Halbert L. White, Jr., 1950-2012

It is with great sadness that I report that UCSD Economics Professor Hal White passed away Saturday morning after an extended struggle with cancer. He was an irreplaceable colleague and dear friend, and we will miss him greatly.

Hal was one of the world’s leading econometricians. One of his core beliefs was that the models and assumptions that we bring to the data are inevitably flawed and misspecified in some way. It might seem that if you believe that, there’s no hope in trying to do econometrics. But some of Hal’s most remarkable discoveries concerned how to form valid inference even if part of what you assumed was fundamentally wrong.

An example arises in ordinary regression analysis, in which a common assumption is that the variance of the regression model’s error is the same for all observations. Suppose that assumption is wrong, and instead the variance depends in an unknown way on the various explanatory variables. Hal found that it is possible to characterize how that dependence would affect the reliability of the inference from the regression, and construct modified t-statistics or F-statistics that take this into account. This was such a useful contribution that it is now a standard option a user can easily select in any decent regression software package. Hal once lamented to me that this was an example of a contribution that became so successful and widespread that people forgot who came up with it in the first place. Hal’s proposed adjustments are often described as “robust standard errors” or “heteroskedasticity-consistent standard errors”, though I have always introduced them to my students as “White standard errors”.

Hal also showed that this idea generalizes much more broadly, as spelled out in his classic article, Maximum Likelihood Estimation of Misspecified Models. The maximum likelihood estimator (affectionately known as the “MLE”) refers to a particular estimate of parameters that is derived from the claim that the researcher knows the family from which the true probability distribution that generated the data comes. Hal’s remarkable contribution here was to examine the properties of that inference if you have assumed the wrong class of probability distributions. He referred to that procedure (using an MLE that is based on an incorrect assumption about the probability distribution) as “quasi maximum likelihood estimation.” Again establishing the properties of such inference seems like (and is!) an astounding result. But when you get into the math, you discover that it makes perfect sense. For example, one could assume (mistakenly, perhaps), that the error terms in the regression model came from a Normal distribution with mean zero and constant variance. If your assumptions were correct, then the MLE turns out to be the usual formula for regression estimation. However, even if your assumption about the probability distribution is wrong, one can show that what you were calling the MLE is usually still giving you a decent estimate of something, namely, an estimate of the best prediction of y if you want to base your prediction on a linear function of x. In fact, White’s robust standard errors for ordinary regression prove to be a special case of his general results for quasi maximum likelihood estimation.

Hal had a host of other very fundamental contributions, ranging from the recognition that neural networks are essentially a statistical inference problem, elegant contributions to asymptotic theory, any number of extremely useful specification tests, and his most recent interest in some very deep ideas about causality and inference. There are I suspect a great many papers by Hal and his co-authors that have not yet been published, but soon will be, as he remained astonishingly productive up to the end, writing papers faster than the journals could publish them.

I used to have lunch each week with Hal, Clive Granger, Rob Engle, and others, at which people would bring up econometrics questions they’d been working on. If you had something important and difficult for which you needed a solution, it was a good idea to save the topic for discussion until Hal got there. I remember a number of occasions when the rest of us would struggle with something for 15 minutes, and then Hal would arrive and provide the key insight within 60 seconds. It was an incredible resource to have somebody like that around.

I must also say that he was one of the kindest and dearest people I have known. He didn’t have insecurities or something to prove about who he was– anybody with any sense would recognize his towering intellect. It was always a joy and honor to sit with him in seminars, and learn yet another new thing from his off-hand remarks and insights. And, since he wrote more in his lifetime than I would be able to read in mine, I can take some comfort in the fact that there is much more that I have yet to learn from this gentle and noble man.


40 thoughts on “Halbert L. White, Jr., 1950-2012

  1. JDH

    Update: A family member called to my attention that I was originally incorrectly reporting that Hal was born in 1951. The correct year is 1950, as now reported.

  2. Brian

    That is truly saddening news. I remember over fifteen years ago sitting in my graduate introductory econometrics course being taught by one of his former students. We used Hal’s 1984 book on asymptotics as the main text aside from course notes. At the time the book was difficult to understand and follow. Now I realize that small book is a masterpiece and remarkably lucid.

