Data

Fable on Legibility

Joy Buchanan1 Comment

Claude Fable is Anthropic’s most capable publicly available “Mythos-class” model. It is optimized for long-running autonomous tasks and deep knowledge work. The roll out of this product has been dramatic. Little people like me have access to it for only two weeks, and I doubt I will be able to afford it thereafter. With my window of access, I posed it the following prompt:

“This article indicates that a much smarter model might not be possible because the universe is opaque. Since Tyler Cowen made this statement, AI has helped people make breakthroughs in math and biology. Write this again in 2026 using the latest state of technology. Is the smartest LLM today much smarter than GPT-4? And is the universe legible?” and I copied in my blog post Is the Universe Legible to Intelligence?

Fable replied in 3 pages of text which you can download as a Word doc here.

One line from Fable’s response: “Notice where the wins clustered: mathematics with checkable proofs, protein structures with experimental ground truth, contest problems with known answers. These are the maximally legible domains — places with a fixed target and a way to verify that you hit it.”

The writing is coherent and contains no obvious hallucinations. Is the answer true, and does it tell the whole truth?

Whenever you read something think about who wrote it, and keep in mind that every author/model has a bias and limitations. In my paper with Will Hickman, we found that just reminding people that a paragraph has an author (whether the author is human or AI) increased the demand for fact checking from readers. LLMs will become more persuasive and closer to (but never completely) correct. Keep reading all things with some skepticism whether they are written by scientists, politicians, or AI.

Regardless, there is definitely such a thing as making the known world more legible to AI today. Thus, people are talking about increasing funding for data availability and the possible demise of the “research paper.”

Research papers are more like stories than facts. The demand for stories is not going away, but I definitely cannot predict the future of the write-for-pay scientist.

AI, potentially, could go and get its own new data, instead of waiting for humans to archive it. Thus, the self-improving AI might take us beyond the current models… unless they run up against something that is not legible to intelligence…

By the Numbers: Florida’s Property Tax Amendment (2026)

Zachary Bartsch2 Comments

Voters this November will face a proposed amendment to the Florida state constitution on property tax reform. Currently, Florida has what’s called a ‘homestead’ exemption of $50,000. If a residential property is your primary residence, then your home’s assessed value is $50k less before taxes are calculated. There is no exemption for rental property or 2nd homes or vacation homes. The proposed amendment increases the exemption to $250k by 2028 and then indexes it to inflation.

First, let’s get an idea of the magnitudes. The median home in Florida is priced at about $400k and the average property tax rate is around 0.8%. Below compares the current consolidated tax bill against that of the proposed amendment. Given current home prices and local tax rates, the new exemption would have a huge impact on municipal governments who get the bulk of their revenue from property tax. In fact, there is no Florida state property tax, so the proposed amendment would adopt a new rule for municipalities and not the state government.

What Motivates the Amendment?

The current homestead exemption of $50k was established in 2008. A subsequent amendment in 2024 allowed half of that to be indexed to CPI-U. The average home price in Florida has risen 114% since 2008 and 84% since 2020. That’s a lot faster than inflation, but the tax burden is partially offset by a maximum of 3% annual increase in assessed value. Regardless, many individuals face a larger tax bill over time even independent of whether their income or use of public services has changed. Plenty people are feeling the squeeze.

What’s the Purpose of the Homestead Exemption?

The exemption is available for primary residences only. That means that rentals and vacation homes do not qualify. It’s important to keep in mind that, given some total revenue, every tax break for one group or activity implies a higher tax rate for others. So, clearly, the effect is to tax residents less and tax seasonal residents and visitors more. Florida doesn’t have an income tax, but it does have a sales tax, gasoline tax, and others that are disproportionately borne by non-residents. Given that higher income individuals tend to have higher home values, the homestead exemption is a way to lower the tax burden of lower income households. Obviously, the lowest income individuals are renters, but so are non-residents who Florida prefers to tax.

