Everybody follows a different path. Sometimes that path includes a late start on saving for retirement. Say that you have $0 in your retirement account right now. Is it too late? What can you get as a result of contributing $100 per month? Maybe more than you think.
Let’s start with an annuity equation that tells us our balance at retirement with some assumptions baked in. Let’s assume that we have zero dollars saved and contribute $100 per month. What rate of return do we earn? The S&P earns an average of 10% per year, which may not keep happening. We can conservatively assume 7.5%, but there are other concerns. Taxes and inflation will both eat away at that. Let’s subtract 2.5% for inflation with the Fisher approximation, leaving a real rate of return of 5%. We’ll chop off 20% due to taxes*. Below is the annuity equation that tells us the balance at retirement, depending on how many years from now you retire.
Assuming that you retire at 65 years of age, the graph below describes your balance at retirement depending on the age at which you started saving $100 per month. Of course, it’s not the balance that most people are worried about. Rather, we care about the implied monthly retirement check. The graph describes that on the right axis too, assuming that constant real payments will be made forever as perpetuity payments. We can see that getting started early matters a lot. But starting at age 40 still gets you real monthly retirement payments that are just shy of $200. That’s not too shabby.
Of course, nobody receives all of the perpetuity payments.
This is an update to a previous post that I did on per-capita real consumption in 1990 vs 2021. As of 2021, we still weren’t sure after the pandemic what was transitory vs structural, and it was unclear whether incomes would keep up with inflation. We now have three more years of data through 2024. News flash: We’re even richer.
I like to use the BEA real quantity indices. Those track what is actually consumed in volumes rather than by deflating total spending by price indices. Divided by population, we can calculate the real quantities of goods and services that people actually consumed per capita.
Even after the pandemic policies have settled down, we are still SO MUCH RICHER – and even richer than we were with all of the pandemic-related stimulus. The worst consumption category since the pandemic has been food and beverage for off-premise consumption, and that is *up* 4.6% since 2020, increasing 31% since 1990. So, while I understand that people can’t enjoy the the low prices of yesteryear, we are still better off in that category than pre-pandemic. In the other categories, everything is awesome.
Since 1990, our consumption of communication services has risen 332%, our houses are 254% better furnished, and we have 118% greater quality-adjusted clothing consumption. All of this is already adjusted for inflation and is per-capita. Since the pandemic, these numbers are still up by 20.4%, 9.8%, and 31.1% respectively. People didn’t like the post-pandemic inflation. I get that. But these improvements in average consumption are mind boggling.
The widespread availability and easy user interface of artificial intelligence (AI) has put great power at everyone’s fingertips. We can do magical things.
Before the internet existed we would use books to help us better interpret the world. Communication among humans is hard. Expressing logic and even phenomena is complex. This is why social skills matter. Among other things, they help us to communicate. The most obvious example of a communication barrier is language. I remember having a pocket-sized English-Spanish dictionary that I used to help me memorize or query Spanish words. The book helped me communicate with others and to translate ideas from one language to another.
Math books do something similar but the translation is English-Math. We can get broader and say that all textbooks are translation devices. They define field-specific terms and ideas to help a person translate among topic domains, usually with a base-language that reaches a targeted generalizability. We can get extreme and say that all books are translators, communicating the content of one person’s head to another.
But sometimes the field-to-general language translation doesn’t work because readers don’t have an adequate grasp of either language. It isn’t necessarily that readers are generally illiterate. It may be that the level of generality and degree of focus of the translation isn’t right for the reader. Anyone who has ever tried to teach anything with math has encountered this. Students say that the book doesn’t translate clearly, and the communication fails. The book gets the reader’s numeracy or understood definitions wrong. Therefore, there is diversity among readers about how ‘good’ a textbook is.
Search engines are so useful because you can enter some keywords and find your destination, even if you don’t know the proper nouns or domain-specific terms. People used to memorize URLs and that’s becoming less common. Wikipedia is so great because if you want to learn about an idea, they usually explain it in 5 different ways. They tell the story of who created something and who they interacted with. They describe the motivation, the math, the logic, the developments, and usually include examples. Wikipedia translates domain-specific ideas to multiple general languages of different cognitive aptitudes or interests. It scatters links along the way to help users level-up their domain-specific understanding so that they can contextualize and translate the part that they care about.
