publicize in the future:

  • Historical patterns of deaf employment, education, human capital, & income
  • The economic impact of the Brooklyn bridge
  • The composition of US interstate migrants relative to their host state
  • Patterns compulsory schooling

IPUMS is so darn rich. I strongly recommend it if you haven’t yet taken advantage of it.

The Tall and Short of Student Experience

Every semester in my intro STAT course I have my students create a variety of survey questions. After I combine their questions into a single survey, they collect responses from the student body at Ave Maria University. Most of the questions are vanilla. Other are not. They typically get in excess of 100 responses from the ~1,100 person student body.

While exploring the data, I found a really beautiful example for the week that we spend on multiple regression and dummy variables.  The survey results illustrate a clear, linear association between student height (inches) and their student experience at AMU (scored 1-10).

So strange! Why might this be? Except for that solitary 7 ft+ student on the basketball team, how in the world might height matter for student experience?

As it turns out a separate relationship holds the key.

Confirmed with a simple unpaired t-test (unequal variances), women rank their student experience much more highly. For this, students have multiple explanations at the ready.

  • Our school is in a rural location and women are more socially satisfied.
  • Men are less happy generally.
  • Men are less studious or have lower grades.
  • Men get less sleep and stay up later

The list goes on and I don’t know what the reasoning is or which ones actually play a role. But what I do know, is how to make fun scatterplots in Stata. As it turns out, if you control for sex, height loses all of its effects on student experience. Men are taller on average and they aren’t happy students relative to women (apparently). We can see in the figure below that all of the action in the two fitted lines occurs in the intercept. The slopes are practically flat for both men and women. In other words, height neither adds nor subtracts from a student’s experience rating.

What’s going on is that neither men’s nor women’s experience is affected by being taller. But, what’s actually going on here – you know – statistically? The simple version is that the bar chart above dominates the scatter plot. If we subtract the mean male experience score from the male values and do the same for the females, then we’re left with what is practically white-noise. How do all those other students of a different height experience the world? Well, as students, not so differently from you.

Compulsory Schooling by Sex

My previous posts focused on the aggregate school attendance and literacy rates for whites before and after state century compulsory schooling laws were enacted. When aggregates fail to deviate from trend after a law is passed, the natural next step is to examine the sub groups.

How did attendance rates differ by sex before and after compulsory school attendance? I’ll illustrate a plausible story. Prior to law enactments, boys attended more school because girls were needed to perform domestic duties and the expectations for female education was lower. As a result, boys had higher literacy rates due to higher school attendance. After law enactments, both girls and boys attended school more and the difference between their attendance rates is eliminated. Similarly, literacy rates converge and differences are eliminated. In short, the story is consistent with an oppressed – or at least disadvantaged – position for girls that was corrected by compulsory schooling.

Formally, the hypotheses are:

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Wait for the Lower Cost Version of Policy

I’ve written previously about initial US state compulsory schooling laws in regard to literacy and in school attendance rates. I ended with a political economy hypothesis. Here’s the logic:

  1. Legislators like lower costs, all else constant (more funding is available for other priorities).
  2. Enforcing truancy and educating an illiterate populous is costly.
  3. Therefore, state legislatures that passed compulsory attendance legislation will already have had relatively high rates of school attendance and literacy.

That’s it. Standard political economy incentives. But is it true? Well, we can’t tell what’s going on in politician heads today, much less 150 years ago. Though, we can observe evidence that might corroborate the story. In plain terms, consistent evidence for the hypothesis would be that school attendance and literacy rates were rising prior to compulsory schooling legislation. The figures below show attendance and literacy rates for children ages 10 to 18.

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School Attendance as State Capacity

Who knows what state capacity was 150 years ago? After all, DMV jokes are only a little out of date. There is a lot of richness and specificity to state capacity. That’s why we can’t look at an identical law in two different places or times and assume that their enforcement and evasion are the same.

Interested readers can see my previous post for a figure that illustrates the timing of compulsory education legislation across US states. The effects on literacy were a bit ambiguous. The explanation might be that effective enforcement by the various states might have differed (substantially). The figure below illustrates the average rates of attendance by age and census year.