The Economics

Homeowners

The exemption is enjoyed by all primary residences, but helps low income owners the most. And, given a stable amount of municipal tax revenue, a higher homestead exemption requires that municipalities replace that revenue. This might take the form of higher local fees and taxes, making life harder for lower income people to, say, own a car or make purchase if taxes on those activities rise. Revenue stability might also be helped by higher property tax rates. The higher the property value is above $250k, the greater the average tax burden that is borne. So, someone with a very high property value may find themselves with an even higher property tax bill after municipalities adjust to the proposed statewide rule. In this sense, the new amendment would be a step in the direction of tax progressivity (a higher proportion taxed from those with higher income/wealth).

Indexing

Normally, I am in favor of indexing nominal values to CPI. In this case, we need to think about what the goal is. Let’s assume that the goals is to provide relief to lower income homeowners specifically and all primary residence homeowners generally. Does indexing to the CPI help? It depends!

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Yes, Americans Probably Are About 46 (or Maybe 65) Times Richer Than in 1776

Jeremy HorpedahlLeave a comment

My post and chart from last week showed the phenomenal growth of average income in the US since the Founding. Using GDP per capita historical estimates and adjusting for inflation, this figure is about 46 times greater today than right around the time we declared independence.

It will probably not surprise you that some folks were skeptical. Could this really be true? Two major objections were raised to using GDP per capita. First, wouldn’t it be better to use a median income value rather than a mean (simple average)? Second, wouldn’t a measure of wages be better than GDP per capita?

I really would like to show you an annual series of median income data back to 1776, but unfortunately it just doesn’t exist. Good median income data are hard to find much before the 1950s, much less the 1770s. However, while median values are often better for showing levels, the growth rates of median wages and mean wages aren’t that different for periods when we have comparable data. Consider the following chart, which compares median wages (as calculated by EPI using CPS data) and mean wages (from BLS’s series for non-supervisory workers) since 1973. I have stated these in nominal terms, so don’t take this as real growth rates, but rather it is a raw comparison of two series (we could apply the same inflation adjustment to both, but that won’t change the picture, only the numbers).

Median wages increased by 667% and mean wages increased by 657%, almost identical. Again, these aren’t inflation adjusted, but that’s not the point of this exercise. The point is that whether you use mean or median wages, at least since 1973, the growth rates are the same. Was this true if we went back another 200 years? We can’t say for sure. But many people have this same skepticism about mean wages in recent decades. I think it is better to use median values when you have them, but we shouldn’t throw up our hands and claim we know nothing if all we have is mean wages.

Next, consider the following chart. It begins in 1790, but instead of using GDP per capita, as I did last week, it uses a measure of average wages from economic historian Lawrence Officer. This measure is for “production workers in manufacturing,” and it is a total compensation measure, meaning that it will include the value of fringe benefits as well — though these aren’t noticeable in the data until the 1930s. This is still an average value, but because it is for manufacturing laborers, it won’t be distorted by the wages of managers and owners in that industry, and it won’t be affected by the growth of new industries that might require more years of education (indeed, manufacturing wages are lowering than overall average wages today, so this is taking the hard case). I have also included a second line, which only includes manufacturing wages (not benefits) that I have blended with Officer’s compensation series starting in the 1930s, in case you think including benefits is somehow “cheating.” (Note the log scale again, as in last week’s chart.)

The trends here are very much in the ballpark from the GDP per capita chart I created last week. Using total compensation, wages are 65 times higher than in 1790. Using only wages, they are 49 times higher. Notice that these are both better than the 46 times multiplier using GDP per capita. How is that possible, since I am using the same price deflator in both cases? First, average hours of work have fallen significantly since the 18th century, so incomes haven’t risen quite as much as wages. Second, there was a bit of a decline in GDP per capita during the Revolutionary War, and if we use 1790 as the baseline for GDP per capita, the multiplier is 63. But again, these numbers are all in the ballpark: whether the true figure for a typical American is 46x, 49x, 63x, or 65x, this is a tremendous amount of economic growth.

