On the Origin of "Frequentist" Statistics

Efron and Hastie note that the "frequentist" term "seems to have been suggested by Neyman as a statistical analogue of Richard von Mises' frequentist theory of probability, the connection being made explicit in his 1977 paper, 'Frequentist Probability and Frequentist Statistics'".  It strikes me that I may have always subconsciously assumed that the term originated with one or another Bayesian, in an attempt to steer toward something more neutral than "classical", which could be interpreted as "canonical" or "foundational" or "the first and best".  Quite fascinating that the ultimate "classical" statistician, Neyman, seems to have initiated the switch to "frequentist".

Bayes, Jeffreys, MCMC, Statistics, and Econometrics

In Ch. 3 of their brilliant book, Efron and Tibshirani (ET) assert that:

Jeffreys’ brand of Bayesianism [i.e., "uninformative" Jeffreys priors] had a dubious reputation among Bayesians in the period 1950-1990, with preference going to subjective analysis of the type advocated by Savage and de Finetti. The introduction of Markov chain Monte Carlo methodology was the kind of technological innovation that changes philosophies. MCMC ... being very well suited to Jeffreys-style analysis of Big Data problems, moved Bayesian statistics out of the textbooks and into the world of computer-age applications.

Interestingly, the situation in econometrics strikes me as rather the opposite.  Pre-MCMC, much of the leading work emphasized Jeffreys priors (RIP Arnold Zellner), whereas post-MCMC I see uniform at best (still hardly uninformative as is well known and as noted by ET), and often Gaussian or Wishart or whatever.  MCMC of course still came to dominate modern Bayesian econometrics, but for a different reason: It facilitates calculation of the marginal posteriors of interest, in contrast to the conditional posteriors of old-style analytical calculations. (In an obvious notation and for an obvious normal-gamma regression problem, for example, one wants posterior(beta), not posterior(beta | sigma).) So MCMC has moved us toward marginal posteriors, but moved us away from uninformative priors.

Statistics in the Computer Age

Efron and Tibshirani's Computer Age Statistical Inference (CASI) is about as good as it gets. Just read it. (Yes, I generally gush about most work in the Efron, Hastie, Tibshirani, Brieman, Friedman, et al. tradition.  But there's good reason for that.)  As with the earlier Hastie-Tibshirani Springer-published blockbusters (e.g., here), the CASI publisher (Cambridge) has allowed ungated posting of the pdf (here).  Hats off to Efron, Tibshirani, Springer, and Cambridge.

New Judea Pearl Causal Inference "Primer"

Should be a fun and informative read. Check out the contents and various chapters here. ("Causal Inference in Statistics - A Primer" by J. Pearl, M. Glymour and N. Jewell. Available now on Kindle; available in print Feb. 26, 2016.)

Latest Draft of Forecasting Book

Latest draft of Forecasting book posted here.  

Superforecasting

A gratis copy of Philip Tetlock and Dan Gardner's new book, Superforecasting, arrived a couple months ago, just before it was published. It's been sitting on my desk until now. With a title like "Superforcasting," perhaps I subconsciously thought it would be pop puffery and delayed looking at it. If so, I was wrong. It's a winner.

Superforecasting is in the tradition of Nate Silver's The Signal and the Noise, but whereas Silver has little expertise (except in politics, baseball and poker, which he knows well) and goes for breadth rather than depth, Tetlock has significant expertise (his own pioneering research, on which his book is built) and goes for depth. Tetlock's emphasis throughout is on just one question: What makes good forecasters good?

Superforecasting is mostly about probabilistic event forecasting, for events much more challenging than those that we econometricians and statisticians typically consider, and for which there is often no direct historical data (e.g., conditional on information available at this moment, what is the probability that Google files for bankruptcy by December 31, 2035?). Nevertheless it contains many valuable lessons for us in forecast construction, evaluation, combination, updating, etc.

You can expect several posts on aspects of Superforecasting in the new year as I re-read it. For now I just wanted to bring it to your attention in case you missed it. Really nice.

DDH Now in Chinese

For my Chinese readers:
A Chinese version of the Diebold-Doherty-Herring risk management book just appeared. Interesting surprise. I knew nothing about it until it arrived in the snail mail, just as with the earlier Chinese version of the Diebold-Rudebusch yield curve book. Ya gotta love Princeton University Press. They take care of business, with minimal hassle.

