Data

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.

Quasi-Relative Measures of Portfolio Performance

Zachary Bartsch1 Comment

Last week I discussed absolute measures of portfolio performance and management, specifically between two portfolios that are composed of different assets (utilities and tech). I began with comparing the basics of return, standard deviation, and Sharpe ratio to some other possible portfolio in the Markowitz cloud. But, simply comparing the difference between these possible portfolios can be sensitive to the spread of stats within a specific Markowitz cloud. In other words, it’s not scale independent. A larger spread of possible stats can make a portfolio look bad due to the spread return/standard deviation/Sharpe ratio alone.

In this post I introduce quasi-relative measures. Again, I lean on the Markowitz cloud. They’re pasted below (Utilities on the left, tech on the right).

If we can somehow express the returns, volatilities, and Sharpe ratios on a common scale that is independent of the level values, then we can make the realized portfolios more comparable. One thing that we can do is to express a stat as a weighted linear average between the maximum and minimum possible values. Conditional on the realized standard deviation, there exists a maximum and minimum of possible return. Something like the below. Rho is the weight on the maximum return. It’s also the proportion of possible conditional returns that are lower than the realized return.

The unconditional version is the same, but would be relative to the global maximum and minimum stats. We can represent the weigh on the maximum return and the percentile among possible returns as gamma.

A final quasi-relative measure of performance is the dissimilarity index between the realized portfolio weights and some reference portfolio weights. This provides a measure of how much the asset weights would need to change in order to adjust the portfolio.  If changing portfolio weights is costly, then it’s also a measure of the transaction cost of reallocation. It’s quasi-relative because it is independent of the spread of possible performance stats.

Below are the quasi-relative measures for each the utility and tech company portfolios.

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The “Reality Index” of Price Inflation Isn’t Grounded in Reality

Jeremy Horpedahl1 Comment

Over the years, many people have tried to create alternatives to the CPI for measuring inflation. Probably the most famous is “Shadow Stats,” which Tim Lee has convincingly shown isn’t actually measuring price inflation (it’s just adding a fixed factor to the CPI).

But the CPI critics keep coming. One that was recently released is called the “Reality Index.” This index tries to improve on the CPI-U in two ways. First, it uses fixed weights for the items in the basket, and importantly it uses the 2024 weights and applies them to past years (this is called a Paasche index). Second, it takes out some BLS prices to avoid using hedonically adjusted prices, and other price calculations that the Reality Index author thinks are weird.

Both of these changes are problematic. I will explain why.

1. Fixed Basket of Goods/Services Doesn’t Make Sense

Many critics of the CPI complain about the shifting weights in the CPI. “We just want to measure the cost of a fixed basket over time.” But measuring a fixed basket over time isn’t actually that useful. I will explain why in a moment. But that’s not even what the Reality Index does! Instead, it takes the 2024 CPI weights (which come from the Consumer Expenditure Survey), and then consistently applies those weights to past years. The Index isn’t measuring the cost of a fixed basket of goods from some past year — it is using the 2024 basket, and assuming that’s what people consumed in the past.

The author of the Reality Index, Tom Elliott, is either confused about this or is being deliberately misleading, for example in a recent WSJ essay promoting the Index, he says “That same basket, the one the government says rose 1.87 times since 2000, has actually risen about 2.4 times.” But that’s false. To do that calculation, you would need to use the 2000 CPI weights and follow them forward to 2024 (this is called a Laspeyres index). Instead, he uses the 2024 weights and follows them backwards. He could do the calculation that he references in the WSJ essay, but he does not.

To see why this is a bad approach, let’s compare the weights in the Reality Index with a few past years. I have done my best to translate the weights for the 10 categories listed on this page to actual BLS categories, though I will admit that none of their category weights matched exactly to what I found at BLS. But I’m pretty confident it is correct.

I am also pretty confident that the “discretionary” category is just a residual for everything that wasn’t in the other 9 categories, though I can’t find them explicitly saying this. Yellow highlighting indicates the category in past years was smaller than the 2024 weights. Green highlighting indicates past years were larger weights.

The first thing you might notice is that the CPI weights have changed significantly over time. Relative to 1970, housing/shelter gets almost twice as much weight today. Conversely, groceries/food at home gets about half the weight today as it had in 1970. The “discretionary” category (the residual to make it add to 100%) used to be 30 percent of a household budget, using this approach! That should really give you pause: do we really think a typical household in 1970 considered 30% of their budget to be “discretionary”? I highly doubt it. That discretionary category includes clothing, which was over 10% of household spending in 1970 (it’s around 2% today).