Just as an increasing number of states began to enact compulsory school attendance, we can see that school attendance rates rose over time. But we can’t tell from the figure whether attendance laws caused or were merely coincident with increasing attendance.

One hint is to group the people by whether their state had compulsory attendance laws on the books. See the figure below.

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Reading Literacy Data

The story that I’ve heard is this:

            In the US, we care about education. We believe that all people should receive one, regardless of their family status. Therefore, states provide education directly.

There you have it. We provide education in the US so that everyone gets a more fair shake at education. We might disagree about the purpose of an education. Maybe it’s for improved job prospects, for a more informed citizenry, or for more unified values and experiences. One socially awkward answer is that state schools are, in part, a childcare service that permit parents to work. Except for these couple of reasons, school provision and compulsory education should, at the very least, increase literacy. That’s a low bar.

Given the above reasoning states began to pass compulsory school legislation. Massachusetts was first in 1852. Followed by DC and Vermont in the 1860s. Thirteen more adopted compulsory education legislation by 1880. By the year 1900, most states had compulsory schooling legislation on the books that was applicable to at least some age groups. See the figure. Thus, did the US achieve more equality, so goes the story.

The reasoning behind the story is sound. Without education of some sort, people will surely have less human capital. The vulnerability of the reasoning is that formal schooling is not the only form of education. A person who doesn’t attend school may help a parent at work or have a private tutor – or simply grow in a milieu of thoughtful exposure. Therefore, requiring that a child attend school may not improve human capital by a degree greater than what the child would have been doing otherwise. That’s an empirical matter.

The figure below illustrate the data for ‘white’ people and illustrates literacy between the ages of 20 and 30. Why that interval? At the lower end, we don’t have literacy data for people under the age of 20 in 1850 & 1860. On the higher end, any effects of compulsory schooling will only affect those who were children and subject to the law – older people are immune to compulsory schooling legislation.

The graph illustrates that state literacy rates were rising throughout the period. The main exception is 1870. Maybe the demands of the civil war caused children to work at home or otherwise and forego schooling. So the increase from 1870 to 1880 is more of a catch-up to a previous trend than anything else. While it’s true that several states passed compulsory schooling laws in the 1870s, that doesn’t explain the widespread literacy improvements across most states.

After 1860, we can examine the younger people who were subject to the schooling laws. The figure below for people ages 10-20 tells a similar story to the one above.

My biased reading of the data is that initial compulsory schooling laws had at least an ambiguous effect on the overall trend of improving literacy. I’ll delve deeper in future posts.

PS – The literacy data is from IPUMS.

PPS – The compulsory schooling law dates are allegedly from “Department of Education, National Center for Educational Statistics, Digest of Education Statistics, 2004.” But I couldn’t find the original source. Kudos to anyone in the comments who can find it.

An Economist Learns Piano: Part 1

My life didn’t change all that much due to Covid-19 pandemic. I live in a small university town. I mostly continued to go to work and my kids mostly continued to play with their neighbor friends. After a brief hiatus, I ended up growing much closer to my neighbors. One nearby couple are even the godparents my most recently born child.

The university at which I teach is a liberal arts school…. And I teach economics. I knew that these music-type of students and professors were out there, but I didn’t have much exposure. I recently obtained a zero-priced piano and had a good 2-hour conversation with a music major. This post illustrates part of I’ve learned so far. First, a graph.

Whether we want to or not, many of us know the musical scale thanks to The Sound of Music. What I didn’t know was that there is not a uniform distance between all of those notes. Along the x-axis is the note labels (do re mi fa so la ti do). The pitch is characterized by an increment called a step. Given some arbitrary pitch for the first note, do, each subsequent note is a specific number of steps away. The pattern is that each increment between notes is 1 step, except the step from mi to fa and from ti to do. Those are half steps. The result is a segmented function.

Now, this pattern can be applied to a piano.