The Black Swan Spectrum

Speaking of the newly-updated draft of Econometrics, now for some fun. Here's a question from the Chapter 6 EPC (exercises, problems and complements). Where does your reaction fall on the A-B spectrum below?

Nassim Taleb is a financial markets trader (and Wharton graduate) turned pop author. His book, The Black Swan, deals with many of the issues raised in this chapter. "Black swans"' are seemingly impossible or very low-probability events -- after all, swans are supposed to be white -- that occur with annoying regularity in reality. Read his book. Where does your reaction fall on the A-B spectrum below? 

A. Taleb offers crucial lessons for econometricians, heightening awareness in ways otherwise difficult to achieve. After reading Taleb, it's hard to stop worrying about non-normality, model misspecification, and so on.

B. Taleb belabors the obvious for hundreds of pages, arrogantly "informing"' us that non-normality is prevalent, that all models are misspecified, and so on. Moreover, it takes a model to beat a model, and Taleb offers nothing new.

The book is worth reading, regardless of where your reaction falls on the A-B spectrum.

Open Econometrics Text Updated for Fall Use

I have just posted an update of my introductory undergraduate Econometrics (book, slides, R code, EViews code, data, etc.). Warning: although it is significantly improved, it nevertheless remains highly (alas, woefully) preliminary and incomplete.

I intend to keep everything permanently "open," freely available on the web, continuously evolving and improving.

If you use the materials in your teaching this fall (and even if you don't), I would be grateful for feedback.

Chinese Diebold-Rudebusch Yield Curve Modeling and Forecasting

A Chinese edition of Diebold-Rudebusch, Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach, just arrived. (I'm traveling -- actually at IMF talking about Diebold-Rudebusch among other things -- but Glenn informed me that he received it in San Francisco.) I'm not even sure that I knew it was in the works. Anyway, totally cool. I love the "DNS" ("Dynamic Nelson-Siegel") in the Chinese subtitle. Not sure how/where to buy it. In any event, the English first chapter is available free from Princeton University Press, and the English complete book is available almost for free (USD 39.50 -- as they used to say in MAD Magazine: Cheap!).

Another 180 on Piketty's Measurement

My first Piketty Post unabashedly praised Piketty's measurement (if not his theory):

"Piketty's book truly shines on the data side. ... Its tables and figures...provide a rich and jaw-dropping image, like a new high-resolution photo of a previously-unseen galaxy. I'm grateful to Piketty for sending it our way, for heightening awareness, and for raising important questions."  

Measurement endorsements don't come much stronger.

Then I did a 180. Upon belatedly reading the Financial Times' Piketty piece, I felt I'd been had, truly had. Out poured my second Piketty Post, written in a near-rage, without time to digest Piketty's response.

Now, with the benefit of more time to read, re-read, and reflect, yes, I'm doing another 180. It seems clear that the bulk of the evidence suggests that the FT, not Piketty, is guilty of sloppiness. Piketty's response is convincing, and all-told, his book appears to remain a model of careful social-science measurement (thoughtful discussion, meticulous footnotes, detailed online technical appendix, freely-available datasets, etc. -- see his website).

Ironically, then, as the smoke clears, my first Piketty post remains an accurate statement of my views.

Piketty's Empirics Are as Bad as His Theory

In my earlier Piketty post, I wrote, "If much of its "reasoning" is little more than neo-Marxist drivel, much of its underlying measurement is nevertheless marvelous." The next day, recognizing the general possibility of a Reinhart-Rogoff error, but with no suspicion that that anything was actually remiss, I added "(assuming of course that it's trustworthy)."

Perhaps I really should read some newspapers. Thanks to Boragan Aruoba for noting this, and for educating me. Turns out that the Financial Times -- clearly a centrist publication with no ax to grind -- got hold of Piketty's data (underlying source data, constructed series, etc.) and published a scathing May 23 indictment.

The chart above -- just one example -- is from The Economist, reporting on the FT piece. Somehow Piketty managed to fit the dark blue curves to the light blue dots of source data. Huh? Sure looks like he conveniently ignored a boatload of recent data that happen to work against him. Put differently, his fits appear much more revealing of his sharp prior view than of data-based information. Evidently he forgot to talk about that in his book.

