🧵1/7) On the difference between dynamical systems in #physics vs #economics. Example 1.
The case of Ramsey-Cass-Koopmans (RCK).
Instability and learning the initial condition for c.
The Philippines is a fantastic example of how deep and fast the drop in fertility is nearly everywhere on the planet.
Just last week, on March 30, 2026, the Philippine Statistics Authority released the 2025 National Demographic and Health Survey (NDHS). The total fertility rate for the last three years has reached 1.7 children per woman, a dramatic fall from 4.1 in 1993, and well below the replacement rate (around 2.1 for a country like the Philippines).
Since the NDHS computes the total fertility rate over three years, and it is dropping quickly, the total fertility rate for 2025 alone should be around 1.6, the same level as in the U.S. Let me repeat this: the Philippines and the U.S. have roughly the same total fertility rate.
But U.S. income per capita is about 7.3 times the Philippine income per capita (when adjusted for purchasing power parity). Or to put it differently, Philippine income per capita today is the same as the U.S. had in 1910. In that year, the total fertility rate of the U.S. was around 3.5. At the same level of income per capita, the Philippines has a total fertility rate that is less than half.
In some more urban regions, such as Calabarzon, the total fertility rate is 1.3. Historically, the rest of the country has followed the patterns of regions like Calabarzon with some lag, so the most likely scenario is that in a few years, the Philippines will have a total fertility rate of around 1.3 as well.
Compared with the United Nations World Population Prospects (WPP), the Philippines is now at the fertility level the WPP had forecast for 2047, despite the aggressive reduction it made to the Philippines’ forecast fertility between 2022 and 2024.
The Philippines is interesting because, compared with other Asian countries, it is a relatively religious and rural country without the Confucian obsession with education found in China or South Korea.
It is also a country that many still associate with high fertility. Just yesterday, one reader left a comment on my previous post on fertility, using the Philippines as an example of high fertility, that “refuted” my claims. No, it does not.
Finally, three technical points.
First, I am reporting total fertility, not completed fertility (and yes, I am keenly aware of the difference between the two). Looking at age-specific fertility rates suggests that completed fertility for younger women will actually be below the current total fertility rate.
Second, no, emigration does not matter here. I am talking about fertility rates, not birth rates.
Third, the official release:
https://t.co/jlzpYOsYYk
Let me explain why I believe modern economics is such a powerful tool for understanding the world. I’ll do this by discussing a great paper by Simone Cerreia-Vioglio, @UncertainLars, Fabio Maccheroni, and Massimo Marinacci, “Making Decisions Under Model Misspecification,” published in the Review of Economic Studies a few months ago.
Imagine I want to drive from UC San Diego to UCLA, but I’ve never driven that route before. I need to build a “model of the world” to guide me, which we usually call a map. Maps are simplified representations of reality. They can’t include every detail if they’re to be useful. Borges, in his short story On Exactitude in Science, makes this point beautifully. (In practice, I don’t draw the map myself—I use an app—but someone still had to make it.)
Because maps simplify, I can’t fully rely on them. Maybe last night’s storm knocked down a tree and closed a street, or there’s construction and the ramp off the highway in LA is shut down.
This uncertainty matters. Suppose I’m driving to UCLA for an important talk at 11 a.m. If the ramp is closed, I might need 15 extra minutes. When should I set my alarm to arrive on time, while still getting enough sleep to give a good talk?
The problem is that I can’t assign precise probabilities to all these contingencies. How likely is the fallen tree? Or new roadwork? Even the best traffic apps can’t capture every disruption, and some might happen after I’ve already left.
In economic terms, my “model of the world” (the map) is misspecified—and no matter how hard I try, I can’t fully fix that.
But sitting down and crying about misspecification doesn’t answer my basic question: when do I set the alarm? Too early, and I’m exhausted. Too late, and I’m late.
Simone and his co-authors offer a way to think about this. They start from the idea that we often hold several structured models of an economic phenomenon, grounded in theory. For example, a central bank might use a standard New Keynesian model and a search-and-matching model of money.
Yet, aware that each model is misspecified by design, the bank adds a protective belt of unstructured models—statistical constructs that help it gauge the consequences of misspecification.
The beauty of the paper is that it provides an axiomatic foundation for this protective belt (and even generalizes it to include a Bayesian approach). It shows that if a decision-maker’s preferences meet certain conditions —reflecting both rational and behavioral features— then those preferences can be represented by an augmented utility function that formally accounts for misspecification.
Crucially, we don’t assume that augmented utility function; we derive it. We start with general, plausible properties of preferences and prove that they imply such a representation.
That’s real progress. Instead of writing endless critiques of expected utility or rational expectations (as many have done for decades, with little to show), we now have a formal way to reason about misspecification—precise definitions, clear boundaries of validity, and awareness of what we still don’t know.
Take, for instance, a brilliant Penn graduate student on the market, Alfonso Maselli
https://t.co/rl2gu95V7t
His job-market paper pushes this frontier further. He studies cases where a decision-maker not only faces model misspecification but is also unsure which model best fits the data and can’t assign probabilities to them—what we call model ambiguity. In my example, the central bank is unsure whether the New Keynesian or the search-and-matching model fits better, and it worries that both might be incorrect.
If you read Simone et al. or Alfonso’s paper, you’ll see how misguided—and, frankly, cartoonish—many of the recent criticisms of economics on X have been.
First: the idea that economists don’t understand math or have “physics envy.” The math in these papers is subtle and advanced—utterly different from what physicists do (neither better nor worse, just distinct). An engineer transitioning into economics would find these tools unfamiliar.
Second: claims of ideological bias are unfounded. I have no idea about the political views of the authors, and I’d be surprised if anyone could infer them from the analysis—beyond vague guesses about typical academics.
Third: This has almost nothing to do with what one learns as an undergraduate, or even in first-year graduate school. If your knowledge of economics stops at an intro textbook, it’s best not to pontificate on the field’s frontiers.
Fourth: Is this science? Debating that word’s boundaries is pointless; every definition of “science” breaks down somewhere.
The Germans solved this long ago with the idea of Wissenschaft—the systematic pursuit of knowledge, whether of nature, society, or the humanities. By that measure, modern mainstream economics is clearly a Wissenschaft: a disciplined, cumulative, and highly useful effort to understand how the world works. Simone and his co-authors have demonstrated that beyond any reasonable doubt.
Unfortunately, indiscriminate use of the term "fixed effects" to describe any set of mutually exclusive and exhaustive dummy variables seems to be generating confusion about nonlinear models and the incidental parameters problem.
#metricstotheface
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Here is my little Bob Lucas anecdote.
It's about Bob's incredible gift as a writer and his generosity toward his students.
It's the fall of 2009 and I'm a grad student at the University of Chicago. Bob is on my thesis committee.