There are a total of 88 keys on a piano. Some are black, others are white. But all of them are a half-step increment from the prior and subsequent key. IDK why there are small black keys and big white ones. But pianos would be a lot bigger without the narrower black keys. Every single white key on a piano is labeled with a letter. The letter *does not move*. A ‘C’ is always a ‘C’.

What can move is the scale label, do, which can be any key. The pattern identified in the graph above must be maintained. To play ‘in the key of C’ means that ‘C’ is identified as do. The remaining keys can be labeled.

The key of ‘C’ is easy because the entire scale can be played on all white keys.

Those two half steps that we mentioned earlier? Those might have been on a black key – except that there is no black key between ‘B’ and ‘C’ or between ‘E’ and ‘F’. The B-C keys are adjacent. That means that their pitch is a half-step apart – exactly what is necessary for the pitch difference between mi and fa. The same is true for the E-F step and the pitch difference between ti and do.

What about the black keys? We can see their roll by placing do on a different lettered key. We can start on ‘D.  

do to re is a full step, from ‘D’ to ‘E’ – skipping the black half-step that’s between them. For re to mi we need to skip a key, all keys are a half step apart. So? To the black key! We skip ‘F’ and land on the subsequent black key. Then, fa falls on ‘G’, a half step and a single key higher in pitch. ‘A is a full step away from ‘G’, so that’s so. la is another full step away on ‘B‘. Recall that all of the keys are separated by a half-step – the key colors are 100% unimportant. ti is a full step higher – but there is no key separating ‘B’ and ‘C’. So, we skip up to the black key again just as we did with mi. Finally, do is a single key and a half step more.

There you have it! One of the things that a pianists can do is play the entire scale, from do to do, starting from any lettered key on the piano. I can’t do that yet, but golly I certainly feel like I have a better handle of what I’m even looking at.

PS – My conversation took a long time and I had to nail down the difference between 1) The note label, 2) the pitch step increments, & 3) the piano key letter labels. Key letter labels and the note labels are ordinal variables while the steps are cardinal. So, the graph at the top of this post isn’t the only important relationship. The graph below includes the relationship between the step and key letter labels. A graph of the note label and the key letter labels requires a rudimentary knowledge of flats and sharps (with two different do’s).

Sunk Costs and The Sense of Self

My 3 year-old will scream. She will lay on the floor, thrash about, and make demands as an infant would if they could communicate and develop the motor control adequate to do so. It doesn’t matter whether she can remember the reason for her disposition – she will continue. My wife and I usually sense the situation. We could get angry and threaten punishments. Alternatively, we know that no amount of reasoning and attempts at persuasion will convert our daughter’s behavior into the sweet, desirable sort. We have found that smothering her with love works best. And when the demands of other children prevent such single-minded attention, we at least try to act lovingly toward her.

My wife is quite beside herself. Why is this happening? (Truth be told, it’s all my fault. It’s in the genes.) Sometimes we see the momentary consideration of a calmer world in our daughter’s face. Then, she rejects it like there is no goodness left in the world. To be clear: I see my daughter know that she can stop her comprehensive riot and instead enjoy some other activity, then definitively decline the opportunity. She has cognitive dissonance.

My child is not crazy. One might say that she is irrational. The entirety of her behavior up to that point is a sunk cost. She could just stop the outburst and feel better. But she doesn’t. Why the heck doesn’t she?

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Age-Old Dads

Do you know how old you are?

I’m 33. Specifically, I’m 33 years, 29 days old. I don’t know the time of day that I was born, but my mom probably remembers within a couple of hours. My dad did not keep track of my age. Growing up, it was normal for him to take me to a sports registration event and need to ask me for plenty of my details in order to complete the paperwork.

Do you know the age of your children? Is it normal for parents to lose track? Or is it just the dads?  …Or just my dad? I have no idea what is typical.

But I do have some decent evidence that, had my dad lived in 1850, he would not have been such an anomaly. Consider exhibit A: A histogram of US ages in 1850. The population was only about 23 million at the time and we have the age for about 19 million of those people. So the graph is relatively representative (IPUMS census data).

Do you notice anything weird about the graph?

That’s the question I asked my Western Economic History class.

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