If you want to look at that chart pessimistically, you will see that there is some reduction in growth rates in the past few decades. That’s true whether we use wages or compensation. This is a well known issue, and has been discussed endlessly in academic papers and on social media. I don’t want to glaze over it here, but I mostly will: the long-run trend of growth in the US is amazing. That’s true whether you use GDP per capita, or wages or compensation for production workers.

So once again, Happy 250th Birthday to the USA and all of you living in the wake of that amazing 250 years of economic growth!

Fiscal Trends: USA’s 250th (And the Government’s 237th)

Zachary BartschLeave a comment

We celebrate 250 years since the Declaration of Independence was signed on July 4th, 1776. That’s the day that we celebrate our country’s birth. So, it’s very American of us to celebrate the day that we merely declared independence (not the day that the revolutionary war ended). We simply said we were independent from the crown. Regardless, we celebrate 250 years as a people. BUT, our government is only 237 years old.  The current constitution replaced the articles of confederation in 1789.  So there are some caveats to the whole semiquincentennial thing.

An important distinction that is baked into the American pie is that we are not our government. Our government is younger than we are. Our government has a piggy bank called ‘US Treasury’. It can spend and borrow for the US national government. It can also impose tax liabilities on the population in order to service those outlays. Now that it’s the government’s 237th birthday, what’s its basic financial track record?

I like to think in the long run, for better or for worse, and I don’t like to get hysterical. So, let’s look at the full span of the 237 years – well – 235 years. The oldest annual data that we have is from Bicentennial Historical Statistics, which goes back to 1792. Below are the series for Federal Receipts and Outlays (revenue and spending).

The blue line is in nominal dollars and the orange line is the natural log so that we can see the changes in growth rates more easily. These aren’t inflation adjusted numbers, so we should expect to see some inflationary patterns. Long-run inflation was pretty stable prior to the 1913 Federal Reserve act and wee can see that reflected in both series. There was some drift upward in terms of revenue and expenditures. But the primary pattern was one of punctuated rises followed by plateaus. That’s a pretty standard ratcheting leviathan pattern. There’s a bump up for the big events in the first half of our history: the War of 1812, Civil War in 1861, and World War I in 1917.

Then, after the great depression and leaving the gold standard (mostly), in about 1933 a new and positive trend in cash flows began. In fact, it’s amazing how consistent the raw nominal series is.  We can see where World War II is in the series, but after that we appear to have traded punctuated increases for steady increases. Even the higher inflation rates of the 1970s look pretty muted and on trend (Btw, the blip in 1976 is a record-keeping artifact. There was a 3 month gap-period when the US government changed its fiscal year start/end). Even the new growth in total cashflows seems to be slightly bending downward and growing a little more slowly.

But rest assured, spending has exceeded revenues. Below is the long run deficit. I don’t take the log for this one since there are negative numbers. It’s hard to tell from the line graph, but the first big and persist swing in the deficit arrived after the Fed was established and the onset of WWI. The deficit hit $9 billion in 1918, which was 10x the prior peak of $0.9 billion at the end of the civil war in 1865. Notice that the above government revenues stayed flat or fell after 1920, but the outlays began trending upward before the revenues. The deficit doesn’t really start its long, steady march until 1932. Of course, for the past quarter century, the national government has been in a deficit mess (even if you measure the proportion of GDP).

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Happy Birthday, USA

Jeremy Horpedahl4 Comments

For America’s 250th birthday, my present to all of you is this chart showing our economic history. Average income in the US has increased dramatically since the country was founded. This chart attempts to provide one, continuous series, using the best available income data and inflation adjustments (well, mostly continuous — before 1790 there are just a few estimates). Sources are listed at the bottom of the chart. The y-axis is a log scale.