  3. QB

    One measure of impact: his 1980 heteroskedasticity paper is the most-cited Econometrica paper in economics.
    And Hal was also a hell of a jazz trumpet player. (His car’s license plate: “DR JAZZ”.) I regret I never had the chance to discuss music with him.

  4. Tom Fomby

    Hal was a towering intellect. He was always excited about new contributions to the econometrics literature, especially those of his students and young scholars. Of course, his own contributions to the literature made us all excited. I am so pleased that Advances in Econometrics had the opportunity to dedicate a volume (#17) in honor of his work. Hal’s work will live on in his papers, books, students and friends. May he rest in peace.

  5. Margarita

    A very sad turn of events. Those of us who were lucky to be his students will always be grateful for his dedication and help. My sincerest condolences to his family and colleagues. May he rest in peace.

  6. Richard Portes

    Hal was an undergraduate student of mine in Princeton – clearly outstanding even then. More important, he babysat our children, then age 2 and 4. He was sensible, caring, totally trustworthy – who would have thought he would become one of the world’s great econometricians? A sad loss indeed.

  7. Pierre Siklos

    My deepest sympathies to Hal and his family. Everything Jim says is true. I still cherish my stays at UCSD and listening to his interventions at lunch or in a seminar setting. While I did not know or talk to Hal as often as I did Clive or Rob I did attend one of his classes and learned a great deal from him and his work.

  8. Alejandro

    Terrible news. I took his graduate class in 95. He was a great teacher, sometimes even a bit intimidating. I remember him very fondly. My sincerest condolences to his family.

  9. Barkley Rosser

    A great loss indeed. Since nobody else has said the obvious yet, I will: he deserved the Swedish Bank Prize in Economic Science in Honor of Alfred Nobel, and I am sure that if he had lived a few more years he would have received it.

  10. Kerry

    I am one of many students privileged to take Professor White’s Intermediate Micro course at UCSD. Obviously, he was a great researcher, but he was also an incredible teacher. I learned so much from him and often brag to my fellow grad students that I was able to take his class as an undergrad. My thoughts and prayers are with his family and friends.

  11. Bob Hall

    Hal was about the brightest and the most likable of all the great students I taught at MIT. We will miss him sorely.

  12. Joao Issler

    Very sad news and very nice words by Jim. UCSD graduates will miss him a lot. He was a great intellect and a very generous scholar.
    I exchanged some emails with him a while ago. Did not know the end was near. My condolences to his family.

  13. Aren M.

    Indeed, Hal deserved the Nobel (possibly with J. Hausman), and I wish he had gotten it last year. I think most people will agree that Hal will be remembered for many decades to come, not just for his contributions to econometric theory, but also because he was just a genuinely nice person whom everybody liked. This is truely a big loss for UCSD and the economics community.

  14. westslope

    Wow. Prof. White was a big chunk of my econometrics education. To the surviving members of the ‘lunch bunch’, colleagues, professors, family and friends, you have my deepest sympathies. How do you right by a guy like Hal White? Work harder?

  15. Ray Chou

    For me, taking Hal’s class of Econometrics (D) was an eye-opening experience in the early 80′s. Although I did not get into econometrics theory, Hal’s class gave me the confidence that no matter how intimidatingly complicated the econometric theoretical papers may be, Hal’s books had it all!

  16. Nassim Sarraf

    I am deeply saddened, yet so humbled to have worked for Hal for over 7 years at Bates White. My respect for him grew every day, and I truly am honored to have known such a beautiful and brilliant being.

  17. Gabriel Perez

    I also had the opportunity to enjoy his classes. He was a great professor and a great person. A big loss for all the UCSD family.

  18. Simone Manganelli

    Thanks Jim for your beatiful words. Hal was a remarkable person and he will be badly missed. Like Clive and Rob, he had a rare combination of intelligence, kindness and dedication to his students. His example has shaped many generations of researchers and will outlive him for many years to come.
    To have him as a co-author was incredibly reassuring. I knew I could always count on him for any doubt was hampering our work. I would drop him an email in the evening, and magically the morning after (due to the time zone) I would find his solution in my inbox.
    My deepest condolences to his family and friends.