In my view, Reinhart-Rogoff was a one-off and innocent (if unfortunate) mistake, whereas the FT analysis clearly suggests that Piketty's "mistakes," in contrast, are systematic and egregious.

More on Piketty -- Oh God No, Please, No...

Piketty, Piketty, Piketty! How did the Piketty phenomenon happen? Surely Piketty must be one of the all-time great economists. Maybe even as great as Marx.

Yes, parts of the emerging backlash against Piketty's Capital resonate with me. Guido Menzio nails its spirit in a recent post, announcing to the Facebook universe that he'll "send you $10 and a nice Hallmark card with kitties if you refrain from talking/writing about Piketty's book for the next six months." (The irony of my now writing this Piketty post has not escaped me.)

As I see it, the problem is that Piketty's book is popularly viewed as a landmark contribution to economic theory, which it most definitely is not. In another Facebook post, leading economic theorist David Levine gets it right:

People keep referring to economists who have favorable views of Piketty's book. Leaving aside Krugman, I would be interested in knowing the name of any economist who asserts that Piketty's reasoning ... is other than gibberish.

    So the backlash is focused on dubious "reasoning" touted as penetrating by a book-buying
    public that unfortunately can't tell scientific wheat from chaff. I'm there.

But what of Piketty's data and conclusion? I admire Piketty's data -- more on that below.  I also agree with his conclusion, which I interpret broadly to be that the poor in developed countries have apparently become relatively much more poor since 1980, and that we should care, and that we should try to understand why. 

In my view, Piketty's book truly shines on the data side. If much of its "reasoning" is little more than neo-Marxist drivel, much of its underlying measurement is nevertheless marvelous (assuming of course that it's trustworthy). Its tables and figures -- there's no need to look at anything else -- provide a rich and jaw-dropping image, like a new high-resolution photo of a previously-unseen galaxy. I'm grateful to Piketty for sending it our way, for heightening awareness, and for raising important questions. Now we just need those questions answered.

Yield Curve Modeling Update

An earlier post, DNS/AFNS Yield Curve Modeling FAQs, ended with:

"What next? Job 1 is flexible incorporation of stochastic volatility, moving from \(A_0(N)\) to \(A_x(N)\) for \(x>0\), as bond yields are most definitely conditionally heteroskedastic. Doing so is important for everything from estimating time-varying risk premia to forming correctly-calibrated interval and density forecasts. Work along those lines is starting to appear. Christensen-Lopez-Rudebusch (2010), Creal-Wu (2013) and Mauabbi (2013) are good recent examples."

Good news. Creal-Wu (2013) is now Creal-Wu (2014), revised and extended to allow both spanned and unspanned stochastic volatility. Really nice stuff.

Student Advice I: Some Good Reading for Good Writing (and Good Graphics)

                            

Good writing is good thinking, so when you next hear some pretentious moron boast that ``I don't like to write, I like to think," rest assured, he's surely a bad writer and a bad thinker. Again, good writing is good thinking. If you like "to do research" but don't like "to write it up," then you're not thinking clearly. Research and writing are inextricably intertwined.

How to get there? Read and absorb McCloskey's Rhetoric of Economics, and Strunk and White's Elements of Style. There's no real need to read or absorb much else (about writing). But do bolt the Chicago Manual of Style to your desk. Then get going. Think about what you want to say, why, and to whom. Think hard and critically about logical structure and flow, at all scales, small and large. Revise and edit, again and again. Make things easy for your readers.  Listen to your words; push your prose toward poetry. 

Good graphics is also good thinking, and precisely the same advice holds. Read and absorb Tufte's Visual Display of Quantitative Information. Notice, by the way, how well Tufte writes (even if he sometimes goes overboard with the poetry thing). It's no accident. As Tufte says: show the data, and appeal to the viewer. Recognize that your first cut using default software settings will never, ever, be satisfactory. (If that statement doesn't instantly resonate with you, then you're in desperate need of a Tufte infusion.) So revise and edit, again and again. And again. 

