At the Conference on Frontiers in Machine Learning and Economics (2025), Professor Tamara Broderick from MIT gave a brilliant keynote, based on the paper An Automatic Finite-Sample Robustness Metric. It’s a metric that measures how sensitive are conclusions to the removal of just a small fraction of data? Motivation Even dropping a vanishingly small proportion of observations can matter. We should worry if removing a fraction $\alpha \in (0,1)$ of the data:...

I got perfect 4.0s for a series of advanced-level statistics courses through my undergrad. Still today during our Empirical Economics class I was spellbound by the concept of confidence interval.

Macro is all about vibes. If you can vibe the math, it’d be super cool.

Here’s another lovely Saturday night spent at the Chicago Symphony Orchestra: There’s a Ravel in the crowd yelling Bravi — can you spot him? Tonight’s program is splendid — the orchestra begins with Camille Pépin’s Les Eaux célestes. Anticipating upcoming Ravel, I was not surprised to catch a sense of oriental chords within the surreal, dreamy, beauuuuuutiful music. Turns out, the piece it was inspired by the ancient Chinese legend 牵牛织女鹊桥会 (a love story, read CSO’s official comment)....

In China, business deals are often made over dinners, where the essential informal/implicit consensus are reached. Drinking alcohol (especially, BaiJiu) in formal business dinner is not only for enjoyment, but more of a cultural etiquette—drinking with the the party is a way to show respect and commitment. Here’s a really interesting behavioral economics paper about the effect of alcohol intoxication affecting people strike a deal in business: The idea is golden — and the paper is only 15 pages!...

The 2025 Econ Camp is taught by Professor Emir Kamenica for incoming PhD students at Booth. This year, first-years from Griffin and Harris also joined, making the room a cross-department gala of future scholars craving for free coffee. The camp runs for an intensive week, with three hours of lectures every morning. At the Econ Department… Thanks to Professor Kamenica’s exceptionally clean logical organization, these notes preserve the blackboard style....

Comparisons of Distributions We study random variables on $\mathbb{R}$ (aka lotteries). Each lottery can be identified with its cumulative distribution function (cdf): $$ F(z) = \Pr(Z \leq z). $$ First-Order Stochastic Dominance (FOSD) Definition. For two distributions characterized by their cdf $F, G$, $$ F \succeq_\text{FOSD} G \iff \int u(x) dF(x) \geq \int u(x) dG(x), \quad \forall \text{increasing } u. $$ Theorem (Characterization of FOSD). $$ F \succeq_\text{FOSD} G \iff F(x) \leq G(x) \quad \forall x....

People don’t cherish the things that they obtained without a cost. Here’s an interesting research from the 2025 AI in Social Science Conference, by Jason Sockin from Cornell University. The paper’s not online yet, but an abstract can be found at NBER Interviews (which seems to be a tentative title…?) Elliott Ash, ETH Zurich. Soumitra Shukla, Harvard University. Jason A. Sockin, Cornell University Interviews allow employers to learn about workers, but do they also enable workers to learn about firms?...

Expected Utility Theory Suppose the space of alternatives has a little more structure: $$ X = X_1 \times X_2 \times \cdots \times X_n. $$ We define Lottery Space on this $X$: Let $\mathcal{L} = \Delta(X)$ = set of lotteries on $X$ (probability distributions). Expected Utility Representation Definition. A preference $\succeq$ on lottery space $\mathcal{L}$ admits an expected utility form if $\exists u:X\to\mathbb{R}$ such that $\forall L,L’\in\mathcal{L}$: $U(L) = \sum_{x\in X} p^L_x u(x)$, $L\succeq L’ \iff U(L)\geq U(L’)$....

Here’s a very interesting matrix completion method and result, which is a direct corollary from Koltchinskii, Lounici and Tsybakov (2011) paper. Consider the following matrix estimation problem: for input matrix $A\in \mathbb R^{m_1\times m_2}$, assume $m_1 < m_2$ and $\text{rank}(A) = r \ll m_2$. $n$ entries of $A$ are observed at uniformly at random, with independent noise $\epsilon_{ij}$. Denote as $\Omega$ the index set of observed entries of $A$, define the scaled observation matrix $Y = [y_{ij}]$ as $$ y_{ij} = \frac{m_1 m_2}n \begin{cases} a_{ij} +\epsilon_{ij} & (i, j) \in \Omega\cr 0 & (i, j)\notin \Omega \end{cases},\quad (i, j)\in [m_1]\times [m_2]....