What the Fed Knew, and When

Zachary BartschLeave a comment

I’ve recently gone back and started listening to the archived episodes of the ‘Macro Musings’ podcast hosted by David Beckworth. The show started in 2016. At that time, there was still a sense of malaise after the 2007-2008 Great Financial Crisis (GFC) and the slow recovery that followed it. We were also in a prolonged low-interest rate environment.

A recurring theme is whether the Fed should have engaged in expansionary policy earlier than they did in response to the GFC. There are multiple ways to answer. It’s not helpful to say ‘knowing what we know now’. The Fed didn’t have that opportunity. It’s a little bit more helpful to say ‘if the Fed had a different target or different tools’.  The target and tools are higher-order policy decisions and changing them can be helpful in the future. But they typically can’t be changed with the flip of a switch. After all, the 2% inflation target itself rolled out over the course of decades.

The most awkward/damning question is “Given the target, tools, and data that the fed actually had, did they make the right decision?”. If the answer is ‘no’, then that warrants a serious investigation of individuals, groups, processes, etc. I don’t mean a legal investigation. I mean the decentralized kind in which public and expert trust can be affected.

A concept that Beckworth often mentions concerning Fed culpability/performance during the GFC is the problem of data revisions. Currently, we know what the revised data says about NGDP, inflation, employment, etc. But the Fed only had the contemporary numbers and immediate revisions. In a world where economic growth is lousy or stellar in a range of 1-3%, small revisions can matter a lot. For example, below are the 2001q1 NGDP revision values over time.

Revisions occurred twice by 2002q2, revising NGDP down by more than 2%. Subsequent revisions raised the value on record to nearly +3% of the initial estimate, before settling at a less elevated value. Sheesh! In a world where a 1% swing is a big deal, how can we possibly expect the Fed to succeed at managing aggregate demand?

Things are not so scary as they might seem. The Fed doesn’t much care about revisions to an individual quarter. Rather, they care about the direction of change over time. Whether future revisions increase GDP by 2% is unimportant. What’s important is whether one period’s value is lower relative to the earlier value. That’s the relevant difference that tells us how the economy is changing.

Now, in 2026, our current understanding of NGDP during the GFC follows the below pattern starting in 2005q1 (lest I omit important pre-trends). NGDP growth had weakened in 2007q4, turning negative in 2008q1. Weak growth resumed in 2008q2. Then we had near-zero or negative growth for the next five quarters. Of course, we’re now approaching twenty years later, so we have the huge benefit of hindsight and revisions. Keep in mind that the contemporary numbers aren’t available until the subsequent quarter. By the yard stick of NGPD, the Fed should have been loosening by Q3 or certainly Q4 of 2008 if they cared about supporting total spending. Maybe as early as Q2 is they were especially sensitive.  

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Consumer Debt Delinquency & Write-Offs

Zachary BartschLeave a comment

I wrote a post about debt delinquency way back in 2023. At the time, people were concerned about an impending recession. I argued that, if there were to be a recession, then debt defaults would not be the cause. The delinquency numbers were low and stable. Though delinquencies did rise some, no recession materialized. I’ll say a little more about how to interpret the numbers and give an update.

There exists a stock of loan balances. Most loans are in good standing with scheduled payments being made. This is good debt. Some debt is delinquent, meaning that payments are not being made. This is bad debt. What happens to bad debt? Sometimes those borrowers catch up on their payments and their loan balances switch to being good debt. Borrowers can also transform their bad debt into good debt by restructuring it with new terms. Temporary administrative adjustments can also change the classification from bad to good debt. At any moment, the total stock of debt is composed of good and delinquent debt. We can express these as proportions of all debt.

But the lenders also recognize that not all bad debt will be made good. For one reason or another, sometimes borrowers just don’t repay. It doesn’t make sense to list delinquent debt as a balance sheet asset if it will never be paid. Rather than accumulating more bad debt every year that will never be paid, banks ‘charge off’ some of that bad debt. Charging off bad debt lets banks realize losses and makes for a more realistic balance sheet. The flow of charge offs is deducted from the stock of delinquent debt.