Hastie-Tibshirani Statistical Learning Course Now Open

Machine learning is hot, hot, hot. I can't imagine better instructors (or scholars) in the area than H&T (great videos), and the course is also a fine way to learn R. It's happening now (started just last week) and runs through late March. Just go to the course site to register. The book is James, Witten, Hastie and Tibshirani (JWHT), Introduction to Statistical Learning, with Applications in R, Springer, 2013. The book homepage has a free pdf download as well as a variety of related information.

DNS/AFNS Yield Curve Modeling FAQ's

It's hard to believe that I haven't yet said anything about yield-curve modeling and forecasting in the dynamic Nelson-Siegel (DNS) tradition, whether the original Diebold-Li (2006) DNS version or the Christensen-Diebold-Rudebusch (2011) arbitrage-free version (AFNS). Here are a few thoughts about where we are and where we're going, expressed as answers to FAQ's, drawn in part from the epilogue of a recent book, Diebold and Rudebusch (2012).

1. What's wrong with unrestricted affine equilibrium models?

The classic affine equilibrium models, although beautiful theoretical constructs, perform poorly in empirical practice. In particular, the maximally-flexible canonical \(A_0(N)\) models have notoriously recalcitrant likelihood surfaces. (Notation: \(A_x(N)\) means a model with \(N\) factors, \(x\) of which have stochastic volatility.) See Hamilton-Wu (2012) et al.

2. What's right with DNS/AFNS?

DNS/AFNS just puts a bit of structure on factor loadings while still maintaining significant flexibility. That gets us to a very good place, involving both theoretical rigor (via imposition of no-arb in AFNS) and empirical tractability. That's all. It really is that simple.

3. Is AFNS the only tractable \(A_0(3)\) model?

Not any longer, as recent important work has opened new doors. In particular, Joslin-Singleton-Zhu (2011) develop a well-behaved (among other things, identified!) family of Gaussian term structure models, for which trustworthy estimation is very simple, just as with AFNS. Moreover, it turns out that AFNS is nested within their canonical form, corresponding to three extra constraints relative to the maximally-flexible model.

4. If AFNS is no longer the only tractable \(A_0(3)\) model, is it nevertheless still of special interest?

Yes! AFNS's structure conveys several important and useful characteristics, which are presently difficult or impossible to achieve in competing frameworks. First, as regards specializations, AFNS parametric simplicity makes it easy to impose restrictions. Second, as regards extensions, AFNS simplicity makes it similarly easy to increase the number of AFNS latent factors if desired or necessary, as for example with the five-factor model of Christensen-Diebold-Rudebusch (2009). Third, as regards varied uses, the flexible AFNS continuous basis functions facilitate relative pricing, curve interpolation between observed yields, and risk measurement for arbitrary bond portfolios.

And there's more. Fascinating recent work studying AFNS from an approximation-theoretic perspective shows that the Nelson-Siegel form is a low-ordered Taylor-series approximation to an arbitrary \(A_0(N)\) model. See Krippner (in press).

5. What next?

Job 1 is flexible incorporation of stochastic volatility, moving from \(A_0(N)\) to \(A_x(N)\) for \(x>0\), as bond yields are most definitely conditionally heteroskedastic. Doing so is important for everything from estimating time-varying risk premia to forming correctly-calibrated interval and density forecasts. Work along those lines is starting to appear. Christensen-Lopez-Rudebusch (2010), Creal-Wu (2013) and Mauabbi (2013) are good recent examples.

Elements of Statistical Learning: A Stunningly Good Job of LaTeX to pdf to Web

  

A very Happy New Year to all! Here's a little thing to start us off.

I happened to be thinking about principal-component regression vs. ridge regression yesterday, so as usual I consulted the Hastie-Tibshirani-Friedman (HTF) classic, Elements of Statistical Learning. Where did I get that gorgeous book pdf? (Look through it; the form is as wonderful as the substance, and see also the similarly-wonderful new James, Witten, Hastie and Tibshirani (JWHT), Introduction to Statistical Learning, with Applications in R.) Both are freely (and legally!) available as pdf on the web. Interestingly, both are also for sale by Springer in the usual ways.

So what's up? In path-breaking arrangements, HTF and JWHT negotiated deals in which they're free to post the book and Springer is free to sell it. And by all accounts the outcomes have been superb for all. Thanks, HTF and JWHT, for promoting best-practice science, and thanks Springer, for doing the right thing.  May many more follow suit.

