Bob Hallinen’s body of work spanned several decades at the Anchorage Daily News and continued to expand long after he retired. The renowned and prolific photojournalist died Sunday at the age of 77. Here's a small sample of his work: https://t.co/J8YN7M6zRr
@kaptenblu@ernietedeschi If we are talking CRRA, this still makes sense with standard levels of risk aversion if their initial wealth (i.e, level of consumption in the absence of the payment) is low.
What happens when nursing homes know inspections are coming?
In the latest episode of The Pie, Maggie Shi joins host Tess Vigeland to discuss how predictable inspections shape nursing home behavior—and what that means for resident health.
🎧 Listen: https://t.co/pQ0nCEBqah
We now have data from 19 states showing how many fewer children are receiving SNAP in the wake of these cuts. The steepest drops in those states:
-49% in AZ (-182,058 kids)
-23% in LA (-82,064 kids)
-18% in TX (-317,316 kids)
-18% in MA (-61,647 kids)
https://t.co/cEyZJidKSM
If you ever took a course in economic history, chances are you heard the argument that the trade embargo of 1807, the subsequent non-importation measures, and the War of 1812 gave a big boost to U.S. manufacturers. I certainly did!
This is a common argument in favor of tariffs, since it illustrates the importance of protecting infant industries.
In a wonderful paper just out in the Economic History Review, Joseph Davis and Douglas Irwin, @D_A_Irwin, show that there is no evidence of this effect in the data. The trend growth of industrial output does not change. You do see some reallocation across sectors, though, as one would expect.
I have made a similar argument on many occasions:
https://t.co/GduuAUZNrP
Are there examples of industrial policies (e.g., aggressive tariff protection) that raise trend growth? Yes. But every single one of them, every single one of them, every single one of them, involves some form of wage repression (i.e., wages below what the market allocation would have delivered).
There was no wage repression in the U.S. in 1807–1815, and hence no positive effect on industrial growth.
Now, remember: wage repression is a necessary condition for industrial policy to work, not a sufficient one. There are plenty of examples of industrial policies with wage repression that did not work. But without wage repression, you do not even have a chance.
Link here:
https://t.co/vEeRInN5Lz
This fantastic figure by @jburnmurdoch is Exhibit 1 of what an aging society means for the political game: public investment, which is choosing future rewards over present consumption, gets squeezed out.
Still not convinced this is a first-order challenge?
US visas issued to international students fell by roughly a third in 2025. Today, DHS finalized changes to a rule known as "Duration of Status" — a move that will help lock that decline in place. The fallout for the STEM workforce, innovation, and economic growth could be severe.
A sustained one-third decline in foreign STEM graduates entering the US labor force would shrink the high-skill STEM workforce by 6.2% overall and by 11.5% at the PhD level. Over a decade, that would cut annual US GDP by $240 billion to $481 billion, comparable to losing an entire state's economy.
That's the estimate from @AmyMNice, in a guest research brief for Hoover's Immigration Initiative, drawing on research she co-authored with @m_clem and @JeremyLNeufeld.
Read the full brief: https://t.co/zo8NmEsI4x
The Department of Economics at University of Notre Dame invites applications for an open-rank, tenure-track position to begin in the Fall of 2027 whose research program will support the Strengthening Families Research Initiative. Apply to join our wonderful department!
Monotone Comparative Statics (MCS) deals with how the solutions to an optimization problem change with its parameters. It can deliver interesting results under relatively weak assumptions. One of its main tools is Topkis’ Theorem https://t.co/7wBsgYpYYa. It allows us to derive MCS without differentiability assumptions and without explicitly solving the model👇
Key concepts to understand the theorem:
First of all, we have to talk about vector ordering. In one dimensional real vectors, it’s trivial to see if a>b. What about vectors of dimension n? Let a,b ∈ ℝⁿ.
(a ∧ b)=(min{a1,b1},…,min{an,bn}) is called the meet of a and b.
(a ∨ b)=(max{a1,b1},…,max{an,bn}) is called the join of a and b.
A set A ⊆ ℝⁿ is greater than a set B ⊆ ℝⁿ in the strong set order if, for any a ∈ A and any b ∈ B,
a ∨ b ∈ A,
a ∧ b ∈ B.