If banks charge off some delinquent debt, then the proportion of delinquent debt should be lower in the next period, all else constant. But all else isn’t constant. Some good debt will become delinquent and some delinquent debt will become good. Though, after a charge off it’s true that delinquent debt is less than it would have been otherwise. Below, I denote the net flow of good & bad debt transitions as ‘r’ and solve for it.

The variable ‘r’ is the net transition to good or to bad debt after charge offs. If r>0, then net new delinquencies occurred faster than banks realized their losses with charge offs. Is that good or bad? A higher rate of net new delinquencies can be bad because it reflects that people aren’t paying their contractually obligated debts. But it can also be good if the new delinquencies are a result of experimental entrepreneurship and an innovative economy. The bad interpretation is probably relevant cyclically as a short or medium run variable. The innovation interpretation probably changes in the medium or long run as a structural variable.

Let’s look at the numbers. There are several categories of loans, but let’s start with just consumer loans.

The delinquency rate is higher than it was after the pandemic stimulus checks, but is still lower than historical rates. The charge off rate is also near the historical average. Below right graphs ‘r’ and it’s always greater than zero, meaning that there’s always more people transitioning from good debt to delinquency than the reverse. There was more debt becoming delinquent as post-pandemic interest rates rose, but net delinquency transitions have been falling since 2024q1 until 2026q1 when they mildly up-ticked. In other words, the aggregate consumer debt picture looks pretty average except for the secular decline in rates of delinquency. I don’t know why that is. Maybe banks have gotten better are identifying risk? Or maybe newer forbearance rules are friendlier to borrowers who need to pause payments?

Below are the same two graphs for single-family residential mortgages. These delinquencies are close to historical lows and charge offs are average. However, the ‘r’ graph below has been rising for a decade and is currently at a twelve-year high. Since the data only goes back so far, it’s hard to say whether the low numbers of the late twenty-teens were an aberration of the post GFC, low interest rate environment or whether we should be concerned. It is worth noting that the ‘r’ values are often below zero, which means that people do often come back from delinquency. We know it’s not simply charge offs doing the work there since the charge off rate has been steady and very low.

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Berries Are Probably Not Making Parents Go Broke

Jeremy Horpedahl1 Comment

The Washington Post recently ran a fun, data-filled article on berry consumption and parenting. Lots of good tidbits in the article, including that Americans eat a lot more berries than in the recent past, and that a lot of the availability is thanks to foreign trade and imports. But despite being somewhat light-hearted, the article does seem very negative, especially in the title and introduction, about how parents are spending a lot of money on berries.

First things first, are berries breaking the budget for parents? Probably not. While the Consumer Expenditure Survey doesn’t give us data on specific types of berry spending, the broader category of Fresh Fruits is a very small share of consumer spending. It has pretty consistently consumed between 0.30% and 0.45% of income for families with children over the past 4 decades. That’s less than $1 out of every $200 of income. True, there has been a slight rise since over the past 20 years or so, but this is still a small share of the budget.

On average, families with children are spending around $600 per year on Fresh Fruit. And that’s all fruit, not just berries! Just a little over $10 per week. But even for an item that families spend a small share of their income on, such as eggs, perhaps the fact that prices have increased so much recently makes families stand up and notice. Berry spending might seem out of control, even if it’s a small share of income.

What does the price data on berries show? My usual source on this the BLS average price data that forms the basis for the CPI, but they only publicly publishes a series for strawberries, not the other famous berries (blueberries, raspberries, etc.). There is one chart on prices in the WaPo article, but it only compares strawberries to bananas over time (they got both of these from BLS). Because banana prices have been very stable in nominal prices over time, it looks like strawberry prices are exploding! But it’s really more notable that banana prices haven’t rise.