Related to that, you may also notice that categories which have had above average inflation over this time frame — such as housing, healthcare, and education — all have bigger weights today than in the past. Meanwhile, food and clothing have seen less price inflation, but they are weighted much less. This process will tend to overstate inflation of the past, as the CPI in 1970 placed less weight on, say, housing, so when you put more weight on it, of course the inflation rate will go up. And indeed, as the Reality Index’s historical analysis shows, the biggest gaps in inflation between the RI and CPI were in the 1970s (4.9% gap in 1979 and 4.7% gap in 1978). But this is ahistorical: people were not spending 37% of their budget on shelter in the 1970s! In fact, they were spending almost as much on groceries in 1970 as they did on shelter.

The Reality Index is essentially projecting backwards to a fake reality of the past, because it uses the 2024 weights in all past years. But this isn’t capturing anything real about the world, and it is at best an interesting thought experiment. Of course, part of the reason people now spend more of their budget on housing and healthcare is because they have gotten more expensive and to some extent crowded out other spending. But they are also categories we might expect demand to increase as incomes increase (normal goods). And notice this is the opposite of the standard critique of the CPI: as things get more expensive, critics claim the CPI assumes people spend less on those items. Instead, the CPI-U weights are updated each year based on the latest Consumer Expenditure Survey data, and goods/services with higher rates of inflation now consumer more of the weight of the CPI than in the past.

(*Note: the “pet” category is listed as 0% in 1970 because BLS didn’t itemize it separately due to it being so small. That’s of little consequence, since it is such a small share in every year — I’m surprised they didn’t just stuff pets in the discretionary category.)

2. Swapping Quality-Adjusted Measures for Nominal Prices is Often a Bad Idea

Using the 2024 weights for past years is reason enough to not find the Reality Index useful. But let me just say a few words about the substitute prices that the Reality Index uses. The changes are either trying to use something that isn’t hedonically adjusted for quality, or to overcome some of the strange calculations, especially for housing and health care.

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Absolute Measures of Portfolio Performance

Zachary Bartsch1 Comment

The basic idea is that we want to compare the performance of different portfolios or their managers. This is relatively easy as long as the portfolios contain the same assets. Then, the portfolios are simply characterized by the different weights among the different assets. But how do we compare the performance of portfolios whose assets are different? In finance, we usually assume that everyone can invest in everything. But there are plenty of cases in which that’s a bad assumption: when clients want exposure to particular industries, when there are statutory limitations on holding certain assets, or when an individual company is considering specific projects within the same company under conditions of scarce financing.

The most primitive step is to compare the return and standard deviation of two different portfolios. However, higher risk investments tend to have higher returns in dynamic equilibrium. So, if we were to compare the returns of a tech company to a utility company, then we’d often see the tech companies performing better. But, if we compare the volatilities, then the utility companies would tend to perform better. Sharpe stepped in with a ratio to express the excess return (benefit) per standard deviation (the cost). This way, we can compare the price of volatilities between two portfolios. We’ll stick with just these basic 3 measures: return, standard deviation, and Sharpe ratio. (Others do exist)

Let’s put some meat on this with an example. Say that we have two portfolios, each composed of different assets. There’s a utility portfolio that’s composed of NEE, DUK, and SO. There’s also a tech portfolio that’s composed of AMD, MSFT, and NVDA. Both portfolios have weights of (0.33, 0.33, 0.34).  The results of the utility versus the tech portfolio are:

  • Returns: 14.2% vs 136.3%
  • Standard Deviation: 14.9% vs 32%
  • Sharpe: 0.684 vs 4.134

Goodness me! The tech portfolio returns much more in absolute terms and much more per unit of risk. It’s twice as volatile as the utility portfolio, but the returns are almost ten times as high. If you could, then many of us would choose the tech portfolio over the utility portfolio. But, what if, for one reason or another, you can only invest in one of the two industries? Or, what if you want to invest your money with a skilled manager, rather than a risky one?

One way to tackle this problem is to introduce the Markowitz cloud. Specifically, we can essentially list out all of the possible portfolios along with their return and standard deviations. Then, we can compare the actual performance to the entire menu of possible performances within each set of assets. Below are the possible performances for the utility (left) versus the tech (right) portfolio. The actual portfolios are marked with an X.

One way to evaluate the two portfolios is to compare their return, standard deviation, and Sharpe ratio to the other candidates that were achievable with the same assets. As we can see, conditional on the assets, neither portfolio minimized the volatility, maximized return, nor maximized the Sharpe ratio. Furthermore, assuming that the realized rate of return was the goal, neither portfolio minimized the conditional volatility. Assuming that the realized volatility was the goal, neither portfolio maximized the conditional return. Below are two tables that describe some candidate alternatives and how they differ from the realized portfolio.

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