Historical translation technology was largely for the audience. More recently, translation technology has empowered the transmitters.
I have a good friend who is a professor in philosophy at another university. He was telling me about the struggle among his colleagues to determine the recipient of their annual department award. Every year the department chooses from among the graduating philosophy major students one to recognize for excellence. This year, they faced the challenge of incommensurables.
One student had a high GPA in the major, but had a severe case of senioritis and had phoned-in her senior courses. A second had a slightly worse GPA, but had face-planted the senior thesis. Still a 3rd student had merely a good GPA, but wrote an excellent publishable thesis.
The philosophy faculty could not agree. They each shared stories and arguments about the relative weights of the performance indicators and the relative value of the performances. I don’t know if you know any academics, but suffice it to say that they both A) tend not to be good administrators and B) tend not to be invited to productive meetings. I’m glad that I wasn’t in the room.
In fact, the faculty met twice! They were at an impasse. The department award winner is usually no contest. The person who excels in one area tends to also excel in the others. This year, the decision was so unclear and the faculty were so divided that they even seriously considered withholding the award entirely. None of the candidates was excellent on all counts.
Finally, trying to come to a decision – if not an agreement – they decided to adopt something that they’d heard good things about: Ranked Choice Voting. I was thrilled to hear this. What an opportunity to exhibit the nuance and beauty of this collective choice method! They agreed to adopt whatever the outcome would be. As my friend told me this, I was giddy with anticipation. What an exciting story! More good experiences with ranked choice voting may improve its popularity and make widespread its adoption.
If you don’t know, Ranked Choice Voting involves everyone ranking the candidates in order of preference. In this case 1 is most preferred and 3 is least preferred. Then, the candidate with the fewest first-ranked votes is eliminated from the running. The voters whose first preference was nixed now have their votes reallocated to their 2nd preferred candidates. Since only two candidates remain, one of them has won the majority and the election ends with an outcome that is usually considered better than the simple ‘just choose your favorite’ version that most of us use at our local polls.
This post is co-written with John Olis, History major at Ave Maria University.
There is a popular myth that manufacturing jobs of the past provided a leg-up to young people. The myth goes like this. Manufacturing jobs had low barriers to entry so anyone could join. Once there, the job paid well and provided opportunities for fostering skills and a path toward long-term economic success. There is more to the myth, but let’s stop there for the moment. Is the myth true?
One of my students, John Olis, did a case study on Connecticut in 1920-1930 using cross sectional IPUMS data of white working age individuals to evaluate the ‘Manufacturing Myth’. We are not talking causal inference here, but the weight of the evidence is non-zero. The story above has some predictions if not outright theoretical assertions.
Manufacturing jobs paid better than non-manufacturing jobs for people with less human capital.
Manufacturing jobs yielded faster income growth than non-manufacturing jobs.
Implicitly, manufacturing jobs provided faster income growth for people with less human capital.
Using only one state and two decades of data obviously makes the analysis highly specific. Expanding the breadth or the timescale could confirm or falsify the results. But historical Connecticut is a particularly useful population because 1) it had a large manufacturing sector, 2) existed prior to the post WWII boom in manufacturing that resulted from the destruction of European capacity, and 3) had large identifiable populations with different levels of human capital.
Who had less human capital on average? There are two groups who are easy to identify: 1) immigrants and 2) illiterate people. Immigrants at the time often couldn’t speak English with native proficiency or lacked the social norms that eased commercial transactions in their new country (on average, not always). Illiterate people couldn’t read or write. Therefore, having a comparative advantage in manual labor, we’d expect these two groups to be well served by manufacturing employment vs the alternative.
Being cross-sectional, the individuals are not linked over time, so we can’t say what happened to particular people. But we can say how people differed by their time and characteristics. Interaction variables help to drill-down to the relevant comparisons. There are two specifications for explaining income*, one that interacts manufacturing employment with immigrant status and one that interacts the status of illiteracy. The baseline case is a 1920 non-operative native or literate person. Let’s start with the below snapshot of 1920. The term used in the data is ‘operative’ rather than ‘manufacturer’, referring to people who operate machines of one sort or another. So, it’s often the same as manufacturing, but can also be manufacturing-adjacent. The below charts illustrate the effect of lower human capital in pink and the additional subpopulation impacts of manufacturing in blue.