Financial Regulation, Part Three: The Known, the Unknown and the Unknowable

Dick Herring, Neil Doherty and I recently worked on an eye-opening research project that resulted in our book, The Known, the Unknown and the Unknowable in Financial Risk Management. I always liked the cover art (thanks to Princeton University Press, which did its usual fine job throughout).  I feel bad for the poor guy in the necktie, in the maze. But that's life in financial markets.

Poor Little Guy

We abbreviate the known, the unknown and the unknowable by K, u and U, respectively. Roughly, K is risk (known outcomes, known probabilities), u is uncertainty (known outcomes, unknown probabilities), and U is ignorance (unknown outcomes, unknown probabilities).

The book blurb on my web page reads as follows:

"On the successes and failures of various parts of modern financial risk management, emphasizing the known (K), the unknown (u) and the unknowable (U). We illustrate a KuU-based perspective for conceptualizing financial risks and designing effective risk management strategies. Sometimes we focus on K, and sometimes on U, but most often our concerns blend aspects of K and u and U. Indeed K and U are extremes of a smooth spectrum, with many of the most interesting and relevant situations interior."

The blurb continues:

"Statistical issues emerge as central to risk measurement, and we push toward additional progress. But economic issues of incentives and strategic behavior emerge as central for risk management, as we illustrate in a variety of contexts."

The book's table of contents reveals the breadth of that insight, from risk management, asset allocation, and asset pricing, to insurance, crisis management, real estate, corporate governance, monetary policy, and private investing:

TABLE OF CONTENTS

Chapter 1: Introduction by Francis X. Diebold, Neil A. Doherty, and Richard J. Herring 1

Chapter 2: Risk: A Decision Maker's Perspective by Sir Clive W. J. Granger 31

Chapter 3: Mild vs. Wild Randomness: Focusing on Those Risks That Matter by Benoit B. Mandelbrot and Nassim Nicholas Taleb 47

Chapter 4: The Term Structure of Risk, the Role of Known and Unknown Risks, and Nonstationary Distributions by Riccardo Colacito and Robert F. Engle 59

Chapter 5: Crisis and Non-crisis Risk in Financial Markets: A Unified Approach to Risk Management by Robert H. Litzenberger and David M. Modest 74

Chapter 6: What We Know, Don't Know, and Can't Know about Bank Risk: A View from the Trenches by Andrew Kuritzkes and Til Schuermann 103

Chapter 7: Real Estate through the Ages: The Known, the Unknown, and the Unknowable by Ashok Bardhan and Robert H. Edelstein 145

Chapter 8: Reflections on Decision-making under Uncertainty by Paul R. Kleindorfer 164

Chapter 9: On the Role of Insurance Brokers in Resolving the Known, the Unknown, and the Unknowable by Neil A. Doherty and Alexander Muermann 194

Chapter 10: Insuring against Catastrophes by Howard Kunreuther and Mark V. Pauly 210

Chapter 11: Managing Increased Capital Markets Intensity: The Chief Financial Officer's Role in Navigating the Known, the Unknown, and the Unknowable by Charles N. Bralver and Daniel Borge 239

Chapter 12: The Role of Corporate Governance in Coping with Risk and Unknowns by Kenneth E. Scott 277

Chapter 13: Domestic Banking Problems by Charles A. E. Goodhart 286

Chapter 14: Crisis Management: The Known, The Unknown, and the Unknowable by Donald L. Kohn 296

Chapter 15: Investing in the Unknown and Unknowable by Richard J. Zeckhauser 304

I say that the project was "eye opening" (for me) because I went into it thinking about econometrics, but I came out of it thinking about economics.  Econometrics is invaluable for risk measurement, systemic aspects of which are embodied for example in the Diebold-Yilmaz network connectedness framework, or in parts of Rob Engle's V-Lab. But risk management, in particular risk prevention, is equally (or more) about creating incentives to guide strategic behavior, particularly in situations of u and U.

The real question, then, is how to write contracts (design organizations, design policies, design rules) that incent firms to "do the right thing," whatever that might mean, in myriad situations, many of which may be inconceivable at present -- that is, across the KuU spectrum.

How to do it?

To be continued...