  19. Chris Neely

    Hal White was a truly outstanding econometrician. It is a shame to lose him at such a young age.
    My prayers will be with his family.

  20. Celeste White

    As Hal’s sister, reading this wonderful tribute and all the moving comments from his friends and colleagues, makes this terrible loss a little more bearable. Thank you to all who have offered their condolences to his family. As you can no doubt imagine, all the qualities that made Hal a wonderful teacher and colleague made him the most wonderful brother anyone could have. His humor, humility, kindness, playfulness, talent, and brilliant, restless, endlessly creative mind … those qualities were all present from his earliest years. My deep sympathy to all of you who are feeling Hal’s loss. We were all so lucky to know such a remarkable man; his absence will be sorely felt.

  21. Fred Joutz

    It is a sad passing for his family and a loss the the profession. Like I prefer(red) emphasizing to my students these are the White HAC tests.

  22. Douglas Palmer

    I will miss Hal. I worked with him in the late 80s and early 90s on neural network models. He had the best grasp of the fundamentals of anyone at that time. He understood the linearization inherent in learning processes. He will be sorely missed.

  23. goca

    I never met Prof. White, but like many others was introduced to White’s test for heteroskedasticity correction, and of course Asymptotic Theory for Econometricans. However, given the typical insularity of economics faculty at many of the top tier institutions, its refreshing to see Prof. White eulogized with such humanity and dignity.

  24. Gary Cottrell

    I learned a great deal from Hal. As a neural network researcher, I was impressed to learn from him that back propagation would, in the end, not only fit the function it was trying to match, but all of the derivatives of the function. Hal was, as everyone here has said, incredibly nice and generous. I will always remember him as “our theoretician of neural nets” at UCSD. His result that, if you added hidden units at the proper rate, you could approximate any Borel-measurable function to an arbitrary degree of accuracy with one hidden layer, has stuck with me forever. I had assumed he had won his battle with this cancer. It is such a shock to learn that he did not. My condolences not to just his family, but to all of his friends and colleagues as well, of which there are thousands, I am sure.

  25. Kleinbogen

    Took his graduate course years ago and it was a challenge. Radon-Nikodym theorem, asymptotic theorems, etc. His books are very hard but received much with respect from us. Great guy overall!

  26. Samuuel Myers

    A terrific classmate and life-long friend. He will be missed. My deepest sympathy to his family.

  27. Mark Plutowski

    In 1992 I was enrolled in the 8am seminar where Hal proved his rigorous result that, in his words, neural networks = statistics. Half-way through the course after filling the board with various equations and symbols he had exhausted all the Latin and Greek characters. So for his next variable he used Happy Face. Everything he had proved up to that point had just been distilled down into that one profound yet unassuming variable. My memory of Hal = Happy Face.

  28. Jerry White

    I went through grade school(Border Star)and high school(Southwest)in Kansas City with Hal. We always new he was smart but his humble ways, he was just Hal and one of the boys. It was not till later in life that we learned how smart and how capeable he really was.
    Sorry his life was so short. We have many class reunions to come and he will be missed.
    Jerry White (no relation)

  29. J. Stan Freeman

    I was fortunate to know Hal long before his ground-breaking work in econometrics–he was a high school friend at KC Southwest, and we hiked together in Montana’s Bob Marshall Wilderness Area during our college years. We learned so much from Hal on so many things, and he was a brilliant, yet genuine individual & a talented musician. Hal can never be replaced, and he will never be forgotten by those he touched. My sincere condolences to his family.