In the left-hand specification, native operatives made 2.2% less than the baseline population. That is, being an operative was slightly harmful to individual earnings. Being an immigrant lowered earnings a substantial 16.8%, but being an operative recovered most of the gap so that immigrant operatives made only 6.1pp less than the baseline population and only 3.9pp less than native operatives. In the right-hand specification, unsurprisingly, being illiterate was terrible for one’s earnings to the tune of 23.4pp. And while being an operative resulted in a 1.2% earnings boost among natives, being an operative entirely eliminated the harm that illiteracy imposed on earnings.
Both graphs show that manufacturing had tiny effects for a typical native or literate individual. But manufacturing mattered hugely for people who had less human capital. So, prediction 1) above is borne out by the data: Manufacturing is great for people with less-than-average human capital.
I just learned about the Bayesian Dawid-Skene method. This is a summary.
Some things are confidently measurable. Other things are harder to perceive or interpret. An expert researcher might think that they know an answer. But there are two big challenges: 1) The researcher is human and can err & 2) the researcher is finite with limited time and resources. Even artificial intelligence has imperfect perception and reason. What do we do?
A perfectly sensible answer is to ask someone else what they think. They might make a mistake too. But if their answer is formed independently, then we can hopefully get closer to the truth with enough iterations. Of course, nothing is perfectly independent. We all share the same globe, and often the same culture or language. So, we might end up with biased answer. We can try to correct for bias once we have an answer, so accepting the bias in the first place is a good place to start.
The Bayesian Dawid-Skene (henceforth DS) method helps to aggregate opinions and find the truth of a matter given very weak assumptions ex ante. Here I’ll provide an example of how the method works.
Let’s start with a very simple question, one that requires very little thought and logic. It may require some context and social awareness, but that’s hard to avoid. Say that we have a list of n=100 images. Each image has one of two words written on it, “pass” and “fail”. If typed, then there is little room for ambiguity. Typed language is relatively clear even when the image is substantially corrupted. But these words are written, maybe with a variety of pens, by a variety of hands, and were stored under a variety of conditions. Therefore, we might be a little less trusting of what a computer would spit out by using optical character recognition (OCR). Given our own potential for errors and limited time, we might lean on some other people to help interpret the scripts.
There was a recent Planet Money Podcast episode that includes a fun exercise. An NPR employee produces a dozen chicken eggs and wants to sell them at cost to another employee for $5. That’s the setup. How does the employee decide who should receive the eggs? Clearly, the price mechanism won’t work since the price is fixed. A lottery is also not allowed. The egg recipient could engage in arbitrage, reselling the eggs for a higher price. But that’s not very likely and would be socially awkward. The egg producer wants to make someone happy. Who would he make the happiest?
That’s the challenge that the Planet Money team tries to solve.
First, they started with a survey. Rather than asking coworkers to rank a long list of things that includes eggs, the survey adopts a more robust method of pairwise comparisons. Do you prefer toast vs eggs? Eggs vs oatmeal? Toast vs oatmeal? and so on. One problem that they encounter, however, is that there is a lot of diversity among preparations methods. My oatmeal is better than my eggs. But my brother’s oatmeal is not. As it turns out, there is not a standard quality of prepared oatmeal and prepared eggs. So the survey is a flop.
Then they consult an economist. They decide to try to measure “willingness to pay”, which is an economic concept that identifies the maximum that a person could pay for something without becoming worse off. They couldn’t really ask the coworkers what their WTP is. People are social creatures and have many reasons to lie, mislead, signal, and to simply not know. Since someone’s WTP reflects preferences and values, we need a way to solicit the true preference while avoiding lies and most mistakes. Here’s how the economist suggested that they reveal the coworker preferences.
Step 1: Tell the coworker these rules.
Step 2: Coworker reports their WTP for a single egg in dollars
Step 3: A random price will be chosen by a machine. If the price is above the self-reported WTP, the coworker is not allowed to buy the egg. If the price is below the WTP, then the coworker must buy the egg at the random price.
