We’re thrilled to announce that Postdoctoral Research Fellow Ludvig Sinander has been awarded the prestigious Aliprantis Prize – which is awarded for excellent work by a new researcher – by the Society for the Advancement of Economic Theory (SAET). Ludvig has been recognised for his paper ‘The Converse Envelope Theorem’, published in Econometrica in November 2022.
We asked Ludvig about the process that led to this prize-winning research, and his response demonstrates that the reality behind awards and academic recognition is effort, support and determination (perhaps he would say stubbornness!)
This paper began in 2017 during my PhD at Northwestern University, while I was working as a research assistant to John Quah and Bruno Strulovici, helping them to write a book on the theory of monotone comparative statics. John and Bruno wrote several influential papers on this topic during their time in Oxford in the 2000s, and I myself learned about the topic from a course that John taught at Oxford in 2014 when I was an MPhil student.
I wrote a section in the book showing how comparative-statics theory may be used to prove one direction of the celebrated Spence–Mirrlees characterisation of incentive-compatibility in mechanism design (due to Mike Spence and Oxford’s own Jim Mirrlees). For completeness, I wished to prove the other direction from first principles. I had in mind an argument that seemed “clearly correct” from an economic perspective; it had to do with the envelope theorem, one of the fundamental mathematical results underpinning economic theory (from the theory of the consumer to the theory of incentives).
Upon reflection, however, I realised that when expressed formally (in the language of mathematics), my “clearly correct” economic argument was not invoking the envelope theorem at all, but rather the converse of the envelope theorem! (The envelope theorem claims that optimal decision-making implies that a certain differential equation, the envelope formula, must be satisfied; my “converse” claim was that because the envelope formula is satisfied, decision-making must be at least locally optimal.) The trouble was that there was no such thing as a converse of the envelope theorem.
At this point, it would perhaps have been sensible to give up, but I was stubborn: the argument was clearly “economically” right, and thus (I felt) it just had to be mathematically correct. I therefore spent a few afternoons on the patio of a café in Chicago wrestling with the problem, and of course I discussed it with some colleagues, most importantly Gregorio Curello (at that time a DPhil student at Oxford). Eventually I cracked it: I proved that the envelope theorem has a very general converse.
The paper then mostly wrote itself. The trickiest part was, ironically, the Spence–Mirrlees application of my general converse envelope theorem, which had motivated the investigation in the first place: I spent several more (frankly painful) months over the next three years figuring out the mathematical intricacies of how the Spence–Mirrlees result could best be obtained from my general converse envelope theorem. This involved learning a great deal about a diverse range of topics in mathematics, which was very interesting. Although, perhaps inevitably, only a small fraction of what I learned ended up actually being useful!
The Department would like to extend our warmest congratulations to Ludvig for this well-deserved recognition of his work.