  30. David DeMers

    Hal made real contributions to making the world a better place.
    I was fortunate that he agreed to be on my dissertation committee. I recall his encyclopedic understanding of many fields. Having a 15 minute meeting with him, I might express some difficulty with an issue in statistical inference. He’d suggest a paper to look at, and walk over to his massive wall o’papers and pull it out for me.
    His profound understanding of the issues involved in statistical modeling, beyond the formal math into specification and estimation issues, gave me bootstrapped maturity (i.e. I didn’t have to make all of the basic mistakes, only new and innovative mistakes…) about inferential modeling, which was hugely influential in my success as a quantitative portfolio manager. As Box said and Hal had deep understanding, “all models are wrong, but some are useful”
    thanks, Hal, for your generosity and insights. sorry that we won’t have the opportunity to chat with you again.

  31. Esfandiar Maasoumi

    In Memoriam:
    Halbert L. White, Jr., The Econometrician
    Oh Hal, another hasty departure, far too soon, leaving your friends and audience thirsty for more.
    The last hug, just last May, at the conference in your honor, with those familiar piercing bright eyes, warm smile, a touch of shyness, and oh so full of all too generous words. You were so good at lifting others with kind words, making them feel comfortable, like they may be in the presence of just another “regular guy”!
    We just toasted you on your 60th birthday. Many of your adoring former students, and so many delighted colleagues and friends, showing up at your conference in San Diego, aptly titled “Causality, Specification and Forecasting”, a mere attempt to encapsulate your boundless interests and areas of influence. I took time from my own presentation to offer you some personal words of appreciation, time far better spent than to speak of my token contribution to the conference. I spoke of only three themes: your “teaching” the profession in the broadest terms, and through your over 53 Ph.D students, a stunning legacy, a “galaxy of stars”, and “a beautiful thing, Hal, that nothing can take away” (not even death), and finally, the most faithful and consistent adherence to the truism that “all models are mis-specified”. Almost everyone subscribes to that truism, but few, perhaps no other, has written in so much compliance to it. Information theory, and its little acknowledged contribution to the concept of “pseudo true” parameters, was well known to Hal and liberated his work and thoughts from “true models” from his earliest writings, and throughout his texts.
    Hal became the personification of “rigorous econometrics” right off the gate. His influence in this respect, like so much else, went well beyond what he imparted to his minions of students and coworkers. Two or more textbooks on this topic witness Hal’s desire to share widely and to guide. He led by example, and his most cited paper in economics, on robust estimation and testing for Heteroscedasticity of unknown form, is more than a classic. It set the standard for rigor and innovativeness, applied to a meaningful problem of interest to every econometrician, technical or empirical. There lied his genius, meaningful solutions to meaningful problems, with no compromise on rigorous statistical inference.
    His model specification searches, through neural nets in which he led by some distance, and ingenious tests and proper “snooping methods”, to some of the deepest forays into forecasting, causality and conditional (in) dependence, and to the last minutes with numerous ongoing papers and collaborations, he was a dizzying and stupendous productivity phenomenon.
    Not often mentioned, perhaps, is Hal’s enormous influence on the standards of statistical and economic consulting, mostly through the highly regarded enterprise, Bates and White, with Charlie Bates, whom I first met in Bloomington, Indiana, with a freshly completed Ph.d thesis (1983) under Hal, on International Trade (!), and some of the most rigorous work then on nonlinear econometrics! Hal had then recently moved to UC San Diego (from Rochester!), “mostly for the beach”, as our other beloved departed colleague, Clive Granger, used to say. The “threesome”, Clive, Rob Engle, and Hal put UCSD on the top of the econometrics map for a generation, surely an unmatched academic journey.
    I heard you play your tune in May, with a good band, soulful, and as good as ever. It is not a little sad, and too restrained to say: we will miss you Hal.
    Esfandiar (Essie) Maasoumi
    Emory University
    April 2, 2012

  32. Merrill Wm Day

    Hal and I shared classes together in Band and Orchestra in High School and though I was few years his senior,I was really impressed with this kid right a way for his devotion and love of music and always had that smile!.His smarts and academic were known to me and of course through the years it became even more apparent,but his humility, congeniality and love of live impressed me even more.The one fault Hal had was there was only one of him.I guess Dr.Jazz was needed for some gig out of town,and I’m sure he’s already got that joint jumpin! My condolences to to the family.~Dubby

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