Generally, decisions to spend federal funds come is the authority of congress. But the Trump administration has very publicly made clear that it will try to cut the things that are within its authority (or that it thinks should be within that authority). Truly, the fiscal year with the new Republican unified government won’t begin until October of 2025. So, the last quarter is when we’ll see what the Republicans actually want – for better or for worse. In the meantime, we can look past the hyperbole and see what the accounting records say. The most recent data includes 95 days after inauguration. First, for context, total spending is up $134 billion or 5.8% from this time last year to $2.45 trillion.
The Trump administration has been making news about their desire and success in cutting. Which programs have been cut the most? As a proportion of their budgets, below is a graph of were the five biggest cuts have happened by percent. The Cuts to the FCC and CPB reflect long partisan stances by Republicans. The cuts to the Federal Financing Bank reflect fewer loans administered by the US government and reflect the current bouts to cut spending. Cuts in the RRB- Misc refer to some types of railroad payments to employees. In the spirit of whiplash, the cuts to the US International Development Finance Corporation reverse the course set by the first Trump administration. This government corporation exists to facilitate US investment in strategically important foreign countries.
But some programs have *increased* spending since 2024. The five largest increases include the USDA, the US contributions to multilateral assistance, claims and judgments against the US, the federal railroad administration, and the international monetary fund. Funding for farmers and railroads reflect the old agricultural and new union Republican constituencies. The multilateral assistance and IMF spending reflects greater international involvement of the administration, despite its autarkic lip service.
Recently, I learned what humidity is. That might sound stupid, so let me clarify. I knew that humidity is the water content of the air. I also knew that the higher the number, the more humid. Finally, I also knew that the dew point is the temperature at which the water falls out of the air. But, now I understand all of this in a way that I hadn’t previously.
First, what does it mean for there to be 70% humidity? As it turns out, it’s a moving target. There are two types of humidity: specific and relative. Specific humidity is the mass of water in, say, a kilogram of air. So, more humidity means more water. This is obvious. There’s a related concept called absolute humidity, which is more like mass of water per volume of air (sometimes used in place of specific humidity). Again, more humidity means more water. Neither of these is the way that humidity is reported on the weather channel.
Relative humidity is the number that you see in your weather app. What’s that? Relative to what? First, we need to know that warm air can hold more water than cool air. Pressure also matters, but atmospheric pressure doesn’t change enough to make its effect on humidity significant on relevant margins. So, all of this discussion, and the number in your phone, is at atmospheric pressure. Below is a graph that illustrates the maximum amount of water that can be in the air at different temperatures (red line). So, at 30 degrees Celsius (86 degrees Fahrenheit), there can be as much as 27 grams (0.95 oz or ~2 tablespoons) of water in the air.
Your Function Keys Are Cooler Than You Think by someone who used to press F1 by mistake
Ever notice the F keys on your keyboard? F1 through F12. Sitting at the top like unused shelf space. If you’re at a computer now, take a glance. I used to think they did nothing, or at least nothing for me. Maybe experts used them. Experts who know what BIOS and DOS are. But for me, just little space fillers with no purpose. I frequently pressed F1 by accident rather than escape. A help window would pop up, wasting half a second of my life until I closed it.
But the Fn keys (function keys) are sneaky useful. They can save you serious time. No clicking. No dragging. No fumbling with touchpad mis-clicks.
When using a web browser, F5 refreshes the web page. Windows has added the same functionality for folders too, updating recently edited files. Fast and easy. F11 changes your web browser view to full screen. Great for long reads or historical documents. F12 shows the guts of a webpage. That’s perfect if you web scrape or need to know what things are called behind the scenes. Ctrl + F4 closes a tab. Alt + F4 shuts the whole application instance down. That last one works for almost all applications.
Excel? F4 saves so much of your life. It toggles absolute cell, row, and column references. Have you ever watched someone try to click on the right spot with their touchpad and manually press the ‘$’ sign… twice? I can feel myself slowly creeping toward death as my life wastes away. Whereas pressing F4 lets you get on with your life. F12 in most Microsoft applications is ‘Save As’. No need to find the floppy disk image on that small laptop screen. PowerPoint has its own tricks—F5 begins the presentation. Shift + F5 starts it from the current slide. Not bad. And don’t forget F7! That’s the spellcheck hotkey. But now it’s been expanded to include grammar, clarity, concision, and inclusivity.
Economist Writing Every Day 