USDA does have some fruit and vegetable specific retail price data, but it only goes from 2013 to 2023. That’s shorter than I would normally like, but it can give us a clue about whether there has been some recent explosion in berry prices. And ending in 2023 isn’t ideal either, but overall inflation has been moderate since 2023, so it’s probably an OK source to use. Here’s what the data shows (prices are for fresh berries, except cranberries which are for dried):

Relative to median wages, berries of all kinds are now more affordable than a decade ago. Parents may still feel squeezed by all the berries their kids are eating, but in terms of affordability and share of the family budget, there is probably no need for a Berry Panic.

Consumer Prices in the US Took About 27 Years to Double

Jeremy HorpedahlLeave a comment

Two years ago I wrote about post about how long it took consumer prices to double in the US. The most recent time period looked pretty good compared to most of the 20th century. But lately I’ve seen a lot of social media posts talking about prices doubling (e.g., “you need twice as much income as the 1990s to match the standard of living back then”), so it’s worth looking at again.

The results aren’t that different:

Using the CPI-U, consumer prices in the US doubled in the most recent 321 months. Not only is that a longer period of time to double than most of the 20th century, in the prior 321 months (November 1972 to August 1999) consumer prices doubled twice: nominal prices were almost 4 times higher in August 1999 than in November 1972!

While the CPI-U does slightly overstate inflation, we don’t get much different results if we used chained indexes. For example, using the PCEPI, it took 390 months for prices to double between October 1993 and April 2026. Either way, prices roughly doubling from some time in the 1990s to today is accurate. But wages have more than doubled since then: you only have to go back to July 2005 for average wages to double (they are up 139% since August 1999 and 190% since October 1993). Or if we use a median wage series (such as EPI’s using CPI data), nominal wages doubled from 2002 to 2025 (I have readjusted that series back to nominal wages). In real terms, median wages are 22 percent since 1999 and 29 percent since 1993.

Of course, it would be better if prices weren’t doubling over any time frame! But the most recent doubling of prices that we lived through is the longest period to double in the lifetime of almost everyone alive in the US today.

Joy Explains how to integrate AI into a statistics class

Joy BuchananLeave a comment

I have put a working paper on SSRN describing three ways I incorporated AI into my Business Statistics 200-level class for undergraduates at Samford University in Spring 2026. Read the paper at the link.

Connecting Classroom Econometrics and Excel Training with Large Language Models (SSRN)

Abstract
Economics education almost always includes a component of statistics. Most undergraduate economics curricula require an upper-division econometrics course, and many economists teach data analysis. These courses help students become conversant with major contributions in economics research, but they can be challenging to teach. On its own, the mathematics of regression, error minimization, and statistical software may not feel exciting to students, especially compared with the intuitive economic reasoning that often draws them into the discipline. At the same time, students are increasingly interested in artificial intelligence and large language models. This note describes three practical teaching exercises designed to connect ordinary least squares, Excel training, and LLMs. The goal is to use students’ curiosity about AI to motivate classic statistical reasoning and practical spreadsheet skills.

The image is from ChatGPT 5.5 Thinking mode and it took over a minute to generate. The fact that their laptop screen is pointing away from them is funny (unrealistic). The portrayal of Tom Holland and Zendaya is good, which is what the audience cares about. So, this seems like a case of AI hallucinating up the thing that people want.

I posted back in February about the LLM Telephone game: Telephone Classroom Game for Teaching Large Language Models

Citation:
Buchanan, Joy, “Connecting Classroom Econometrics and Excel Training with Large Language Models” (May 27, 2026). Available at SSRN: https://ssrn.com/abstract=6839039

Note: I have been posting my papers to SSRN for a long time as a way to distribute them faster and more widely. I have heard rumors that SSRN might stop working, for my purposes. If anyone has suggestions for what I should do about the papers I have up there, please let me know! Or, if you are readying this post-summer-2026 and want a copy, send me a message at my Samford email so I can send you a copy.