A lattice is a set X ⊆ ℝⁿ such that x ∨ y ∈ X and x ∧ y ∈ X for all x,y ∈ X.
A function f has increasing differences in (x,ø) if, whenever xH ≥ xL and ø’≥ ø, we have
f(xH, ø’)-f(xL, ø’) ≥ f(xH, ø)-f(xL, ø)
Increasing differences captures complementarity between the choice variable x and the parameter ø. Intuitively: the increment in f from a higher x is weakly larger when the parameter ø is larger.
Supermodularity: A function f: X x Ø → ℝ is supermodular in x if, for all x,y ∈ X and ø ∈ Ø, we have
f(x ∨ y, ø)−f(x, ø) ≥ f(y, ø)−f(x ∧y, ø)
Supermodularity captures complementarity among the components of the choice vector x. Intuitively: the increment in f from increasing some components of x is weakly larger when the remaining components of x are higher.
Given the complementarity meanings of these concepts, it’s not surprising that they’re widely used in Economic Theory. Now let’s get to one of the main results of MCS⬇️
⚫️Topkis’ Theorem (1978): Let x ∈ X and ø ∈ Ø. If X ⊆ ℝⁿ is a lattice, Ø ⊆ ℝᵐ and f: X x Ø → ℝ has increasing differences in (x, ø) and is supermodular in x, then the solution set X*(ø) is increasing in the strong set order.
Application: If the function f has increasing differences in (x, ø) and is supermodular in x, higher values of the parameter ø make optimal values of x weakly higher.
Now, I’ll review an application to Economic Theory based on Amir’s survey on Supermodularity and Complementarity in Economics https://t.co/3cxkzd67AD in a one-dimensional case that is useful to understand the intuition better, but modifying it to not use differentiability:
Example: Consumer Theory
A consumer maximizing U(x1, x2) from goods x1 and x2 with prices p1 and p2, respectively, and has income m. We want to derive conditions under which x1 is a normal good (the demand for increases in m). The problem is
max {U(x1, x2): p1x1 + p2x2 = m}
If U is increasing in x2, the budget constraint binds. Hence, solving for x2 in the budget constraint, we get x2 = (m − p1x1)/p2, so the consumer’s problem can be rewritten as
max {U(x1,(m−p1x1)/p2) : x1 ∈ [0,m/p1]}
Since x1 is one-dimensional, supermodularity in x1 is automatically satisfied: if x ≥ y, x ∨ y = x and x ∧ y = y, so the supermodularity inequality becomes
f(x, ø)−f(x, ø) ≥ f(y, ø)−f(y, ø), which is 0 ≥ 0 and is trivially satisfied. Hence, in the one-dimensional case, the key conditions are increasing differences in (x, ø) and monotonicity of the feasible set.
The feasible set [0,m/p1] is increasing in m: when income rises, the upper bound m/p1 rises.
Define F(x1,m) = U(x1, (m−p1x1)/p2). Does F have increasing differences? That would mean that if x1H ≥ x1L, mH ≥ mL,
F(x1H, mH) - F(x1L, mH) ≥ F(x1H, ml) - F(x1L, mL), that is, U(x1H ,(mH−p1x1H)/p2) - U(x1L ,(mH−p1x1L)/p2) ≥ U(x1H ,(mL−p1x1H)/p2) - U(x1L ,(mL−p1x1L)/p2).
If this holds, Topkis’ theorem implies that the demand correspondence
X*(m) = argmax F(x1, m) where x1 ∈ [0, m/p1]
is increasing in the strong set order. If the maximizer is single-valued, this reduces to x1*(mH) ≥ x1*(mL), so x1 is a normal good.
Thrilled to share a project I've been refining: a complete, open-source repository on "Deep Learning for Solving and Estimating Dynamic Models in Economics and Finance."
I've cleaned up the materials from my PhD classes and summer schools into one coherent resource. 🧵 1/6
Tonight, the Secretary of the Treasury is personally vetting and approving each company that gets access to the most advanced U.S. AI model, because the risks of the model being misused to hurt US national security are so high.
Also tonight, Jensen Huang is flying on Air Force One with President Trump to Beijing to sell China the AI chips it will use to develop its own Mythos-level AI model as soon as possible.
The administration’s AI policy remains inconsistent and incoherent. It is impossible to justify these two approaches simultaneously.